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The spurious states found in numerical implementations of envelope function models for semiconductor heterostructures and nanostructures have been shown to be readily removed by employing a first-order difference scheme. This approach is…
A novel framework for resolving discontinuous solutions of conservation laws, e.g., contact lines, shock waves, and interfaces, using implicit tracking and a high-order discontinuous Galerkin (DG) discretization was introduced in [38].…
This article addresses the question concerning the existence of global entropy solution for generalized Eulerian droplet models with air velocity depending on both space and time variables. When $f(u)=u,$ $\kappa(t)=const.$ and…
We consider a system of two conservation laws and provide a detailed description of both classical and non-classical self-similar Riemann solutions. In particular, we demonstrate the existence of overcompressive delta shocks as singular…
We consider the initial value problem for a nonlinear shallow water model in horizontal dimension d = 2 and in the presence of a fixed partially immersed solid body on the water surface. We assume that the bottom of the solid body is the…
In this paper, we extend the ROM-based approach for inverse scattering with Neumann boundary conditions, introduced by Druskin at. al. (Inverse Problems 37, 2021), to the 1D Schr{\"o}dinger equation with impedance (Robin) boundary…
Tracking signals in dynamic environments presents difficulties in both analysis and implementation. In this work, we expand on a class of subspace tracking algorithms which utilize the Grassmann manifold -- the set of linear subspaces of a…
We study the Rayleigh-Stokes problem for a generalized second-grade fluid which involves a Riemann-Liouville fractional derivative in time, and present an analysis of the problem in the continuous, space semidiscrete and fully discrete…
We consider dispersive shock wave to the focusing nonlinear Schr\"odinger equation generated by a discontinuous initial condition which is periodic or quasi-periodic on the left semi-axis and zero on the right semi-axis. As an initial…
Reliable tracking of moving boundaries is important for the simulation of compressible fluid flows and there are a lot of contributions in literature. We recognize from the classical piston problem, a typical moving boundary problem in gas…
In this paper, we mainly discuss the convergence behavior of diffuse domain method (DDM) for solving semilinear parabolic equations with Neumann boundary condition defined in general irregular domains. We use a phasefield function to…
We study the behavior of perturbations in a compressible one-dimensional inviscid gas with an ambient state consisting of constant pressure and periodically-varying density. We show through asymptotic analysis that long-wavelength…
Recent advances in nonlinear dynamical systems theory provide a new insight into numerical properties of discrete algorithms developed to solve nonlinear initial value problems. Basic features like accuracy and stability are well pointed…
We study the resolution of discontinuous singularities in gas dynamics via multi-dimensional rarefaction waves. While the mechanism is well-understood in one spatial dimension, the rigorous construction in higher dimensions has remained a…
The capability to accurately predict flood flows via numerical simulations is a key component of contemporary flood risk management practice. However, modern flood models lack the capacity to accurately model flow interactions with linear…
A method is presented for solving the characteristic initial value problem for the collision and subsequent nonlinear interaction of plane gravitational or gravitational and electromagnetic waves in a Minkowski background. This method…
In this thesis, we present new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions: - Single-Source Reachability…
In this paper, we study the convergence behavior of the diffuse domain method (DDM) for solving a class of second-order parabolic partial differential equations with Neumann boundary condition posed on general irregular domains. The DDM…
This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…
Theoretical studies on linear shear instabilities often use simple velocity and density profiles (e.g. constant, piecewise) for obtaining good qualitative and quantitative predictions of the initial disturbances. Furthermore, such simple…