Related papers: Mean-Field Theory and Sandpile Models
The phase behavior of the primitive model of electrolytes is studied in the framework of various mean field approximations obtained recently by means of methods pertaining to statistical field theory (CAILLOL, J.-M., 2004, \textit{J. Stat.…
Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (non-conservative) local dynamics on the…
A two-offspring branching annihilating random walk model, with finite reaction rates, is studied in one-dimension. The model exhibits a transition from an active to an absorbing phase, expected to belong to the $DP2$ universality class…
The paper describes and compares three approaches to modeling an epidemic spread. The first approach is a well-known system of SIR ordinary differential equations. The second is a mean-field model, in which an isolation strategy for each…
In this paper, we consider mean-field games where the interaction of each player with the mean-field takes into account not only the states of the players but also their collective behavior, To do so, we develop a random variable framework…
In this work we discuss an Mean Field Games approach to traffic management on multi-lane roads. Such approach is particularly indicated to model self driven vehicles with perfect information of the domain. The mathematical interest of the…
The mean field theory, in its different hues, form one of the most useful tools for calculating the single-body physical properties of a many-body system. It provides important information, like critical exponents, of the systems that do…
We introduce a family of glassy models having a parameter, playing the role of an interaction range, that may be varied continuously to go from a system of particles in d dimensions to a mean-field version of it. The mean-field limit is…
We consider a class of spin systems on $\Z^d$ with vector valued spins $(\bS_x)$ that interact via the pair-potentials $J_{x,y} \bS_x\cdot\bS_y$. The interactions are generally spread-out in the sense that the $J_{x,y}$'s exhibit either…
A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…
With a toppling rule which generates metastable sites, we explore the properties of a gradient-driven sandpile that is minimally perturbed at one boundary. In two dimensions we find that the transport of grains takes place along deep…
The use of Mean-Field theory to unwrap principal phase patterns has been recently proposed. In this paper we generalize the Mean-Field approach to process phase patterns with arbitrary degree of undersampling. The phase unwrapping problem…
We typically interact in groups, not just in pairs. For this reason, it has recently been proposed that the spread of information, opinion or disease should be modelled over a hypergraph rather than a standard graph. The use of hyperedges…
Psychological disorders like major depressive disorder can be seen as complex dynamical systems. By looking at symptom activation patterns, we can investigate the dynamic behaviour of individuals to see whether or not they are at risk for…
By analogy with the Landau-Ginzburg theory of ordinary zero-form symmetries, we introduce and develop a Landau-Ginzburg theory of one-form global symmetries, which we call mean string field theory. The basic dynamical variable is a string…
How a system initially at infinite temperature responds when suddenly placed at finite temperatures is a way to check the existence of phase transitions. It has been shown in [R. da Silva, IJMPC 2023] that phase transitions are imprinted in…
Mean field games is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play non-cooperative dynamic games…
We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The existence of optimal policies is shown and the limiting mean-field problem is derived when the…
We study layered systems and heterostructures of s-wave superconductors by means of a suitable generalization of Dynamical Mean-Field Theory. In order to reduce the computational effort, we consider an embedding scheme in which a relatively…
An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points…