Related papers: The self-consistent quantum-electrostatic problem …
The accuracy of quasilinear theory applied to the electron bump-on-tail instability, a classic model problem, is explored with conservative high-order discontinuous Galerkin methods applied to both the quasilinear equations and to a direct…
We study the existence and stability of stationary solutions of Poisson-Nernst- Planck equations with steric effects (PNP-steric equations) with two counter-charged species. These equations describe steady current through open ionic…
We present a real-space adaptive-coordinate method, which combines the advantages of the finite-difference approach with the accuracy and flexibility of the adaptive coordinate method. The discretized Kohn-Sham equations are written in…
We present a general formalism for the construction of thermodynamically consistent stochastic models of non-linear electronic circuits. The devices constituting the circuit can have arbitrary I-V curves and may include tunnel junctions,…
Recent spatially resolved measurements of the electrostatic-potential variation across a Hall bar in strong magnetic fields, which revealed a clear correlation between current-carrying strips and incompressible strips expected near the…
We address the weak interaction of a pair of well-separated pure-quartic solitons (PQSs), which are solutions to a generalized nonlinear Schrodinger equation (NLSE) with the quartic-only dispersion. An asymptotic technique is applied to…
The study of the non-equilibrium dynamics of many-body systems after a quantum quench received a considerable boost and a deep theoretical understanding from the path integral formulation in imaginary time. However, the celebrated problem…
Structure-preserving numerical schemes for a nonlinear parabolic fourth-order equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation…
We study a self-similar solution of the kinetic equation describing weak wave turbulence in Bose-Einstein condensates. This solution presumably corresponds to an asymptotic behavior of a spectrum evolving from a broad class of initial data,…
Ion transport, often described by the Poisson--Nernst--Planck (PNP) equations, is ubiquitous in electrochemical devices and many biological processes of significance. In this work, we develop conservative, positivity-preserving, energy…
The formalism of Ursell operators provides a self-consistent integral equation for the one-particle reduced operator. In three dimensions this technique yields values of the shift in the Bose-Einstein condensation (BEC) transition…
We study the stationary nonequilibrium states of N point particles moving under the influence of an electric field E among fixed obstacles (discs) in a two dimensional torus. The total kinetic energy of the system is kept constant through a…
All complex fluid motions, such as transition and turbulence, obeying the Navier-Stokes equations are non-linear phenomena. Some aspects of the non-linear terms of these equations are not well understood and are, in fact, misunderstood. The…
Stability of electro-hydrodynamic processes between ion-exchange membranes is investigated. Solutions of the equilibrium problem are commonly described in the one-dimensional (1D) steady-state approximation. In the present work, a novel…
We consider the stationary one dimensional Schr\"odinger-Poisson system on a bounded interval with a background potential describing a quantum well. Using a partition function which forces the particles to remain in the quantum well, the…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
Solving the stationary nonlinear Fokker-Planck equations is important in applications and examples include the Poisson-Boltzmann equation and the two layer neural networks. Making use of the connection between the interacting particle…
A variational approach is used to develop a robust numerical procedure for solving the nonlinear Poisson-Boltzmann equation. Following Maggs et al., we construct an appropriate constrained free energy functional, such that its…
We investigate the transport through a few-level quantum system described by a Markovian master equation with temperature- and particle-density dependent chemical potentials. From the corresponding Onsager relations we extract linear…
We propose an unconditionally energy-stable, orthonormality-preserving, component-wise splitting iterative scheme for the Kohn-Sham gradient flow based model in the electronic structure calculation. We first study the scheme discretized in…