dissertation.bib

@article{mueth_force_1998,
	title = {Force distribution in a granular medium},
	volume = {57},
	copyright = {force distributions},
	issn = {1063-651X, 1095-3787},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.57.3164},
	doi = {10.1103/PhysRevE.57.3164},
	number = {3},
	urldate = {2020-07-02},
	journal = {Physical Review E},
	author = {Mueth, Daniel M. and Jaeger, Heinrich M. and Nagel, Sidney R.},
	month = mar,
	year = {1998},
	pages = {3164--3169},
	file = {Mueth et al. - 1998 - Force distribution in a granular medium.pdf:C\:\\Users\\craig\\Zotero\\storage\\G987F6UH\\Mueth et al. - 1998 - Force distribution in a granular medium.pdf:application/pdf},
}

@article{liarte_jamming_2019,
	title = {Jamming as a {Multicritical} {Point}},
	volume = {122},
	copyright = {EMT connection stuff? (sean)},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.128006},
	doi = {10.1103/PhysRevLett.122.128006},
	number = {12},
	urldate = {2020-07-02},
	journal = {Physical Review Letters},
	author = {Liarte, Danilo B. and Mao, Xiaoming and Stenull, Olaf and Lubensky, T. C.},
	month = mar,
	year = {2019},
	file = {Liarte et al. - 2019 - Jamming as a Multicritical Point.pdf:C\:\\Users\\craig\\Zotero\\storage\\HV74K96B\\Liarte et al. - 2019 - Jamming as a Multicritical Point.pdf:application/pdf},
}

@article{zaccone_approximate_2011,
	title = {Approximate analytical description of the nonaffine response of amorphous solids},
	volume = {83},
	copyright = {EMT dz share mod},
	issn = {1098-0121, 1550-235X},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.83.184205},
	doi = {10.1103/PhysRevB.83.184205},
	number = {18},
	urldate = {2020-07-01},
	journal = {Physical Review B},
	author = {Zaccone, Alessio and Scossa-Romano, Enzo},
	month = may,
	year = {2011},
	file = {Zaccone and Scossa-Romano - 2011 - Approximate analytical description of the nonaffin.pdf:C\:\\Users\\craig\\Zotero\\storage\\RCG7DK9T\\Zaccone and Scossa-Romano - 2011 - Approximate analytical description of the nonaffin.pdf:application/pdf},
}

@article{wyart_rigidity_2005,
	title = {On the rigidity of amorphous solids},
	volume = {30},
	copyright = {not sure (from sean) (probably mattheiu's thesis)},
	issn = {0003-4169, 1286-4838},
	url = {http://www.annphys.org/10.1051/anphys:2006003},
	doi = {10.1051/anphys:2006003},
	abstract = {We poorly understand the properties of amorphous systems at small length scales, where a continuous elastic description breaks down. This is apparent when one considers their vibrational and transport properties, or the way forces propagate in these solids. Little is known about the microscopic cause of their rigidity. Recently it has been observed numerically that an assembly of elastic particles has a critical behavior near the jamming threshold where the pressure vanishes. At the transition such a system does not behave as a continuous medium at any length scales. When this system is compressed, scaling is observed for the elastic moduli, the coordination number, but also for the density of vibrational modes. In the present work, we derive theoretically these results, and show that they apply to various systems such as granular matter and silica, but also to colloidal glasses. In particular we show that: (i) these systems present a large excess of vibrational modes at low frequency in comparison with normal solids, called the “boson peak” in the glass literature. The corresponding modes are very different from plane waves, and their frequency is related to the system coordination; (ii) rigidity is a non-local property of the packing geometry, characterized by a length scale which can be large. For elastic particles this length diverges near the jamming transition; (iii) for repulsive systems the shear modulus can be much smaller than the bulk modulus. We compute the corresponding scaling laws near the jamming threshold. Finally, we discuss the implications of these results for the glass transition, the transport, and the geometry of the random close packing.},
	number = {3},
	urldate = {2020-02-14},
	journal = {Annales de Physique},
	author = {Wyart, M.},
	year = {2005},
	pages = {1--96},
	file = {Wyart - 2005 - On the rigidity of amorphous solids.pdf:C\:\\Users\\craig\\Zotero\\storage\\RG4UYZJ9\\Wyart - 2005 - On the rigidity of amorphous solids.pdf:application/pdf},
}

@article{liarte_jamming_2019-1,
	title = {Jamming as a {Multicritical} {Point}},
	volume = {122},
	copyright = {"recent tom"},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.128006},
	doi = {10.1103/PhysRevLett.122.128006},
	number = {12},
	urldate = {2020-06-30},
	journal = {Physical Review Letters},
	author = {Liarte, Danilo B. and Mao, Xiaoming and Stenull, Olaf and Lubensky, T. C.},
	month = mar,
	year = {2019},
	file = {Liarte et al. - 2019 - Jamming as a Multicritical Point.pdf:C\:\\Users\\craig\\Zotero\\storage\\7VL22FIQ\\Liarte et al. - 2019 - Jamming as a Multicritical Point.pdf:application/pdf},
}

@article{wyart_effects_2005,
	title = {Effects of compression on the vibrational modes of marginally jammed solids},
	volume = {72},
	copyright = {EMT scalings},
	issn = {1539-3755, 1550-2376},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.72.051306},
	doi = {10.1103/PhysRevE.72.051306},
	number = {5},
	urldate = {2020-06-22},
	journal = {Physical Review E},
	author = {Wyart, Matthieu and Silbert, Leonardo E. and Nagel, Sidney R. and Witten, Thomas A.},
	month = nov,
	year = {2005},
	file = {Wyart et al. - 2005 - Effects of compression on the vibrational modes of.pdf:C\:\\Users\\craig\\Zotero\\storage\\CJKE43ZD\\Wyart et al. - 2005 - Effects of compression on the vibrational modes of.pdf:application/pdf},
}

@article{ciamarra_statistical_2012,
	title = {Statistical mechanics for static granular media: open questions},
	volume = {8},
	copyright = {compactivity bounds + ??? // unimportant?},
	issn = {1744-683X, 1744-6848},
	shorttitle = {Statistical mechanics for static granular media},
	url = {http://xlink.rsc.org/?DOI=c2sm06898b},
	doi = {10.1039/c2sm06898b},
	number = {38},
	urldate = {2018-11-27},
	journal = {Soft Matter},
	author = {Ciamarra, Massimo Pica and Richard, Patrick and Schröter, Matthias and Tighe, Brian P.},
	year = {2012},
	pages = {9731},
	file = {Ciamarra et al. - 2012 - Statistical mechanics for static granular media o.pdf:C\:\\Users\\craig\\Zotero\\storage\\VSZWR2VF\\Ciamarra et al. - 2012 - Statistical mechanics for static granular media o.pdf:application/pdf},
}

@article{liu_jamming_1998,
	title = {Jamming is not just cool any more: {Nonlinear} dynamics},
	volume = {396},
	copyright = {density being important // unimportant?},
	issn = {0028-0836, 1476-4687},
	shorttitle = {Jamming is not just cool any more},
	url = {http://www.nature.com/articles/23819},
	doi = {10.1038/23819},
	number = {6706},
	urldate = {2018-11-27},
	journal = {Nature},
	author = {Liu, Andrea J. and Nagel, Sidney R.},
	month = nov,
	year = {1998},
	pages = {21--22},
	file = {Liu and Nagel - 1998 - Jamming is not just cool any more Nonlinear dynam.pdf:C\:\\Users\\craig\\Zotero\\storage\\PDDM497J\\Liu and Nagel - 1998 - Jamming is not just cool any more Nonlinear dynam.pdf:application/pdf},
}

@article{onoda_random_1990,
	title = {Random loose packings of uniform spheres and the dilatancy onset},
	volume = {64},
	copyright = {compactivity bounds // unimportant?},
	issn = {0031-9007},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.64.2727},
	doi = {10.1103/PhysRevLett.64.2727},
	number = {22},
	urldate = {2018-11-27},
	journal = {Physical Review Letters},
	author = {Onoda, George Y. and Liniger, Eric G.},
	month = may,
	year = {1990},
	pages = {2727--2730},
	file = {Onoda and Liniger - 1990 - Random loose packings of uniform spheres and the d.pdf:C\:\\Users\\craig\\Zotero\\storage\\3ZL6LAFH\\Onoda and Liniger - 1990 - Random loose packings of uniform spheres and the d.pdf:application/pdf},
}

@article{bennett_efficient_1976,
	title = {Efficient estimation of free energy differences from {Monte} {Carlo} data},
	volume = {22},
	copyright = {overlapping histograms original},
	issn = {00219991},
	url = {https://linkinghub.elsevier.com/retrieve/pii/0021999176900784},
	doi = {10.1016/0021-9991(76)90078-4},
	number = {2},
	urldate = {2019-05-09},
	journal = {Journal of Computational Physics},
	author = {Bennett, Charles H},
	month = oct,
	year = {1976},
	pages = {245--268},
	file = {Bennett - 1976 - Efficient estimation of free energy differences fr.pdf:C\:\\Users\\craig\\Zotero\\storage\\C7RF632E\\Bennett - 1976 - Efficient estimation of free energy differences fr.pdf:application/pdf},
}

@article{mcnamara_measurement_2009,
	title = {Measurement of granular entropy},
	volume = {80},
	copyright = {use of overlapping hists},
	issn = {1539-3755, 1550-2376},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.80.031301},
	doi = {10.1103/PhysRevE.80.031301},
	number = {3},
	urldate = {2018-11-27},
	journal = {Physical Review E},
	author = {McNamara, Sean and Richard, Patrick and de Richter, Sébastien Kiesgen and Le Caër, Gérard and Delannay, Renaud},
	month = sep,
	year = {2009},
	file = {McNamara et al. - 2009 - Measurement of granular entropy.pdf:C\:\\Users\\craig\\Zotero\\storage\\IHHGJFP4\\McNamara et al. - 2009 - Measurement of granular entropy.pdf:application/pdf},
}

@article{henkes_statistical_2009,
	title = {A statistical mechanics framework for static granular matter},
	volume = {79},
	copyright = {field theory angoricity prediction},
	issn = {1539-3755, 1550-2376},
	url = {http://arxiv.org/abs/0810.5715},
	doi = {10.1103/PhysRevE.79.061301},
	abstract = {The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming diagram [1]. This work focuses on the case of static granular matter, where we have constructed a statistical ensemble [2] which mirrors equilibrium statistical mechanics. This ensemble, which is based on the conservation properties of the stress tensor, is distinct from the original Edwards ensemble and applies to packings of deformable grains. We combine it with a field theoretical analysis of the packings, where the field is the Airy stress function derived from the force and torque balance conditions. In this framework, Point J characterized by a diverging stiffness of the pressure fluctuations. Separately, we present a phenomenological mean-field theory of the jamming transition, which incorporates the mean contact number as a variable. We link both approaches in the context of the marginal rigidity picture proposed by [3, 4].},
	number = {6},
	urldate = {2018-11-15},
	journal = {Physical Review E},
	author = {Henkes, S. and Chakraborty, B.},
	month = jun,
	year = {2009},
	note = {arXiv: 0810.5715},
	keywords = {Condensed Matter - Statistical Mechanics, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Soft Condensed Matter},
	annote = {Comment: 21 pages, 15 figures},
	file = {Henkes and Chakraborty - 2009 - A statistical mechanics framework for static granu.pdf:C\:\\Users\\craig\\Zotero\\storage\\BHLIMCLV\\Henkes and Chakraborty - 2009 - A statistical mechanics framework for static granu.pdf:application/pdf},
}

@article{edwards_granular_2002,
	title = {Granular materials: {Towards} the statistical mechanics of jammed configurations},
	volume = {51},
	copyright = {stat mech // compactivity is lacking},
	issn = {0001-8732, 1460-6976},
	shorttitle = {Granular materials},
	url = {http://www.tandfonline.com/doi/abs/10.1080/0001873021000030780},
	doi = {10.1080/0001873021000030780},
	abstract = {The properties of granular materials can be well de®ned, that is be a branch of physics, but conventional statistical mechanics is inadequate to handle what amounts to the physics of disordered packings of hard-core particles, either static or driven by external forces. A new approach that employs statistical-mechanical concepts is o ered for the description of such systems. An analysis of the stress ®eld in static granular packings is given within the framework of this approach. There are more conventional systems such as polymer glasses which have a rather similar statistical physics to granular media, and some speculative ideas are o ered which are a real departure from conventional glass theories.},
	number = {8},
	urldate = {2018-11-15},
	journal = {Advances in Physics},
	author = {Edwards, S. F. and Grinev, D. V.},
	month = dec,
	year = {2002},
	pages = {1669--1684},
	file = {Edwards and Grinev - 2002 - Granular materials Towards the statistical mechan.pdf:C\:\\Users\\craig\\Zotero\\storage\\4DZJ24J2\\Edwards and Grinev - 2002 - Granular materials Towards the statistical mechan.pdf:application/pdf},
}

@article{edwards_distribution_2008,
	title = {The distribution of forces in a granular system under external stress is a spinglass problem},
	volume = {41},
	copyright = {angoricity proposal},
	issn = {1751-8113, 1751-8121},
	url = {http://stacks.iop.org/1751-8121/41/i=32/a=324019?key=crossref.91301149080e11e0fb4cc0316f09b324},
	doi = {10.1088/1751-8113/41/32/324019},
	abstract = {There is now ample experimental and computational evidence that a welldefined and reproducible state can be achieved in a granular system under a repeated disturbance, e.g., if subjected to disturbance of amplitude A and frequency ω, a volume V (A, ω) is found which will be returned to if the system is subjected to A , ω and then to A, ω. A microcanonical ensemble defines the entropy from volume V , where V equals the volume function W , just as E equals H in conventional statistical physics. A canonical version exists via a compactivity ∂V /∂S. Granular systems also have a distribution of intergranular forces generated by external forces or gravity. This paper shows that the idea that the configurations are determined by the Gibbsian formula exp(−W (∂S/∂V )) can be extended to the distribution of forces with a microcanonical condition P (external) = (force moments in grains)/V via exp(− (∂S/∂P )). The canonical ensemble immediately gives the exponential distribution of intergranular forces, found experimentally. The distribution must depend on the configuration and any physical property will have a value averaged over configurations, i.e. will give rise to a spinglass problem.},
	number = {32},
	urldate = {2018-08-21},
	journal = {Journal of Physics A: Mathematical and Theoretical},
	author = {Edwards, Sam F},
	month = aug,
	year = {2008},
	pages = {324019},
	file = {Edwards - 2008 - The distribution of forces in a granular system un.pdf:C\:\\Users\\craig\\Zotero\\storage\\88DUV95V\\Edwards - 2008 - The distribution of forces in a granular system un.pdf:application/pdf},
}

