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An overview of advanced dynamical algorithms capable of spanning the widely disparate time scales that govern the decay of metastable phases in discrete spin models is presented. The algorithms discussed include constrained transfer-matrix,…
First of all, this paper presents some improvements of DSMC method in the form of new schemes and approaches, that, for a wide class of problems, increase performance and reduce the demands on computer resources. The most important…
This paper develops three linear and energy-stable schemes for a modified phase field crystal model with a strong nonlinear vacancy potential (VMPFC model). This sixth-order phase-field model enables realistic crystal growth simulation.…
Sequential Monte Carlo (SMC) algorithms represent a suite of robust computational methodologies utilized for state estimation and parameter inference within dynamical systems, particularly in real-time or online environments where data…
There is growing interest in warm dense matter (WDM) -- an exotic state on the border between condensed matter and plasmas. Due to the simultaneous importance of quantum and correlation effects WDM is complicated to treat theoretically. A…
A simple and efficient algorithm of the molecular-dynamics simulation of the hard disk system based on the Event-Driven method is developed. From the analysis of algorithm, the complexity is O(log N) per 1 event, and the constant…
To better understand the capture process by a nanopore, we introduce an efficient Kinetic Monte Carlo (KMC) algorithm that can simulate long times and large system sizes by mapping the dynamic of a point-like particle in a 3D spherically…
Simulation-guided design represents a fundamental contribution towards the development of modern semiconductor devices aiming to reach high-performance particle detection, identification and tracking, and constitutes a strategic element of…
Recently-proposed particle MCMC methods provide a flexible way of performing Bayesian inference for parameters governing stochastic kinetic models defined as Markov (jump) processes (MJPs). Each iteration of the scheme requires an estimate…
We study the Edwards-Anderson model on a simple cubic lattice with a finite constant external field. We employ an indicator composed of a ratio of susceptibilities at finite wavenumbers, which was recently proposed to avoid the difficulties…
In this work we investigate the ground state and the dissipative quantum dynamics of interacting charged particles in an external potential at finite temperature. The recently devised time-dependent quantum Monte Carlo (TDQMC) method allows…
Mean field-like approximations (including naive mean field, Bethe and Kikuchi and more general Cluster Variational Methods) are known to stabilize ordered phases at temperatures higher than the thermodynamical transition. For example, in…
This work addresses uncertainty quantification of electromagnetic devices determined by the eddy current problem. The multilevel Monte Carlo (MLMC) method is used for the treatment of uncertain parameters while the devices are discretized…
We present a quantum mechanical / molecular mechanics (QM/MM) to tackle chemical reactions with substantial molecular reorganization. For this, molecular dynamics simulations with smoothly switched interaction models are used to suggest…
In this Ph.D. thesis quantum Monte Carlo methods are applied to investigate the properties of a number of ultracold quantum systems. In Chapter 1 we discuss the analytical approaches and approximations used in the subsequent Chapters; also…
In this work we propose a new approach for the numerical simulation of kinetic equations through Monte Carlo schemes. We introduce a new technique which permits to reduce the variance of particle methods through a matching with a set of…
Warm dense matter systems created in the laboratory are highly dynamical. In such cases electron dynamics is often needed to accurately simulate the evolution and properties of the system. Large systems force one to make simple…
Molecular Dynamic (MD) approach is applied to study the converging cylindrical shock waves in a dense Lennard-Jones (LJ) fluid. MD method is based on tracking of the atom motions and hence it has an fundamental advantages over hydrodynamic…
Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. Here, we present a new acceleration algorithm based on…
The recently introduced method of excess collisions (MEC) is modified to estimate diffusion-controlled reaction times inside systems of arbitrary size. The resulting MEC-E equations contain a set of empirical parameters, which have to be…