arXiv subjects

M. Wyart

Publications and source records attributed to M. Wyart.

8 recordsLinked to original sources

arXiv2018

Comparing Dynamics: Deep Neural Networks versus Glassy Systems

We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems. The two main issues we address are (1) the complexity of the loss landscape and of the dynamics within it, and (2) to what extent DNNs share similarities with glassy systems. Our findings, obtained for different architectures and datasets, suggest that during the training process the dynamics slows down because of an increasingly large number of flat directions. At large times, when the loss is approaching zero, the system diffuses at the bottom of the landscape. Despite some similarities with the dynamics of mean-field glassy systems, in particular, the absence of barrier crossing, we find distinctive dynamical behaviors in the two cases, showing that the statistical properties of the corresponding loss and energy landscapes are different. In contrast, when the network is under-parametrized we observe a typical glassy behavior, thus suggesting the existence of different phases depending on whether the network is under-parametrized or over-parametrized.

stat.ML↗

arXiv2017

Friction law and hysteresis in granular materials

The macroscopic friction of particulate materials often weakens as the flow rate is increased, leading to potentially disastrous intermittent phenomena including earthquakes and landslides. We theoretically and numerically study this phenomenon in simple granular materials. We show that velocity-weakening, corresponding to a non-monotonic behavior in the friction law $μ(I)$, is present even if the dynamic and static microscopic friction coefficients are identical, but disappears for softer particles. We argue that this instability is induced by endogenous acoustic noise, which tends to make contacts slide, leading to faster flow and increased noise. We show that soft spots, or excitable regions in the materials, correspond to rolling contacts that are about to slide, whose density is described by a nontrivial exponent $θ_s$. We build a microscopic theory for the non-monotonicity of $μ(I)$, which also predicts the scaling behavior of acoustic noise, the fraction of sliding contacts $χ$ and the sliding velocity, in terms of $θ_s$. Surprisingly, these quantities have no limit when particles become infinitely hard, as confirmed numerically. Our analysis rationalizes previously unexplained observations and makes new experimentally testable predictions.

cond-mat.soft↗

arXiv2017

Effect of Friction on Dense Suspension Flows of Hard Particles

We use numerical simulations to study the effect of particle friction on suspension flows of non-Brownian hard particles. By systematically varying the microscopic friction coefficient $μ_p$ and the viscous number $J$, we build a phase diagram that identifies three regimes of flow: Frictionless, Frictional Sliding, and Rolling. Using energy balance in flow, we predict relations between kinetic observables, confirmed by numerical simulations. For realistic friction coefficient and small viscous numbers (below $J\sim 10^{-3}$) we show that the dominating dissipative mechanism is sliding of frictional contacts, and we characterize asymptotic behaviors as jamming is approached. Outside this regime, our observations support that flow belongs to the universality class of frictionless particles. We discuss recent experiments in the context of our phase diagram.

cond-mat.soft↗

arXiv2016

Phase Diagram for Inertial Granular Flows

Flows of hard granular materials depend strongly on the interparticle friction coefficient $μ_p$ and on the inertial number ${\cal I}$, which characterizes proximity to the jamming transition where flow stops. Guided by numerical simulations, we derive the phase diagram of dense inertial flow of spherical particles, finding three regimes for $10^{-4} \lesssim {\cal I} \lesssim 10^{-1}$: \textit{ frictionless, frictional sliding, } and {\it rolling}. These are distinguished by the dominant means of energy dissipation, changing from collisional to sliding friction, and back to collisional, as $μ_p$ increases from zero at constant ${\cal I}$. The three regimes differ in their kinetics and rheology; in particular, the velocity fluctuations and the stress ratio both display non-monotonic behavior with $μ_p$, corresponding to transitions between the three regimes of flow. We rationalize { the phase boundaries between these regimes}, show that energy balance yields scaling relations { between microscopic properties} in each of them, and { derive the strain scale at which particles lose memory of their velocity. For the frictional sliding regime most relevant experimentally, we find for ${\cal I}\geq 10^{-2.5}$ that the growth of the macroscopic friction $μ({\cal I})$ with ${\cal I}$ is induced by an increase of collisional dissipation. This implies in that range that $μ({\cal I})-μ(0)\sim {\cal I}^{1-2b}$, where $b\approx 0.2$ is an exponent that characterizes both the dimensionless velocity fluctuations ${\cal L}\sim {\cal I}^{-b}$ and the density of sliding contacts $χ\sim {\cal I}^b$.

