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Interview with D. H. Mellor (2001)
This article is the text of an interview with D. H. Mellor conducted in Cambridge on 30 May 2001 by Anna-Sofia Maurin and Johannes Persson for the philosophical journal Theoria.
Published by: Theoria
Stored energy functions for phase transitions in crystals
Johannes Zimmer
May 01, 2004
A method is presented to construct nonconvex free energies that are invariant under a symmetry group. Algebraic and geometric methods are used to determine invariant functions with the right location of minimizers. The methods...
Stored energy functions for phase transitions in crystals
Johannes Zimmer
May 01, 2004
A method is presented to construct nonconvex free energies that are invariant under a symmetry group. Algebraic and geometric methods are used to determine invariant functions with the right location of minimizers. The methods...
Rate-independent processes with linear growth energies and time-dependent boundary conditions
A rate-independent evolution problem is considered for which the stored energy density depends on the gradient of the displacement. The stored energy density does not have to be quasiconvex and is assumed to exhibit linear...
Kinetic relations for a lattice model of phase transitions
The aim of this article is to analyse travelling waves for a lattice model of phase transitions, specifically the Fermi-Pasta-Ulam chain with piecewise quadratic interaction potential. First, for fixed, sufficiently large...
Travelling lattice waves in a toy model of Lennard-Jones interaction
We consider an infinite lattice model, where particles interact with nearest neighbour (NN) and next-to-nearest neighbours (NNN); the NN and NNN springs act against each other to mimic the Lennard-Jones potential. The existence...
Geometrical interpretation of fluctuating hydrodynamics in diffusive systems
We discuss geometric formulations of hydrodynamic limits in diffusive systems. Specifically, we describe a geometrical construction in the space of density profiles - the Wasserstein geometry - which allows the deterministic...
Kinetic relations for a lattice model of phase transitions
The aim of this article is to analyse travelling waves for a lattice model of phase transitions, specifically the Fermi-Pasta-Ulam chain with piecewise quadratic interaction potential. First, for fixed, sufficiently large...
Existence of subsonic heteroclinic waves for the Frenkel-Kontorova model with piecewise quadratic on-site potential
We give an existence proof for heteroclinic wave solutions to the Frenkel-Kontorova model of dislocation dynamics. The on-site potential is assumed to be piecewise quadratic. The framework employed here allows us to determine...
Travelling wavefronts in nonlocal diffusion equations with nonlocal delay effects
This paper deals with the existence, monotonicity, uniqueness and asymptotic behaviour of travelling wavefronts for a class of temporally delayed, spatially nonlocal diffusion equations.
Travelling lattice waves in a toy model of Lennard-Jones interaction
We consider an infinite lattice model, where particles interact with nearest neighbour (NN) and next-to-nearest neighbours (NNN); the NN and NNN springs act against each other to mimic the Lennard-Jones potential. The existence...
Entropic and gradient flow formulations for nonlinear diffusion
Nonlinear diffusion ∂tρ= (increment)(Φ(ρ)) is considered for a class of nonlinearities Φ. It is shown that for suitable choices of Φ, an associated Lyapunov functional can be interpreted as thermodynamic entropy....
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