Related papers: Coarse Stability and Bifurcation Analysis Using St…
We present a lattice Monte Carlo algorithm based on the one originally proposed by Maggs and Rossetto for simulating electrostatic interactions in inhomogeneous dielectric media. The original algorithm is known to produce attractive…
We present an application of equation-free computation to the coarse-grained feedback linearization problem of nonlinear systems described by microscopic/stochastic simulators. Feedback linearization with pole placement requires the…
Biochemical reactions with oscillatory behavior play an essential role in synthetic biology at the microscopic scale. Although a robust stability theory for deterministic chemical oscillators in the macroscopic limit exists, the dynamical…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
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…
Solvent-free coarse grained models represent one of the most promising approaches for molecular simulations of mesoscopically large membranes. In these models, the size of the simulated membrane is limited by the slow relaxation time of…
We demonstrate a data-driven method to solve for the invariant probability density function of a randomly perturbed dynamical system. The key idea is to replace the boundary condition of numerical schemes by a least squares problem…
This paper introduces the novel class of modulated cyclostationary processes, a class of non-stationary processes exhibiting frequency coupling, and proposes a method of their estimation from repeated trials. Cyclostationary processes also…
We show how to extend a recently proposed multi-level Monte Carlo approach to the continuous time Markov chain setting, thereby greatly lowering the computational complexity needed to compute expected values of functions of the state of the…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
We establish, through coarse-grained computation, a connection between traditional, continuum numerical algorithms (initial value problems as well as fixed point algorithms) and atomistic simulations of the Larson model of micelle…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
We propose a kinetic Ising model to study phase separation driven by surface diffusion. This model is referred to as "Model S", and consists of the usual Kawasaki spin-exchange kinetics ("Model B") in conjunction with a kinetic constraint.…
In this paper we consider the possibility to use numerical simulations for a computer assisted analysis of integrability of dynamical systems. We formulate a rather general method of recovering the obstruction to integrability for the…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
In traffic flow modeling, incorporating uncertainty is crucial for accurately capturing the complexities of real-world scenarios. In this work we focus on kinetic models of traffic flow, where a key step is to design effective numerical…
When simulating resistive-capacitive circuits or electroquasistatic problems where conductors and insulators coexist, one observes that large time steps or low frequencies lead to numerical instabilities, which are related to the condition…
Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The basic idea is to apply the method of numerical continuation to a feedback-controlled physical experiment. Since in an…
We introduce a novel method of efficiently simulating the non-equilibrium steady state of large many-body open quantum systems with highly non-local interactions, based on a variational Monte Carlo optimization of a matrix product operator…
Recent years have seen a growing interest in the thermodynamic cost of dissipative structures formed by active particles. Given the strong finite-size effects of such systems, it is essential to develop efficient numerical approaches that…