International Workshop on Multi-Rate Processes and Hysteresis

Abstract

We are interested in singular perturbation problems and hysteresis as common strongly nonlinear phenomena that occur in many industrial, physical and economic systems. The wording `strongly nonlinear' means that linearization will not encapsulate the observed phenomena. Often these two types of phenomena are manifested for different stages of the same or similar processes. A number of fundamental hysteresis models can be considered as limit cases of time relaxation processes, or admit an approximation by a differential equation which is singular with respect to a particular parameter. However, the amount of interaction between practitioners of theories of systems with time relaxation and systems with hysteresis (and between the `relaxation' and `hysteresis' research communities) is still low, and cross-fertilization is small. In recent years Ireland has become a home for a series of prestigious International Workshops in Singular Perturbations and Hysteresis: International Workshop on Multi-rate Processes and Hysteresis (University College Cork, Ireland, 3–8 April 2006). Proceedings are published in Journal of Physics: Conference Series, volume 55. See further information at http://euclid.ucc.ie/murphys2008.htm International Workshop on Hysteresis and Multi-scale Asymptotics (University College Cork, Ireland, 17–21 March 2004). Proceedings are published in Journal of Physics: Conference Series, volume 22. See further information at http://euclid.ucc.ie/murphys2006.htm International Workshop on Relaxation Oscillations and Hysteresis (University College Cork, Ireland, 1–6 April 2002). The related collection of invited lectures, was published as a volume Singular Perturbations and Hysteresis, SIAM, Philadelphia, 2005. See further information at http://euclid.ucc.ie/hamsa2004.htm International Workshop on Geometrical Methods of Nonlinear Analysis and Semiconductor Laser Dynamics (University College Cork, Ireland, 5–5 April 2001). A collection of invited papers has been published as a special issue of Proceedings of the Russian Academy of Natural Sciences: Nonlinear dynamics of laser and reacting systems, and is available online at http://www.ins.ucc.ie/roh2002.htm. See further information at http://www.ins.ucc.ie/roh2002.htm Among the aims of these workshops were to bring together leading experts in singular perturbations and hysteresis phenomena in applied problems; to discuss important problems in areas such as reacting systems, semiconductor lasers, shock phenomena in economic modelling, fluid mechanics, etc with an emphasis on hysteresis and singular perturbations; to learn and to share modern techniques in areas of common interest. The `International Workshop on Multi-Rate Processes and Hysteresis' (University College Cork, Ireland, April 3–8, 2006) brought together more than 70 scientists (including more than 10 students), actively researching in the areas of dynamical systems with hysteresis and singular perturbations, to analyze those phenomena that occur in many industrial, physical and economic systems. The countries represented at the Workshop included Czech Republic, England, France, Germany, Hungary, Ireland, Israel, Italy, Poland, Romania, Russia, Scotland, South Africa, Switzerland and USA.All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.The Workshop has been sponsored by Science Foundation Ireland (SFI), KE Consulting group, Drexel University, Philadelphia, USA, University College Cork (UCC), Boole Centre for Research in Informatics, UCC, Cork, School of Mathematical Sciences, UCC, Cork, Irish Mathematical Society, Tyndall National Institute, Cork, University of Limerick, Cork Institute of Technology, and Heineken. The supportive affiliation of the European Geophysics Society, International Association of Hydrological Sciences, and Laboratoire Poncelet is gratefully acknowledged.The Editors and the Organizers of the Workshop wish to place on record their sincere gratitude to Mr Andrew Zhezherun and Mr Alexander Pimenov of University College Cork for both the assistance which he provided to all the presenters at the Workshop, and for the careful formatting of all the manuscripts prior to their being forwarded to the Publisher. More information about the Workshop can be found at http://euclid.ucc.ie/murphys2006.htm Michael P Mortell, Robert E O'Malley Jr, Alexei Pokrovskii, Dmitrii Rachinskii and Vladimir Sobolev Editors