The London Mathematical Society
Department of Mathematics, University of York
Organisers: Z. Brzezniak (York), K. D. Elworthy (Warwick), X.-M. Li (Warwick)
and H.Z. Zhao (Loughborough)
Date: Friday 29th May 2009
Venue: P/T/005 Lecture Room and P/L/002 Lecture Theatre (Physics Department)
A one-day meeting will be held in the Department of Mathematics at the University of York as part of the LMS funded programme of the East Midlands Stochastic Analysis.
14:15 Olaf Wittich (Eindhoven, The Netherlands): Brownian motion conditioned to submanifolds (P/T/005)
15:15 Martin Hairer (Courant): How hot can a heat bath get? (P/L/002)
16:15 Refreshments in G/109
16:45 Roy Chantrell (York): Stochastic models of ultrafast magnetisation reversal at elevated temperatures. (P/L/002)
Olaf Wittich: As an example for the construction of probability measures on infinite dimensional sets, we consider the path measure of Brownian motion in an ambient manifold M which is conditioned not to leave a closed submanifold L of M up to some finite time T. We present two possible ways to construct this measure, one is based on approximation at subsequent times using Trotters product formula, the other on a homogenization result for small tubes around the submanifold.
Martin Hairer: We consider one of the simplest possible models of non-equilibrium statistical mechanics: two coupled oscillators in contact with two Langevin heat baths. The twist is that one of the heat baths is at"infinite" temperature in the sense that no friction acts on the corresponding degree of freedom. We explore the question of the existence of a stationary state in this situation and its properties if it exists. In particular, we will see that the question "Is the corresponding degree of freedom at infinite temperature?" can have a surprising variety of answers.
Roy Chantrell: Laser induced ultrafast magnetisation processes are currently the subject of intense research interest, in part because of potential applications such as Heat Assisted Magnetic Recording. In addition, recent experimental studies have shown that magnetisation reversal can be induced using circularly polarized laser light with no externally applied field, which is of considerable fundamental importance. Further, reversal is believed to take place on the picosecond timescale which makes this phenomenon important for potential applications as data transfer rates increase. It is known that the continuum theory of magnetization reversal (micromagnetics) is not capable of dealing with phase transitions without introducing some atomic level information. Computational models at the atomistic level are currently under development and have already given important insight, for example into the properties of materials for ultra-high density recording media. The basis of atomistic models will be outlined. Essentially this consists of the use of a Heisenberg effective spin model and the solution of a set of coupled stochastic PDEs to describe the time evolution of the ensemble of coupled spins. The model enables representation of the temperature dependent magnetic properties and complete magnetic excitation spectrum. We also review a recent extension of the formalism which introduces the coloured noise which might be expected to feature at the sub-picosecond timescale. Finally we will review the progress in linking atomistic and micromagnetic models in a step toward creating macroscopic models of magnetic materials at temperatures approaching the Curie temperature. This is important since the understanding of macroscopic reversal process cannot realistically be achieved with atomistic models. Our previous work has shown that the (macrospin) Landau-Lifshitz-Bloch (LLB) equation describes the physics of high temperature processes better than the macrospin LLG equation. Here it is shown that the LLB equation gives a reasonable description of Ultrafast dynamic processes. In particular it is demonstrated that the models predict an entirely new ultrafast reversal path via a strongly non-equlibrium, magnetic state. This is highly significant since it could lead to new information storage technologies with high information density and data transfer rates up to two orders of magnitude faster than currently possible.
For more information on speakers and events, please contact: Zdzislaw Brzezniak
For accommodation information, please contact: Christine Cockett
Department of MathematicsThe University of YorkHeslington, York YO10 5DD, UKUnited Kingdom
Brzezniak: +44 (0) 1904 434154Cockett: +44 (0) 1904 433071Fax: +:44 (0) 1904 433071