Mathematical Models And Methods For Smart Materials

Mauro Fabrizio, Barbara Lazzari, Angelo Morro

• Publisher: World Scientific
• Year: 2002
• Print ISBN: 9789812382351, 9789812382351
• eBook ISBN: 9789812776273
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

This book contains the papers presented at the conference on "Mathematical Models and Methods for Smart Materials", held in Italy in 2001. The papers are divided into four parts:"Methods in Materials Science" deals mainly with mathematical techniques for the investigation of physical systems, such as liquid crystals, materials with internal variables, amorphous materials, and thermoelastic materials. Also, techniques are exhibited for the analysis of stability and controllability of classical models of continuum mechanics and of dynamical systems."Modelling of Smart Materials" is devoted to models of superfluids, superconductors, materials with memory, nonlinear elastic solids, and damaged materials. In the elaboration of the models, thermodynamic aspects play a central role in the characterization of the constitutive properties."Well-Posedness in Materials with Memory" deals with existence, uniqueness and stability for the solution of problems, most often expressed by integrodifferential equations, which involve materials with fading memory. Also, attention is given to exponential decay in viscoelasticity, inverse problems in heat conduction with memory, and automatic control for parabolic equations."Analytic Problems in Phase Transitions" discusses nonlinear partial differential equations associated with phase transitions, and hysteresis, possibly involving fading memory effects. Particular applications are developed for the phase-field model with memory, the Stefan problem with a Cattaneo-type equation, the hysteresis in thermo-visco-plasticity, and the solid-solid phase transition.

Table of contents

• Contents
• Preface
• Obituary
• Temperance for order/disorder transition in nematics
• Null Lagrangians and surface interaction potentials in nonlinear elasticity
• Automatic control problems for integrodifferential parabolic equations
• Asymptotic partition in the linear thermoelasticity backward in time
• Internal parameters and superconductive phase in metals
• Phase relaxation problems with memory and their optimal control
• Some inverse problems related to the heat equation with memory in non smooth spatial domains
• On the minimal free energy and the Saint-Venant principle in linear viscoelasticity
• Gentili's norm on the process and state spaces in linear viscoelasticity
• Unified dynamics of particles and photons
• The problem of the rate of thermalization, and the relations between classical and quantum mechanics
• Solid-solid phase transition in a mechanical system
• The minimum free energy of compressible viscoelastic fluids
• KAM methods for nonautonomous Schrödinger operators
• Phase-field systems with memory effects in the order parameter dynamics
• Elliptic problems depending on a parameter in plane curvilinear polygons
• Fractional diffusion and wave equations
• Exponential decay on the mean in linear viscoelasticity
• Recovering a memory kernel in an integrodifferential Stefan problem
• The fundamental solutions of the time-fractional diffusion equation
• Some results of pointwise stability for solutions to the Navier-Stokes system
• Asymptotic behavior for a model of transverse vibration of a bar with linear memory
• Balance equations in two-fluid models of helium II
• Thermoelastic plate with thermal interior control
• A non-stationary model in superconductivity
• Counterexample to the exponential decay for systems with memory
• Convergence to the Stefan problem of the hyperbolic phase relaxation problem and error estimates
• On a thermodynamical model for type-II high-Tc superconductors. Theory and applications.
• Decay of the energy to partially viscoelastic materials
• Some remarks on the conserved Penrose-Fife phase field model with memory effects
• Local solution to Frémond's full model for irreversible phase transitions
• A scalar model of viscoelasticity with singular memory
• An existence result for semilinear equations in viscoelasticity:The case of regular kernels
• Phase transitions and hysteresis in one-dimensional thermo-plasticity
• Longterm dynamics of a conserved phase-field system with memory