Related papers: Mean-Field Theory and Sandpile Models
We model the dynamics of avalanches in granular assemblies in partly filled rotating cylinders using a mean-field approach. We show that, upon varying the cylinder angular velocity $\omega$, the system undergoes a hysteresis cycle between…
The Bak-Tang-Wiesenfeld sandpile model provdes a simple and elegant system with which to demonstate self-organized criticality. This model has rather remarkable mathematical properties first elucidated by Dhar. I demonstrate some of these…
The role of turbulent effects for dynamos in the Sun and stars continues to be debated. Mean-field (MF) theory provides a broadly used framework to connect these effects to fundamental magnetohydrodynamics. While inaccessible…
This paper investigates the use of transformers to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomena across physics, biology, and…
We introduce a simple one-dimensional sandpile model that undergoes relaxation oscillations. A single model can account for self-organized critical behavior and relaxation oscillations, depending on the manner in which it is driven,…
Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a…
We study sandpile models as closed systems, with conserved energy density $\zeta$ playing the role of an external parameter. The critical energy density, $\zeta_c$, marks a nonequilibrium phase transition between active and absorbing…
We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability measures which includes an interaction term. Our main insight…
Microtubules are dynamic intracellular fibers that have been observed experimentally to undergo spontaneous self-alignment. We formulate a 3D mean-field theory model to analyze the nematic phase transition of microtubules growing and…
Mean-field models approximate large stochastic systems by simpler differential equations that are supposed to approximate the mean of the larger system. It is generally assumed that as the stochastic systems get larger (i.e., more people or…
We construct a driven sandpile slope model and study it by numerical simulations in one dimension. The model is specified by a threshold slope $\sigma_c\/$, a parameter $\alpha\/$, governing the local current-slope relation (beyond…
We formulate the dynamical mean field theory directly in the continuum. For a given definition of the local Green's function, we show the existence of a unique functional, whose stationary point gives the physical local Green's function of…
Incorporating social interactions is essential to an accurate modeling of epidemic spreading. This work proposes a novel local mean-field density functional theory model by using the sum-of-exponential approximation of convolution kernels…
We present an analysis of the classical contact process on scale-free networks. A mean-field study, both for finite and infinite network sizes, yields an absorbing-state phase transition at a finite critical value of the control parameter,…
In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified…
The mean-field theory (MFT) of simple glasses, which is exact in the limit of infinite spatial dimensions, $d\rightarrow\infty$, offers theoretical insight as well as quantitative predictions about certain features of $d=3$ systems. In…
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…
We present a mean-field dynamical theory for single semiflexible polymers which can precisely capture, without fitting parameters, recent fluorescence correlation spectroscopy results on single monomer kinetics of DNA strands in solution.…
A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some…
The mean-field theory of Kinetically-Constrained-Models is developed by considering the Fredrickson-Andersen model on the Bethe lattice. Using certain properties of the dynamics observed in actual numerical experiments we derive asymptotic…