相关论文: Generalized Dielectric Breakdown Model

A hybrid percolation transition (HPT) exhibits both discontinuity of the order parameter and critical behavior at the transition point. Such dynamic transitions can occur in two ways: by cluster pruning with suppression of loop formation of…

We study the brittle fragmentation of spheres by using a three-dimensional Discrete Element Model. Large scale computer simulations are performed with a model that consists of agglomerates of many particles, interconnected by beam-truss…

We review the critical behavior of nonequilibrium systems, such as directed percolation (DP) and branching-annihilating random walks (BARW), which possess phase transitions into absorbing states. After reviewing the bulk scaling behavior of…

In mechanical systems it is of interest to know the onset of fracture in dependence of the boundary conditions. Here we study a one-dimensional model which allows for an underlying heterogeneous structure in the discrete setting. Such…

We introduce a multi-scale diagonalization scheme to study the transition between the many-body localized and the ergodic phase in disordered quantum chains. The scheme assumes a sharp dichotomy between subsystems that behave as localized…

Cellular bioelectricity describes the biological phenomenon in which cells in living tissue generate and maintain patterns of voltage gradients induced by differing concentrations of charged ions. A growing body of research suggests that…

We summarize and to discuss briefly the geometrical practice of modeling attitudes so far popular in treating reaction kinetics of solid-state processes. The model equations existing in the literature have been explored to describe the…

Breakage is generally understood in mechanical terms, yet nano-structures can rupture not only under external loads but also via thermal activation. Here we treat in a general framework the statistical mechanics of thermally induced…

A microcanonical multifragmentation model (MMM) is used for investigating whether equilibration really occurs in the dynamical evolution of two heavy ion collisions simulated via a stochastic mean field approach (SMF). The standard…

We consider the scalar sector of the most general renormalizable two-Higgs-doublet model at non-zero temperature. We calculate the largest finite temperature corrections to the free-energy density and study thermal evolution of the ground…

In this paper we consider an approach, which allows researching a processes of order-disorder transition in various systems (with any distribution of the exchange integrals signs) in the frame of Ising model. A new order parameters, which…

Self-organization and nonequilibrium phase transitions are well known to occur in two- and three- dimensional dissipative systems. Here, instead, we provide numerical evidence that these phenomena also occur in a one-dimensional Hamiltonian…

We construct transported PDEs on self-similar fractal domains from reference equations posed on the unit interval, and derive explicit self-similar interacting particle systems that approximate the resulting dynamics. The construction…

Although diffusion models now occupy a central place in generative modeling, introductory treatments commonly assume Euclidean data and seldom clarify their connection to discrete-state analogues. This article is a self-contained primer on…

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion…

Searches for the permanent electric dipole moments (EDMs) of molecules, atoms, nucleons and nuclei provide powerful probes of CP violation both within and beyond the Standard Model (BSM). The interpretation of experimental EDM limits…

We investigate the application of conformable derivatives to model critical phenomena near continuous phase transitions. By incorporating a deformation parameter into the differential structure, we derive unified expressions for…

The formation and dissolution of a droplet is an important mechanism related to various nucleation phenomena. Here, we address the droplet formation-dissolution transition in a two-dimensional Lennard-Jones gas to demonstrate a consistent…

In the ordered phase of the 3D Ising model, minority spin clusters are surrounded by a boundary of dual plaquettes. As the temperature is raised, these spin clusters become more numerous, and it is found that eventually their boundaries…

Modeling microstructure evolution in electrochemical systems is vital for understanding the mechanism of various electrochemical processes. In this work, we propose a general phase field framework that is fully variational and thus…