Related papers: Beyond single-stream with the Schr\"odinger method
Based on the notion of a construction process consisting of the stepwise addition of particles to the pure fluid, a discrete model for the apparent viscosity as well as for the maximum packing fraction of polydisperse suspensions of…
We present analytical results and numerical simulations for a class of nonlinear dispersive equations in two spatial dimensions. These equations are of (derivative) nonlinear Schr\"odinger type and have recently been obtained in \cite{DLS}…
For simulations that deal only with dark matter or stellar systems, the conventional N-body technique is fast, memory efficient, and relatively simple to implement. However when including the effects of gas physics, mesh codes are at a…
The complex processes underlying the generation of a coherent-like emission from the multiple-scattering of photons and wave-localization in the presence of structural disorder are still mostly un-explored. Here we show that a single…
In this paper, we develop an ultra-weak discontinuous Galerkin (DG) method to solve the one-dimensional nonlinear Schr\"odinger equation. Stability conditions and error estimates are derived for the scheme with a general class of numerical…
The Euler Poisson equations describe important physical phenomena in many applications such as semiconductor modeling and plasma physics. This paper is to advance our understanding of critical threshold phenomena in such systems in the…
We study the dispersive blow-up phenomena for the Schr\"odinger-Korteweg-de Vries (S-KdV) system. Roughly, dispersive blow-up has being called to the development of point singularities due to the focussing of short or long waves. In…
In this study, we focus on the modelling of coupled systems of shallow water flows and solute transport with source terms due to variable topography and friction effect. Our aim is to propose efficient and accurate numerical techniques for…
In this article, we study a collisionless kinetic model for plasmas in the neighborhood of a cylindrical metallic Langmuir probe. This model consists in a bi-species Vlasov-Poisson equation in a domain contained between two cylinders with…
Conditional generative models represent a significant advancement in the field of machine learning, allowing for the controlled synthesis of data by incorporating additional information into the generation process. In this work we introduce…
Nonlinearity in the Schr\"odinger equation gives rise to rich phenomena such as soliton formation, modulational instability, and self-organization in diverse physical systems. Motivated by recent advances in engineering nonlinear gauge…
The collision of two equilibrium ground state solutions of the Schr\"odinger-Poisson (SP) system, in orthogonal states, is proposed as a formation mechanism of mixed state solutions of the SP system with spherical and first dipolar…
We discuss spacetime singularities of a solution to the Schr\"odinger equation with a metric perturbation and a sublinear potential. The quasi-homogeneous wave front set, due to Lascar (1977), of a solution is characterized by that of the…
In this paper, we study the existence problem of bound states of one dimensional Schrodinger system via the blow-up method.
This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a…
We employ a multi-phase smoothed particle hydrodynamics (SPH) method to study droplet dynamics in shear flow. With an extensive range of Reynolds number, capillary number, wall confinement, and density/viscosity ratio between the droplet…
This work outlines a new three-dimensional diffuse interface finite volume method for the simulation of multiple solid and fluid components featuring large deformations, sliding and void opening. This is achieved by extending an existing…
In this paper we are studying the scattering of massless Dirac fermions by Schwarzschild and Reissner-Nordstr\"om black holes. This is done by applying the partial wave analysis to the scattering modes obtained after solving the massless…
We review some recent results on the theory of scattering and more precisely on the local Cauchy problem at infinity in time for some long range nonlinear systems including some form of the Schr"odinger equation. We consider in particular…
We investigate the dynamics of localized solutions of the relativistic cold fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed…