We study spectral and scattering properties of the Laplacian H = −∆ in L2(R+) corresponding to the boundary condition ∂u ∂ν + σu = 0 for a wide class of periodic functions σ. The Floquet decomposition leads to problems on an unbounded cell which are analyzed in detail. We prove that the wave operators W±(H ,H) exist. 2000 Mathematics Subject Classification: Primary 35J10; Secondary 35J25, 35P05...

The effective dynamic of a quantum particle on the tubular neighbourhood of some closed submanifold of a riemannian manifold can be described by an effective dynamic on the submanifold as the diameter of the tube decreases to zero. It depends whether Dirichletor Neumann conditions are imposed at the boundary of the tube.

A transient two-dimensional model is developed and numericaUy solved to specifically investigate the effects of CNC motion and workpiece boundary on cutting front mobility and temperature in reactive-gas assisted C01 laser cutting. Co-ordinated motion systems must ramp up and down to their desired speeds, and therefore the initial actuator acceleration is considered for its effect on the cuttin...

This paper introduces the immersive visualisation of nano-indentation simulation of Cu. The molecular dynamics simulation is performed in a system consisting of 326,592 atoms of size 18.6 × 17.0 × 18.4 nm, under periodic boundary conditions. Based on the coordination number calculation, a practical method for the extraction of “extraordinary” atoms is developed. The simulation has been visualis...

This paper investigates the global dynamics of a mean field model of the electroencephalogram developed by Liley et al., 2002. The model is presented as a system of coupled ordinary and partial differential equations with periodic boundary conditions. Existence, uniqueness, and regularity of weak and strong solutions of the model are established in appropriate function spaces, and the associate...

In this paper we show the existence of regular solutions of the Rothe–approximation of the unsteady Navier–Stokes equations with periodic boundary condition in arbitrary dimension. The result relies on techniques developed by the authors in the study of the higher–dimensional steady Navier–Stokes equations.

We apply the method of self-consistent bounds to prove the existence of multiple steady state bifurcations for Kuramoto-Sivashinski PDE on the line with odd and periodic boundary conditions.

where t ≥ 0 denotes time and x ∈ Ω ⊂ R position typical within a d−dimensional bounded domain Ω with “sufficiently smooth” boundary or Ω = R. The states u = (u1, . . . , um), i = 1, . . . , m describe the concentrations or densities of substances/populations ui = ui(t, x). The functions di(t, x) are called diffusion coefficients or diffusivities. On a bounded domain Ω the eqs. (1) have to be co...

Vacuum structures of supersymmetric (SUSY) Yang-Mills theories in 1 + 1 dimensions are studied with the spatial direction compactified. SUSY allows only periodic boundary conditions for both fermions and bosons. By using the Born-Oppenheimer approximation for the weak coupling limit, we find that the vacuum energy vanishes, and hence the SUSY is unbroken. Other boundary conditions are also stud...

Let Ω ⊂ Rd be a bounded domain with smooth boundary and let A ⊂⊂ Ω be a smooth, compactly embedded subdomain. Consider the operator − 1 2 ∆ in Ω − Ā with the Dirichlet boundary condition at ∂A and the Neumann boundary condition at ∂Ω, and let λ0(Ω, A) > 0 denote its principal eigenvalue. We discuss the question of monotonicity of λ0(Ω, A) in its dependence on the domain Ω. The main point of thi...