@article{bitzek_structural_2006,
	title = {Structural {Relaxation} {Made} {Simple}},
	volume = {97},
	copyright = {FIRE},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.97.170201},
	doi = {10.1103/PhysRevLett.97.170201},
	number = {17},
	urldate = {2018-11-15},
	journal = {Physical Review Letters},
	author = {Bitzek, Erik and Koskinen, Pekka and Gähler, Franz and Moseler, Michael and Gumbsch, Peter},
	month = oct,
	year = {2006},
	file = {Bitzek et al. - 2006 - Structural Relaxation Made Simple.pdf:C\:\\Users\\craig\\Zotero\\storage\\UWGBCSM4\\Bitzek et al. - 2006 - Structural Relaxation Made Simple.pdf:application/pdf},
}

@article{edwards_theory_1989,
	title = {Theory of powders},
	volume = {157},
	copyright = {fomulates compactivity},
	issn = {03784371},
	url = {http://linkinghub.elsevier.com/retrieve/pii/0378437189900344},
	doi = {10.1016/0378-4371(89)90034-4},
	number = {3},
	urldate = {2018-11-15},
	journal = {Physica A: Statistical Mechanics and its Applications},
	author = {Edwards, S.F. and Oakeshott, R.B.S.},
	month = jun,
	year = {1989},
	pages = {1080--1090},
	file = {Edwards and Oakeshott - 1989 - Theory of powders.pdf:C\:\\Users\\craig\\Zotero\\storage\\GGRS8YYK\\Edwards and Oakeshott - 1989 - Theory of powders.pdf:application/pdf},
}

@article{tetrode_chemische_1912,
	title = {Die chemische {Konstante} der {Gase} und das elementare {Wirkungsquantum}},
	volume = {343},
	copyright = {Sackur-Tetrode original},
	issn = {1521-3889},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/andp.19123430708},
	doi = {10.1002/andp.19123430708},
	number = {7},
	urldate = {2018-11-27},
	journal = {Annalen der Physik},
	author = {Tetrode, H.},
	month = jan,
	year = {1912},
	pages = {434--442},
	file = {Submitted Version:C\:\\Users\\craig\\Zotero\\storage\\8V4K7GUL\\Tetrode - 1912 - Die chemische Konstante der Gase und das elementar.pdf:application/pdf;Snapshot:C\:\\Users\\craig\\Zotero\\storage\\QDABRJ26\\andp.html:text/html},
}

@article{parisi_robustness_2018,
	title = {Robustness of mean field theory for hard sphere models},
	volume = {97},
	copyright = {mean field prediction not true},
	issn = {2470-0045, 2470-0053},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.97.063003},
	doi = {10.1103/PhysRevE.97.063003},
	number = {6},
	urldate = {2020-05-18},
	journal = {Physical Review E},
	author = {Parisi, Giorgio and Pollack, Yoav G. and Procaccia, Itamar and Rainone, Corrado and Singh, Murari},
	month = jun,
	year = {2018},
	file = {Parisi et al. - 2018 - Robustness of mean field theory for hard sphere mo.pdf:C\:\\Users\\craig\\Zotero\\storage\\6HTIP7NQ\\Parisi et al. - 2018 - Robustness of mean field theory for hard sphere mo.pdf:application/pdf},
}

@article{skoge_packing_2006,
	title = {Packing {Hyperspheres} in {High}-{Dimensional} {Euclidean} {Spaces}},
	volume = {74},
	copyright = {phi j {\textasciitilde} d log d},
	issn = {1539-3755, 1550-2376},
	url = {http://arxiv.org/abs/cond-mat/0608362},
	doi = {10.1103/PhysRevE.74.041127},
	abstract = {We present the first study of disordered jammed hard-sphere packings in four-, five- and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed (MRJ) states for space dimensions \$d=4\$, 5 and 6 to be \${\textbackslash}phi\_\{MRJ\} {\textbackslash}simeq 0.46\$, 0.31 and 0.20, respectively. To a good approximation, the MRJ density obeys the scaling form \${\textbackslash}phi\_\{MRJ\}= c\_1/2{\textasciicircum}d+(c\_2 d)/2{\textasciicircum}d\$, where \$c\_1=-2.72\$ and \$c\_2=2.56\$, which appears to be consistent with high-dimensional asymptotic limit, albeit with different coefficients. Calculations of the pair correlation function \$g\_\{2\}(r)\$ and structure factor \$S(k)\$ for these states show that short-range ordering appreciably decreases with increasing dimension, consistent with a recently proposed ``decorrelation principle,'' which, among othe things, states that unconstrained correlations diminish as the dimension increases and vanish entirely in the limit \$d {\textbackslash}to {\textbackslash}infty\$. As in three dimensions (where \${\textbackslash}phi\_\{MRJ\} {\textbackslash}simeq 0.64\$), the packings show no signs of crystallization, are isostatic, and have a power-law divergence in \$g\_\{2\}(r)\$ at contact with power-law exponent \${\textbackslash}simeq 0.4\$. Across dimensions, the cumulative number of neighbors equals the kissing number of the conjectured densest packing close to where \$g\_\{2\}(r)\$ has its first minimum. We obtain estimates for the freezing and melting desnities for the equilibrium hard-sphere fluid-solid transition, \${\textbackslash}phi\_F {\textbackslash}simeq 0.32\$ and \${\textbackslash}phi\_M {\textbackslash}simeq 0.39\$, respectively, for \$d=4\$, and \${\textbackslash}phi\_F {\textbackslash}simeq 0.19\$ and \${\textbackslash}phi\_M {\textbackslash}simeq 0.24\$, respectively, for \$d=5\$.},
	number = {4},
	urldate = {2020-05-12},
	journal = {Physical Review E},
	author = {Skoge, M. and Donev, A. and Stillinger, F. H. and Torquato, S.},
	month = oct,
	year = {2006},
	note = {arXiv: cond-mat/0608362},
	keywords = {Condensed Matter - Statistical Mechanics, Condensed Matter - Disordered Systems and Neural Networks},
	pages = {041127},
	annote = {Comment: 28 pages, 9 figures. To appear in Physical Review E},
	file = {Skoge et al. - 2006 - Packing Hyperspheres in High-Dimensional Euclidean.pdf:C\:\\Users\\craig\\Zotero\\storage\\YY6CRAIS\\Skoge et al. - 2006 - Packing Hyperspheres in High-Dimensional Euclidean.pdf:application/pdf},
}

@article{parisi_mean-field_2010,
	title = {Mean-field theory of hard sphere glasses and jamming},
	volume = {82},
	copyright = {mean field review {\textbar} phi j {\textasciitilde} d log d},
	issn = {0034-6861, 1539-0756},
	url = {https://link.aps.org/doi/10.1103/RevModPhys.82.789},
	doi = {10.1103/RevModPhys.82.789},
	number = {1},
	urldate = {2020-01-21},
	journal = {Reviews of Modern Physics},
	author = {Parisi, Giorgio and Zamponi, Francesco},
	month = mar,
	year = {2010},
	pages = {789--845},
	file = {Parisi and Zamponi - 2010 - Mean-field theory of hard sphere glasses and jammi.pdf:C\:\\Users\\craig\\Zotero\\storage\\TMBPJ3WP\\Parisi and Zamponi - 2010 - Mean-field theory of hard sphere glasses and jammi.pdf:application/pdf},
}

@article{parisi_amorphous_2006,
	title = {Amorphous packings of hard spheres for large space dimension},
	volume = {2006},
	copyright = {phi j {\textasciitilde} d log d},
	issn = {1742-5468},
	url = {https://iopscience.iop.org/article/10.1088/1742-5468/2006/03/P03017},
	doi = {10.1088/1742-5468/2006/03/P03017},
	abstract = {In a recent paper we derived an expression for the replicated free energy of a liquid of hard spheres based on the hypernetted chain (HNC) free energy functional. An approximate equation of state for the glass and an estimate of the random close packing density were obtained for d = 3. Here we show that the HNC approximation is not needed: the same expression can be obtained from the full diagrammatic expansion of the replicated free energy. Then, we consider the asymptotics of this expression when the space dimension d is very large. In this limit, the entropy of the hard sphere liquid has been computed exactly. Using this solution, we derive asymptotic expressions for the glass transition density and for the random close packing density for hard spheres for large space dimension.},
	number = {03},
	urldate = {2020-05-12},
	journal = {Journal of Statistical Mechanics: Theory and Experiment},
	author = {Parisi, Giorgio and Zamponi, Francesco},
	month = mar,
	year = {2006},
	pages = {P03017--P03017},
	file = {Parisi and Zamponi - 2006 - Amorphous packings of hard spheres for large space.pdf:C\:\\Users\\craig\\Zotero\\storage\\AYIS4PQD\\Parisi and Zamponi - 2006 - Amorphous packings of hard spheres for large space.pdf:application/pdf},
}

@article{fan_particle_2017,
	title = {Particle rearrangement and softening contributions to the nonlinear mechanical response of glasses},
	volume = {96},
	copyright = {plasticity},
	issn = {2470-0045, 2470-0053},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.96.032602},
	doi = {10.1103/PhysRevE.96.032602},
	number = {3},
	urldate = {2020-05-07},
	journal = {Physical Review E},
	author = {Fan, Meng and Zhang, Kai and Schroers, Jan and Shattuck, Mark D. and O'Hern, Corey S.},
	month = sep,
	year = {2017},
	file = {Fan et al. - 2017 - Particle rearrangement and softening contributions.pdf:C\:\\Users\\craig\\Zotero\\storage\\VN3RLZ73\\Fan et al. - 2017 - Particle rearrangement and softening contributions.pdf:application/pdf},
}

@article{sartor_direct_2020,
	title = {Direct measurement of force configurational entropy in jamming},
	volume = {101},
	copyright = {self},
	issn = {2470-0045, 2470-0053},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.101.050902},
	doi = {10.1103/PhysRevE.101.050902},
	number = {5},
	urldate = {2020-05-04},
	journal = {Physical Review E},
	author = {Sartor, James D. and Corwin, Eric I.},
	month = may,
	year = {2020},
	file = {Sartor and Corwin - 2020 - Direct measurement of force configurational entrop.pdf:C\:\\Users\\craig\\Zotero\\storage\\SBCAZMBU\\Sartor and Corwin - 2020 - Direct measurement of force configurational entrop.pdf:application/pdf},
}

@article{shimada_low-frequency_2019,
	title = {Low-frequency vibrations of jammed packings in large spatial dimensions},
	copyright = {prestress},
	url = {http://arxiv.org/abs/1910.07238},
	abstract = {Amorphous packings prepared in the vicinity of the jamming transition play a central role in theoretical studies of the vibrational spectrum of glasses. Two mean-field theories predict that the vibrational density of states \$g({\textbackslash}omega)\$ obeys a characteristic power law, \$g({\textbackslash}omega){\textbackslash}sim{\textbackslash}omega{\textasciicircum}2\$, called the non-Debye scaling in the low-frequency region. Numerical studies have however reported that this scaling breaks down at low frequencies, due to finite dimensional effects. In this study, we prepare amorphous packings of up to \$128000\$ particles in spatial dimensions from \$d=3\$ to \$d=9\$ to characterise the range of validity of the non-Debye scaling. Our numerical results suggest that the non-Debye scaling is obeyed down to a frequency that gradually decreases as \$d\$ increases, and possibly vanishes for large \$d\$, in agreement with mean-field predictions. We also show that the prestress is an efficient control parameter to quantitatively compare packings across different spatial dimensions.},
	urldate = {2020-05-04},
	journal = {arXiv:1910.07238 [cond-mat]},
	author = {Shimada, Masanari and Mizuno, Hideyuki and Berthier, Ludovic and Ikeda, Atsushi},
	month = oct,
	year = {2019},
	note = {arXiv: 1910.07238},
	keywords = {Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Soft Condensed Matter},
	annote = {Comment: 15 pages, 11 figures},
	file = {Shimada et al. - 2019 - Low-frequency vibrations of jammed packings in lar.pdf:C\:\\Users\\craig\\Zotero\\storage\\BSICUMV8\\Shimada et al. - 2019 - Low-frequency vibrations of jammed packings in lar.pdf:application/pdf},
}

@article{morse_two_nodate,
	title = {Two classes of events in sheared particulate matter},
	copyright = {network events vs. rearrangements},
	author = {Morse, Peter K and Wijtmans, Sven and van Deen, Merlijn and van Hecke, Martin and Manning, M Lisa},
	pages = {9},
	file = {Morse et al. - Two classes of events in sheared particulate matte.pdf:C\:\\Users\\craig\\Zotero\\storage\\C7WN5AQF\\Morse et al. - Two classes of events in sheared particulate matte.pdf:application/pdf},
}

@article{berthier_perspective_2019,
	title = {Perspective: {Gardner} {Physics} in {Amorphous} {Solids} and {Beyond}},
	volume = {151},
	copyright = {mean field (gardner)},
	issn = {0021-9606, 1089-7690},
	shorttitle = {Perspective},
	url = {http://arxiv.org/abs/1902.10494},
	doi = {10.1063/1.5097175},
	abstract = {One of the most remarkable predictions to emerge out of the exact infinite-dimensional solution of the glass problem is the Gardner transition. Although this transition was first theoretically proposed a generation ago for certain mean-field spin glass models, its materials relevance was only realized when a systematic effort to relate glass formation and jamming was undertaken. A number of nontrivial physical signatures associated to the Gardner transition have since been considered in various areas, from models of structural glasses to constraint satisfaction problems. This Perspective surveys these recent advances and discusses the novel research opportunities that arise from them.},
	number = {1},
	urldate = {2020-04-27},
	journal = {The Journal of Chemical Physics},
	author = {Berthier, Ludovic and Biroli, Giulio and Charbonneau, Patrick and Corwin, Eric I. and Franz, Silvio and Zamponi, Francesco},
	month = jul,
	year = {2019},
	note = {arXiv: 1902.10494},
	keywords = {Condensed Matter - Statistical Mechanics, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Soft Condensed Matter},
	pages = {010901},
	annote = {Comment: 17 pages, 9 figures},
	file = {Berthier et al. - 2019 - Perspective Gardner Physics in Amorphous Solids a.pdf:C\:\\Users\\craig\\Zotero\\storage\\I64BP3XU\\Berthier et al. - 2019 - Perspective Gardner Physics in Amorphous Solids a.pdf:application/pdf},
}

