Stability analysis of fronts in a tristable reaction-diffusion system

A stability analysis is performed analytically for the tristable reaction-diffusion equation, in which a quintic reaction term is approximated by a piecewise linear function. We obtain growth rate equations for two basic types of propagating fronts, monotonous and nonmonotonous ones. Their solutions show that the monotonous front is stable whereas the nonmonotonous one is unstable. It is found that there are two values of the growth rate for the most dangerous modes (corresponding to the longest possible wavelengths), and , for the monotonous front, so that at the perturbation eigenfunction is positive whereas when it changes sign. It is also noted that the eigenvalue becomes negative in an inhomogeneous system with a particular (stabilizing) inhomogeneity. Counting arguments for the number of eigenmodes of the linear stability operator are presented.Received: 9 August 2004, Published online: 23 December 2004PACS: 05.45.-a Nonlinear dynamics and nonlinear dynamical systems - 47.20.Ma Interfacial instability - 47.54. + r Pattern selection; pattern formation     

Die Einwirkung des Morphins, sowie des Acetanilids auf Mischungen von Eisenoxydsalzen und Ferridcyankalium

Ohne Zusammenfassung     

Die Verwendung von Natriumsuperoxyd

Ohne Zusammenfassung     

Phase field modeling of fast crack propagation

We present a continuum theory which predicts the steady state propagation of cracks. The theory overcomes the usual problem of a finite time cusp singularity of the Grinfeld instability by the inclusion of elastodynamic effects which restore selection of the steady state tip radius and velocity. We developed a phase-field model for elastically induced phase transitions; in the limit of small or vanishing elastic coefficients in the new phase, fracture can be studied. The simulations confirm analytical predictions for fast crack propagation.     

Quantum diffusion on a lattice with gaussian fluctuating site energies

In this article, the motion of a single quantum particle on a lattice with stochastically fluctuating site energies is investigated. The model is characterized by three parameters: the matrix elementJ for coherent energy transfer between nearest neighbours and the strength and correlation time 1/ of the fluctuations. Because of the simple structure of its Hamiltonian, expressions for stochastic moments such as the mean square displacement can be derived, which are valid for strong fluctuations, no matter how slow their decay, and for weak fluctuations, in the short correlation time limit. The basic idea of the method is to treat the deterministic part of the motion as perturbation acting on the stochastic part. While this method was previously used to obtain the diffusion constant for fluctuations represented by dichotomic Markov processes (DMPs), now the more realistic situation of Gaussian Markov processes is treated. The resulting diffusion constants are compared with those of dichotomic systems. Major differences appear for strong fluctuations and long correlation times. Contrary to the DMP case, the diffusion constant turns out to be a monotonously increasing function of the inverse correlation time (withJ, fixed), for all values of . Anderson localization is observed at =0 but disappears as increases.     

Influence of coloured noise on the diffusion of a quantum particle. Part I: General results

A general stochastic model for the diffusion of a quantum particle on a fluctuating lattice is considered and several exact results useful in the calculation of transport properties are given. First, we derive a new type of integral equation for the density operator using a time-dependent projection operator and disentangling the stochastic, not the deterministic part of the motion in contrast to previous treatments. The mean square displacement is then expressed by the kernel of this equation in the case of diagonal fluctuations. We obtain an equation of motion for this kernel similar in structure to equations known from Green's function theory and containing a self-energy like quantity. Finally, two general statements concerning the exact solution of correlated models are given.