International Workshop on Multi-Rate processes and Hysterisis

Abstract

We are interested in singular perturbationproblems and hysteresis as common strongly nonlinear phenomenathat occur in many industrial, physical and economic systems. Thewording `strongly nonlinear' means that linearization will notencapsulate the observed phenomena. Often these two types ofphenomena are manifested for different stages of the same orsimilar processes. A number of fundamental hysteresis models canbe considered as limit cases of time relaxation processes, oradmit an approximation by a differential equation which issingular with respect to a particular parameter. However, theamount of interaction between practitioners of theories of systemswith time relaxation and systems with hysteresis (and between the`relaxation' and `hysteresis' research communities) is still low.In recent years Ireland has become a home for a series ofprestigious International Workshops in Singular Perturbations andHysteresis: International Workshop on Hysteresis and Multi-scaleAsymptotics (University College Cork, Ireland, 17–21 March 2004). Proceedings are published in Journal of Physics: ConferenceSeries 22. International Workshop on Relaxation Oscillations andHysteresis (University College Cork, Ireland, 1–6 April 2002).The related collection of invited lectures, was published as avolume Singular Perturbations and Hysteresis, SIAM,Philadelphia, 2005. International Workshop on Geometrical Methods ofNonlinear Analysis and Semiconductor Laser Dynamics (UniversityCollege Cork, Ireland, 5–5 April 2001). A collection of invitedpapers has been published as a special issue of Proceedings of theRussian Academy of Natural Sciences: Nonlinear dynamics of laserand reacting systems.Among the aims of these workshops were to bring together leading experts in time relaxation andhysteresis phenomena in applied problems; to discuss important problems in areas such as reactingsystems, semiconductor lasers, shock phenomena in economicmodelling, fluid mechanics, etc with an emphasis on hysteresisand singular perturbations; to learn and to share modern techniques in areas of commoninterest.The `International Workshop on Multi-Rate Processes andHysteresis' (University College Cork, Ireland, April 3–8, 2006)brought together more than 50 scientists, actively researching inthe areas of dynamical systems with hysteresis and singularperturbations, to analyze these phenomena that occur in manyindustrial, physical and economic systems.The Workshop has been sponsored by the University College Cork(UCC), the Boole Centre for Research in Informatics, UCC, Cork,the School of Mathematical Sciences UCC, Cork, Science FoundationIreland and the Irish Mathematical Society. The supportiveaffiliation of the UK and Republic of Ireland SIAM Section isgratefully acknowledged.The Editors and the Organizers of the Workshop wish to place onrecord their sincere gratitude to Mr Andrew Zhezherun ofUniversity College Cork for both the assistance which he providedto all the presenters at the Workshop, and for the carefulformatting of all the manuscripts prior to their being forwardedto the Publisher.More information about the Workshop can be found at http://euclid.ucc.ie/murphys2006.htm Michael P Mortell, Robert E O'Malley, Alexei Pokrovskiiand Vladimir Sobolev Editors