Mean-field avalanches in jammed spheres

Franz, Silvio; Spigler, Stefano

doi:10.1103/physreve.95.022139

Cited by 55 publications

(71 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our results are also consistent with the scaling analysis of [11]. These results, together with the results on the vibrational spectrum obtained in [16,17], and the study of avalanches performed in [19], provide a complete study of all the properties of the random perceptron that are relevant for the study of the glass and jamming transition at the mean field level.…”

Section: Discussionsupporting

confidence: 88%

“…4 we compare the cumulative distri- We conclude by mentioning that one can also study the vibrational spectrum, both in the SAT and UNSAT phases [16,17], to discuss the presence of soft modes associated to both fullRSB and jamming, and connect the density of states with these critical exponents as it is also observed in sphere packings [40]. Also, it has been shown in [19] that the asymptotic behavior of the function y(q), related to the exponent κ, controls the scaling of the avalanches at the jamming point, which is therefore different than the scaling in the UNSAT phase.…”

Section: Force and Gap Distributionsmentioning

confidence: 89%

“…Furthermore, in [17] it has been shown how to study systematically the free energy landscape of the model using a Thouless-Anderson-Palmer approach [18] to obtain, in particular, the vibrational spectrum in the SAT phase. In [19], the avalanches characterizing the glassy phase around jamming have also been studied. Thanks to these studies, the non-convex perceptron now emerges as the simplest model that captures, at the mean field level, all the most important features of the glass and jamming transitions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems

et al. 2017

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionsupporting

confidence: 88%

Section: Force and Gap Distributionsmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Scale-free avalanche dynamics often appear near yielding or unjamming transitions, such as in the intermittent motion of dislocations in crystalline solids [9][10][11] or the rearrangements of particles at yielding in amorphous materials [12][13][14][15]. For loose assemblies of particles such as grains or bubbles, the shear modulus becomes finite above a density f j when a jamming transition occurs [16,17], and it is known that in such systems, the dynamics become increasingly intermittent as the jamming point is approached, producing power law distributions in a variety of dynamic quantities [18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Avalanche dynamics for active matter in heterogeneous media

Reichhardt

2018

New J. Phys.

View full text Add to dashboard Cite

Using numerical simulations, we examine the dynamics of run-and-tumble disks moving in a disordered array of fixed obstacles. As a function of increasing active disk density and activity, we find a transition from a completely clogged state to a continuous flowing phase, and in the large activity limit, we observe an intermittent state where the motion occurs in avalanches that are power law distributed in size with an exponent of b = 1.46. In contrast, in the thermal or low activity limit we find bursts of motion that are not broadly distributed in size. We argue that in the highly active regime, the system reaches a self-jamming state due to the activity-induced self-clustering, and that the intermittent dynamics is similar to that found in the yielding of amorphous solids. Our results show that activity is another route by which particulate systems can be tuned to a nonequilibrium critical state.

show abstract

“…This phenomenon is of capital importance for engineering applications as it is responsible for the brittleness typical of glassy materials, in particular metallic glasses [18], whose potential for practical use is stymied by their tendency to shear-band and fracture [17,19,20]. Measurements of plastic events occurring after yield reveal scale-free energy or stress drops, typically characterized by power-law statistics [21,22]. The aim of this paper is to present the current understanding of this scale-free behavior which, as said above, is suspected to be related to some criticality.…”

Section: Introductionmentioning

confidence: 99%

Mechanical failure in amorphous solids: Scale-free spinodal criticality

2017

View full text Add to dashboard Cite

The mechanical failure of amorphous media is a ubiquitous phenomenon from material engineering to geology. It has been noticed for a long time that the phenomenon is "scale-free", indicating some type of criticality. In spite of attempts to invoke "Self-Organized Criticality", the physical origin of this criticality, and also its universal nature, being quite insensitive to the nature of microscopic interactions, remained elusive. Recently we proposed that the precise nature of this critical behavior is manifested by a spinodal point of a thermodynamic phase transition. Moreover, at the spinodal point there exists a divergent correlation length which is associated with the system-spanning instabilities (known also as shear bands) which are typical to the mechanical yield. Demonstrating this requires the introduction of an 'order parameter' that is suitable for distinguishing between disordered amorphous systems, and an associated correlation function, suitable for picking up the growing correlation length. The theory, the order parameter, and the correlation functions used are universal in nature and can be applied to any amorphous solid that undergoes mechanical yield. Critical exponents for the correlation length divergence and the system size dependence are estimated. The phenomenon is seen at its sharpest in athermal systems, as is explained below; in this paper we extend the discussion also to thermal systems, showing that at sufficiently high temperatures the spinodal phenomenon is destroyed by thermal fluctuations.

show abstract

Mean-field avalanches in jammed spheres

Cited by 55 publications

References 47 publications

Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems

Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems

Avalanche dynamics for active matter in heterogeneous media

Mechanical failure in amorphous solids: Scale-free spinodal criticality

Contact Info

Product

Resources

About