This edited volume consists of twelve contributions related to the EU Marie Curie Transfer of Knowledge Project Cooperation of Estonian and Norwegian Scienti c Centres within Mathematics and its Applications, CENS-CMA (2005-2009), – der contract MTKD-CT-2004-013909, which ?nanced exchange visits to and from CENS, the Centre for Nonlinear Studies at the Institute of Cybernetics of Tallinn University of Technology in Estonia. Seven contributions describe research highlights of CENS members, two the work of members of CMA, the Centre of Mathematics for Applications, Univ- sity of Oslo, Norway, as the partner institution of CENS in the Marie Curie project, and three the ?eld of work of foreign research fellows, who visited CENS as part of theproject. Thestructureofthebookre?ectsthedistributionofthetopicsaddressed: Part I Waves in Solids Part II Mesoscopic Theory Part III Exploiting the Dissipation Inequality Part IV Waves in Fluids Part V Mathematical Methods The papers are written in a tutorial style, intended for non-specialist researchers and students, where the authors communicate their own experiences in tackling a problem that is currently of interest in the scienti?c community. The goal was to produce a book, which highlights the importance of applied mathematics and which can be used for educational purposes, such as material for a course or a seminar. To ensure the scienti?c quality of the contributions, each paper was carefully – viewed by two international experts. Special thanks go to all authors and referees, without whom making this book would not have been possible.
Mục lục
CENS, CMA and the CENS-CMA Project.- Waves in Solids.- Overview.- Deformation Waves in Solids.- The Perturbation Technique for Wave Interaction in Prestressed Material.- Waves in Inhomogeneous Solids.- Mesoscopic Theory.- Overview.- Dynamics of Internal Variables from the Mesoscopic Background for the Example of Liquid Crystals and Ferrofluids.- Towards a Description of Twist Waves in Mesoscopic Continuum Physics.- Exploiting the Dissipation Inequality.- Overview.- Weakly Nonlocal Non-equilibrium Thermodynamics – Variational Principles and Second Law.- Waves in Fluids.- Overview.- Long Ship Waves in Shallow Water Bodies.- Modelling of Ship Waves from High-speed Vessels.- New Trends in the Analytical Theory of Long Sea Wave Runup.- Mathematical Methods.- Overview.- The Pseudospectral Method and Discrete Spectral Analysis.- Foundations of Finite Element Methods for Wave Equations of Maxwell Type.- An Introduction to the Theory of Scalar Conservation Laws with Spatially Discontinuous Flux Functions.
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