Related papers: Directed Fixed Energy Sandpile Model

We present and analyze a model of an evolving sandpile surface in (2 + 1) dimensions where the dynamics of mobile grains ({\rho}(x, t)) and immobile clusters (h(x, t)) are coupled. Our coupling models the situation where the sandpile is…

A phase-field model that takes into account the bending energy of fluid vesicles is presented. The Canham-Helfrich model is derived in the sharp-interface limit. A dynamic equation for the phase-field has been solved numerically to find…

This paper presents a generalization of the sandpile model, called the parallel symmetric sandpile model, which inherits the rules of the symmetric sandpile model and implements them in parallel. In this new model, at each step the…

We investigate the origin of the difference, which was noticed by Fey {\it et al.} [Phys. Rev. Lett. {\bf 104}, 145703 (2010)], between the steady state density of an Abelian sandpile model (ASM) and the transition point of its…

Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations…

We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called stochastic modified…

We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically…

We introduce and study a deterministic lattice model describing the motion of an infinite system of oppositely charged particles under the action of a constant electric field. As an application this model represents a traffic flow of cars…

We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…

Coarse-graining is central to reducing dimensionality in molecular dynamics, and is typically characterized by a mapping which projects the full state of the system to a smaller class of variables. While extensive literature has been…

Energy-Based Models (EBMs) have proven to be a highly effective approach for modelling densities on finite-dimensional spaces. Their ability to incorporate domain-specific choices and constraints into the structure of the model through…

We consider the dynamics of a 1D system evolving according to a deterministic drift and randomly forced by two types of jumps processes, one representing an external, uncontrolled forcing and the other one a control that instantaneously…

Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In…

Atmospheric self-organization and activator-inhibitor dynamics in biology provide examples of checkerboard-like spatio-temporal organization. We study a simple model for local activation-inhibition processes. Our model, first introduced in…

The solidification of polycrystalline materials can be modelled by orientation-field models, which are formulated in terms of two continuous fields: a phase field that describes the thermodynamic state and an orientation field that…

We consider the directed Abelian sandpile model in the presence of sink sites whose density f_t at depth t below the top surface varies as c~1/t^chi. For chi>1 the disorder is irrelevant. For chi<1, it is relevant and the model is no longer…

In this paper, the variable wind power is incorporated into the dynamic model for long-term stability analysis. A theory-based method is proposed for power systems with wind power to conduct long-term stability analysis, which is able to…

Directed paths have been used extensively in the scientific literature as a model of a linear polymer. Such paths models in particular the conformational entropy of a linear polymer and the effects it has on the free energy. These directed…

We discuss a model for directed percolation in which the flux of material along each bond is a dynamical variable. The model includes a physically significant limiting case where the total flux of material is conserved. We show that the…

Energy landscapes play a crucial role in shaping dynamics of many real-world complex systems. System evolution is often modeled as particles moving on a landscape under the combined effect of energy-driven drift and noise-induced diffusion,…