Calculation of the Potential Distribution for a Three-Layer Spherical Volume Conductor

Electroencephalography (EEG) and magnetoencephalography (MEG) are non-invasive methods of studying the functional activity of the human brain with millisecond temporal resolution. Much of the work in EEG and MEG in the last few decades has been focused on estimating the properties of the internal sources of the fields from the external measurements, i.e. on solving the inverse problem of EEG and MEG. To handle this task one must first study the forward problem, i.e. how the fields arise from a known source. For practical purposes, one also has to choose appropriate models for the source and the head as a conductor. The most straightforward model for describing the surface evoked potential or the external evoked magnetic field is the single equivalent current dipole. In EEG models the volume conductor properties of the head are commonly modelled by three or four concentric spherical shells with different electrical conductivities representing the brain, the cerebrospinal fluid, the skull, and the scalp. While more accurate geometric models have been applied, such asymmetric models are limited in accuracy by knowledge of boundaries and resistivities of various tissues. In this article we consider a three-layer spherical volume conductor model and calculate the dipole-induced potential by analytical methods. This calculation requires the symbolic solution of a system of linear equations which is not complicated but that would be a pain when done by pencil and paper. We use Maple for setting up the system of model equations, solve it symbolically, and then generate numerical code to obtain a fast program for the evaluation of the potential. Finally, the dipole-envoked electric potential is plotted for realistic EEG model parameters

Calculation of Chemical Equilibrium Compositions

The catalytic reaction between steam and hydrocarbon into mixtures of hydrogen, carbon monoxide, carbon dioxide and methane forms the basic feedstock (synthesis gas) to produce ammonia, methanol and other chemicals. For reactor design and to find the most economic reaction conditions it is necessary to study theoretically the reaction behaviour with respect to the operating parameters. In the present thermodynamic study we examine the temperature dependence of chemical compositions at equilibrium. The mathematical computation system Maple is used for the symbolic and numerical calculations, for generating the graphics and formatting the document

Algorithms of mixed symbolic-numeric type for rational approximation

This paper describes the implementation of recursive algorithms for approximation and summation processes using the Maple programming language for symbolic computation. The programs are collected in the Maple package trans which contains most of the currently known algorithms (transformations) for the construction of rational approximations. The advantages of employing mixed symbolic-numeric computation techniques are indicated and demonstrated by some numerical examples

Education for Simulation and HPC at JSC

Fostering a sound education for students and young researchers at bachelor, master and PhD level in simulation and high-performance computing (HPC) is an essential task of the Jülich Supercomputing Centre (JSC). Applied mathematics education plays a crucial part in these activities. This talk will give an overview of the joint degree programmes with nearby universities and informs on guest student programmes and the Joint Laboratory for Extreme Scale Computing (JLESC) tailored for master and PhD students with interest in HPC

On Solving the McConnell Equations in Biochemistry

In recent years, in vivo nuclear magnetic resonance (NMR) spectroscopy has allowed to measure rate constants of transport and diffusion across living cell membranes. For the study of bacterial systems a special NMR technique -inversion transfer- is used. The theoretical basis for the analysis of inversion transfer experiments is a system of differential equations first formulated by McConnell. These equations describe the rate of change of nuclear spin magnetization of a single nuclear species which is transferred back and forth between two different magnetic environments by kinetic processes. In this article we demonstrate various ways how the McConnell equations can be solved analytically using the symbolic computation system Maple, and verify solutions found in the literature. Furthermore, computation techniques of mixed symbolic-numeric type for the determination of the formal parameters involved in the solutions are indicated

CSE education at JSC

Fostering a sound education of students and young researchers at bachelor, master and PhD level in high-performance computing, mathematics and computational science is an essential task of the Jülich Supercomputing Centre (JSC). This talk will give an overview of the educational activities and structures at JSC and informs about the guest student programme, the summer/winter schools for PhD students, joint bachelor and master courses with universities and the German Research School for Simulation Sciences (GRS)

Maple programs for converting series expansions to rational functions using the Levin transformation automatic generation of FORTRAN functions for numerical applications

MAPLE procedures for converting Taylor series expansions and asymptotic series expansions to rational functions using Levin's u, t or v transformation are presented. FORTRAN functions can be generated automatically for the resulting rational functions

Approximating functions by means of symbolic computation and a general extrapolation method

Using a general extrapolation algorithm we present MAPLE procedures for the generation of polynomial and rational approximations to functions having formal series expansions. This algorithm, which has been called E algorithm or Brezinski-Håvie (BH) protocol, includes most of the series (sequence) transformations actually known. MAPLE's ability to perform all calculations in rational arithmetic eliminates the numerical instability of the E algorithm. For numerical purposes the approximating functions can be transformed into optimized FORTRAN programs