Related papers: An alternative approach to efficient simulation of…
We present a new Monte Carlo method for obtaining solutions of the Boltzmann equation for describing phonon transport in micro and nanoscale devices. The proposed method can resolve arbitrarily small signals (e.g. temperature differences)…
We present and discuss a variance-reduced stochastic particle method for simulating the relaxation-time model of the Boltzmann transport equation. The present paper focuses on the dilute gas case, although the method is expected to directly…
An algorithm is proposed to calculate traveling dissipative solitons for the FitzHugh-Nagumo equations. It is based on the application of the steepest descent method to a certain functional. This approach can be used to find solitons…
Monte Carlo statistical ray-tracing methods are commonly employed to simulate carrier transport in nanostructured materials. In the case of a large degree of nanostructuring and under linear response (small driving fields), these…
Mesoscopic numerical simulation has become an important tool in thermal management and energy harvesting at the micro/nano scale, where the Fourier's law failed. However, it is not easy to efficiently solve the phonon Boltzmann transport…
Different techniques of event biasing have been implemented in the particle-based Monte Carlo simulations of a 15nm n-channel MOSFET. The primary goal is to achieve enhancement in the channel statistics and faster convergence in the…
Recently the general form of a translation-covariant quantum Boltzmann equation has been derived which describes the dynamics of a tracer particle in a quantum gas. We develop a stochastic wave function algorithm that enables full…
This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substantial computational cost of solving the Boltzmann equation…
Energy-transport equations for the transport of fermions in optical lattices are formally derived from a Boltzmann transport equation with a periodic lattice potential in the diffusive limit. The limit model possesses a formal gradient-flow…
A Full Band Monte Carlo simulator has been developed to consider phonon transmission across interfaces that are perpendicular to the heat flux. This solver of the Boltzmann transport equation which does not require any assumption on the…
We have developed a Monte Carlo simulation for ion transport in hot background gases, which is an alternative way of solving the corresponding Boltzmann equation that determines the distribution function of ions. We consider the limit of…
MCBTE solves the linearized Boltzmann transport equation for phonons in three dimensions using a variance-reduced Monte Carlo solution approach. The algorithm is suited for both transient and steady-state analysis of thermal transport in…
Numerical simulation of turbulent fluid dynamics needs to either parameterize turbulence-which introduces large uncertainties-or explicitly resolve the smallest scales-which is prohibitively expensive. Here we provide evidence through…
In this book chapter we provide the definition of "Simulating Nanoscale Heat Transport", broadly regarded as modeling heat conduction beyond Fourier's law. We primarely focus on incoherent transport, which is dominated by scattering between…
We develop a computational framework, based on the Boltzmann transport equation, with the ability to compute the thermal transport in nanostructured materials of any geometry using as the only input the bulk thermal conductivity…
Inspired by the Boltzmann kinetics, we propose a collision-based dynamics with a Monte Carlo solution algorithm that approximates the solution of the multi-marginal optimal transport problem via randomized pairwise swapping of sample…
The Boltzmann transport equation is one of the most relevant framework to study the heat transport at the nanoscale, beyond the diffusive regime and up to the micrometer-scale. In the general case of three-dimensional devices, the particle…
The direct simulation Monte Carlo (DSMC) method is a widely used stochastic particle approach to solving the Boltzmann equation. However, its computational cost remains a major drawback, which can be attributed to statistical errors when…
The Boltzmann equation has been a driving force behind significant mathematical research over the years. Its challenging theoretical complexity, combined with a wide variety of current scientific and technological problems that require…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…