@article{stanifer_simple_2018,
	title = {Simple random matrix model for the vibrational spectrum of structural glasses},
	volume = {98},
	copyright = {ethan lisa ?},
	issn = {2470-0045, 2470-0053},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.98.042908},
	doi = {10.1103/PhysRevE.98.042908},
	number = {4},
	urldate = {2020-04-27},
	journal = {Physical Review E},
	author = {Stanifer, E. and Morse, P. K. and Middleton, A. A. and Manning, M. L.},
	month = oct,
	year = {2018},
	file = {Stanifer et al. - 2018 - Simple random matrix model for the vibrational spe.pdf:C\:\\Users\\craig\\Zotero\\storage\\5PN295GZ\\Stanifer et al. - 2018 - Simple random matrix model for the vibrational spe.pdf:application/pdf},
}

@article{charbonneau_universal_2016,
	title = {Universal {Non}-{Debye} {Scaling} in the {Density} of {States} of {Amorphous} {Solids}},
	volume = {117},
	copyright = {mean field confirmation},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.117.045503},
	doi = {10.1103/PhysRevLett.117.045503},
	number = {4},
	urldate = {2020-04-27},
	journal = {Physical Review Letters},
	author = {Charbonneau, Patrick and Corwin, Eric I. and Parisi, Giorgio and Poncet, Alexis and Zamponi, Francesco},
	month = jul,
	year = {2016},
	file = {Charbonneau et al. - 2016 - Universal Non-Debye Scaling in the Density of Stat.pdf:C\:\\Users\\craig\\Zotero\\storage\\P2HH6236\\Charbonneau et al. - 2016 - Universal Non-Debye Scaling in the Density of Stat.pdf:application/pdf},
}

@article{charbonneau_jamming_2015,
	title = {Jamming {Criticality} {Revealed} by {Removing} {Localized} {Buckling} {Excitations}},
	volume = {114},
	copyright = {isostaticity sweep},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.114.125504},
	doi = {10.1103/PhysRevLett.114.125504},
	number = {12},
	urldate = {2020-04-23},
	journal = {Physical Review Letters},
	author = {Charbonneau, Patrick and Corwin, Eric I. and Parisi, Giorgio and Zamponi, Francesco},
	month = mar,
	year = {2015},
	file = {Charbonneau et al. - 2015 - Jamming Criticality Revealed by Removing Localized.pdf:C\:\\Users\\craig\\Zotero\\storage\\U4TVLDNQ\\Charbonneau et al. - 2015 - Jamming Criticality Revealed by Removing Localized.pdf:application/pdf},
}

@article{charbonneau_glass_2017,
	title = {Glass and {Jamming} {Transitions}: {From} {Exact} {Results} to {Finite}-{Dimensional} {Descriptions}},
	volume = {8},
	copyright = {review: finite vs infinite},
	issn = {1947-5454, 1947-5462},
	shorttitle = {Glass and {Jamming} {Transitions}},
	url = {http://www.annualreviews.org/doi/10.1146/annurev-conmatphys-031016-025334},
	doi = {10.1146/annurev-conmatphys-031016-025334},
	abstract = {Despite decades of work, gaining a first-principles understanding of amorphous materials remains an extremely challenging problem. However, recent theoretical breakthroughs have led to the formulation of an exact solution of a microscopic glass-forming model in the mean-field limit of infinite spatial dimension. Numerical simulations have remarkably confirmed the dimensional robustness of some of the predictions. This review describes these latest advances. More specifically, we consider the dynamical and thermodynamic descriptions of hard spheres around the dynamical, Gardner, and jamming transitions. Comparing mean-field predictions with the finitedimensional simulations, we identify robust aspects of the theory and uncover its more sensitive features. We conclude with a brief overview of ongoing research.},
	number = {1},
	urldate = {2020-04-21},
	journal = {Annual Review of Condensed Matter Physics},
	author = {Charbonneau, Patrick and Kurchan, Jorge and Parisi, Giorgio and Urbani, Pierfrancesco and Zamponi, Francesco},
	month = mar,
	year = {2017},
	pages = {265--288},
	file = {Charbonneau et al. - 2017 - Glass and Jamming Transitions From Exact Results .pdf:C\:\\Users\\craig\\Zotero\\storage\\XT9BWQVK\\Charbonneau et al. - 2017 - Glass and Jamming Transitions From Exact Results .pdf:application/pdf},
}

@article{dennis_jamming_2020,
	title = {Jamming {Energy} {Landscape} is {Hierarchical} and {Ultrametric}},
	volume = {124},
	copyright = {cam ultrametricity},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.124.078002},
	doi = {10.1103/PhysRevLett.124.078002},
	number = {7},
	urldate = {2020-04-21},
	journal = {Physical Review Letters},
	author = {Dennis, R. C. and Corwin, E. I.},
	month = feb,
	year = {2020},
	file = {Dennis and Corwin - 2020 - Jamming Energy Landscape is Hierarchical and Ultra.pdf:C\:\\Users\\craig\\Zotero\\storage\\6PFL8CAE\\Dennis and Corwin - 2020 - Jamming Energy Landscape is Hierarchical and Ultra.pdf:application/pdf},
}

@article{makse_why_1999,
	title = {Why {Effective} {Medium} {Theory} {Fails} in {Granular} {Materials}},
	volume = {83},
	copyright = {not sure (from sean)},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.83.5070},
	doi = {10.1103/PhysRevLett.83.5070},
	number = {24},
	urldate = {2020-02-14},
	journal = {Physical Review Letters},
	author = {Makse, Hernán A. and Gland, Nicolas and Johnson, David L. and Schwartz, Lawrence M.},
	month = dec,
	year = {1999},
	pages = {5070--5073},
	file = {Makse et al. - 1999 - Why Effective Medium Theory Fails in Granular Mate.pdf:C\:\\Users\\craig\\Zotero\\storage\\7SWCLIFZ\\Makse et al. - 1999 - Why Effective Medium Theory Fails in Granular Mate.pdf:application/pdf},
}

@article{arceri_vibrational_2019,
	title = {Vibrational properties of hard and soft spheres are unified at jamming},
	copyright = {cecco vibrational},
	url = {http://arxiv.org/abs/1912.05697},
	abstract = {The unconventional thermal properties of jammed amorphous solids are directly related to their density of vibrational states. While the vibrational spectrum of jammed soft sphere solids has been fully described, the vibrational spectrum of hard spheres, a model for colloidal glasses, is still unknown due to the difficulty of treating the non-analytic interaction potential. We bypass this difficulty using the recently described effective interaction potential for the free energy of thermal hard spheres. By minimizing this effective free energy we mimic a quench and produce typical configurations of low temperature colloidal glasses. We measure the resulting vibrational spectrum and characterize its evolution towards the jamming point where configurations of hard and soft spheres are trivially unified. For densities approaching jamming from below, we observe low frequency modes which agree with those found in numerical simulations of jammed soft spheres. Our measurements of the vibrational structure demonstrate that the jamming universality extends away from jamming: hard sphere thermal systems below jamming exhibit the same vibrational spectra as thermal and athermal soft sphere systems above the transition.},
	urldate = {2020-01-22},
	journal = {arXiv:1912.05697 [cond-mat]},
	author = {Arceri, Francesco and Corwin, Eric I.},
	month = dec,
	year = {2019},
	note = {arXiv: 1912.05697},
	keywords = {Condensed Matter - Soft Condensed Matter},
	annote = {Comment: 7 pages (supplement in the last page), 7 figures (5 in the main text, 2 in the supplement)},
	file = {Arceri and Corwin - 2019 - Vibrational properties of hard and soft spheres ar.pdf:C\:\\Users\\craig\\Zotero\\storage\\GT8DV6EC\\Arceri and Corwin - 2019 - Vibrational properties of hard and soft spheres ar.pdf:application/pdf},
}

@article{franz_universality_2017,
	title = {Universality of the {SAT}-{UNSAT} (jamming) threshold in non-convex continuous constraint satisfaction problems},
	volume = {2},
	copyright = {mean field predictions},
	issn = {2542-4653},
	url = {https://scipost.org/10.21468/SciPostPhys.2.3.019},
	doi = {10.21468/SciPostPhys.2.3.019},
	abstract = {Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical physics of disordered systems and computer science has brought new light into the realm of computational complexity theory, by introducing the notion of clustering of solutions, related to replica symmetry breaking. However, the class of problems in which clustering has been studied often involve discrete degrees of freedom: standard random CSPs are random K-SAT (aka disordered Ising models) or random coloring problems (aka disordered Potts models). In this work we consider instead problems that involve continuous degrees of freedom. The simplest prototype of these problems is the perceptron. Here we discuss in detail the full phase diagram of the model. In the regions of parameter space where the problem is non-convex, leading to multiple disconnected clusters of solutions, the solution is critical at the SAT/UNSAT threshold and lies in the same universality class of the jamming transition of soft spheres. We show how the critical behavior at the satisfiability threshold emerges, and we compute the critical exponents associated to the approach to the transition from both the SAT and UNSAT phase. We conjecture that there is a large universality class of non-convex continuous CSPs whose SAT-UNSAT threshold is described by the same scaling solution.},
	number = {3},
	urldate = {2020-01-18},
	journal = {SciPost Physics},
	author = {Franz, Silvio and Parisi, Giorgio and Sevelev, Maxime and Urbani, Pierfrancesco and Zamponi, Francesco},
	month = jun,
	year = {2017},
	file = {Franz et al. - 2017 - Universality of the SAT-UNSAT (jamming) threshold .pdf:C\:\\Users\\craig\\Zotero\\storage\\4NK6N58X\\Franz et al. - 2017 - Universality of the SAT-UNSAT (jamming) threshold .pdf:application/pdf},
}

@article{charbonneau_universal_2012,
	title = {Universal {Microstructure} and {Mechanical} {Stability} of {Jammed} {Packings}},
	volume = {109},
	copyright = {pyCudaPacking/phiC estimates in high D},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.109.205501},
	doi = {10.1103/PhysRevLett.109.205501},
	number = {20},
	urldate = {2018-11-27},
	journal = {Physical Review Letters},
	author = {Charbonneau, Patrick and Corwin, Eric I. and Parisi, Giorgio and Zamponi, Francesco},
	month = nov,
	year = {2012},
	file = {Charbonneau et al. - 2012 - Universal Microstructure and Mechanical Stability .pdf:C\:\\Users\\craig\\Zotero\\storage\\TNQDGVSD\\Charbonneau et al. - 2012 - Universal Microstructure and Mechanical Stability .pdf:application/pdf},
}

@book{parisi_theory_2020,
	address = {New York},
	title = {Theory of {Simple} {Glasses}: {Exact} {Solutions} in {Infinite} {Dimensions}},
	copyright = {Francesco Z's book},
	isbn = {978-1-107-19107-5},
	shorttitle = {Theory of {Simple} {Glasses}},
	abstract = {This pedagogical and self-contained text describes the modern mean field theory of simple structural glasses. The book begins with a thorough explanation of infinite-dimensional models in statistical physics, before reviewing the key elements of the thermodynamic theory of liquids and the dynamical properties of liquids and glasses. The central feature of the mean field theory of disordered systems, the existence of a large multiplicity of metastable states, is then introduced. The replica method is then covered, before the final chapters describe important, advanced topics such as Gardner transitions, complexity, packing spheres in large dimensions, the jamming transition, and the rheology of glass. Presenting the theory in a clear and pedagogical style, this is an excellent resource for researchers and graduate students working in condensed matter physics and statistical mechanics.},
	publisher = {Cambridge University Press},
	author = {Parisi, Giorgio and Urbani, Pierfrancesco and Zamponi, Francesco},
	month = feb,
	year = {2020},
}

@article{liu_jamming_2010,
	title = {The {Jamming} {Transition} and the {Marginally} {Jammed} {Solid}},
	volume = {1},
	copyright = {jamming review. contact number stuff},
	issn = {1947-5454, 1947-5462},
	url = {http://www.annualreviews.org/doi/10.1146/annurev-conmatphys-070909-104045},
	doi = {10.1146/annurev-conmatphys-070909-104045},
	abstract = {When a system jams it undergoes a transition from a flowing to a rigid state. Despite this important change in the dynamics, the internal structure of the system remains disordered in the solid as well as the fluid phase. In this way jamming is very different from crystallization, the other common way in which a fluid solidifies. Jamming is a paradigm for thinking about how many different types of fluids – from molecular liquids to macroscopic granular matter –develop rigidity. Here we review recent work on the jamming transition. We start with perhaps the simplest model of frictionless spheres interacting via repulsive finite-range forces at zero temperature. In this highly-idealized case, the transition has aspects of both first- and second-order transitions. From studies of the normal modes of vibration for the marginally jammed solid, new physics has emerged for how a material can be rigid without having the elastic properties of a normal solid. We first survey the simulation data and theoretical arguments that have been proposed to understand this behavior. We then review work that has systematically gone beyond the ideal model to see whether the scenario developed there is more generally applicable.},
	number = {1},
	urldate = {2020-01-18},
	journal = {Annual Review of Condensed Matter Physics},
	author = {Liu, Andrea J. and Nagel, Sidney R.},
	month = aug,
	year = {2010},
	pages = {347--369},
	file = {Liu and Nagel - 2010 - The Jamming Transition and the Marginally Jammed S.pdf:C\:\\Users\\craig\\Zotero\\storage\\55JKQ395\\Liu and Nagel - 2010 - The Jamming Transition and the Marginally Jammed S.pdf:application/pdf},
}

@article{bitzek_structural_2006-1,
	title = {Structural {Relaxation} {Made} {Simple}},
	volume = {97},
	copyright = {FIRE},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.97.170201},
	doi = {10.1103/PhysRevLett.97.170201},
	number = {17},
	urldate = {2018-11-15},
	journal = {Physical Review Letters},
	author = {Bitzek, Erik and Koskinen, Pekka and Gähler, Franz and Moseler, Michael and Gumbsch, Peter},
	month = oct,
	year = {2006},
}

