In this work, we consider a convexity splitting scheme for a coupled phase field and energy equation, a modification of Stefan problem. The Stefan problem is a free boundary value problem that models the temperature in a homogeneous multiphase medium. Each phase is modeled using a heat diffusion parabolic partial...
The first part of this work presents an executive system for
steady state process systems analysis. The executive is developed
to promote maximum flexibility, generality and a high degree of
man-machine interaction by allowing the user to write a Fortran
main calling program which permits special logic and control to...
The Euler-MacLaurin sum formula has appeared in the titles
of two quite recent papers whose authors were primarily interested
in certain applications. In this paper a somewhat different approach
to the myriad of formulas for summation, integration, differentiation,
etc. , is based on the simple identity which defines the set...
In this thesis, we investigate the problem of simulating Maxwell's equations in dispersive dielectric media. We begin by explaining the relevance of Maxwell's equations to
21st century problems. We also discuss the previous work on the numerical simulations of
Maxwell's equations. Introductions to Maxwell's equations and the Yee finite difference...
This thesis examines the mixing times for one-dimensional interacting particle systems. We use the coupling method to study the mixing rates for particle systems on the circle which move according to specific permutations e.g., transpositions and 3-cycles.
Conclusion: The first part of this note deals with problems of propagation of error and the latter part with questions commonly identified as "model validation" questions. It is concluded that all validation questions can be resolved into two parts: (1) strategic aspects, involving logical and inferential structures and (2) tactical...
Accurate modeling and simulation of wave propagation in dispersive dielectrics such as water, human tissue and sand, among others, has a variety of applications. For example in medical imaging, electromagnetic waves are used to interrogate human tissue in a non-invasive manner to detect anomalies that could be cancerous. In non-destructive...
A numerical method based on the the method of characteristics for hyperbolic systems
of partial differential equations in four independent variables is developed and used
for solving time domain Maxwell's equations. The method uses the characteristic
hypersurfaces and the characteristic conditions to derive a set of independent equations
relating the...