A recent paper by Patel and Kosko (2008) demonstrated stochastic resonance (SR) for general feedback continuous and spiking neuron models using additive Lévy noise constrained to have finite second moments. In this brief, we drop this constraint and show that their result extends to general LEvy noise models. We achieve this by showing that "large jump" discontinuities in the noise can be contr...

This paper is dedicated to the study of stochastic finite-time stability (SFTS) and control synthesis for a class of nonlinear Markovian jump stochastic systems with impulsive effects. By introducing a time-varying stochastic Lyapunov function with discontinuities at impulse times, an improved criterion for SFTS is derived in terms of linear matrix inequalities (LMIs). Based on the new SFTS cri...

New finite element methods based on Cartesian triangulations are presented for two dimensional elliptic interface problems involving discontinuities in the coefficients. The triangulations in these methods do not need to fit the interfaces. The basis functions in these methods are constructed to satisfy the interface jump conditions either exactly or approximately. Both non-conforming and confo...

Edge is a boundary between two homogeneous regions. Edge detection is a preprocessing step in image analysis. It is a most difficult task in image processing. Edge in an image are with strong intensity contrast. A jump in intensity from one pixels to the very next, which effects in the quality of the picture. A quality of picture is characterized by the sharp discontinuities in an image. Hence ...

We consider piecewise smooth viscosity solutions to a Hamilton-Jacobi equation, for which the Hamiltonian is the maximum of a finite number of smooth concave functions. We describe the possible types of “basic” singularities, namely jump discontinuities in the derivative of either the solution or the Hamiltonian which occur across a smooth hypersurface. Each such type of singularity is describe...

A finite element method for elasticity systems with discontinuities in the coefficients and the flux across an arbitrary interface is proposed in this paper. The method is based on a Cartesian mesh with local modifications to the mesh. The total degrees of the freedom of the finite element method remains the same as that of the Cartesian mesh. The local modifications lead to a quasi-uniform bod...

Abstract We develop a novel nonlocal model of dislocations based on the framework peridynamics. By embedding interior discontinuities into constitutive law, displacement jump in Volterra dislocation is reproduced, intrinsic singularities classical elasticity are regularized, and surface effect previous peridynamics models avoided. The extended embedded discontinuity overcomes unphysical dissipa...

Abstract. We are concerned with the detection of edges – the location and amplitudes of jump discontinuities of piecewise smooth data realized in terms of its discrete grid values. We discuss the interplay between two approaches. One approach, realized in the physical space, is based on local differences and is typically limited to low-order of accuracy. An alternative approach developed in our...

A mesh refinement method is described for solving optimal control problems using Legendre-Gauss-Radau collocation. The detects discontinuities in the solution by employing an edge detection scheme based on jump function approximations. When are identified, refined with a targeted h-refinement approach whereby discontinuity locations bracketed points. remaining smooth portions of previously deve...

Localized deformation such as shear bands, compaction bands, dilation bands, combined shear/compaction or shear/dilation bands, fractures, and joint slippage are commonly found in rocks. Thus, modeling their inception, development and propagation, and effect on stress response is important with regard to making informed engineering design decisions involving these materials. Following a GulfRoc...