@article{pellegrino_structural_1993,
	title = {Structural computations with the singular value decomposition of the equilibrium matrix},
	volume = {30},
	copyright = {singular value decomposition},
	issn = {0020-7683},
	url = {http://www.sciencedirect.com/science/article/pii/002076839390210X},
	doi = {10.1016/0020-7683(93)90210-X},
	abstract = {The Singular Value Decomposition of the equilibrium matrix makes it possible to answer any question of a static, kinematic, or static/kinematic nature for any structural assembly, within a unified computational framework. The paper introduces this decomposition, relates it to the physical properties of a given assembly, and derives formulae for stresses, displacements, etc. A simple example illustrates the calculations.},
	number = {21},
	urldate = {2020-02-14},
	journal = {International Journal of Solids and Structures},
	author = {Pellegrino, S.},
	month = jan,
	year = {1993},
	pages = {3025--3035},
	file = {ScienceDirect Snapshot:C\:\\Users\\craig\\Zotero\\storage\\HV24B36J\\002076839390210X.html:text/html},
}

@article{dagois-bohy_soft-sphere_2012,
	title = {Soft-{Sphere} {Packings} at {Finite} {Pressure} but {Unstable} to {Shear}},
	volume = {109},
	copyright = {excess contact def},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.109.095703},
	doi = {10.1103/PhysRevLett.109.095703},
	number = {9},
	urldate = {2018-11-27},
	journal = {Physical Review Letters},
	author = {Dagois-Bohy, Simon and Tighe, Brian P. and Simon, Johannes and Henkes, Silke and van Hecke, Martin},
	month = aug,
	year = {2012},
	file = {Dagois-Bohy et al. - 2012 - Soft-Sphere Packings at Finite Pressure but Unstab.pdf:C\:\\Users\\craig\\Zotero\\storage\\55KCS8UJ\\Dagois-Bohy et al. - 2012 - Soft-Sphere Packings at Finite Pressure but Unstab.pdf:application/pdf},
}

@article{goodrich_scaling_2016,
	title = {Scaling ansatz for the jamming transition},
	volume = {113},
	copyright = {excess scaling, e {\textasciitilde} p{\textasciicircum}1/2},
	issn = {0027-8424, 1091-6490},
	url = {http://www.pnas.org/lookup/doi/10.1073/pnas.1601858113},
	doi = {10.1073/pnas.1601858113},
	number = {35},
	urldate = {2019-05-09},
	journal = {Proceedings of the National Academy of Sciences},
	author = {Goodrich, Carl P. and Liu, Andrea J. and Sethna, James P.},
	month = aug,
	year = {2016},
	pages = {9745--9750},
	file = {Goodrich et al. - 2016 - Scaling ansatz for the jamming transition.pdf:C\:\\Users\\craig\\Zotero\\storage\\JPV62R23\\Goodrich et al. - 2016 - Scaling ansatz for the jamming transition.pdf:application/pdf},
}

@article{ohern_random_2002,
	title = {Random {Packings} of {Frictionless} {Particles}},
	volume = {88},
	copyright = {scaling stuff},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.88.075507},
	doi = {10.1103/PhysRevLett.88.075507},
	number = {7},
	urldate = {2020-01-18},
	journal = {Physical Review Letters},
	author = {O'Hern, Corey S. and Langer, Stephen A. and Liu, Andrea J. and Nagel, Sidney R.},
	month = jan,
	year = {2002},
	file = {O'Hern et al. - 2002 - Random Packings of Frictionless Particles.pdf:C\:\\Users\\craig\\Zotero\\storage\\8742Y9FH\\O'Hern et al. - 2002 - Random Packings of Frictionless Particles.pdf:application/pdf},
}

@article{mangeat_quantitative_2016,
	title = {Quantitative approximation schemes for glasses},
	volume = {93},
	copyright = {10 is not high D.},
	issn = {2470-0045, 2470-0053},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.93.012609},
	doi = {10.1103/PhysRevE.93.012609},
	number = {1},
	urldate = {2019-09-18},
	journal = {Physical Review E},
	author = {Mangeat, Matthieu and Zamponi, Francesco},
	month = jan,
	year = {2016},
	file = {Mangeat and Zamponi - 2016 - Quantitative approximation schemes for glasses.pdf:C\:\\Users\\craig\\Zotero\\storage\\HXEVR9TV\\Mangeat and Zamponi - 2016 - Quantitative approximation schemes for glasses.pdf:application/pdf},
}

@article{lubensky_phonons_2015,
	title = {Phonons and elasticity in critically coordinated lattices},
	volume = {78},
	copyright = {not sure (from sean)},
	issn = {0034-4885, 1361-6633},
	url = {http://stacks.iop.org/0034-4885/78/i=7/a=073901?key=crossref.ed7e2e7f699a1e53049f16f3a85fc3dc},
	doi = {10.1088/0034-4885/78/7/073901},
	abstract = {Much of our understanding of vibrational excitations and elasticity is based upon analysis of frames consisting of sites connected by bonds occupied by central-force springs, the stability of which depends on the average number of neighbors per site z. When z  {\textless}  zc  ≈  2d, where d is the spatial dimension, frames are unstable with respect to internal deformations. This pedagogical review focuses on the properties of frames with z at or near zc, which model systems like randomly packed spheres near jamming and network glasses. Using an index theorem, N0  −NS  =  dN  −NB relating the number of sites, N, and number of bonds, NB, to the number, N0, of modes of zero energy and the number, NS, of states of self stress, in which springs can be under positive or negative tension while forces on sites remain zero, it explores the properties of periodic square, kagome, and related lattices for which z  =  zc and the relation between states of self stress and zero modes in periodic lattices to the surface zero modes of finite free lattices (with free boundary conditions). It shows how modifications to the periodic kagome lattice can eliminate all but trivial translational zero modes and create topologically distinct classes, analogous to those of topological insulators, with protected zero modes at free boundaries and at interfaces between different topological classes.},
	number = {7},
	urldate = {2020-02-14},
	journal = {Reports on Progress in Physics},
	author = {Lubensky, T C and Kane, C L and Mao, Xiaoming and Souslov, A and Sun, Kai},
	month = jul,
	year = {2015},
	pages = {073901},
	file = {Lubensky et al. - 2015 - Phonons and elasticity in critically coordinated l.pdf:C\:\\Users\\craig\\Zotero\\storage\\U8S4492X\\Lubensky et al. - 2015 - Phonons and elasticity in critically coordinated l.pdf:application/pdf},
}

@article{charbonneau_glass_2011,
	title = {Glass {Transition} and {Random} {Close} {Packing} above {Three} {Dimensions}},
	volume = {107},
	copyright = {phiC estimates in high D},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.107.185702},
	doi = {10.1103/PhysRevLett.107.185702},
	number = {18},
	urldate = {2019-09-20},
	journal = {Physical Review Letters},
	author = {Charbonneau, Patrick and Ikeda, Atsushi and Parisi, Giorgio and Zamponi, Francesco},
	month = oct,
	year = {2011},
	file = {Charbonneau et al. - 2011 - Glass Transition and Random Close Packing above Th.pdf:C\:\\Users\\craig\\Zotero\\storage\\6L9RBP48\\Charbonneau et al. - 2011 - Glass Transition and Random Close Packing above Th.pdf:application/pdf},
}

@article{goodrich_finite-size_2012,
	title = {Finite-{Size} {Scaling} at the {Jamming} {Transition}},
	volume = {109},
	copyright = {excess contacts // maxwell counting},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.109.095704},
	doi = {10.1103/PhysRevLett.109.095704},
	number = {9},
	urldate = {2018-11-27},
	journal = {Physical Review Letters},
	author = {Goodrich, Carl P. and Liu, Andrea J. and Nagel, Sidney R.},
	month = aug,
	year = {2012},
	file = {Goodrich et al. - 2012 - Finite-Size Scaling at the Jamming Transition.pdf:C\:\\Users\\craig\\Zotero\\storage\\NURGT42V\\Goodrich et al. - 2012 - Finite-Size Scaling at the Jamming Transition.pdf:application/pdf},
}

@article{mailman_using_2012,
	title = {Using point-to-set correlations to probe unjamming of frictionless grains},
	volume = {2012},
	doi = {10.1088/1742-5468/2012/05/P05001},
	abstract = {We present a detailed analysis of the unjamming transition in 2D frictionless disk packings using a static correlation function that has been widely used to study disordered systems. We show that this point-to-set (PTS) correlation function exhibits a dominant length scale that diverges as the unjamming transition is approached through decompression. In addition, we identify deviations from mean-field predictions, and present detailed analysis of the origin of non-mean-field behavior. A mean-field bulk-surface argument is reviewed. Corrections to this argument are identified, which lead to a change in the functional form of the critical PTS boundary size R0. An entropic description of the origin of the correlations is presented, and simple rigidity assumptions are shown to predict the functional form of R0 as a function of the pressure P.},
	journal = {Journal of Statistical Mechanics-theory and Experiment - J STAT MECH-THEORY EXP},
	author = {Mailman, M and Chakraborty, Bulbul},
	month = may,
	year = {2012},
	file = {Full Text PDF:C\:\\Users\\craig\\Zotero\\storage\\SGP62XL4\\Mailman and Chakraborty - 2012 - Using point-to-set correlations to probe unjamming.pdf:application/pdf},
}

@article{bililign_protocol_2019,
	title = {Protocol {Dependence} and {State} {Variables} in the {Force}-{Moment} {Ensemble}},
	volume = {122},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.038001},
	doi = {10.1103/PhysRevLett.122.038001},
	number = {3},
	urldate = {2019-12-07},
	journal = {Physical Review Letters},
	author = {Bililign, Ephraim S. and Kollmer, Jonathan E. and Daniels, Karen E.},
	month = jan,
	year = {2019},
	pages = {038001},
	file = {Bililign et al. - 2019 - Protocol Dependence and State Variables in the For.pdf:C\:\\Users\\craig\\Zotero\\storage\\5CL8YKYA\\Bililign et al. - 2019 - Protocol Dependence and State Variables in the For.pdf:application/pdf},
}

@article{puckett_equilibrating_2013,
	title = {Equilibrating {Temperaturelike} {Variables} in {Jammed} {Granular} {Subsystems}},
	volume = {110},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.110.058001},
	doi = {10.1103/PhysRevLett.110.058001},
	number = {5},
	urldate = {2019-12-07},
	journal = {Physical Review Letters},
	author = {Puckett, James G. and Daniels, Karen E.},
	month = jan,
	year = {2013},
	pages = {058001},
	file = {Puckett and Daniels - 2013 - Equilibrating Temperaturelike Variables in Jammed .pdf:C\:\\Users\\craig\\Zotero\\storage\\VLIWL6WZ\\Puckett and Daniels - 2013 - Equilibrating Temperaturelike Variables in Jammed .pdf:application/pdf},
}

@article{grimus_100th_2013,
	title = {100th anniversary of the {Sackur}–{Tetrode} equation},
	volume = {525},
	issn = {1521-3889},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/andp.201300720},
	doi = {10.1002/andp.201300720},
	number = {3},
	urldate = {2019-12-07},
	journal = {Annalen der Physik},
	author = {Grimus, Walter},
	year = {2013},
	pages = {A32--A35},
	file = {Full Text PDF:C\:\\Users\\craig\\Zotero\\storage\\GRHPUZT3\\Grimus - 2013 - 100th anniversary of the Sackur–Tetrode equation.pdf:application/pdf;Snapshot:C\:\\Users\\craig\\Zotero\\storage\\KY9JCKCD\\andp.html:text/html},
}

@article{gao_enumeration_2007,
	title = {Enumeration of distinct mechanically stable disk packings in small systems},
	volume = {87},
	copyright = {enumeration of packings},
	issn = {1478-6435, 1478-6443},
	url = {http://www.tandfonline.com/doi/abs/10.1080/14786430600851760},
	doi = {10.1080/14786430600851760},
	number = {3-5},
	urldate = {2019-07-18},
	journal = {Philosophical Magazine},
	author = {Gao, G.-J. and Blawzdziewicz, J. and O'Hern, C. S.},
	month = jan,
	year = {2007},
	pages = {425--431},
	file = {Gao et al. - 2007 - Enumeration of distinct mechanically stable disk p.pdf:C\:\\Users\\craig\\Zotero\\storage\\6LQV9IR3\\Gao et al. - 2007 - Enumeration of distinct mechanically stable disk p.pdf:application/pdf},
}

@article{ohern_jamming_2003,
	title = {Jamming at zero temperature and zero applied stress: {The} epitome of disorder},
	volume = {68},
	copyright = {pressure definition AND shitty excess contacts comparison (table pg 9)},
	issn = {1063-651X, 1095-3787},
	shorttitle = {Jamming at zero temperature and zero applied stress},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.68.011306},
	doi = {10.1103/PhysRevE.68.011306},
	number = {1},
	urldate = {2019-05-09},
	journal = {Physical Review E},
	author = {O’Hern, Corey S. and Silbert, Leonardo E. and Liu, Andrea J. and Nagel, Sidney R.},
	month = jul,
	year = {2003},
	file = {O’Hern et al. - 2003 - Jamming at zero temperature and zero applied stres.pdf:C\:\\Users\\craig\\Zotero\\storage\\VTZQDYXN\\O’Hern et al. - 2003 - Jamming at zero temperature and zero applied stres.pdf:application/pdf},
}

@article{goodrich_solids_2014,
	title = {Solids between the mechanical extremes of order and disorder},
	volume = {10},
	copyright = {justifying claim that amorphous and crrystalline are different},
	issn = {1745-2473, 1745-2481},
	url = {http://www.nature.com/articles/nphys3006},
	doi = {10.1038/nphys3006},
	number = {8},
	urldate = {2021-07-08},
	journal = {Nature Physics},
	author = {Goodrich, Carl P. and Liu, Andrea J. and Nagel, Sidney R.},
	month = aug,
	year = {2014},
	pages = {578--581},
	file = {Goodrich et al. - 2014 - Solids between the mechanical extremes of order an.pdf:C\:\\Users\\craig\\Zotero\\storage\\QLMLJS7U\\Goodrich et al. - 2014 - Solids between the mechanical extremes of order an.pdf:application/pdf},
}

