Related papers: Time evolution of nanoscale systems by finite diff…
The rotation profile of a magnetized plasma cylinder composed of multiple fluids is investigated analytically, expanding on previous results. The analytic steady-state solution is used as a benchmark for a time-dependent multiple-fluid…
System identification through learning approaches is emerging as a promising strategy for understanding and simulating dynamical systems, which nevertheless faces considerable difficulty when confronted with power systems modeled by…
The most popular methods for self-consistent simulation of fields interacting with charged species is using finite difference time domain (FDTD) methods together with Newton's laws of motion to evolve locations and velocities of particles.…
A coupled BEM/FEM formulation for the transient interaction between an acoustic field and a piezoelectric scatterer is proposed. The scattered part of the acoustic wave is represented in terms of retarded layer potentials while the elastic…
Multiderivative time integrators have a long history of development for ordinary differential equations, and yet to date, only a small subset of these methods have been explored as a tool for solving partial differential equations (PDEs).…
This survey is an in-depth development of the theoretical aspects of the method of Evolving Sets, a method which has been used in several of my papers. It is fairly esoteric as to a large degree it stems from my efforts to ascertain whether…
The evolution equation for inhomogeneous and anisotropic temperature fluctuation inside a medium is derived within the ambit of Boltzmann Transport Equation (BTE) for a hot gas of massless particles. Also, specializing to a situation…
Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods (MFEM) in space for simulating…
In this work we prove that a family of explicit numerical finite-difference methods is convergent when applied to a nonlinear Volterra equation with a power-type nonlinearity. In that case the kernel is not of Lipschitz type, therefore the…
We examine the temporal evolution of the modular entropy and capacity (in particular, the fluctuation of the entanglement entropy) for systems of time-dependent oscillators coupled by a (time-dependent) parameter. Such models, through the…
We consider a strongly nonlinear PDE system describing solid-solid phase transitions in shape memory alloys. The system accounts for the evolution of an order parameter (related to different symmetries of the crystal lattice in the phase…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
We derive a nonlinear integro-differential transport equation describing collective evolution of weights under gradient descent in large-width neural-network-like models. We characterize stationary points of the evolution and analyze…
We consider discrete-time (DT) systems S in which a DT input is first tranformed to a continuous-time (CT) format by phase-amplitude modulation, then modified by a non-linear CT dynamical transformation F, and finally converted back to DT…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
Flow of molecular gas into a complex vacuum system is investigated by a lumped parameter model to estimate the time evolution of gas pressure $p_g$, which for the first time takes into account the realistic effect of time-delay arising due…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
The calculation of time-dependent charge and energy currents in nanoscale systems is a challenging task. Nevertheless it is crucial for gaining a deep understanding of the relevant processes at the nanoscale. We extend the auxiliary-mode…
Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…
A coercivity property of temporal convolution operators is an essential tool in the analysis of time-dependent boundary integral equations and their space and time discretisations. It is known that this coercivity property is inherited by…