Related papers: Numerical Stability Improvements for the Pseudo-Sp…
Across many plasma applications, the underlying phenomena and interactions among the involved processes are known to exhibit three-dimensional characteristics. Furthermore, the global properties and evolution of plasma systems are often…
Recent advancements in photon induced near-field electron microscopy (PINEM) enable the preparation, coherent manipulation and characterization of free-electron quantum states. The available measurement consists of electron energy…
We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time retains the explicit computational cycle and conserves…
Uncertainties have become a major concern in integrated circuit design. In order to avoid the huge number of repeated simulations in conventional Monte Carlo flows, this paper presents an intrusive spectral simulator for statistical circuit…
The present paper is devoted to the convergence analysis of a class of asymptotic preserving particle schemes [Filbet \& Rodrigues, SIAM J. Numer. Anal., 54 (2) (2016)] for the Vlasov equation with a strong external magnetic field. In this…
We use particle-in-cell (PIC) simulations of a collisionless, electron-ion plasma with a decreasing background magnetic field, $B$, to study the effect of velocity-space instabilities on the viscous heating and thermal conduction of the…
The procedure of comprehensive analysis of instability of current sheathes in a wide range of frequencies and wave lengths in the electrically neutral approximation has been developed. This comprehensive analysis of instability is based on…
We discuss the scalable parallel solution of the Poisson equation within a Particle-In-Cell (PIC) code for the simulation of electron beams in particle accelerators of irregular shape. The problem is discretized by Finite Differences.…
We introduce a new electrostatic particle-in-cell algorithm capable of using large timesteps compared to particle gyro-period under a uniform external magnetic field. The algorithm extends earlier electrostatic fully implicit PIC…
We investigate the stability of probabilistic error cancellation (PEC) outcomes in the presence of non-stationary noise, which is an obstacle to achieving accurate observable estimates. Leveraging Bayesian methods, we design a strategy to…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
The Nystr\"om method is a widely used technique for improving the scalability of kernel-based algorithms, including kernel ridge regression, spectral clustering, and Gaussian processes. Despite its popularity, the numerical stability of the…
We use particle-in-cell (PIC) simulations to study the nonlinear evolution of ion velocity space instabilities in an idealized problem in which a background velocity shear continuously amplifies the magnetic field. We simulate the…
Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical…
The traditional finite-difference time-domain (FDTD) method is constrained by the Courant-Friedrich-Levy (CFL) condition and suffers from the notorious staircase error in electromagnetic simulations. This paper proposes a three-dimensional…
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…
We consider the stability analysis of a large class of linear 1-D PDEs with polynomial data. This class of PDEs contains, as examples, parabolic and hyperbolic PDEs, PDEs with boundary feedback and systems of in-domain/boundary coupled…
We present a geometric Particle-in-Cell (PIC) algorithm on two-dimensional (2D) unstructured meshes for studying electrostatic perturbations in magnetized plasmas. In this method, ions are treated as fully kinetic particles, and electrons…
We present the parallel particle-in-cell (PIC) code Apar-T and, more importantly, address the fundamental question of the relations between the PIC model, the Vlasov-Maxwell theory, and real plasmas. First, we present four validation tests:…
A new approach to nonperturbative calculations in quantum electrodynamics is proposed. The approach is based on a regular iteration scheme for solution of Schwinger-Dyson equations for generating functional of Green functions. The approach…