Related papers: Generalized Dielectric Breakdown Model
We investigate the thermodynamic properties of a Restricted Boltzmann Machine (RBM), a simple energy-based generative model used in the context of unsupervised learning. Assuming the information content of this model to be mainly reflected…
A theoretical model of the formation of an amorphous phase during the quenching of a metallic melt is proposed. It has been shown that the appearance of a significant temperature gradient during the quenching of a metallic melt leads to…
Molecular dynamics (MD) simulations were conducted using the generalized replica exchange method (gREM) on the 4-cyano-4$^{\prime}$-$n$-alkylbiphenyl ($n$CB) system with $n=5$, 6, 7, and 8, which exhibits a nematic-isotropic (NI) phase…
This study addresses ductile fracture of single grains in metals by modeling of the formation and propagation of transgranular cracks. A proposed model integrates gradient extended hardening, phase-field modeling for fracture, and crystal…
Dislocation pileups directly impact the material properties of crystalline solids through the arrangement and collective motion of interacting dislocations. We study the statistical mechanics of these ordered defect structures embedded in…
A systematics of grain boundary (GB) segregation transitions and critical phenomena has been derived to expand the classical GB segregation theory. Using twist GBs as an example, this study uncovers when GB layering vs. prewetting…
We examine in full generality the phase behavior of systems whose constituent particles interact by means of potentials which do not diverge at the origin, are free of attractive parts and decay fast enough to zero as the interparticle…
Diffusion models (DMs) are capable of generating remarkably high-quality samples by iteratively denoising a random vector, a process that corresponds to moving along the probability flow ordinary differential equation (PF ODE).…
We develop a data-driven characterization of the pilot-wave hydrodynamic system in which a bouncing droplet self-propels along the surface of a vibrating bath. We consider drop motion in a confined one-dimensional geometry, and apply the…
We study the effects of spatially inhomogeneous diffusion on the non-equilibrium phase transition in the contact process. The directed-percolation critical point in the contact process is known to be stable against the addition of a…
Different branching and annihilating random walk models are investigated by cluster mean-field method and simulations in one and two dimensions. In case of the A -> 2A, 2A -> 0 model the cluster mean-field approximations show diffusion…
Dielectric spectroscopy measurements over a broad range of temperature and pressure were carried out on poly(oxybutylene) (POB), a type-A polymer (dielectrically-active normal mode). There are three dynamic processes appearing at lower…
By developing data augmentation methods unique to the negative binomial (NB) distribution, we unite seemingly disjoint count and mixture models under the NB process framework. We develop fundamental properties of the models and derive…
Interacting systems can be studied as the networks where nodes are system units and edges denote correlated interactions. Although percolation on network is a unified way to model the emergence and propagation of correlated behaviours, it…
We introduce a three-dimensional model for jamming and glasses, and prove that the fraction of frozen particles is discontinuous at the directed-percolation critical density. In agreement with the accepted scenario for jamming- and…
Kinetic facilitated models and the Mode Coupling Theory (MCT) model B are within those systems known to exhibit a discontinuous dynamical transition with a two step relaxation. We consider a general scaling approach, within mean field…
We study the universal properties of eigenstate entanglement entropy across the transition between many-body localized (MBL) and thermal phases. We develop an improved real space renormalization group approach that enables numerical…
Material properties controlled by evolving defect structures, such as mechanical response, often involve processes spanning many length and time scales which cannot be modeled using a single approach. We present a variety of new results…
Static and dynamical properties of elastic phase transitions under the influence of short--range defects, which locally increase the transition temperature, are investigated. Our approach is based on a Ginzburg--Landau theory for…
The paper suggests a generalisation of the diffusion-limited aggregation (DLA) based on using a general stochastic process to control particle movements before sticking to a growing cluster. This leads to models with variable…