Narrow Results

We consider a ferromagnetic Ising spin system, consisting of m+1, d-dimensional, layers with “–” boundary condition on the bottom layer and “+” on the top layer. When β is larger than β_cr, the inverse critical temperature for the d-dimensional Ising model, the interface generated by the boundary conditions is expected to be halfway between bottom and top, for m odd, and just above or below the middle layer, for m even (each possibility with probability ). In this paper, we prove the above assertion under the condition that β≥const . m and partly for β>β_cr.

We find the probe D5-brane solution on the black hole space–time which is asymptomatically ${\mathrm{\text{AdS}}}_5\times S^5$. These black holes have spherical, hyperbolic and toroidal structures. Depending on the gauge flux on the D5-brane, the D5-brane behaves differently. By adding the fundamental string, the potential energy of the interface solution and the Wilson loop is given in the case of nonzero gauge flux.

We develop a class of Hamiltonian-preserving numerical schemes for high frequency elastic waves in heterogeneous media. The approach is based on the high frequency approximation governed by the Liouville equations with singular coefficients due to material interfaces. As previously done by Jin and Wen [10, 12], we build into the numerical flux the wave scattering information at the interface, and use the Hamiltonian preserving principle to couple the wave numbers at both sides of the interface. This gives a class of numerical schemes that allows a hyperbolic CFL condition, is positive and l^∞ stable, and captures correctly wave scattering at the interface with a sharp numerical resolution. We also extend the method to curved interfaces. Numerical experiments are carried out to study the numerical convergence and accuracy.