@article{maxwell_calculation_1864,
	title = {On the calculation of the equilibrium and stiffness  of  frames.},
	volume = {27},
	copyright = {maxwell count},
	url = {http://ebooks.cambridge.org/ref/id/CBO9780511698095},
	number = {182},
	urldate = {2021-07-08},
	journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science},
	author = {Maxwell, James Clerk},
	year = {1864},
	doi = {10.1017/CBO9780511698095},
	pages = {294--299},
	file = {Maxwell - 2011 - The Scientific Papers of James Clerk Maxwell.pdf:C\:\\Users\\craig\\Zotero\\storage\\KD54A576\\Maxwell - 2011 - The Scientific Papers of James Clerk Maxwell.pdf:application/pdf},
}

@article{sartor_mean-field_2021,
	title = {Mean-{Field} {Predictions} of {Scaling} {Prefactors} {Match} {Low}-{Dimensional} {Jammed} {Packings}},
	volume = {126},
	copyright = {me},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.126.048001},
	doi = {10.1103/PhysRevLett.126.048001},
	abstract = {No known analytic framework precisely explains all the phenomena observed in jamming. The replica theory for glasses and jamming is a mean-field theory which attempts to do so by working in the limit of infinite dimensions, such that correlations between neighbors are negligible. As such, results from this mean-field theory are not guaranteed to be observed in finite dimensions. However, many results in mean field for jamming have been shown to be exact or nearly exact in low dimensions. This suggests that the infinite dimensional limit is not necessary to obtain these results. In this Letter, we perform precision measurements of jamming scaling relationships between pressure, excess packing fraction, and number of excess contacts from dimensions 2–10 in order to extract the prefactors to these scalings. While these prefactors should be highly sensitive to finite dimensional corrections, we find the mean-field predictions for these prefactors to be exact in low dimensions. Thus the mean-field approximation is not necessary for deriving these prefactors. We present an exact, first-principles derivation for one, leaving the other as an open question. Our results suggest that mean-field theories of critical phenomena may compute more for d≥du than has been previously appreciated.},
	number = {4},
	urldate = {2021-06-09},
	journal = {Physical Review Letters},
	author = {Sartor, James D. and Ridout, Sean A. and Corwin, Eric I.},
	month = jan,
	year = {2021},
	pages = {048001},
	file = {APS Snapshot:C\:\\Users\\craig\\Zotero\\storage\\WFZ785P4\\PhysRevLett.126.html:text/html},
}

@article{f._hagh_broader_2019,
	title = {A broader view on jamming: from spring networks to circle packings},
	volume = {15},
	copyright = {rigidity matrix stuff},
	issn = {1744-683X, 1744-6848},
	shorttitle = {A broader view on jamming},
	url = {http://xlink.rsc.org/?DOI=C8SM01768A},
	doi = {10.1039/C8SM01768A},
	abstract = {Jammed packings can be generated by pruning elastic networks and mapping them into circle packings.
          , 
            
              Jamming occurs when objects like grains are packed tightly together (
              e.g.
              grain silos). It is highly cooperative and can lead to phenomena like earthquakes, traffic jams,
              etc.
              In this paper we point out the paramount importance of the underlying contact network for jammed systems; the network must have one contact in excess of isostaticity and a finite bulk modulus. Isostatic means that the number of degrees of freedom is exactly balanced by the number of constraints. This defines a large class of networks that can be constructed without the necessity of packing particles together compressively (either in the lab or computationally). One such construction, which we explore here, involves setting up the Delaunay triangulation of a Poisson disk sampling and then removing edges to maximize the bulk modulus until the isostatic plus one edge is reached. This construction works in any dimensions and here we give results in 2D where we also show how such networks can be transformed into disk packs.},
	number = {15},
	urldate = {2019-12-07},
	journal = {Soft Matter},
	author = {F. Hagh, Varda and Corwin, Eric I. and Stephenson, Kenneth and Thorpe, M. F.},
	year = {2019},
	pages = {3076--3084},
	file = {F. Hagh et al. - 2019 - A broader view on jamming from spring networks to.pdf:C\:\\Users\\craig\\Zotero\\storage\\XQA33IHT\\F. Hagh et al. - 2019 - A broader view on jamming from spring networks to.pdf:application/pdf},
}

@article{sussman_spatial_2016,
	title = {Spatial structure of states of self stress in jammed systems},
	volume = {12},
	copyright = {spatial structure of sss},
	issn = {1744-683X, 1744-6848},
	url = {http://xlink.rsc.org/?DOI=C6SM00094K},
	doi = {10.1039/C6SM00094K},
	number = {17},
	urldate = {2021-04-20},
	journal = {Soft Matter},
	author = {Sussman, Daniel M. and Goodrich, Carl P. and Liu, Andrea J.},
	year = {2016},
	pages = {3982--3990},
	file = {Sussman et al. - 2016 - Spatial structure of states of self stress in jamm.pdf:C\:\\Users\\craig\\Zotero\\storage\\Y2QTUBAG\\Sussman et al. - 2016 - Spatial structure of states of self stress in jamm.pdf:application/pdf},
}

@article{taylor_mechanism_1934,
	title = {The mechanism of plastic deformation of crystals. {Part} {I}.—{Theoretical}},
	volume = {145},
	copyright = {crystal defects},
	issn = {0950-1207, 2053-9150},
	url = {https://royalsocietypublishing.org/doi/10.1098/rspa.1934.0106},
	doi = {10.1098/rspa.1934.0106},
	abstract = {Experiments on the plastic deformation of single crystals, of metals and of rock salt have given results which differ in detail but possess certain common characteristics. In general the deformation of a single crystal in tension or compression consists of shear strain in which sheets of the crystal parallel to a crystal plane slip over one another, the direction of motion being some simple crystal-lographic axis. The measure of this strain, which will be represented by
              s
              , is the ration of the relative lateral movement of two parallel planes of slip to the distance between them. Thus it is defined in the same way as the shear strain considered in the theory of elasticity.},
	number = {855},
	urldate = {2021-04-21},
	journal = {Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character},
	author = {Taylor, G},
	month = jul,
	year = {1934},
	pages = {362--387},
	file = {1934 - The mechanism of plastic deformation of crystals. .pdf:C\:\\Users\\craig\\Zotero\\storage\\QTL8Y2ZL\\1934 - The mechanism of plastic deformation of crystals. .pdf:application/pdf},
}

@article{schoenholz_understanding_2014,
	title = {Understanding {Plastic} {Deformation} in {Thermal} {Glasses} from {Single}-{Soft}-{Spot} {Dynamics}},
	copyright = {defects},
	author = {Schoenholz, S S and Liu, A J and Riggleman, R A and Rottler, J},
	year = {2014},
	pages = {11},
	file = {Schoenholz et al. - 2014 - Understanding Plastic Deformation in Thermal Glass.pdf:C\:\\Users\\craig\\Zotero\\storage\\VLXVMUQT\\Schoenholz et al. - 2014 - Understanding Plastic Deformation in Thermal Glass.pdf:application/pdf;PhysRevLett.95.098301(1).pdf:C\:\\Users\\craig\\Zotero\\storage\\7YAQNBDA\\PhysRevLett.95.098301(1).pdf:application/pdf},
}

@article{manning_vibrational_2011,
	title = {Vibrational {Modes} {Identify} {Soft} {Spots} in a {Sheared} {Disordered} {Packing}},
	volume = {107},
	copyright = {defects},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.107.108302},
	doi = {10.1103/PhysRevLett.107.108302},
	number = {10},
	urldate = {2021-04-20},
	journal = {Physical Review Letters},
	author = {Manning, M. L. and Liu, A. J.},
	month = aug,
	year = {2011},
	pages = {108302},
	file = {Manning and Liu - 2011 - Vibrational Modes Identify Soft Spots in a Sheared.pdf:C\:\\Users\\craig\\Zotero\\storage\\MZBB5IYG\\Manning and Liu - 2011 - Vibrational Modes Identify Soft Spots in a Sheared.pdf:application/pdf},
}

@article{ding_soft_2014,
	title = {Soft spots and their structural signature in a metallic glass},
	volume = {111},
	copyright = {defects},
	issn = {0027-8424, 1091-6490},
	url = {http://www.pnas.org/lookup/doi/10.1073/pnas.1412095111},
	doi = {10.1073/pnas.1412095111},
	number = {39},
	urldate = {2021-04-20},
	journal = {Proceedings of the National Academy of Sciences},
	author = {Ding, Jun and Patinet, Sylvain and Falk, Michael L. and Cheng, Yongqiang and Ma, Evan},
	month = sep,
	year = {2014},
	pages = {14052--14056},
	file = {Ding et al. - 2014 - Soft spots and their structural signature in a met.pdf:C\:\\Users\\craig\\Zotero\\storage\\3GV2C7CY\\Ding et al. - 2014 - Soft spots and their structural signature in a met.pdf:application/pdf},
}

@article{cubuk_identifying_2015,
	title = {Identifying {Structural} {Flow} {Defects} in {Disordered} {Solids} {Using} {Machine}-{Learning} {Methods}},
	volume = {114},
	copyright = {defects},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.114.108001},
	doi = {10.1103/PhysRevLett.114.108001},
	number = {10},
	urldate = {2021-04-20},
	journal = {Physical Review Letters},
	author = {Cubuk, E. D. and Schoenholz, S. S. and Rieser, J. M. and Malone, B. D. and Rottler, J. and Durian, D. J. and Kaxiras, E. and Liu, A. J.},
	month = mar,
	year = {2015},
	pages = {108001},
	file = {Cubuk et al. - 2015 - Identifying Structural Flow Defects in Disordered .pdf:C\:\\Users\\craig\\Zotero\\storage\\K39DLGVL\\Cubuk et al. - 2015 - Identifying Structural Flow Defects in Disordered .pdf:application/pdf},
}

@article{wijtmans_disentangling_2017,
	title = {Disentangling defects and sound modes in disordered solids},
	volume = {13},
	copyright = {defects (vibrational)},
	issn = {1744-683X, 1744-6848},
	url = {http://xlink.rsc.org/?DOI=C7SM00792B},
	doi = {10.1039/C7SM00792B},
	abstract = {Adding an artificial potential to simulations of disordered solids isolates localized excitations from phonon-like modes in the vibrational spectrum. These structural defects predict locations and displacements in particle rearrangements.
          , 
            We develop a new method to isolate localized defects from extended vibrational modes in disordered solids. This method augments particle interactions with an artificial potential that acts as a high-pass filter: it preserves small-scale structures while pushing extended vibrational modes to higher frequencies. The low-frequency modes that remain are “bare” defects; they are exponentially localized without the quadrupolar tails associated with elastic interactions. We demonstrate that these localized excitations are excellent predictors of plastic rearrangements in the solid. We characterize several of the properties of these defects that appear in mesoscopic theory of plasticity, including their distribution of energy barriers, number density, and size, which is a first step in testing and revising continuum models for plasticity in disordered solids.},
	number = {34},
	urldate = {2021-04-20},
	journal = {Soft Matter},
	author = {Wijtmans, Sven and Manning, M. Lisa},
	year = {2017},
	pages = {5649--5655},
	file = {Wijtmans and Manning - 2017 - Disentangling defects and sound modes in disordere.pdf:C\:\\Users\\craig\\Zotero\\storage\\6JT947IG\\Wijtmans and Manning - 2017 - Disentangling defects and sound modes in disordere.pdf:application/pdf},
}

@article{barber_quickhull_1996,
	title = {The quickhull algorithm for convex hulls},
	volume = {22},
	copyright = {qhull},
	issn = {00983500},
	url = {http://portal.acm.org/citation.cfm?doid=235815.235821},
	doi = {10.1145/235815.235821},
	number = {4},
	urldate = {2018-11-27},
	journal = {ACM Transactions on Mathematical Software},
	author = {Barber, C. Bradford and Dobkin, David P. and Huhdanpaa, Hannu},
	month = dec,
	year = {1996},
	pages = {469--483},
	file = {Barber et al. - 1996 - The quickhull algorithm for convex hulls.pdf:C\:\\Users\\craig\\Zotero\\storage\\VYKSJ439\\Barber et al. - 1996 - The quickhull algorithm for convex hulls.pdf:application/pdf},
}

@article{bi_statistical_2015,
	title = {The {Statistical} {Physics} of {Athermal} {Materials}},
	volume = {6},
	copyright = {review // compactivity bounds // edwards ensemble},
	issn = {1947-5454, 1947-5462},
	url = {http://arxiv.org/abs/1404.1854},
	doi = {10.1146/annurev-conmatphys-031214-014336},
	abstract = {At the core of equilibrium statistical mechanics lies the notion of statistical ensembles: a collection of microstates, each occurring with a given a priori probability that depends only on a few macroscopic parameters such as temperature, pressure, volume, and energy. In this review article, we discuss recent advances in establishing statistical ensembles for athermal materials. The broad class of granular and particulate materials is immune from the effects of thermal fluctuations because the constituents are macroscopic. In addition, interactions between grains are frictional and dissipative, which invalidates the fundamental postulates of equilibrium statistical mechanics. However, granular materials exhibit distributions of microscopic quantities that are reproducible and often depend on only a few macroscopic parameters. We explore the history of statistical ensemble ideas in the context of granular materials, clarify the nature of such ensembles and their foundational principles, highlight advances in testing key ideas, and discuss applications of ensembles to analyze the collective behavior of granular materials.},
	number = {1},
	urldate = {2018-08-21},
	journal = {Annual Review of Condensed Matter Physics},
	author = {Bi, Dapeng and Henkes, Silke and Daniels, Karen E. and Chakraborty, Bulbul},
	month = mar,
	year = {2015},
	note = {arXiv: 1404.1854},
	keywords = {Condensed Matter - Statistical Mechanics, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Soft Condensed Matter},
	pages = {63--83},
	file = {Bi et al. - 2015 - The Statistical Physics of Athermal Materials.pdf:C\:\\Users\\craig\\Zotero\\storage\\25X59XHI\\Bi et al. - 2015 - The Statistical Physics of Athermal Materials.pdf:application/pdf},
}

