AVO analysis of seismic data is based on the assumption that transitions in the earth consist of jump discontinuities only. The generalization of this type of transition to a more realistic class of transitions shows a drastic change in observed AVO behavior, especially for the large angles currently attained by increasing cable lengths. We propose a simple approach that accounts for this anoma...

This paper shows the advantages of the material failure process simulation by improve finite elements with embedded discontinuities, using a new definition of traction vector, dependent on the discontinuity length and the angle. Particularly, two families of this kind of elements are compared: kinematically optimal symmetric and statically and kinematically optimal non-symmetric. The constituti...

In this article the problem of the American option valuation in a Lévy process setting is analysed. The perpetual case is first considered. Without possible discontinuities (i.e. with negative jumps in the call case), known results concerning the currency option value as well as the exercise boundary are obtained with a martingale approach. With possible discontinuities of the underlying proces...

Recent developments in the context of minimum residual finite element methods are paving way for designing quasi-optimal discretization non-standard function spaces, such as q -type Sobolev spaces. For ? 1, these have demonstrated huge potential avoiding notorious Gibbs phenomena, i.e. , occurrence spurious non-physical oscillations near thin layers and jump discontinuities. In this work we pro...

Edge detection has traditionally been associated with detecting physical space jump discontinuities in one dimension, e.g. seismic signals, and two dimensions, e.g. digital images. Hence most of the research on edge detection algorithms is restricted to these contexts. High dimension edge detection can be of significant importance, however. For instance, stochastic variants of classical differe...

We present a class of augmented approximate Riemann solvers for the shallow water equations in the presence of a variable bottom surface. These belong to the class of simple approximate solvers that use a set of propagating jump discontinuities, or waves, to approximate the true Riemann solution. Typically, a simple solver for a system of m conservation laws uses m such discontinuities. We pres...

At interfaces between different fluids, properties such as density, viscosity, and molecular cohesion are discontinuous. To animate small-scale details of incompressible viscous multi-phase fluids realistically, we focus on the discontinuities in the state variables that express these properties. Surface tension of both free and bubble surfaces is modeled using the jump condition in the pressur...

Artificial discontinuity is a kind of singularity at a parametric point in computing the Gröbner basis of a specialized parametric ideal w.r.t. a certain term order. When it occurs, though parameters change continuously at the point and the properties of the parametric ideal have no sudden changes, the Gröbner basis will still have a jump at the parametric point. This phenomenon can cause insta...

A mathematical model is presented to simulate water and solute transport in a highly viscous fluid with a water-permeable, elastic immersed membrane. In this model, fluid motion is described by Stokes flow, whereas water fluxes across the membrane are driven by transmural pressure and solute concentration differences. The elastic forces, arising from the membrane being distorted from its relaxe...

In the past of two decades, wavelet methods have been adopted enthusiastically in many engineering applications such as signal and image processing. However, like most of the classic orthogonal expansions, wavelet expansions also exhibit Gibbs phenomenon around discontinuities of the original signals. Therefore, the recovered signals using wavelet expansions could be corrupted by the overshoot ...