cond-mat.soft↗

arXiv2015

Unified Theory of Inertial Granular Flows and Non-Brownian Suspensions

Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases, both for aerial granular flows dominated by inertia, and for over-damped suspensions. Concomitantly, the lengthscale characterizing velocity correlations appears to diverge at jamming. Here we introduce a theoretical framework that proposes a tentative, but potentially complete scaling description of stationary flows. Our analysis, which focuses on frictionless particles, applies {\it both} to suspensions and inertial flows of hard particles. We compare our predictions with the empirical literature, as well as with novel numerical data. Overall we find a very good agreement between theory and observations, except for frictional inertial flows whose scaling properties clearly differ from frictionless systems. For over-damped flows, more observations are needed to decide if friction is a relevant perturbation or not. Our analysis makes several new predictions on microscopic dynamical quantities that should be accessible experimentally.

cond-mat.soft↗

arXiv2015

Theory of the Jamming Transition at Finite Temperature

A theory for the microscopic structure and the vibrational properties of soft sphere glass at finite temperature is presented. With an effective potential, derived here, the phase diagram and vibrational properties are worked out around the Maxwell critical point at zero temperature $T$ and pressure $p$. Variational arguments and effective medium theory identically predict a non-trivial temperature scale $T^*\sim p^{(2-a)/(1-a)}$ with $a \approx 0.17$ such that low-energy vibrational properties are hard-sphere like for $T \gtrsim T^*$, and zero-temperature soft-sphere like otherwise. However, due to crossovers in the equation of state relating $T$, $p$, and the packing fraction $ϕ$, these two regimes lead to four regions where scaling behaviors differ when expressed in terms of $T$ and $ϕ$. Scaling predictions are presented for the mean-squared displacement, characteristic frequency, shear modulus, and characteristic elastic length in all regions of the phase diagram.

cond-mat.soft↗

arXiv2014

The distribution of forces affects vibrational properties in hard sphere glasses

We study theoretically and numerically the elastic properties of hard sphere glasses, and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero-temperature, we argue that the presence of certain pairs of particles interacting with a small force $f$ soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting $P(f)\sim f^{θ_e}$ the force distribution of such pairs and $ϕ_c$ the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale $ω^*$, rising up to it as $D(ω) \sim ω^{2+a}$, and decaying above $ω^*$ as $D(ω)\sim ω^{-a}$ where $a=(1-θ_e)/(3+θ_e)$ and $ω$ is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with $\langle δR^2\rangle\sim1/μ\sim (ϕ_c-ϕ)^κ $ where $κ=2-2/(3+θ_e)$, and (iii) continuum elasticity breaks down on a scale $\ell_c \sim1/\sqrt{δz}\sim (ϕ_c-ϕ)^{-b}$ where $b=(1+θ_e)/(6+2θ_e)$ and $δz=z-2d$, where $z$ is the coordination and $d$ the spatial dimension. We numerically test (i) and provide data supporting that $θ_e\approx 0.41$ in our bi-disperse system, independently of system preparation in two and three dimensions, leading to $κ\approx1.41$, $a \approx 0.17$, and $b\approx 0.21$. Our results for the mean-square displacement are consistent with a recent exact replica computation for $d=\infty$, whereas some observations differ, as rationalized by the present approach.

cond-mat.soft↗

arXiv2008

A coordination-based approach to elasticity of floppy and stiff random networks

We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of the network coordination relative to that of an isostatic network $δz$; a floppy network has $δz<0$, while a stiff network has $δz>0$. Under the influence of an externally applied load we observe that the response of both floppy and rigid network are controlled by the same critical point, corresponding to the onset of rigidity. We use numerical simulations to compute the exponents which characterize the shear modulus, the amplitude of non-affine displacements, and the network stiffening as a function of $δz$, derive these theoretically and make predictions for the mechanical response of glasses and fibrous networks.

cond-mat.soft↗