Related papers: Solving equations of motion by using Monte Carlo M…
We present a new numerical Monte Carlo approach to determine the scaling behavior of lattice field theories far from equilibrium. The presented methods are generally applicable to systems where classical-statistical fluctuations dominate…
In this paper, we suggest a novel sampling method for Monte Carlo molecular simulations. In order to perform efficient sampling of molecular systems, it is advantageous to avoid extremely high energy configurations while also retaining the…
Particle methods based on evolving the spatial derivatives of the solution were originally introduced to simulate reaction-diffusion processes, inspired by vortex methods for the Navier--Stokes equations. Such methods, referred to as…
This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…
We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit…
A first-order, Monte Carlo ensemble method has been recently introduced for solving parabolic equations with random coefficients in [26], which is a natural synthesis of the ensemble-based, Monte Carlo sampling algorithm and the…
Path integrals with complex actions are encountered for many physical systems ranging from spin- or mass-imbalanced atomic gases and graphene to quantum chromo-dynamics at finite density to the non-equilibrium evolution of quantum systems.…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
In this work, we introduce a simple modification of the Monte Carlo algorithm, which we call step Monte Carlo (sMC). The sMC approach allows to simulate processes far from equilibrium and obtain information about the dynamic properties of…
We present a method which extends Monte Carlo studies to situations that require a large dynamic range in particle number. The underlying idea is that, in order to calculate the collisional evolution of a system, some particle interactions…
We propose a fast potential splitting Markov Chain Monte Carlo method which costs $O(1)$ time each step for sampling from equilibrium distributions (Gibbs measures) corresponding to particle systems with singular interacting kernels. We…
We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, mechatronic systems. We derive the equations of motion for some typical mechatronic systems using deterministic principles…
Recently, a class of efficient spectral Monte-Carlo methods was developed in \cite{Feng2025ExponentiallyAS} for solving fractional Poisson equations. These methods fully consider the low regularity of the solution near boundaries and…
This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…
We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition…
This paper deals with nonlinear mechanics of an elevator brake system subjected to uncertainties. A deterministic model that relates the braking force with uncertain parameters is deduced from mechanical equilibrium conditions. In order to…
We present a new approach to determine the small-scale statistical behavior of hydrodynamic turbulence by means of lattice simulations. Using the functional integral representation of the random-force-driven Burgers equation we show that…
We introduce a Monte-Carlo algorithm for the simulation of charged particles moving in the continuum. Electrostatic interactions are not instantaneous as in conventional approaches, but are mediated by a constrained, diffusing electric…
We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide.…
We study the Monte Carlo method for solving a linear system of the form $x = H x + b$. A sufficient condition for the method to work is $\| H \| < 1$, which greatly limits the usability of this method. We improve this condition by proposing…