@article{charbonneau_jamming_2015-1,
	title = {Jamming {Criticality} {Revealed} by {Removing} {Localized} {Buckling} {Excitations}},
	volume = {114},
	copyright = {rigidity matrix},
	issn = {0031-9007, 1079-7114},
	url = {http://arxiv.org/abs/1411.3975},
	doi = {10.1103/PhysRevLett.114.125504},
	abstract = {Recent theoretical advances offer an exact, first-principle theory of jamming criticality in infinite dimension as well as universal scaling relations between critical exponents in all dimensions. For packings of frictionless spheres near the jamming transition, these advances predict that nontrivial power-law exponents characterize the critical distribution of (i) small inter-particle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the inter-particle gaps is known to be constant in all spatial dimensions \$d\$ -- including the physically relevant \$d=2\$ and 3, but the value of the weak force exponent remains the object of debate and confusion. Here, we resolve this ambiguity by numerical simulations. We construct isostatic jammed packings with extremely high accuracy, and introduce a simple criterion to separate the contribution of particles that give rise to localized buckling excitations, i.e., bucklers, from the others. This analysis reveals the remarkable dimensional robustness of mean-field marginality and its associated criticality.},
	number = {12},
	urldate = {2018-11-16},
	journal = {Physical Review Letters},
	author = {Charbonneau, P. and Corwin, E. I. and Parisi, G. and Zamponi, F.},
	month = mar,
	year = {2015},
	note = {arXiv: 1411.3975},
	keywords = {Condensed Matter - Statistical Mechanics, Condensed Matter - Disordered Systems and Neural Networks},
	file = {Charbonneau et al. - 2015 - Jamming Criticality Revealed by Removing Localized.pdf:C\:\\Users\\craig\\Zotero\\storage\\Q5FMQDV3\\Charbonneau et al. - 2015 - Jamming Criticality Revealed by Removing Localized.pdf:application/pdf},
}

@article{ellenbroek_rigidity_2015,
	title = {Rigidity {Loss} in {Disordered} {Systems}: {Three} {Scenarios}},
	volume = {114},
	copyright = {rigidity matrix},
	issn = {0031-9007, 1079-7114},
	shorttitle = {Rigidity {Loss} in {Disordered} {Systems}},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.114.135501},
	doi = {10.1103/PhysRevLett.114.135501},
	number = {13},
	urldate = {2018-11-27},
	journal = {Physical Review Letters},
	author = {Ellenbroek, Wouter G. and Hagh, Varda F. and Kumar, Avishek and Thorpe, M. F. and van Hecke, Martin},
	month = apr,
	year = {2015},
	file = {Ellenbroek et al. - 2015 - Rigidity Loss in Disordered Systems Three Scenari.pdf:C\:\\Users\\craig\\Zotero\\storage\\X8GXAWFW\\Ellenbroek et al. - 2015 - Rigidity Loss in Disordered Systems Three Scenari.pdf:application/pdf},
}

@article{snoeijer_force_2004,
	title = {Force {Network} {Ensemble}: {A} {New} {Approach} to {Static} {Granular} {Matter}},
	volume = {92},
	copyright = {FNE original paper},
	issn = {0031-9007, 1079-7114},
	shorttitle = {Force {Network} {Ensemble}},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.92.054302},
	doi = {10.1103/PhysRevLett.92.054302},
	number = {5},
	urldate = {2018-11-24},
	journal = {Physical Review Letters},
	author = {Snoeijer, Jacco H. and Vlugt, Thijs J. H. and van Hecke, Martin and van Saarloos, Wim},
	month = feb,
	year = {2004},
	file = {Snoeijer et al. - 2004 - Force Network Ensemble A New Approach to Static G.pdf:C\:\\Users\\craig\\Zotero\\storage\\KR5ZV4IU\\Snoeijer et al. - 2004 - Force Network Ensemble A New Approach to Static G.pdf:application/pdf},
}

@article{tighe_stress_2011,
	title = {Stress fluctuations in granular force networks},
	volume = {2011},
	copyright = {FNE // sep of scales},
	issn = {1742-5468},
	url = {http://stacks.iop.org/1742-5468/2011/i=04/a=P04002?key=crossref.ec4d93d62266e3242532ceb8b8079f6f},
	doi = {10.1088/1742-5468/2011/04/P04002},
	abstract = {The heterogeneous force networks in static granular media are distinguished from other network structures in that they must satisfy constraints of mechanical equilibrium on every vertex/grain. Here we study the statistics of ensembles of hyperstatic frictionless force networks, which are composed of more forces than can be determined uniquely from force balance. Hyperstatic force networks possess degrees of freedom that rearrange one balanced network into another. We calculate the equation of state and demonstrate that the number of rearrangements governs the macroscopic statistical properties of the ensemble, in particular the macroscopic fluctuations of stress, which scale with distance to the isostatic point. We then show that a maximum entropy postulate allows one to quantitatively capture many features of the microscopic statistics. All predictions are tested against highly accurate Monte Carlo numerical simulations employing umbrella sampling.},
	number = {04},
	urldate = {2018-08-21},
	journal = {Journal of Statistical Mechanics: Theory and Experiment},
	author = {Tighe, Brian P and Vlugt, Thijs J H},
	month = apr,
	year = {2011},
	pages = {P04002},
	file = {Tighe and Vlugt - 2011 - Stress fluctuations in granular force networks.pdf:C\:\\Users\\craig\\Zotero\\storage\\EDL6G6ZT\\Tighe and Vlugt - 2011 - Stress fluctuations in granular force networks.pdf:application/pdf},
}

@article{tighe_force_2010,
	title = {The force network ensemble for granular packings},
	volume = {6},
	copyright = {FNE \#2, sep of scales},
	issn = {1744-683X, 1744-6848},
	url = {http://xlink.rsc.org/?DOI=b926592a},
	doi = {10.1039/b926592a},
	abstract = {The idea of sampling all possible configurations goes back to Edwards, who advocated considering ensembles of all grain configurations consistent with some set of boundary conditions.34 In general this is hard or impossible to do explicitly. The FNE can be seen as a restricted Edwards ensemble,17 with an extensive measure of the stress playing a role analogous to energy in equilibrium statistical mechanics.35,36 The ensemble then allows one to explore the consequences of and limits to the Edwards approach. For example, we will see that one popular notion, namely that entropy maximization implies robustly exponential force statistics,37 does not survive confrontation with the FNE.},
	number = {13},
	urldate = {2018-08-21},
	journal = {Soft Matter},
	author = {Tighe, Brian P. and Snoeijer, Jacco H. and Vlugt, Thijs J. H. and van Hecke, Martin},
	year = {2010},
	pages = {2908},
	file = {Tighe et al. - 2010 - The force network ensemble for granular packings.pdf:C\:\\Users\\craig\\Zotero\\storage\\72NCJCWM\\Tighe et al. - 2010 - The force network ensemble for granular packings.pdf:application/pdf},
}

@article{rissone_long-range_2020,
	title = {Long-range anomalous decay of the correlation in jammed packings},
	copyright = {angle correlation},
	url = {http://arxiv.org/abs/2012.10181},
	abstract = {We numerically study the structure of the interactions occurring in three-dimensional systems of hard spheres at jamming, focusing on the large-scale behavior. Given the fundamental role they play in the configuration of jammed packings, we analyze the propagation through the system of the weak forces and of the variation of the coordination number w.r.t. the isostaticity condition, \{{\textbackslash}Delta\}Z. We show that these correlations can be successfully probed by introducing a correlation function weighted on the density-density fluctuations. The results of this analysis can be further improved by introducing a representation of the system based on the contact points between particles. In particular, we find evidence that the weak forces and the \{{\textbackslash}Delta\}Z fluctuations support the hypothesis of randomly jammed packings of spherical particles being hyperuniform by exhibiting an anomalous long-range decay. Moreover, we find that the large-scale structure of the density-density correlation exhibits a complex behavior due to the superimposition of two exponentially damped oscillating signals propagating with linearly depending frequencies.},
	urldate = {2021-04-20},
	journal = {arXiv:2012.10181 [cond-mat]},
	author = {Rissone, Paolo and Corwin, Eric I. and Parisi, Giorgio},
	month = dec,
	year = {2020},
	note = {arXiv: 2012.10181},
	keywords = {Condensed Matter - Statistical Mechanics, Condensed Matter - Soft Condensed Matter},
	file = {Rissone et al. - 2020 - Long-range anomalous decay of the correlation in j.pdf:C\:\\Users\\craig\\Zotero\\storage\\FDJE5LP8\\Rissone et al. - 2020 - Long-range anomalous decay of the correlation in j.pdf:application/pdf},
}

@article{cubuk_structural_2016,
	title = {Structural {Properties} of {Defects} in {Glassy} {Liquids}},
	volume = {120},
	copyright = {softness defects},
	issn = {1520-6106, 1520-5207},
	url = {https://pubs.acs.org/doi/10.1021/acs.jpcb.6b02144},
	doi = {10.1021/acs.jpcb.6b02144},
	abstract = {At zero temperature a disordered solid corresponds to a local minimum in the energy landscape. As the temperature is raised or the system is driven with a mechanical load, the system explores different minima via dynamical events in which particles rearrange their relative positions. We have shown recently that the dynamics of particle rearrangements are strongly correlated with a structural quantity associated with each particle, “softness”, which we can identify using supervised machine learning. Particles of a given softness have a well-defined energy scale that governs local rearrangements; because of this property, softness greatly simplifies our understanding of glassy dynamics. Here we investigate the correlation of softness with other commonly used structural quantities, such as coordination number and local potential energy. We show that although softness strongly correlates with these properties, its predictive power for rearrangement dynamics is much higher. We introduce a useful metric for quantifying the quality of structural quantities as predictors of dynamics. We hope that, in the future, authors introducing new structural measures of dynamics will compare their proposals quantitatively to softness using this metric. We also show how softness correlations give insight into rearrangements. Finally, we explore the physical meaning of softness using unsupervised dimensionality reduction and reduced curve-fitting models, and show that softness can be recast in a form that is amenable to analytical treatment.},
	number = {26},
	urldate = {2021-04-20},
	journal = {The Journal of Physical Chemistry B},
	author = {Cubuk, Ekin D. and Schoenholz, Samuel S. and Kaxiras, Efthimios and Liu, Andrea J.},
	month = jul,
	year = {2016},
	pages = {6139--6146},
	file = {Cubuk et al. - 2016 - Structural Properties of Defects in Glassy Liquids.pdf:C\:\\Users\\craig\\Zotero\\storage\\WALDY5GG\\Cubuk et al. - 2016 - Structural Properties of Defects in Glassy Liquids.pdf:application/pdf},
}

@article{schoenholz_structural_2016,
	title = {A structural approach to relaxation in glassy liquids},
	volume = {12},
	copyright = {sussman softness},
	issn = {1745-2473, 1745-2481},
	url = {http://www.nature.com/articles/nphys3644},
	doi = {10.1038/nphys3644},
	number = {5},
	urldate = {2021-04-20},
	journal = {Nature Physics},
	author = {Schoenholz, S. S. and Cubuk, E. D. and Sussman, D. M. and Kaxiras, E. and Liu, A. J.},
	month = may,
	year = {2016},
	pages = {469--471},
	file = {Schoenholz et al. - 2016 - A structural approach to relaxation in glassy liqu.pdf:C\:\\Users\\craig\\Zotero\\storage\\KE2QAF48\\Schoenholz et al. - 2016 - A structural approach to relaxation in glassy liqu.pdf:application/pdf},
}

@article{brizin_finite_1985,
	title = {Finite size effects in phase transitions},
	volume = {257},
	copyright = {sean requested},
	doi = {10.1016/0550-3213(85)90379-7},
	journal = {Nuclear Physics B},
	author = {Brizin, E and Zinn-Justin, J},
	year = {1985},
	pages = {27},
	file = {Brizin and Zinn-Justin - FINITE SIZE EFFECTS IN PHASE TRANSITIONS.pdf:C\:\\Users\\craig\\Zotero\\storage\\VS4X3GXV\\Brizin and Zinn-Justin - FINITE SIZE EFFECTS IN PHASE TRANSITIONS.pdf:application/pdf},
}

@article{blote_universality_1997,
	title = {Universality and the five-dimensional {Ising} model},
	volume = {38},
	copyright = {sean requested},
	issn = {0295-5075, 1286-4854},
	url = {https://iopscience.iop.org/article/10.1209/epl/i1997-00284-x},
	doi = {10.1209/epl/i1997-00284-x},
	abstract = {We solve the long-standing discrepancy between Monte Carlo results and the renormalization prediction for the Binder cumulant of the five-dimensional Ising model. Our conclusions are based on accurate Monte Carlo data for systems with linear sizes up to L = 22. A detailed analysis of the corrections to scaling allows the extrapolation of these results to L = ∞. Our determination of the critical point, Kc = 0.1139150 (4), is more than an order of magnitude more accurate than previous estimates.},
	number = {8},
	urldate = {2020-10-27},
	journal = {Europhysics Letters (EPL)},
	author = {Blöte, H. W. J and Luijten, E},
	month = jun,
	year = {1997},
	pages = {565--570},
	file = {Blöte and Luijten - 1997 - Universality and the five-dimensional Ising model.pdf:C\:\\Users\\craig\\Zotero\\storage\\ZK3NP5JX\\Blöte and Luijten - 1997 - Universality and the five-dimensional Ising model.pdf:application/pdf},
}

@article{parisi_scaling_1996,
	title = {Scaling above the upper critical dimension in {Ising} models},
	volume = {54},
	copyright = {scaling of ising model at 5D},
	issn = {0163-1829, 1095-3795},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.54.R3698},
	doi = {10.1103/PhysRevB.54.R3698},
	number = {6},
	urldate = {2020-10-26},
	journal = {Physical Review B},
	author = {Parisi, Giorgio and Ruiz-Lorenzo, Juan J.},
	month = aug,
	year = {1996},
	pages = {R3698--R3701},
	file = {Parisi and Ruiz-Lorenzo - 1996 - Scaling above the upper critical dimension in Isin.pdf:C\:\\Users\\craig\\Zotero\\storage\\WVG7HWZN\\Parisi and Ruiz-Lorenzo - 1996 - Scaling above the upper critical dimension in Isin.pdf:application/pdf},
}

@book{privman_universal_1991,
	title = {Universal {Critical}-{Point} {Amplitude} {Relations}, in "{Phase} transition and critical phenomena" vol. 14, {C}. {Domb} and {JL} {Lebowitz} eds},
	copyright = {book with percolation exact formula},
	publisher = {Academic Press},
	author = {Privman, V and Hohenberg, P. C. and Aharony, A},
	year = {1991},
}

