By introducing a boundary condition for the quantum wire, the Hubbard model is solved exactly by means of the Bethe ansatz. The wave function for the bounded state is clearly defined, and the secular equation for the spectrum is exactly obtained. The ground state and low-lying excited states are studied in the thermodynamic limit. The ground-state energy in the strong coupling limit is obtained...

The nonlinear reflection curve due to a van der Pol type boundary condition at the right end becomes a multivalued relation when one of the parameters (α) exceeds the characteristic impedance value (α = 1). From stability and continuity considerations, we prescribe kinematic admissibility and define hysteresis iterations with memory effects, whose dynamical behavior is herein investigated. Assu...

We numerically investigate periodic travelling wave solutions for a diffusive predator–prey system with landscape features. The landscape features are modelled through the homogeneous Dirichlet boundary condition which is imposed at the edge of the obstacle domain. To effectively treat the Dirichlet boundary condition, we employ a robust and accurate numerical technique by using a boundary cont...

We analyze the multisymplectic Preissman scheme for the KdV equation with the periodic boundary condition and show that the unconvergence of the widely-used iterative methods to solve the resulting nonlinear algebra system of the Preissman scheme is due to the introduced potential function. A artificial numerical condition is added to the periodic boundary condition. The added boundary conditio...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

The fluctuating elastic boundary (FEB) model for molecular dynamics has recently been developed and validated through simulations of liquid argon. In the FEB model, a flexible boundary which consists of particles connected by springs is used to confine the solvated system, thereby eliminating the need for periodic boundary conditions. In this study, we extend this model to the simulation of bul...

We study two types of asymptotic problems whose common feature and difficultyis to exhibit oscillating Dirichlet boundary conditions : the main contribution of this article is to show how to recover the Dirichlet boundary condition for the limiting equation. These two types of problems are (i) periodic homogenization problems for fully nonlinear, second-order elliptic partial differential equat...

Abstract In Smoothed Particle Hydrodynamics (SPH) methods for fluid flow, incompressibility may be imposed by a projection method with an artificial homogeneous Neumann boundary condition for the pressure Poisson equation. This is often inconsistent with physical conditions at solid walls and inflow and outflow boundaries. For this reason open-boundary flows have rarely been computed using SPH....

In this paper we prove the existence of weak periodic solutions for a nonlinear parabolic equations with the Robin periodic boundary condition. The aim will be achieved by reformulating the problem in abstract form and applying some results of the maximal monotone mapping theory joint with the Schauder fixed point theorem.

This article concerns a multi-dimensional Cahn-Hilliard equation subject to Neumann boundary condition. We show existence of the periodic solutions by using the viscosity approach. By applying the Schauder fixed point theorem, we show existence of the solutions to the suitable approximate problem and then obtain the solutions of the considered periodic problem using a priori estimates. Our resu...