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We apply Prediction-Based control (PBC) in order to stabilize globally a positive equilibrium of a planar Ricker's equation. We construct a closed invariant set in a strictly positive domain for the controlled map and derive conditions on…
A recent paper by Huang et al. [Computer Physics Communications 207, 123 (2016)] thoroughly analyzed the Finite Grid Instability(FGI) and spectral fidelity of standard Particle-In-Cell (PIC) methods. Numerical experiments were carried out…
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…
The use of explicit particle-in-cell (PIC) method for relativistic plasma simulations is restricted by numerical heating and instabilities that may significantly constrain the choice of time and space steps. To partially eliminate these…
The accurate prediction of occurrence and strength of kinetic instabilities in plasmas remains a significant challenge in nuclear fusion research. To accurately capture the plasmas dynamics one is required to solve the Vlasov equation for…
A novel theoretical framework, the inverse problem approach, is proposed to calculate non-perturbative quantities in quantum chromodynamics (QCD). Based on the dispersion relation of quantum field theory, this approach determines unknown…
Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These…
Plasma instabilities are a major concern in plasma science, for applications ranging from particle accelerators to nuclear fusion reactors. In this work, we consider the possibility of controlling such instabilities by adding an external…
Particle-in-cell (PIC) is the most used algorithm to perform self-consistent tracking of intense charged particle beams. It is based on depositing macro-particles on a grid, and subsequently solving on it the Poisson equation. It is well…
This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…
Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining…
While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy.…
This paper presents a nonlinear model predictive control strategy for stochastic systems with general (state and input dependent) disturbances subject to chance constraints. Our approach uses an online computed stochastic tube to ensure…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
We solve principal component regression (PCR), up to a multiplicative accuracy $1+\gamma$, by reducing the problem to $\tilde{O}(\gamma^{-1})$ black-box calls of ridge regression. Therefore, our algorithm does not require any explicit…
We study the Richtmyer--Meshkov (RM) instability of a relativistic perfect fluid by means of high order numerical simulations with adaptive mesh refinement (AMR). The numerical scheme adopts a finite volume Weighted Essentially…
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…
This paper discusses a novel fully implicit formulation for a 1D electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov-Poisson…
Petrov-Galerkin formulations with optimal test functions allow for the stabilization of finite element simulations. In particular, given a discrete trial space, the optimal test space induces a numerical scheme delivering the best…
In this article, we introduce a novel dimensionality reduction formulation for the Poisson's equation in the Vlasov-Poisson system that yields a reduced-order particle-in-cell scheme. This scheme allows a remarkable reduction in the…