Summary of Research

My research in Physics is related to field theories in particlephysics and statistical physics. After studying Higgs models onthe lattice, I began in 1987 to work on the one component 4theory in the broken phase. In particular the finite sizeeffects due to the tunneling between the two vacua of the phasewith broken symmetry have been analyzed in detail.

This study clarified the spectrum in a finite volume which allowsto control the energy splitting quantitatively [1]. With thecontrol of the finite size effects the results of M. Lüscherand P. Weisz have been confirmed by calculating the renormalizedquartic coupling from the 4-point functions in a large scale computersimulation [2].

Following the suggestion of Prof. D. Stauffer I applied my experiencewith tunnel effects also to the three-dimensional Ising model[3], where a precise determination of the surface tension hasresolved an old controversy of different results.

Together with Dr. U.-J. Wiese we generalized the methods successfullyapplied to the Ising model also to Z(3) symmetric models to describeinterface effects at first order phase transitions. Ina Z(3) symmetric 4 model we found theinstanton solution near Tc allowing us to determine critical wettingexponents [6,8]. Furthermore we discussed wetting in a generalized6 model and worked out the transfermatrix in models with a Z(3) symmetric potential, leading to differentformulas for the energy splitting in situations with and withoutwetting [6,8].

After generalizing the formulas of [6] to temperatures in thevicinity of a critical point the methods was applied to the SU(3)gauge theory at finite temperatures [11,12,15]. With the helpof Monte Carlo simulation it was demonstrated that the finitesize effects of time slice correlation are well described by theinstanton formulas and that complete wetting is present in quenchedQCD. From the volume dependence of the energy splitting the interfacetension was extracted.

Also the recently proposed multicanonical algorithm was appliedto the SU(3) gauge theory were Binder's method was used to extractthe interface tension [10,14]. The implications of lattice resultsof the interface tension in the finite temperature QCD for cosmologicalinhomogenities are discussed in [21].

Since 1989 I have also worked on Fermion-Higgs models. Together with colleagues in Glasgow we have studied the eigenvaluesof the fermion matrix in SU(2)SU(2) symmetric and Z(2)Z(2) symmetricmodels [4] to get some deeper understanding of an earlier discoveredcrossover.

Together with my colleagues in Aachen we performed large scalecomputer simulations of the SU(2)SU(2) symmetric model with dynamicalfermions.

One aim was to search for a nontrivial fixed point. No positiveevidence for such a point was found and it turned out that therenormalized Yukawa coupling is bounded, which lead together witha triviality argument to an upper bound on a fermion mass [5]. In addition, an explanation of the rich structure in the momentumspace of the scalar propagator was found [7] and we tried to determinethe influence of a heavy fermion on the triviality bound of theHiggs boson mass [7]. With colleagues at DESY in Hamburg we havealso searched for a strong Yukawa coupling in a Fermion-Higgssystem with mirror fermions [13,16]. The relations of the richphase structures in various Fermion-Higgs models and their relationto other models in statistical mechanics was emphasized in [9].

Computer Science

My research in the field of computer science is influenced bythe intensive use of supercomputers.

Effective programming and benchmarking of Monte Carlo simulationson vector and vector parallel computers are described in [18,19]. To study the usage of object oriented programming in scientificcomputer simulations we developed an object oriented lattice gaugetheory programs in C++ [17] and discussed its usage for largescale simulations in [24].

My work in the area of parallel computing was particularlyfocused on parallel algorithms, performance evaluations, parallelprogramming tools and parallel computer environments. In [23]we discuss general strategies for parallelization of applicationsoftware and propose a general classification scheme of parallelapplications. The current trends in the standardization of parallelprogramming models, such as the SPMD model in High PerformanceFortran (HPF) and the Message Passing Interface Standard (MPI),are very exciting. A first experience with HPF is summarized in[20], and some Message Passing Environments are compared in [25].

My research at Optimax Software Inc. lead to the development ofa parallelization tool. A survey of programming tools for parallelcomputers is given in [22]. Optimax 1.0 Fortran uses advancedprogram analysis techniques such as data dependency analysis [22,26]and bank conflict resolution [27] to enable a more efficient interactivetuning of application programs.

Beside the hard core parallel computing I'm increasingly interestedin distributed information processing, as for example appliedto distributed multimedia application.

In addition I'm most interested in complex systems of simple devicessuch as spin glasses and neural networks. Although neural networkshave a long history in computer science, they appear only recentlyin an increasing area of applications and are establishing againthe old computer science domain of learning machines.

Beside my research in the basic understanding of such systems,I currently apply neural networks in two projects. In a projectin collaboration with researchers at the Chemistry Departmentat Dalhousie University we are employing neural networks for thequality control of water analysis. The representation and generalizationcapabilities of mapping neural networks are discussed in [28],where also a recently proposed hybrid algorithm was employed andadvanced.

In a project with researchers at the Psychology Department atDalhousie University and neurophysiologists at Queens Universitywe are modeling the oculomotor system of primates, including brainstem,middbrain, and cortical areas. The major focus of this projectis to determine the target selection mechanism in primates, whichis a first attempt to understand the details of higher organizationsin our brain. The developed neural network models can also beused to simulate brain damage.