No abstract

We present an asymptotic analysis of the Gunn effect in a driftdiffusion model-including electric-field-dependent generation-recombination processes-for long samples of strongly compensated p-type Ge at low temperature and under dc voltage bias. During each Gunn oscillation, there are different stages corresponding to the generation, motion and annihilation of solitary waves. Each stage may be described by one evolution equation for only one degree of freedom (the current density), except for the generation of each new wave. The wave generation is a faster process that may be described by solving a semiinfinite canonical problem. As a result of our study we have found that (depending on the boundary condition) one or several solitary waves may be shed during each period of the oscillation. Examples of numerical simulations validating our analysis are included.

No abstract

Consider a crack propagating in a plane according to a loading that results in antiplane shear deformation. We show here that if the crack path consists of two straight segments making an angle ϕ = 0 at their junction, examples can be provided for which the value of the stress-intensity factor (SIF) actually depends on the previous history of the motion. This is in sharp contrast with the rectilinear case (corresponding to ϕ = 0), where the SIF is known to have a local character, its value depending only on the position and velocity of the crack tip at any given time.

Abstract. This work deals with the linear wave equation considered in the whole plane R 2 except for a rectilinear moving slit, represented by a curve Γ (t) = {(x 1 , 0) : −∞ < x 1 < λ (t)} with t ≥ 0. Along Γ (t) , either homogeneous Dirichlet or Neumann boundary conditions are imposed. We discuss existence and uniqueness for these problems, and derive explicit representation formulae for solutions. The latter have a simple geometrical interpretation, and in particular allow us to derive precise asymptotic expansions for solutions near the tip of the curve. In the Neumann case, we thus recover a classical result in fracture dynamics, namely the form of the stress intensity factor in crack propagation under antiplane shear conditions.