Related papers: Universality in sandpiles
The universal anomalous diffusion scaling is obtained for the semiclassical quantum Hall transition, which has been argued to describe samples with dissipation or correlated impurities. The results explain a discrepancy between existing…
The low temperature physics of disordered systems is governed by the statistics of extremely low energy states. It is thus rather important to discuss the possible universality classes for extreme value statistics. We compare the usual…
One of the theoretical pillars that sustain certain machine learning models are universal approximation theorems, which prove that they can approximate all functions from a function class to arbitrary precision. Independently, classical…
Similar evolutionary variational inequalities appear as convenient formulations for continuous models for sandpile growth, magnetization of type-II superconductors, and evolution of some other dissipative systems characterized by the…
Spatiotemporal patterns, which are of interest in statistical physics and nonlinear dynamics, form on the tape-peeling trace. Recently, we have proposed a mathematical model to describe these pattern formation in the tape-peeling trace. In…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
The number of clusters per site $n(p)$ in percolation at the critical point $p = p_c$ is not itself a universal quantity---it depends upon the lattice and percolation type (site or bond). However, many of its properties, including…
The existence of universal scaling in the vicinity of the jamming transition of sheared granular materials is predicted by a phenomenology. The critical exponents are explicitly determined, which are independent of the spatial dimension.…
Although well described by mean-field theory in the thermodynamic limit, scaling has long been puzzling for finite systems in high dimensions. This raised questions about the efficacy of the renormalization group and foundational concepts…
We study systems with a continuous phase transition that tune their parameters to maximize a quantity that diverges solely at a unique critical point. Varying the size of these systems with dynamically adjusting parameters, the same…
We describe the surface properties of a simple lattice model of a sandpile that includes evolving structural disorder. We present a dynamical scaling hypothesis for generic sandpile automata, and additionally explore the kinetic roughening…
We consider matrix-valued processes described as solutions to stochastic differential equations of very general form. We study the family of the empirical measure-valued processes constructed from the corresponding eigenvalues. We show that…
Plastic yield of amorphous solids occurs by power law distributed slip avalanches whose universality is still debated. Determination of the power law exponents from experiments and molecular dynamics simulations is hampered by limited…
We study the universal properties of distributions of eigenvalues of random matrices in the large $N$ limit. The distributions fall in universality classes characterized entirely by the support of the spectral density.
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
We introduce a new general framework for constructing tilings of Euclidean space, which we call multiscale substitution tilings. These tilings are generated by substitution schemes on a finite set of prototiles, in which multiple distinct…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
The objective of statistical physics is to understand macroscopic behavior of a many-body system from the interactions of the constituents of that system. When many-body systems reach critical states, simple universal and scaling behaviors…
We discuss various critical densities in sandpile models. The stationary density is the average expected height in the stationary state of a finite-volume model; the transition density is the critical point in the infinite-volume…
We study distributions of dissipative and nondissipative avalanches in Manna's stochastic sandpile, in one and two dimensions. Our results lead to the following conclusions: (1) avalanche distributions, in general, do not follow simple…