A free material surface which supports surface diffusion becomes unstable when put under external nonhydrostatic stress. Since the chemical potential on a stressed surface is larger inside an indentation, small shape fluctuations develop because material preferentially diffuses out of indentations. When the bulk of the material is purely elastic one expects this instability to run into a finite...

For a crack impinging upon a bimaterial interface at an angle, the singular stress field is a linear superposition of two modes, usually of unequal exponents, either a pair of complex conjugates, or two unequal real numbers. In the latter case, a stronger and a weaker singularity coexist (known as split singularities). We define a dimensionless parameter, called the local mode mixity, to charac...

The general exact solution describing the dynamics of anisotropic elastic spheres supported only by tangential stresses is reduced to a quadrature using Ori’s mass–area coordinates. This leads to the explicit construction of the root equation governing the nature of the central singularity. Using this equation, we formulate and motivate on physical grounds a conjecture on the nature of this sin...

The viscosity solution of static Hamilton-Jacobi equations with a pointsource condition has an upwind singularity at the source, which makes all formally high-order finite-difference scheme exhibit first-order convergence and relatively large errors. To obtain designed high-order accuracy, one needs to treat this source singularity during computation. In this paper, we apply the factorization i...

Using Einstein’s and Weinberg’s energy complex, we evaluate the energy distribution of the vaccum nonsingularity black hole solution. The energy distribution is positive everywhere and be equal to zero at origin. PACS No.:04.20.-q, 04.50.+h E-mail:[email protected] 1 There are two reasons for evaluting the energy of a system in general relativity. First, the conserved qualitities, l...