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Stochastic and mixed stochastic-deterministic density functional theory (DFT) are promising new approaches for the calculation of the equation-of-state and transport properties in materials under extreme conditions. In the intermediate warm…
Symplectic integrators offer vastly superior performance over traditional numerical techniques for conservative dynamical systems, but their application to \emph{dissipative} systems is inherently difficult due to dissipative systems' lack…
A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
The algorithm for the DPD fluid, the dynamics of which is conceptually a combination of molecular dynamics, Brownian dynamics and lattice gas automata, is designed for simulating rheological properties of complex fluids on hydrodynamic time…
The finite-difference time-domain (FDTD) algorithm is a popular numerical method for solving electromagnetic problems. FDTD simulations can suffer from instability due to the explicit nature of the method. Stability enforcement can be…
In this paper we present splitting methods which are based on iterative schemes and applied to stochastic nonlinear Schroedinger equation. We will design stochastic integrators which almost conserve the symplectic structure. The idea is…
Discrete variational methods show excellent performance in numerical simulations of mechanical systems. In this paper, we adapt discrete variational integrators for the case of mechanical systems with double-bracket dissipation. In…
Even though the Dissipative Particle Dynamics (DPD) has shown its worth in a variety of research areas, it has been rarely used for polymer dynamics, particularly in dilute and semi-dilute conditions and under imposed flow fields. For such…
In this paper we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual…
We examine the formulation and numerical treatment of dissipative particle dynamics (DPD) and momentum-conserving molecular dynamics. We show that it is possible to improve both the accuracy and the stability of DPD by employing a pairwise…
Particle methods are less computationally efficient than grid based numerical solution of the Navier Stokes equation. However, they have important advantages including rigorous mass conservation, momentum conservation and isotropy. In…
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…
This paper is devoted to the study of qualitative geometrical properties of stochastic dynamical systems, namely their symmetries, reduction and integrability. In particular, we show that an SDS which is diffusion-wise symmetric with…
Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…
The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via Ito stochastic calculus is obtained. The stochastic integral representation affords many…
The implementation of a new particle module describing the physics of dust grains coupled to the gas via drag forces is the subject of this work. The proposed particle-gas hybrid scheme has been designed to work in Cartesian as well as in…
The paper provides a tutorial to the conceptual layout of a self-consistently coupled Particle-In-Cell/Test-Particle model for the kinetic simulation of sputtering transport in capacitively coupled plasmas at low gas pressures. It explains…
This work presents the mathematical and computational aspects of a smooth dissipative particle dynamics with dynamic virtual particle allocation method (SDPD-DV) for modeling and simulation of mesoscopic fluids in wall-bounded domains. The…