Related papers: Numerical simulation of random paths with a curvat…
Information geometry is concerned with the application of differential geometry concepts in the study of the parametric spaces of statistical models. When the random variables are independent and identically distributed, the underlying…
We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We are mainly focused on the completion of a table for the protocols of the quantum walk that could simulate different family of the…
In this article, we review the progress made on the statistical mechanics of liquids and fluids embedded in curved space. Our main focus will be on two-dimensional manifolds of constant nonzero curvature and on the influence of the latter…
We review and extend, in a self-contained way, the mathematical foundations of numerical simulation methods that are based on the use of random states. The power and versatility of this simulation technology is illustrated by calculations…
A key open question in the glass transition field is whether a finite temperature thermodynamic transition to the glass state exists or not. Recent simulations of coupled replicas in atomistic models have found signatures of a static…
Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. Identifying…
Transition path theory computes statistics from ensembles of reactive trajectories. A common strategy for sampling reactive trajectories is to control the branching and pruning of trajectories so as to enhance the sampling of low…
The conductance in Coulomb blockade quantum dots exhibits sharp peaks whose spacings fluctuate with the number of electrons. We derive the temperature-dependence of these fluctuations in the statistical regime and compare with recent…
The path probability of stochastic motion of non dissipative or quasi-Hamiltonian systems is investigated by numerical experiment. The simulation model generates ideal one-dimensional motion of particles subject only to conservative forces…
Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…
The paper develops a method for the numerical simulation of a free-surface flow of incompressible viscous fluid around a streamlined body. The body is a rigid stationary construction partially submerged in the fluid. The application we are…
A first-order phase transition is found in two types of intrinsic curvature models defined on dynamically triangulated surfaces of disk topology. The intrinsic curvature energy is included in the Hamiltonian. The smooth phase is separated…
In this paper we outline methodology to efficiently simulate (jump) diffusion bridge sample paths without discretisation error. We achieve this by considering the simulation of conditioned (jump) diffusion bridge sample paths in light of…
Particle diffusion in a two dimensional curved surface embedded in $R_3$ is considered. In addition to the usual diffusion flow, we find a new flow with an explicit curvature dependence. New diffusion equation is obtained in $\epsilon$…
A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular…
Random walk subject to random drive has been extensively employed as a model for physical and biological processes. While equilibrium statistical physics has yielded significant insights into the distributions of dynamical fixed points of…
The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A…
The dynamics of phase transitions plays a crucial r\^ole in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified…
An extrinsic curvature surface model is investigated by Monte Carlo simulations on a disk. We found that the model undergoes a first-order transition separating the smooth phase from the collapsed phase. The results in this paper together…
Numerical modelling of coupled multiphysics phenomena is becoming an increasingly important subject in applied mathematics. The main challenge in teaching this subject is the complexity of both the mathematical models and their numerical…