We present a new way of modeling turbulent thermonuclear deflagration fronts in Chandrasekhar-mass white dwarfs, consisting of carbon and oxygen, undergoing a type Ia supernova explosion. Our approach is a front capturing/tracking hybrid scheme, based on a level set method, which treats the front as a mathematical discontinuity and allows for full coupling between the front geometry and the flo...

UV laser micromachining of metallic materials has been used in microelectronic and other industries. Knowledge and data about the process vary with feature size, material, laser wavelength and pulse duration. This paper reports on experimental and numerical investigation of micromachining of copper using a frequency tripled Nd:YAG laser with 50 ns pulse duration. An axisymmetric model is develo...

This paper discusses a new family of sixth{order continuously imbedded Runge{Kutta{ Sarafyan methods and a mathematical software package DKLAG6 for the numerical solution of systems of functional di erential equations with state dependent delays. The methods used are based on piecewise polynomial approximants which are used for error estimation and stepsize selection, to handle the necessary in...

A two-level method for the solution of nite element schemes on locally reened meshes is introduced. The upper bound on the condition number implies, in some cases, mesh-independent convergence, as is veriied numerically for a diiusion problem with discontinuous coeecients. The discontinuity curves are not necessarily aligned with the coarse mesh; indeed, numerical applications with ten levels o...

Singularities of the Radon transform of a piecewise smooth function f(x), x e R" , n > 2, are calculated. If the singularities of the Radon transform are known, then the equations of the surfaces of discontinuity of f(x) are calculated by applying the Legendre transform to the functions, which appear in the equations of the discontinuity surfaces of the Radon transform of f(x) ; examples are gi...

We study mixing and spreading in a very simple heterogeneous system: a numerical flow cell comprised of two homogeneous porous media separated by a sharp angled interface. The two media have identical porosity, but differing permeability and dispersivity characteristics representing a fine and a coarse medium. We focus on transport in advection-dominated systems as the primary role of the angle...

We have derived an analytical expression in the wavenumber domain for calculating the gravity anomaly caused by an exponential density contrast model for an interface (Xia and Sprowl, 1990), above which the density contrast changes exponentially with depth. Constant density contrast and a linear density contrast are specific cases of the exponential density contrast model. The formula should be...

We propose a new method to construct a four parameter family of quantum-mechanical point interactions in one dimension, which is known as all possible self-adjoint extensions of the symmetric operator T = −∆⌈C 0 (R\{0}). It is achieved in the small distance limit of equally spaced three neighboring Dirac’s δ potentials. The strength for each δ is appropriately renormalized according to the dist...

Quasi-brittle materials such as concrete suffer from cracks during their life cycle, requiring great cost for conventional maintenance or replacement. In the last decades, self-healing materials are developed which are capable of filling and healing the cracks and regaining part of the stiffness and strength automatically after getting damaged, bringing the possibility of maintenance-free mater...

A procedure for measuring the acoustic scattering matrix coefficients of a duct discontinuity for higher order acoustic duct mode propagation conditions is described and tested. The technique requires measurement of pressure waves per mode coming in and out of the discontinuity. Assuming N cut-on modes, the 2N 2 scattering matrix coefficients are determined after repeating the experiment for N ...