131 citations · 217 across the 16 of their papers we have counts for
17 papers
Remarks on the linear wave equation
John M. Ball
We make some remarks on the linear wave equation concerning the existence and uniqueness of weak solutions, satisfaction of the energy equation, growth properties of solutions, the…
Image comparison and scaling via nonlinear elasticity
John M. Ball, Christopher L. Horner
A nonlinear elasticity model for comparing images is formulated and analyzed, in which optimal transformations between images are sought as minimizers of an integral functional. Th…
Slip and twinning in Bravais lattices
John M. Ball
A unified treatment of slip and twinning in Bravais lattices is given, focussing on the case of cubic symmetry, and using the Ericksen energy well formulation, so that interfaces c…
A free discontinuity model for smectic thin films
John M. Ball, Giacomo Canevari, Bianca Stroffolini
We attempt to describe surface defects in smectic A thin films by formulating a free discontinuity problem - that is, a variational problem in which the order parameter is allowed…
Interaction of martensitic microstructures in adjacent grains
John M. Ball, Carsten Carstensen
It is often observed that martensitic microstructures in adjacent polycrystal grains are related. For example, micrographs of Arlt exhibit propagation of layered structures across…
Liquid crystals and their defects
John M. Ball
These lecture notes discuss classical models of liquid crystals, and the different ways in which defects are described according to the different models.
Geometry of polycrystals and microstructure
John M. Ball, Carsten Carstensen
We investigate the geometry of polycrystals, showing that for polycrystals formed of convex grains the interior grains are polyhedral, while for polycrystals with general grain geo…
Discontinuous order parameters in liquid crystal theories
J. M. Ball, S. J. Bedford
The paper is concerned with various issues surrounding the mathematical description of defects in models of liquid crystals, drawing on experience from solid mechanics. The roles p…
Quasiconvexity at the boundary and the nucleation of austenite
John Ball, Konstantinos Koumatos
Motivated by experimental observations of H. Seiner et al., we study the nucleation of austenite in a single crystal of a CuAlNi shape-memory alloy stabilized as a single variant o…
Incompatible sets of gradients and metastability
J. M. Ball, R. D. James
We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a p…
Partial regularity and smooth topology-preserving approximations of rough domains
John M. Ball, Arghir Zarnescu
For a bounded domain of class , the properties are studied of fields of `good directions', that is the directions with respect to which $\part…
Entropy and Convexity for Nonlinear Partial Differential Equations: Introduction
John M. Ball, Gui-Qiang G. Chen
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in…
Nucleation of austenite in mechanically stabilized martensite by localized heating
John M. Ball, Konstantinos Koumatos, Hanus Seiner
The nucleation of bcc austenite in a single crystal of a mechanically stabilized 2H-martensite of Cu-Al-Ni shape-memory alloy is studied. The nucleation process is induced by local…
An investigation of non-planar austenite-martensite interfaces
John M. Ball, Konstantinos Koumatos
Motivated by experimental observations on CuAlNi single crystals, we present a theoretical investigation of non-planar austenite-martensite interfaces. Our analysis is based on the…
On uniqueness for time harmonic anisotropic Maxwell's equations with piecewise regular coefficients
John M. Ball, Yves Capdeboscq, Basang Tsering Xiao
We are interested in the uniqueness of solutions to Maxwell's equations when the magnetic permeability and the permittivity are symmetric positive definite matrix…
An analysis of non-classical austenite-martensite interfaces in CuAlNi
J. M. Ball, K. Koumatos, H. Seiner
Ball and Carstensen theoretically investigated the possibility of the occurrence of non-classical austenite-martensite interfaces and studied the cubic-to-tetragonal case extensive…
Orientability and energy minimization in liquid crystal models
John M. Ball, Arghir Zarnescu
Uniaxial nematic liquid crystals are modelled in the Oseen-Frank theory through a unit vector field . This theory has the apparent drawback that it does not respect the head-to-…