A convection–di$usion system in one space dimension is a partial di"erential equation of the form ut + A(u)ux =(B(u)ux)x: (1.1) Here u∈Rn, and A(u) and B(u) are n×n matrices that we shall assume are C2 functions of u. If we ignore di"usion, we have the convection system ut + A(u)ux =0: (1.2) If A(u)=Df(u) for some 4ux function f : Rn → Rn, then Eq. (1.2) becomes ut + f(u)x =0; (1.3) a system of...

This paper describes an adaptive algorithm for optimal control of time-dependent partial di erentialalgebraic equation (PDAE) systems. A direct method based on a modi ed multiple shooting type technique and sequential quadratic programming (SQP) is used for solving the optimal control problem, while an adaptive mesh re nement (AMR) algorithm is employed to dynamically adapt the spatial integrat...

We examine sample based Bayesian inference from impedance imaging data. We report experiments employing low level pixel based priors with mixed discrete and continuous conductivities. Sampling is carried out using MetropolisHastings Markov chain Monte Carlo, employing both large scale, Langevin updates, and state-adaptive local updates. Computing likelihood ratios of conductivity distributions ...

We consider an elliptic partial di erential operator P (x; @) with analytic coe cients and discuss the unique continuation along an analytic curve. That is, let P (x; @)u = 0 in a simply connected domain R, be an analytic curve and let fxgj2N have an accumulation point. Our main result asserts that if u(x) = 0, j 2 N , then u(x) = 0 for any x 2 . Furthermore we apply such uniqueness to an isotr...

Observers are usually formulated as explicit systems of di erential equations and implemented using standard ODE solvers. In this paper, we show that there can be advantages in formulating the observer as a DAE (Di erential-Algebraic Equation). We review the general idea of DAE observer design of [10]. We give two special normal forms for which DAE observer design yields an observer with linear...

This paper is devoted to the study of periodic boundary value problems for nonlinear third order di¤erential equations subjected to impulsive e¤ects. We provide su¢ cient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one solution. Our approach is based on a priori estimates, the method of upper and lower solutions combined with an iterative te...

Rapid thermal processing (RTP) is a new technique for performing various wafer fabrication operations such as annealing, oxidation and chemical vapor deposition in a single chamber. The success of the RTP depends on the precise control of wafer temperature by adjusting wall heat ̄ux. In the present investigation, an ecient recursive method is developed to solve the inverse heat transfer proble...

The discontinuous Galerkin (dG) method for time integration of the parabolic problem obtained when pricing options using the BlackScholes partial di↵erential equation is presented. By decoupling of the large system of equations needed to be solved in each time step, the time of computation and memory requirement is significantly reduced. Even though there is a discontinuity in the first derivat...

In this paper, an image denoising operator de ned by a non-linear partial di erential equation(PDE) is presented. Similar to the operators proposed by Perona, Malik and Catt e et al., it can remove noise, enhance step-like edges and keep the locality of the edges. Its extra ability is to keep thin edges. The criterion for stopping time is also investigated. The new operator is capable of removi...

The implementation of generation±recombination (g±r) noise in a partial di€erential equation based device simulator is presented. Derived from the Shockley±Read±Hall model, the strength of each local g±r noise source is calculated based on the carrier transition rates between the conduction band, valence band, and trap states. The perturbations of these local g±r noise sources are then transmit...