Choosing good problems is essential for being a good scientist. But what is a good problem, and how do you choose one? The subject is not usually discussed explicitly within our profession. Scientists are expected to be smart enough to figure it out…
Mathematical Modelling and Industrial Mathematics
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The Conjugate Gradient Method is the most prominent iterative method for solving sparse systems of linear equations. Unfortunately, many textbook treatments of the topic are written with neither illustrations nor intuition, and their victims can be…

Introduction This is a concise summary of recommended features in LATEX and a couple of extension packages for writing math formulas. Readers needing greater depth of detail are referred to the sources listed in the bibliography, especially…

Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other selforganizing systems. Ordinarily, the…

Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady…

Despite application of cryogen spray (CS) precooling, customary treatment of port wine stain (PWS) birthmarks with a single laser pulse does not result in complete lesion blanching for a majority of patients. One obvious reason is nonselective…

We are developing a dual panel breastdedicated PET system using LSO scintillators coupled to position sensitive avalanche photodiodes (PSAPD). The charge output is amplified and read using NOVA RENA3 ASICs. This paper shows that the coincidence…

Matrix identities, relations and approximations. A desktop reference for quick overview of mathematics of matrices.

This paper presents an analytical model and a geometric numerical integrator for a tethered spacecraft model that is composed of two rigid bodies connected by an elastic tether. This model includes important dynamic characteristics of tethered…

We present an overview of how the arterial fluid mechanics problems can be modeled with the stabilized space–time fluid–structure interaction (SSTFSI) technique developed by the Team for Advanced Flow Simulation and Modeling (TAFSM). The SSTFSI…

Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and timedependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal…

This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a…

A precise definition of the basic reproduction number, ??? 0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if ??? 0 < 1, then the disease free equilibrium…

Creating amesh is the first step in a wide range of applications, including scientific comput ing and computer graphics. An unstructured simplex mesh requires a choice of meshpoints (vertex nodes) and a triangulation. We want to offer a short and…

This is the only book on spectral methods built around MATLAB programs. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since…

New numerical algorithms are devised (PSC algorithms) for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These…

The term immersed boundary methodwas first used in reference to a method de veloped by Peskin (1972) to simulate cardiac mechanics and associated blood flow. The distinguishing feature of this methodwas that the entire simulationwas carried out on…

Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement…

In this series of lectures, we describe the analytic and computational foundations of fast multipole methods, as well as some of their applications. They are most easily understood, perhaps, in the case of particle simulations, where they reduce the…

The present elaboration of essentially nonoscillatory (ENO) shockcapturing schemes proceeds with a novel, simplified expression for the ENO construction procedure having its basis in numerical fluxes rather than cellaverages. The ENOlocal…
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