The influence of the material texture (substructure) on the force driving the crack tip in complex materials admitting Ginzburg-Landau-like energies is analyzed in a three-dimensional continuum setting. The theory proposed accounts for finite deformations and general coarse-grained order parameters. A modified expression of the J-integral is obtained together with other path-integrals which are...

A new kind of nonlinear nonequilibrium patterns--twisted spiral waves--is predicted for periodically forced oscillatory reaction-diffusion media. We show, furthermore, that, in such media, spatial regions with modified local properties may act as traps where propagating waves can be stored and released in a controlled way. Underlying both phenomena is the effect of the wavelength-dependent prop...

A class of dissipative complex Ginzburg–Landau (DCGL) equations that govern the wave propagation in dissipative nonlinear transmission lines is solved exactly by means of the Hirota bilinear method. Two-soliton solutions of the DCGL equations, from which the one-soliton solutions are deduced, are obtained in analytical form. The modified Hirota method imposes some restrictions on the coefficien...

Weakly nonlocal thermodynamic theories are critically revisited. The irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current. Several classical equations are derived , including Guyer-Krumhansl, Ginzburg-Landau and Cahn-Hilliard type equations.

Using a recent construction of Bezrukavnikov and Etingof, [BE], we prove that there is a factorization of the Etingof-Ginzburg sheaf on the generalized Calogero-Moser space associated to a complex reflection group. In the case W = Sn, this confirms a conjecture of Etingof and Ginzburg, [EG].