Related papers: Provably Stable Full-Spectrum Dispersion Relation …
We develop a stability theory for two-dimensional periodic traveling waves of general parabolic systems, possibly including conservation laws. In particular, we identify a diffusive spectral stability assumption and prove that it implies…
In multi-qubit superconducting systems utilizing flip-chip technology, achieving high accuracy in resonator frequencies is of paramount importance, particularly when multiple resonators share a common Purcell filter with restricted…
This paper discusses aspects of the second order hyperbolic partial differential equation associated with the ideal lossless string under tension and it's relationship to two discrete models. These models are finite differencing in the time…
Using spatial domain techniques developed by the authors and Myunghyun Oh in the context of parabolic conservation laws, we establish under a natural set of spectral stability conditions nonlinear asymptotic stability with decay at Gaussian…
In this paper we study the stability of two different problems. The first one is a one-dimensional degenerate wave equation with degenerate damping, incorporating a drift term and a leading operator in non-divergence form. In the second…
This paper considers the phenomenon of distinct regional frequencies recently observed in some power systems. First, a reduced-order mathematical model describing this behaviour is developed. Then, techniques to solve the model are…
We consider differential operators $A$ that can be represented by means of a so-called closure relation in terms of a simpler operator $A_{\operatorname{ext}}$ defined on a larger space. We analyze how the spectral properties of $A$ and…
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…
In numerical simulations of complex flows with discontinuities, it is necessary to use nonlinear schemes. The spectrum of the scheme used have a significant impact on the resolution and stability of the computation. Based on the approximate…
We give a variational proof of global stability for bistable travelling waves of scalar reaction-diffusion equations on the real line. In particular, we recover some of the classical results by P. Fife and J.B. McLeod without any use of the…
We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both…
Distributed secondary frequency control for power systems, is a problem that has been extensively studied in the literature, and one of its key features is that an additional communication network is required to achieve optimal power…
The stability of a thick planar premixed flame, propagating steadily in a direction transverse to that of unidirectional shear flow, is studied. A linear stability analysis is carried out in the asymptotic limit of infinitely large…
We present a detailed convergence analysis for an operator splitting scheme proposed in [C. Liu et al.,J. Comput. Phys., 436, 110253, 2021] for a reaction-diffusion system with detailed balance. The numerical scheme has been constructed…
In this paper, we study the dispersive properties of the wave equation associated with the shifted Laplace-Beltrami operator on real hyperbolic spaces, and deduce Strichartz estimates for a large family of admissible pairs. As an…
In several recent works \cite{Causley2013a}, \cite{Causley2013}, we developed a new second order, A-stable approach to wave propagation problems based on the method of lines transpose (MOL$^T$) formulation combined with alternating…
A hyperbolic system approach is proposed for robust computation of anisotropic diffusion equations that appear in quasineutral plasmas. Though the approach exhibits merits of high extensibility and accurate flux computation, the…
In this paper we develop linear transfer Perron Frobenius operator-based approach for optimal stabilization of stochastic nonlinear system. One of the main highlight of the proposed transfer operator based approach is that both the theory…
This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating…
Stable matching is a fundamental problem studied both in economics and computer science. The task is to find a matching between two sides of agents that have preferences over who they want to be matched with. A matching is stable if no pair…