Phase Transitions and Hysteresis [electronic resource] : Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, July 13-21, 1993 / by M. Brokate, Yong Zhong Huo, Noboyuki Kenmochi, Ingo Mรผller, Josรฉ F. Rodriguez, Claudio Verdi ; edited by Augusto Visintin
Imprint
Berlin, Heidelberg : Springer Berlin Heidelberg, 1994
1) Phase Transitions, represented by generalizations of the classical Stefan problem. This is studied by Kenmochi and Rodrigues by means of variational techniques. 2) Hysteresis Phenomena. Some alloys exhibit shape memory effects, corresponding to a stress-strain relation which strongly depends on temperature; mathematical physical aspects are treated in Mรผller's paper. In a general framework, hysteresis can be described by means of hysteresis operators in Banach spaces of time dependent functions; their properties are studied by Brokate. 3) Numerical analysis. Several models of the phenomena above can be formulated in terms of nonlinear parabolic equations. Here Verdi deals with the most updated approximation techniques
CONTENT
Hysteresis operators -- Systems of nonlinear PDEs arising from dynamical phase transitions -- Quasiplasticity and pseudoelasticity in shape memory alloys -- Variational methods in the stefan problem -- Numerical aspects of parabolic free boundary and hysteresis problems
Mathematics
Mathematical analysis
Analysis (Mathematics)
Applied mathematics
Engineering mathematics
Numerical analysis
Physics
Mechanics
Condensed matter
Mathematics
Applications of Mathematics
Condensed Matter Physics
Numerical Analysis
Analysis
Theoretical Mathematical and Computational Physics
