Alan E. Berger

Generalized OCI schemes for boundary layer problems

A family of tridiagonal formally fourth-order difference schemes is developed for a class of singular perturbation problems. These schemes have no cell Reynolds number limitation and satisfy a discrete maximum principle. Error estimates and numerical results for this family of methods are given, and are compared with those for several other schemes.

Investigation of molecular structure in solids by two‐dimensional NMR exchange spectroscopy with magic angle spinning

An approach to the investigation of molecular structures in disordered solids, using two‐dimensional (2D) nuclear magnetic resonance (NMR) exchange spectroscopy with magic angle spinning (MAS), is described. This approach permits the determination of the relative orientation of two isotopically labeled chemical groups within a molecule in an unoriented sample, thus placing strong constraints on the molecular conformation. Structural information is contained in the amplitudes of crosspeaks in rotor‐synchronized 2D MAS exchange spectra that connect spinning sideband lines of the two labeled sites. The theory for calculating the amplitudes of spinning sideband crosspeaks in 2D MAS exchange spectra, in the limit of complete magnetization exchange between the labeled sites, is presented in detail. A new technique that enhances the sensitivity of 2D MAS exchange spectra to molecular structure, called orientationally weighted 2D MAS exchange spectroscopy, is introduced. Symmetry principles that underlie the cons...

NUMERICAL SOLUTION OF A DIFFUSION CONSUMPTION PROBLEM WITH A FREE BOUNDARY

We consider the numerical solution of an implicit moving free boundary problem which arises in the study of diffusion and consumption of oxygen in tissue. A fixed domain numerical method is presented which is motivated by a theoretical formulation developed by Rogers. Our numerical method uses any convenient finite difference or finite element scheme which converges to the underlying partial differential equation. The frontal generation appears by way of a simple algebraic comparison operation involving truncation of the computed approximation. Higher space dimensions are treated with equal ease. Results of numerical experiments are presented. A convergence proof for the truncation method is given.

A priori estimates and analysis of a numerical method for a turning point problem

Bounds are obtained for the derivatives of the solution of a turning point problem. These results suggest a modification of the El-Mistikawy Werle finite difference scheme at the turning point. A uniform error estimate is obtained for the resulting method, and illustrative numerical results are given. I. Introduction. We will examine the following two-point boundary value problem with Dirichlet data at the endpoints: (l.la) Ly= -eyx.(x) -p(x)yx(x) +q(x)y(x) =f(x) for -I

The Alternating Phase Truncation Method for Numerical Solution of a Stefan Problem

A numerical scheme for solving heat conduction problems involving a change of phase is presented. The numerical solution is obtained for heat flow in a two phase medium by using a method which treats each phase alternately, The resulting scheme avoids geometrical front tracking, and requires only simple algebraic operations. A maximum principle for the method and results of numerical experiments are given. An analytical version of the algorithm for a one dimensional one phase Stefan problem is shown to have an

A conservative uniformly accurate difference method for a singular perturbation problem in conservation form

O(\Delta t \cdot \ln {{1}/{\Delta t}})^{{1/2}}

Inhalational anthrax(Ames aerosol)in naïve and vaccinated New Zealand rabbits: characterizing the spread of bacteria from lung deposition to bacteremia

rate of convergence. Numerical experiments indicate that this estimate is sharp.

Modeling low-dose mortality and disease incubation period of inhalational anthrax in the rabbit☆

A conservative three point finite difference method is presented for the numerical solution of the singular perturbation problem

Theory of amphiphilic liquid crystals: multiple phase transitions in a model micellar system

\varepsilon u_{xx} + (b(x)u)_x = f(x)

Numerical Solution of Hydrodynamic Free Boundary Problems

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