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Workshop Programme

for period 13 - 14 February 2003

Computational Electromagnetism

13 - 14 February 2003


Thursday 13 February
Session: Computational Electromagnetism
10:00-11:00 Chapman, JN (Glasgow)
  Micromagnetism - some current challenges faced by experimentalists Sem 1

Small magnetic structures play a crucial role in modern storage devices and sensors. To achieve ever improving performance, magnetic films with superior properties and smaller (and frequently more densely packed) magnetic elements are required. When experimenting with new magnetic systems the ideal would be to have a description of the magnetisation distribution throughout the 3-dimensional magnetic system and to understand how it evolves as a function of vector field, temperature and time. Resolution as close as possible to the atomic level, and in any event better than characteristic magnetic length scales, is also highly desirable. Despite the rapid development of existing and the introduction of new magnetic microscopy techniques over the last decade, we still fall far short of these goals. In this talk, I will give examples of some recent imaging investigations with equal emphasis on the information that they do and do not provide.

Among the topics to be discussed will be the extent to which the properties of notionally identical magnetic elements differ as a result of small differences in their physical microstructure. This can be quite complex in elements comprising a single magnetic layer but is inevitably much more so in multilayers where the detailed coupling between the layers themselves remains imperfectly understood. Further challenges arise when the elements are packed closely together as interactions between them become important. Other significant topics are the effect of thermal processes leading to property changes with time, all other parameters remaining constant. Studies of this nature relate, for example, to stability and hence the suitability of particular structures for storage purposes. At the other end of the time spectrum is the phenomenon of ultra-fast switching where it is difficult to simultaneously meet the requirements of high spatial and temporal resolution.

I will discuss how combining information gleaned from experiment and micromagnetic modelling can help to advance the subject.

11:00-11:30 Coffee
11:30-12:30 Schrefl, T (Vienna)
  Time and length scales in computational microgenetics Sem 1

Micromagnetics is a continuum theory to describe magnetization processes on a length scale which is large enough to replace the atomic spins by a continuous magnetization vector and small enough to resolve the magnetization transition inside a domain wall. The characteristic length scale, the domain wall witdh, is in the order of five to ten nanometers, The size of the basic structural units of magnetic devices like sensor or storage elements may extend towards micrometers. The time scale range from sub-nanosecond regime for fast precessional switching to years for thermally activated magnetization reversal. The wide range of time and length scales involved in micromagnetic simulations is a challenge for effective computational tools. In the talk numerical methods for the solution of the LLG equation and the simulation of thermal stability will be reviewed. In particular, the role of the physical microstructure on hysteresis properties will be discussed, and numerical techniques to treat microstructural effects will be proposed.

12:30-14:00 Lunch
14:00-15:00 Prohl, A (Z\"urich)
  Numerical Analysis of stationary and nonstationary micromagnetism Sem 1

Magnetic patterns of ferromagnetic materials are described by the well-accepted model of Landau and Lifshitz. Over the last years, different strategies have been developed to tackle the related non-convex problem: direct minimization, convexification, and relaxation by using Young measures. Nonstationary ferromagnetic effects are considered by the extended model of Landau, Lifshitz and Gilbert (LLG). In the talk, we survey numerical analysis for solving the stationary problem. In the second part, we discuss proper projection/penalization strategies to discretize (LLG).

15:00-15:30 Tea
15:30-16:15 Carbou, G (Bordeaux)
  Weak and regular solutions for Landau-Lifschitz equations: existence and asymptotic behaviour Sem 1

In this talk, we describe existence results for weak and regular solutions of Landau-Lifschitz equations. Furthermore, we present two types of asymptotic behaviour : for large time, we study the $\omega$-limit set of the weak solutions. On the other hand, we perform an asymptotic expansion of the regular solutions when the exchange coefficient goes to zero : it appears a boundary layer described with a BKW method.

16:15-17:00 Monk, P (Delaware)
  An eddy current-micromagnetic model with application to disk write heads Sem 1
17:00-18:00 Wine and Beer Reception
Friday 14 February
Session: Computational Electromagnetism
10:00-11:00 McCulloch, M (Oxford)
  Using PDE's to develop the application of superconductors Sem 1
11:00-11:30 Coffee
11:30-12:30 Chapman, J (Oxford)
  Macroscopic models of superconductivity Sem 1
12:30-14:00 Lunch
14:00-15:00 Du, Q (HKUST)
  Quantized vortices: from Ginzburg-Landau to Gross-Pitaevskii Sem 1

Quantized vortex, a signature of superfluidity, has been studied for more than fifty years in the context of superconductivity and in recent years, it has attracted much attention in the study of the Bose-Einstein condensates.

In this talk, we will discuss some questions related to quantized vortices based on the Ginzburg-Landau models for superconductivity and the Gross-Pitaevskii equations for the Bose-Einstein condensation. Some strikingly similar properties will be illustrated. Both mathematical results concerning these equations and the computational challenges will be presented.

15:00-15:30 Tea
15:30-16:15 Styles, V (Sussex)
  A finite element approximation of a variational formulation of Bean's model for superconductivity Sem 1

We introduce phase field and sharp interface models for bidirectional diffusion induced grain boundary motion with triple junctions. We present numerical discretizations of the models together with some computational simulations.

16:15-17:00 Prigozhin, L (Ben Gurion)
  Solution of critical-state problems in superconductivity Sem 1

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