Homogenization and enhancement for the G-equation

We consider the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection has suitably small spatial divergence, we prove that, as the size of the oscillations diminishes, the solutions homogenize (average out) and converge to the solution of an effective anisotropic first-order (spatio-temporal homogeneous) level set equation. Moreover we obtain a rate of convergence and show that, under certain conditions, the averaging enhances the velocity of the underlying front. We also prove that, at scale one, the level sets of the solutions of the oscillatory problem converge, at long times, to the Wulff shape associated with the effective Hamiltonian. Finally we also consider advection depending on position at the integral scale

d-like Symmetry of the Order Parameter and Intrinsic Josephson Effects in Bi2212 Cross-Whisker Junctions

An intrinsic tunnel junction was made using two Bi-2212 single crystal whiskers. The two whiskers with a cross-angle were overlaid at their c-planes and connected by annealing. The angular dependence of the critical current density along the c-axis is of the d-wave symmetry. However, the angular dependence is much stronger than that of the conventional d-wave. Furthermore, the current vs. voltage characteristics of the cross-whiskers junctions show a multiple-branch structure at any cross-angle, indicating the formation of the intrinsic Josephson junction array.Comment: 4 pages PDF fil