相关论文: Explicit Solutions and Stability Properties of Hom…

An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…

This manuscript presents an efficient solver for the linear system that arises from the Hierarchical Poincar\'e-Steklov (HPS) discretization of three dimensional variable coefficient Helmholtz problems. Previous work on the HPS method has…

In this manuscript we consider the stability of periodic solutions to Lambda-Omega lattice dynamical systems. In particular, we show that an appropriate ansatz casts the lattice dynamical system as an infinite-dimensional fast-slow…

We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many families of groups with polynomial coefficients. This gives two…

This paper provides an algorithmic pipeline for studying the intrinsic structure of a finite discrete dynamical system (DDS) modelling an evolving phenomenon. Here, by intrinsic structure we mean, regarding the dynamics of the DDS under…

We show that any system of ODEs can be modified whilst preserving its homogeneous Darboux polynomials. We employ the result to generalise a hierarchy of integrable Lotka-Volterra systems.

The two-fluid plasma model has a wide range of timescales which must all be numerically resolved regardless of the timescale on which plasma dynamics occurs. The answer to solving numerically stiff systems is generally to utilize…

We study the problem of stabilization for the acoustic system with a spatially distributed damping. Imposing various hypotheses on the structural properties of the damping term, we identify either exponential or polynomial decay of…

Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for…

The paper focuses on the numerical stability and accuracy of implicit time-domain integration (TDI) methods when applied for the solution of a power system model impacted by time delays. Such a model is generally formulated as a set of…

We present a novel, global algorithm for solving polynomial multiparameter eigenvalue problems (PMEPs) by leveraging a hidden variable tensor Dixon resultant framework. Our method transforms a PMEP into one or more univariate polynomial…

Boolean automata networks, genetic regulation networks, and metabolic networks are just a few examples of biological modelling by discrete dynamical systems (DDS). A major issue in modelling is the verification of the model against the…

We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based…

Eigenvalue perturbation theory is applied to justify using complex-valued linear scalar test equations to characterize the stability of implicit-explicit general linear methods (IMEX GLMs) solving autonomous linear ordinary differential…

We consider a hydrodynamic-type system of balance equations which is closed by the dynamic equation of state taking into account the effects of spatial nonlocality. Symmetry and local conservation laws of this system are studied. A system…

A new conservative finite element solver for the three-dimensional steady magnetohydrodynamic (MHD) kinematics equations is presented.The solver utilizes magnetic vector potential and current density as solution variables, which are…

Driven by the challenging task of finding robust discretization methods for Galbrun's equation, we investigate conditions for stability and different aspects of robustness for different finite element schemes on a simplified version of the…

While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of…

In this work, a novel analysis of a hybrid discontinuous Galerkin method for the Helmholtz equation is presented. It uses wavenumber, mesh size and polynomial degree independent stabilisation parameters leading to impedance traces between…

We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…