@article{aronovitz_universal_1987,
	title = {Universal features of the shapes of percolation clusters and lattice animals},
	volume = {20},
	copyright = {percolation comparison},
	issn = {0305-4470, 1361-6447},
	url = {https://iopscience.iop.org/article/10.1088/0305-4470/20/9/038},
	doi = {10.1088/0305-4470/20/9/038},
	abstract = {The shapes of percolation clusters and lattice animals are investigated. The universal quantities Ad and s d , which were introduced to measure the average asymmetry and degree of prolate- or oblateness, respectively, of long-chain polymers, are here computed in an E expansion for percolation clusters and for lattice animals. A,, is computed to O(E ) , while S, is computed to O(1). The clusters are shown to be on average anisotropic and prolate, but less so than polymers. Percolation clusters and lattice animals have identical shapes above eight dimensions. Below d = 8 animals are slightly more anisotropic than percolation clusters.},
	number = {9},
	urldate = {2020-10-26},
	journal = {Journal of Physics A: Mathematical and General},
	author = {Aronovitz, J A and Stephen, M J},
	month = jun,
	year = {1987},
	pages = {2539--2556},
	file = {Aronovitz and Stephen - 1987 - Universal features of the shapes of percolation cl.pdf:C\:\\Users\\craig\\Zotero\\storage\\67CENQ2P\\Aronovitz and Stephen - 1987 - Universal features of the shapes of percolation cl.pdf:application/pdf},
}

@book{allen_computer_1989,
	title = {Computer {Simulation} of {Liquids}},
	copyright = {textbook def of stress tensor},
	isbn = {978-0-19-855645-9},
	abstract = {Computer simulation is an essential tool in studying the chemistry and physics of liquids. Simulations allow us to develop models and to test them against experimental data. They can be used to evaluate approximate theories of liquids, and to provide detailed information on the structure anddynamics of model liquids at the molecular level. This book is an introduction and practical guide to the molecular dynamics and Monte Carlo methods.The first four chapters describe these methods in detail, and provide the essential background in intermolecular forces and statistical mechanics. Chapters 5 and 6 emphasize the practical aspects of writing efficient programs and analysing the simulation results. The remaining chapters coveradvanced techniques, non-equilibrium methods, Brownian dynamics, quantum simulations, and some important applications. FORTRAN code is presented in the text.},
	publisher = {Clarendon Press},
	author = {Allen, M. P. and Allen, M. P. and Tildesley, D. J. and ALLEN, TILDESLEY and Tildesley, D. J.},
	year = {1989},
	keywords = {History / Europe / Ireland, Technology \& Engineering / Chemical \& Biochemical},
}

@article{richard_predicting_2020,
	title = {Predicting plasticity in disordered solids from structural indicators},
	volume = {4},
	copyright = {defects},
	issn = {2475-9953},
	url = {https://link.aps.org/doi/10.1103/PhysRevMaterials.4.113609},
	doi = {10.1103/PhysRevMaterials.4.113609},
	number = {11},
	urldate = {2021-07-13},
	journal = {Physical Review Materials},
	author = {Richard, D. and Ozawa, M. and Patinet, S. and Stanifer, E. and Shang, B. and Ridout, S. A. and Xu, B. and Zhang, G. and Morse, P. K. and Barrat, J.-L. and Berthier, L. and Falk, M. L. and Guan, P. and Liu, A. J. and Martens, K. and Sastry, S. and Vandembroucq, D. and Lerner, E. and Manning, M. L.},
	month = nov,
	year = {2020},
	pages = {113609},
	file = {Richard et al. - 2020 - Predicting plasticity in disordered solids from st.pdf:C\:\\Users\\craig\\Zotero\\storage\\AMS7DWZ5\\Richard et al. - 2020 - Predicting plasticity in disordered solids from st.pdf:application/pdf},
}

@article{falk_dynamics_nodate,
	title = {Dynamics of viscoplastic deformation in amorphous solids},
	author = {Falk, M L and Langer, J S},
	pages = {14},
	file = {Falk and Langer - Dynamics of viscoplastic deformation in amorphous .pdf:C\:\\Users\\craig\\Zotero\\storage\\UBJ7MQNI\\Falk and Langer - Dynamics of viscoplastic deformation in amorphous .pdf:application/pdf},
}

@article{kollmer_betweenness_2019,
	title = {Betweenness centrality as predictor for forces in granular packings},
	volume = {15},
	issn = {1744-683X, 1744-6848},
	url = {http://xlink.rsc.org/?DOI=C8SM01372A},
	doi = {10.1039/C8SM01372A},
	abstract = {A load applied to a jammed frictional granular system is localized into a network of force chains making inter-particle connections throughout the system. While this force network is not unique, likely patterns can be predicted using metric known as betweenness centrality.
          , 
            A load applied to a jammed frictional granular system will be localized into a network of force chains making inter-particle connections throughout the system. Because such systems are typically under-constrained, the observed force network is not unique to a given particle configuration, but instead varies upon repeated formation. In this paper, we examine the ensemble of force chain configurations created under repeated assembly in order to develop tools to statistically forecast the observed force network. In experiments on a gently suspended 2D layer of photoelastic particles, we subject the assembly to hundreds of repeated cyclic compressions. As expected, we observe the non-unique nature of the force network, which differs for each compression cycle, by measuring all vector inter-particle contact forces using our open source PeGS software. We find that total pressure on each particle in the system correlates to its betweenness centrality value extracted from the geometric contact network. Thus, the mesoscale network structure is a key control on individual particle pressures.},
	number = {8},
	urldate = {2021-07-13},
	journal = {Soft Matter},
	author = {Kollmer, Jonathan E. and Daniels, Karen E.},
	year = {2019},
	pages = {1793--1798},
	annote = {this paper they make a bunch of physical systems and find members of the force network ensemble with small deviations},
	file = {Kollmer and Daniels - 2019 - Betweenness centrality as predictor for forces in .pdf:C\:\\Users\\craig\\Zotero\\storage\\GTD4ITUL\\Kollmer and Daniels - 2019 - Betweenness centrality as predictor for forces in .pdf:application/pdf},
}

@article{wyart_geometric_2005,
	title = {Geometric origin of excess low-frequency vibrational modes in weakly connected amorphous solids},
	volume = {72},
	issn = {0295-5075, 1286-4854},
	url = {https://iopscience.iop.org/article/10.1209/epl/i2005-10245-5},
	doi = {10.1209/epl/i2005-10245-5},
	abstract = {Glasses have an excess number of low-frequency vibrational modes in comparison with most crystalline solids. We show that such a feature necessarily occurs in solids with low coordination. In particular, we analyze the density D(ω) of normal-mode frequencies ω and the nature of the low-frequency normal modes of a recently simulated system (O’Hern C., Silbert L. E., Liu A. J. and Nagel S. R., Phys. Rev. E, 68 (2003) 011306) comprised of weakly compressed spheres at zero temperature. We account for the observed a) convergence of D(ω) toward a non-zero constant as the frequency goes to zero, b) appearance of a lowfrequency cutoff ω∗, and c) power law increase of ω∗ with compression. We introduce a length scale l∗ which characterizes the vibrational modes that appear at ω∗.},
	number = {3},
	urldate = {2021-07-13},
	journal = {Europhysics Letters (EPL)},
	author = {Wyart, M and Nagel, S. R and Witten, T. A},
	month = nov,
	year = {2005},
	pages = {486--492},
	file = {Wyart et al. - 2005 - Geometric origin of excess low-frequency vibration.pdf:C\:\\Users\\craig\\Zotero\\storage\\97TSVS62\\Wyart et al. - 2005 - Geometric origin of excess low-frequency vibration.pdf:application/pdf},
}

@article{shimada_spatial_2018,
	title = {Spatial structure of quasilocalized vibrations in nearly jammed amorphous solids},
	volume = {98},
	issn = {2470-0045, 2470-0053},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.98.060901},
	doi = {10.1103/PhysRevE.98.060901},
	number = {6},
	urldate = {2021-07-13},
	journal = {Physical Review E},
	author = {Shimada, Masanari and Mizuno, Hideyuki and Wyart, Matthieu and Ikeda, Atsushi},
	month = dec,
	year = {2018},
	pages = {060901},
	file = {Shimada et al. - 2018 - Spatial structure of quasilocalized vibrations in .pdf:C\:\\Users\\craig\\Zotero\\storage\\A7BIYP8V\\Shimada et al. - 2018 - Spatial structure of quasilocalized vibrations in .pdf:application/pdf},
}

@article{silbert_vibrations_2005,
	title = {Vibrations and {Diverging} {Length} {Scales} {Near} the {Unjamming} {Transition}},
	volume = {95},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.95.098301},
	doi = {10.1103/PhysRevLett.95.098301},
	number = {9},
	urldate = {2021-07-13},
	journal = {Physical Review Letters},
	author = {Silbert, Leonardo E. and Liu, Andrea J. and Nagel, Sidney R.},
	month = aug,
	year = {2005},
	pages = {098301},
	file = {Silbert et al. - 2005 - Vibrations and Diverging Length Scales Near the Un.pdf:C\:\\Users\\craig\\Zotero\\storage\\LABRBA3V\\Silbert et al. - 2005 - Vibrations and Diverging Length Scales Near the Un.pdf:application/pdf},
}

@article{ellenbroek_rigidity_2015-1,
	title = {Rigidity {Loss} in {Disordered} {Systems}: {Three} {Scenarios}},
	volume = {114},
	copyright = {rigidity},
	issn = {0031-9007, 1079-7114},
	shorttitle = {Rigidity {Loss} in {Disordered} {Systems}},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.114.135501},
	doi = {10.1103/PhysRevLett.114.135501},
	number = {13},
	urldate = {2021-07-13},
	journal = {Physical Review Letters},
	author = {Ellenbroek, Wouter G. and Hagh, Varda F. and Kumar, Avishek and Thorpe, M. F. and van Hecke, Martin},
	month = apr,
	year = {2015},
	pages = {135501},
	file = {Ellenbroek et al. - 2015 - Rigidity Loss in Disordered Systems Three Scenari.pdf:C\:\\Users\\craig\\Zotero\\storage\\NISXPEZK\\Ellenbroek et al. - 2015 - Rigidity Loss in Disordered Systems Three Scenari.pdf:application/pdf},
}

@article{hagh_transient_2021,
	title = {Transient degrees of freedom and stability},
	copyright = {ultrastables},
	url = {http://arxiv.org/abs/2105.10846},
	abstract = {The mechanical stability of a physical system plays a crucial role in determining its excitations and response to strain. Recent advances have led to protocols that can create particularly stable amorphous solids. Such systems, whether they be physical systems created using vapor-deposition or numerical model systems created using swap or breathing algorithms, exist in exceptionally deep energy minima marked by the absence of low-frequency quasilocalized modes. We introduce new numerical protocols for creating stable jammed packings that first introduce and subsequently remove degrees of freedom such as particle sizes or particle stiffnesses. We find that different choices for the degrees of freedom can lead to very different results. For jammed packings, degrees of freedom that couple to the jamming transition, e.g., particle sizes, push the system to much more stable and deeper energy minima than those that only couple to interaction stiffnesses.},
	urldate = {2021-07-13},
	journal = {arXiv:2105.10846 [cond-mat]},
	author = {Hagh, Varda F. and Nagel, Sidney R. and Liu, Andrea J. and Manning, M. Lisa and Corwin, Eric I.},
	month = may,
	year = {2021},
	note = {arXiv: 2105.10846},
	keywords = {Condensed Matter - Soft Condensed Matter},
	file = {Hagh et al. - 2021 - Transient degrees of freedom and stability.pdf:C\:\\Users\\craig\\Zotero\\storage\\JLJUMVDT\\Hagh et al. - 2021 - Transient degrees of freedom and stability.pdf:application/pdf},
}

@article{morse_echoes_2017,
	title = {Echoes of the {Glass} {Transition} in {Athermal} {Soft} {Spheres}},
	volume = {119},
	copyright = {log spacing delta phi},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.119.118003},
	doi = {10.1103/PhysRevLett.119.118003},
	number = {11},
	urldate = {2021-08-31},
	journal = {Physical Review Letters},
	author = {Morse, Peter K. and Corwin, Eric I.},
	month = sep,
	year = {2017},
	pages = {118003},
	file = {Morse and Corwin - 2017 - Echoes of the Glass Transition in Athermal Soft Sp.pdf:C\:\\Users\\craig\\Zotero\\storage\\3EWJFX9E\\Morse and Corwin - 2017 - Echoes of the Glass Transition in Athermal Soft Sp.pdf:application/pdf},
}

@article{ozawa_exploring_2017,
	title = {Exploring the jamming transition over a wide range of critical densities},
	volume = {3},
	copyright = {stability stuff},
	issn = {2542-4653},
	url = {https://scipost.org/10.21468/SciPostPhys.3.4.027},
	doi = {10.21468/SciPostPhys.3.4.027},
	abstract = {We numerically study the jamming transition of frictionless polydisperse spheres in three dimensions. We use an efficient thermalisation algorithm for the equilibrium hard sphere fluid and generate amorphous jammed packings over a range of critical jamming densities that is about three times broader than in previous studies. This allows us to reexamine a wide range of structural properties characterizing the jamming transition. Both isostaticity and the critical behavior of the pair correlation function hold over the entire range of jamming densities. At intermediate length scales, we find a weak, smooth increase of bond orientational order. By contrast, distorted icosahedral structures grow rapidly with increasing the volume fraction in both fluid and jammed states. Surprisingly, at large scale we observe that denser jammed states show stronger deviations from hyperuniformity, suggesting that the enhanced amorphous ordering inherited from the equilibrium fluid competes with, rather than enhances, hyperuniformity. Finally, finite size fluctuations of the critical jamming density are considerably suppressed in the denser jammed states, indicating an important change in the topography of the potential energy landscape. By considerably stretching the amplitude of the critical “J-line”, our work disentangles physical properties at the contact scale that are associated with jamming criticality, from those occurring at larger length scales, which have a different nature.},
	number = {4},
	urldate = {2021-08-31},
	journal = {SciPost Physics},
	author = {Ozawa, Misaki and Berthier, Ludovic and Coslovich, Daniele},
	month = oct,
	year = {2017},
	pages = {027},
	file = {Ozawa et al. - 2017 - Exploring the jamming transition over a wide range.pdf:C\:\\Users\\craig\\Zotero\\storage\\4WN3MIVR\\Ozawa et al. - 2017 - Exploring the jamming transition over a wide range.pdf:application/pdf},
}

