We study the effect of boundary conditions on vacuum polarization for charged scalar fields in two space-time dimensions. find that both Dirichlet and Neumann lead to screening. In case, charge density vanishes at boundary, whereas it attains its maximum there conditions. At a critical field strength, diverges conditions, an due instability lowest energy mode presence external field.

We consider a reaction-diffusion system exhibiting diffusion driven instability if supplemented by Dirichlet-Neumann boundary conditions. We impose unilateral conditions given by inclusions on this system and prove that global bifurcation of spatially nonhomogeneous stationary solutions occurs in the domain of parameters where bifurcation is excluded for the original mixed boundary value proble...

This paper analyses the numerical stability of coupling procedures in modelling the thermal diiusion in a solid and uid with continuity of temperature and heat ux at the interface. A simple one-dimensional model is employed with uniform material properties and grid density in each domain. A number of diierent explicit and implicit algorithms are considered for both the interior equations and th...

This paper analyses the numerical stability of coupling procedures in modelling the thermal diiusion in a solid and uid with continuity of temperature and heat ux at the interface. A simple one-dimensional model is employed with uniform material properties and grid density in each domain. A number of diierent explicit and implicit algorithms are considered for both the interior equations and th...

Boundary integral equation methods are well suited to represent the Dirichlet to Neumann maps which are required in the formulation of domain decomposition methods. Based on the symmetric representation of the local Steklov– Poincaré operators by a symmetric Galerkin boundary element method, we describe a stabilized variational formulation for the local Dirichlet to Neumann map. By a strong cou...

The narrow escape problem in diffusion theory is to calculate the mean first passage time of a diffusion process to a small target on the reflecting boundary of a bounded domain. The problem is equivalent to solving the mixed Dirichlet–Neumann boundary value problem for the Poisson equation with small Dirichlet and large Neumann parts. The mixed boundary value problem, which goes back to Lord R...

Monte Carlo remains an effective simulations methodology for the study of MOSFET devices well into the decananometre regime as it captures non-equilibrium and quasi-ballistic transport. The inclusion of quantum corrections further extends the usefulness of this technique without adding significant computational cost. In this paper we examine the impact of boundary conditions at the Ohmic contac...

where Ji = 0 for x0 < 0. The problem is to find necessary and sufficient conditions on B(x, B) such that the initial-boundary value problem (1), (2), (3) is well-posed. Note that all theorems that a;re formulated below will also apply to the case when (1) is a general hyperbolic equation or a hyperbolic system of equations of arbitrary order provided that all components of the characteristic co...

We consider the hp–version interior penalty discontinuous Galerkin finite element method (hp–DGFEM) for semilinear parabolic equations with mixed Dirichlet and Neumann boundary conditions. Our main concern is the error analysis of the hp–DGFEM on shape–regular spatial meshes. We derive error bounds under various hypotheses on the regularity of the solution, for both the symmetric and non–symmet...

Exchange energy is especially sensitive to the numerical representation selected. We compare three discretized exchange energy formulations for 3D numerical micromagnetics on rectangular grids. Explicit formulae are provided for both Neumann and Dirichlet boundary conditions. Results illustrate the convergence order of these methods as a function of discretization cell size and the effect of ce...