High-dimensional optimization under nonconvex excluded volume constraints.

We consider high-dimensional random optimization problems where the dynamical variables are subjected to nonconvex excluded volume constraints. We focus on the case in which the cost function is a simple quadratic cost and the excluded volume constraints are modeled by a perceptron constraint satisfaction problem. We show that depending on the density of constraints, one can have different situations.

Searching for the Gardner Transition in Glassy Glycerol.

We search for a Gardner transition in glassy glycerol, a standard molecular glass, measuring the third harmonics cubic susceptibility χ_{3}^{(3)} from slightly below the usual glass transition temperature down to 10 K. According to the mean-field picture, if local motion within the glass were becoming highly correlated due to the emergence of a Gardner phase then χ_{3}^{(3)}, which is analogous to the dynamical spin-glass susceptibility, should increase and diverge at the Gardner transition temperature T_{G}. We find instead that upon cooling |χ_{3}^{(3)}| decreases by several orders of magnitude and becomes roughly constant in the regime 100-10  K.

Jamming in Multilayer Supervised Learning Models.

Critical jamming transitions are characterized by an astonishing degree of universality. Analytic and numerical evidence points to the existence of a large universality class that encompasses finite and infinite dimensional spheres and continuous constraint satisfaction problems (CCSP) such as the nonconvex perceptron and related models. In this Letter we investigate multilayer neural networks (MLNN) learning random associations as models for CCSP that could potentially define different jamming universality classes.

Critical Jammed Phase of the Linear Perceptron.

Criticality in statistical physics naturally emerges at isolated points in the phase diagram. Jamming of spheres is not an exception: varying density, it is the critical point that separates the unjammed phase where spheres do not overlap and the jammed phase where they cannot be arranged without overlaps. The same remains true in more general constraint satisfaction problems with continuous variables where jamming coincides with the (protocol dependent) satisfiability transition point.

Can a Large Packing be Assembled from Smaller Ones?

We consider zero temperature packings of soft spheres that undergo a jamming to unjamming transition as a function of packing fraction. We compare differences in the structure, as measured from the contact statistics, of a finite subsystem of a large packing to a whole packing with periodic boundaries of an equivalent size and pressure. We find that the fluctuations of the ensemble of whole packings are smaller than those of the ensemble of subsystems.

A stability-reversibility map unifies elasticity, plasticity, yielding, and jamming in hard sphere glasses.

Amorphous solids, such as glasses, have complex responses to deformations, with substantial consequences in material design and applications. In this respect, two intertwined aspects are important: stability and reversibility. It is crucial to understand, on the one hand, how a glass may become unstable due to increased plasticity under shear deformations, and, on the other hand, to what extent the response is reversible, meaning how much a system is able to recover the original configuration once the perturbation is released.

Microscopic Theory of Two-Step Yielding in Attractive Colloids.

Attractive colloids display two distinct amorphous solid phases: the attractive glass due to particle bonding and the repulsive glass due to the hard-core repulsion. By means of a microscopic mean field approach, we analyze their response to a quasistatic shear strain. We find that the presence of two distinct interaction length scales may result in a sharp two-step yielding process, which can be associated with a hysteretic stress response or with a reversible but nonmonotonic stress-strain curve.

Universality of jamming of nonspherical particles.

Amorphous packings of nonspherical particles such as ellipsoids and spherocylinders are known to be hypostatic: The number of mechanical contacts between particles is smaller than the number of degrees of freedom, thus violating Maxwell's mechanical stability criterion. In this work, we propose a general theory of hypostatic amorphous packings and the associated jamming transition. First, we show that many systems fall into a same universality class.

Shear Yielding and Shear Jamming of Dense Hard Sphere Glasses.

We investigate the response of dense hard sphere glasses to a shear strain in a wide range of pressures ranging from the glass transition to the infinite-pressure jamming point. The phase diagram in the density-shear strain plane is calculated analytically using the mean-field infinite-dimensional solution. We find that just above the glass transition, the glass generically yields at a finite shear strain.

Universal spectrum of normal modes in low-temperature glasses.

We report an analytical study of the vibrational spectrum of the simplest model of jamming, the soft perceptron. We identify two distinct classes of soft modes. The first kind of modes are related to isostaticity and appear only in the close vicinity of the jamming transition.

Following the evolution of hard sphere glasses in infinite dimensions under external perturbations: compression and shear strain.

We consider the adiabatic evolution of glassy states under external perturbations. The formalism we use is very general. Here we use it for infinite-dimensional hard spheres where an exact analysis is possible.

Fractal free energy landscapes in structural glasses.

Glasses are amorphous solids whose constituent particles are caged by their neighbours and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers. Here we show, using theory and numerical simulation, that the landscape is much rougher than is classically assumed.

Exact theory of dense amorphous hard spheres in high dimension. II. The high density regime and the Gardner transition.

We consider the theory of the glass phase and jamming of hard spheres in the large space dimension limit. Building upon the exact expression for the free-energy functional obtained previously, we find that the random first order transition (RFOT) scenario is realized here with two thermodynamic transitions: the usual Kauzmann point associated with entropy crisis and a further transition at higher pressures in which a glassy structure of microstates is developed within each amorphous state. This kind of glass-glass transition into a phase dominating the higher densities was described years ago by Elisabeth Gardner, and may well be a generic feature of RFOT.

Static replica approach to critical correlations in glassy systems.

We discuss the slow relaxation phenomenon in glassy systems by means of replicas by constructing a static field theory approach to the problem. At the mean field level we study how criticality in the four point correlation functions arises because of the presence of soft modes and we derive an effective replica field theory for these critical fluctuations. By using this at the gaussian level we obtain many physical quantities: the correlation length, the exponent parameter that controls the mode-coupling dynamical exponents for the two-point correlation functions, and the prefactor of the critical part of the four point correlation functions.

A note on weakly discontinuous dynamical transitions.

We analyze mode coupling discontinuous transition in the limit of vanishing discontinuity, approaching the so called "A(3)" point. In these conditions structural relaxation and fluctuations appear to have universal form independent from the details of the system. The analysis of this limiting case suggests new ways for looking at the mode coupling equations in the general case.

Quantitative field theory of the glass transition.

We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature, we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we analytically study the critical behavior of a set of four-points correlation functions, from which we can extract the dynamical correlation length.