@article{tuckman_contact_2020,
	title = {Contact network changes in ordered and disordered disk packings},
	volume = {16},
	copyright = {network vs rearrangements},
	issn = {1744-683X, 1744-6848},
	url = {http://xlink.rsc.org/?DOI=D0SM01137A},
	doi = {10.1039/D0SM01137A},
	abstract = {There are two ways to transition between different contact networks, point and jump changes, as shown in a packing fraction-strain landscape.
          , 
            We investigate the mechanical response of packings of purely repulsive, frictionless disks to quasistatic deformations. The deformations include simple shear strain at constant packing fraction and at constant pressure, “polydispersity” strain (in which we change the particle size distribution) at constant packing fraction and at constant pressure, and isotropic compression. For each deformation, we show that there are two classes of changes in the interparticle contact networks: jump changes and point changes. Jump changes occur when a contact network becomes mechanically unstable, particles “rearrange”, and the potential energy (when the strain is applied at constant packing fraction) or enthalpy (when the strain is applied at constant pressure) and all derivatives are discontinuous. During point changes, a single contact is either added to or removed from the contact network. For repulsive linear spring interactions, second- and higher-order derivatives of the potential energy/enthalpy are discontinuous at a point change, while for Hertzian interactions, third- and higher-order derivatives of the potential energy/enthalpy are discontinuous. We illustrate the importance of point changes by studying the transition from a hexagonal crystal to a disordered crystal induced by applying polydispersity strain. During this transition, the system only undergoes point changes, with no jump changes. We emphasize that one must understand point changes, as well as jump changes, to predict the mechanical properties of jammed packings.},
	number = {41},
	urldate = {2021-08-31},
	journal = {Soft Matter},
	author = {Tuckman, Philip J. and VanderWerf, Kyle and Yuan, Ye and Zhang, Shiyun and Zhang, Jerry and Shattuck, Mark D. and O’Hern, Corey S.},
	year = {2020},
	pages = {9443--9455},
	file = {Tuckman et al. - 2020 - Contact network changes in ordered and disordered .pdf:C\:\\Users\\craig\\Zotero\\storage\\FH5QS4BD\\Tuckman et al. - 2020 - Contact network changes in ordered and disordered .pdf:application/pdf},
}

@article{kapteijns_fast_2019,
	title = {Fast generation of ultrastable computer glasses by minimization of an augmented potential energy},
	volume = {99},
	copyright = {ultrastable},
	issn = {2470-0045, 2470-0053},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.99.012106},
	doi = {10.1103/PhysRevE.99.012106},
	number = {1},
	urldate = {2021-08-19},
	journal = {Physical Review E},
	author = {Kapteijns, Geert and Ji, Wencheng and Brito, Carolina and Wyart, Matthieu and Lerner, Edan},
	month = jan,
	year = {2019},
	pages = {012106},
	file = {Kapteijns et al. - 2019 - Fast generation of ultrastable computer glasses by.pdf:C\:\\Users\\craig\\Zotero\\storage\\52C93PNJ\\Kapteijns et al. - 2019 - Fast generation of ultrastable computer glasses by.pdf:application/pdf},
}

@article{ninarello_models_2017,
	title = {Models and {Algorithms} for the {Next} {Generation} of {Glass} {Transition} {Studies}},
	volume = {7},
	copyright = {ultrastable},
	issn = {2160-3308},
	url = {http://link.aps.org/doi/10.1103/PhysRevX.7.021039},
	doi = {10.1103/PhysRevX.7.021039},
	number = {2},
	urldate = {2021-08-19},
	journal = {Physical Review X},
	author = {Ninarello, Andrea and Berthier, Ludovic and Coslovich, Daniele},
	month = jun,
	year = {2017},
	pages = {021039},
	file = {Ninarello et al. - 2017 - Models and Algorithms for the Next Generation of G.pdf:C\:\\Users\\craig\\Zotero\\storage\\NEGJYZ6K\\Ninarello et al. - 2017 - Models and Algorithms for the Next Generation of G.pdf:application/pdf},
}

@article{rocks_learning-based_2021,
	title = {Learning-based approach to plasticity in athermal sheared amorphous packings: {Improving} softness},
	volume = {9},
	copyright = {coordination \#},
	issn = {2166-532X},
	shorttitle = {Learning-based approach to plasticity in athermal sheared amorphous packings},
	url = {https://aip.scitation.org/doi/10.1063/5.0035395},
	doi = {10.1063/5.0035395},
	abstract = {The plasticity of amorphous solids undergoing shear is characterized by quasi-localized rearrangements of particles. While many models of plasticity exist, the precise relationship between the plastic dynamics and the structure of a particle’s local environment remains an open question. Previously, machine learning was used to identify a structural predictor of rearrangements called “softness.” Although softness has been shown to predict which particles will rearrange with high accuracy, the method can be difficult to implement in experiments where data are limited and the combinations of descriptors it identifies are often difficult to interpret physically. Here, we address both of these weaknesses, presenting two major improvements to the standard softness method. First, we present a natural representation of each particle’s observed mobility, allowing for the use of statistical models that are both simpler and provide greater accuracy in limited datasets. Second, we employ persistent homology as a systematic means of identifying simple, topologically informed, structural quantities that are easy to interpret and measure experimentally. We test our methods on two-dimensional athermal packings of soft spheres under quasi-static shear. We find that the same structural information that predicts small variations in the response is also predictive of where plastic events will localize. We also find that an excellent accuracy is achieved in athermal sheared packings using simply a particle’s species and the number of nearest neighbor contacts.},
	number = {2},
	urldate = {2021-08-13},
	journal = {APL Materials},
	author = {Rocks, Jason W. and Ridout, Sean A. and Liu, Andrea J.},
	month = feb,
	year = {2021},
	pages = {021107},
	file = {Rocks et al. - 2021 - Learning-based approach to plasticity in athermal .pdf:C\:\\Users\\craig\\Zotero\\storage\\HYLM8GYS\\Rocks et al. - 2021 - Learning-based approach to plasticity in athermal .pdf:application/pdf},
}

@article{ridout_correlation_2020,
	title = {Correlation of plastic events with local structure in jammed packings across spatial dimensions},
	copyright = {coordination \#},
	url = {http://arxiv.org/abs/2011.13049},
	abstract = {In jammed packings, it is usually thought that local structure only plays a significant role in specific regimes. The standard deviation of the relative excess coordination, \${\textbackslash}sigma\_Z/ Z\_{\textbackslash}mathrm\{c\}\$, decays like \$1/{\textbackslash}sqrt\{d\}\$, so that local structure should play no role in high spatial dimensions. Furthermore, in any fixed dimension \$d {\textbackslash}geq 2\$, there are diverging length scales as the pressure vanishes approaching the unjamming transition, again suggesting that local structure should not be sufficient to describe response. Here we challenge the assumption that local structure does not matter in these cases. In simulations of jammed packings under athermal, quasistatic shear, we use machine learning to identify a local structural variable, softness, that correlates with rearrangements in dimensions \$d=2\$ to \$d=5\$. We find that softness - and even just the coordination number \$Z\$ - are quite predictive of rearrangements over a wide range of pressures, all the way down to unjamming, in all \$d\$ studied. This result provides direct evidence that local structure can play a role in higher spatial dimensions.},
	urldate = {2021-08-13},
	journal = {arXiv:2011.13049 [cond-mat]},
	author = {Ridout, Sean A. and Rocks, Jason W. and Liu, Andrea J.},
	month = nov,
	year = {2020},
	note = {arXiv: 2011.13049},
	keywords = {Condensed Matter - Soft Condensed Matter},
	annote = {Comment: 8 pages, 8 figures},
	file = {Ridout et al. - 2020 - Correlation of plastic events with local structure.pdf:C\:\\Users\\craig\\Zotero\\storage\\VATN3W7L\\Ridout et al. - 2020 - Correlation of plastic events with local structure.pdf:application/pdf},
}

@article{morse_differences_2020,
	title = {Differences in plasticity between hard and soft spheres},
	volume = {2},
	copyright = {86\% of contact changes are reversible},
	issn = {2643-1564},
	url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.023179},
	doi = {10.1103/PhysRevResearch.2.023179},
	number = {2},
	urldate = {2021-07-31},
	journal = {Physical Review Research},
	author = {Morse, Peter and Wijtmans, Sven and van Deen, Merlijn and van Hecke, Martin and Manning, M. Lisa},
	month = may,
	year = {2020},
	pages = {023179},
	file = {Morse et al. - 2020 - Differences in plasticity between hard and soft sp.pdf:C\:\\Users\\craig\\Zotero\\storage\\BHGASY6X\\Morse et al. - 2020 - Differences in plasticity between hard and soft sp.pdf:application/pdf},
}

@article{jordan_essai_1875,
	title = {Essai sur la géométrie à \$n\$ dimensions},
	volume = {2},
	copyright = {angle between planes},
	issn = {0037-9484, 2102-622X},
	url = {http://www.numdam.org/item?id=BSMF_1875__3__103_2},
	doi = {10.24033/bsmf.90},
	urldate = {2021-07-29},
	journal = {Bulletin de la Soci\&\#233;t\&\#233; math\&\#233;matique de France},
	author = {Jordan, Camille},
	year = {1875},
	pages = {103--174},
	file = {Jordan - 1875 - Essai sur la géométrie à \$n\$ dimensions.pdf:C\:\\Users\\craig\\Zotero\\storage\\ER3ZIC5Y\\Jordan - 1875 - Essai sur la géométrie à \$n\$ dimensions.pdf:application/pdf},
}

@article{hales_overview_1998,
	title = {An overview of the {Kepler} conjecture},
	copyright = {packing density proof},
	url = {http://arxiv.org/abs/math/9811071},
	abstract = {This is the first in a series of papers giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than \${\textbackslash}pi/{\textbackslash}sqrt\{18\}{\textbackslash}approx 0.74048...\$. This is the oldest problem in discrete geometry and is an important part of Hilbert's 18th problem. An example of a packing achieving this density is the face-centered cubic packing. This paper has a historical overview and a synopsis of the rest of the series. The other papers in the series are math.MG/9811072, math.MG/9811073, math.MG/9811074, math.MG/9811075, math.MG/9811076, math.MG/9811077, and math.MG/9811078.},
	urldate = {2021-09-14},
	journal = {arXiv:math/9811071},
	author = {Hales, Thomas C.},
	month = nov,
	year = {1998},
	note = {arXiv: math/9811071
version: 1},
	keywords = {Mathematics - Metric Geometry},
	annote = {Comment: 16 pages. First in a series},
	file = {arXiv Fulltext PDF:C\:\\Users\\craig\\Zotero\\storage\\V398K7H3\\Hales - 1998 - An overview of the Kepler conjecture.pdf:application/pdf;arXiv.org Snapshot:C\:\\Users\\craig\\Zotero\\storage\\32RHXQYA\\9811071.html:text/html},
}

@misc{kepler_strena_1611,
	title = {Strena {Seu} de {Nive} {Sexangula}},
	copyright = {kepler conjecture FCC},
	url = {https://www.goodreads.com/book/show/27591698-strena-seu-de-nive-sexangula},
	abstract = {"Strena seu de nive sexangula," from Iohannes Kepler. Iohannes Kepler (1571-1630), germanice astronomus et matematicus.},
	urldate = {2021-09-14},
	author = {Kepler, Johannes},
	year = {1611},
	file = {Snapshot:C\:\\Users\\craig\\Zotero\\storage\\IJ5F8B5H\\27591698-strena-seu-de-nive-sexangula.html:text/html},
}

@misc{gunter_photo_2021,
	title = {Photo by {Jen} {Gunter} on {Unsplash}},
	copyright = {oranges},
	url = {https://unsplash.com/photos/A4BBdJQu2co},
	abstract = {Fresh oranges from a Farmer's Market in California. Download this photo by Jen Gunter on Unsplash},
	language = {en},
	urldate = {2021-09-21},
	journal = {Unsplash},
	author = {Gunter, Jen},
	month = jan,
	year = {2021},
	file = {Snapshot:C\:\\Users\\craig\\Zotero\\storage\\GBW74YU8\\A4BBdJQu2co.html:text/html},
}

@misc{louw_soul_1967,
	title = {Soul {City} ({Pyramid} of {Oranges})},
	copyright = {oranges},
	url = {https://www.tate.org.uk/art/artworks/louw-soul-city-pyramid-of-oranges-t13881},
	abstract = {Artwork page for ‘Soul City (Pyramid of Oranges)’, Roelof Louw, 1967 This sculpture starts as a pyramid made from about 5800 oranges. The shape is similar to an oversized market stall display. Viewers are invited to take one orange each, gradually consuming the work. Even if no one takes them, the work will still eventually rot and disintegrate. In the late 1960s, Louw was one of the artists connected to London’s Saint Martin’s School of Art who radically pushed the boundaries of sculpture. In his own words, he wanted ‘to ask questions about the direct “interactive” relationship between sculptural works …},
	language = {en-GB},
	urldate = {2021-09-21},
	journal = {Tate},
	author = {Louw, Roelof},
	year = {1967},
	note = {Section: Art \& artists},
	file = {Snapshot:C\:\\Users\\craig\\Zotero\\storage\\ZUDN67DY\\louw-soul-city-pyramid-of-oranges-t13881.html:text/html},
}

@article{sartor_predicting_2021,
	title = {Predicting {Defects} in {Soft} {Sphere} {Packings} {Near} {Jamming} {Using} {The} {Force} {Network} {Ensemble}},
	copyright = {me},
	url = {http://arxiv.org/abs/2108.09385},
	abstract = {Amorphous systems of soft particles above jamming have more contacts than are needed to achieve mechanical equilibrium. The force network of a granular system with a fixed contact network is thus underdetermined, and can be characterized as a random instantiation within the space of the force network ensemble. In this work, we show that by examining the boundaries of this space of allowed force networks, defect contacts which are not necessary for stability of the system can be uniquely identified. We further show that in the near jamming limit, this identification is nearly always correct and the defect contacts are broken under decompression of the system.},
	urldate = {2021-09-21},
	journal = {arXiv:2108.09385 [cond-mat]},
	author = {Sartor, James D. and Corwin, Eric I.},
	month = sep,
	year = {2021},
	note = {arXiv: 2108.09385},
	keywords = {Condensed Matter - Soft Condensed Matter},
	file = {arXiv Fulltext PDF:C\:\\Users\\craig\\Zotero\\storage\\W2ME9J5R\\Sartor and Corwin - 2021 - Predicting Defects in Soft Sphere Packings Near Ja.pdf:application/pdf;arXiv.org Snapshot:C\:\\Users\\craig\\Zotero\\storage\\CB34E6HR\\2108.html:text/html},
}