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Prof Sir John Ball FRS FRSE

Fellow in Mathematics

Sedleian Professor of Natural Philosophy

Introduction

I took my undergraduate degree in Mathematics at Cambridge before obtaining my DPhil in 1972 at the University of Sussex. Prior to starting at Queen’s in 1996 I was Professor of Applied Analysis at Heriot-Watt University in Edinburgh. I have held visiting professorships at the University of California at Berkeley, at the Université Pierre at Marie Curie, Paris, at the Tata Institute of Fundamental Research, Bangalore, at the Institute for Advanced Study, Princeton, and at the University of Montpellier II. I am a former President of the International Mathematical Union and am currently a member of the Executive Board of the International Council for Science.

Teaching

I am currently teaching a survey course on Nonlinear Analysis and Applications for the Centre for Doctoral Training in Partial Differential Equations: Analysis and Applications. Other recent courses include Dynamics and Energy Minimization and Mathematical Foundations of Elasticity Theory.

Research

My main research areas lie in the calculus of variations, nonlinear partial differential equations, infinite-dimensional dynamical systems and their applications to nonlinear mechanics. In solid mechanics, I am especially interested in the mathematics of microstructure arising from phase transformations in solids, using models based on nonlinear elasticity, where the problem of predicting microstructure morphology is related to deep unsolved questions of the multi-dimensional calculus of variations such as understanding quasiconvexity. Another main interest is in the mathematics of liquid crystals, in particular concerning how defects can be studied using different models.

Publications

J.M. Ball. Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rat. Mech. Anal., 63:337--403, 1977.

J.M. Ball. Discontinuous equilibrium solutions and cavitation in nonlinear elasticity. Phil. Trans. Royal Soc. London A, 306:557--611, 1982.

J.M. Ball and V.J. Mizel. One-dimensional variational problems whose minimizers do not satisfy  the Euler-Lagrange equations. Arch. Rat. Mech. Anal., 90:325--388, 1985.

J.M. Ball, J. Carr, and O. Penrose. The Becker-Doring cluster equations: basic properties and  asymptotic behaviour of solutions. Comm. Math. Phys., 104:657--692, 1986.

J.M. Ball and R.D. James. Fine phase mixtures as minimizers of energy. Arch. Rat. Mech. Anal., 100:13--52, 1987

J.M. Ball and R.D. James. Proposed experimental tests of a theory of fine microstructure, and  the two-well problem, Phil. Trans. Roy. Soc. London A, 338:389--450, 1992.

J.M. Ball. Global attractors for damped semilinear wave equations, Discrete and Continuous Dynamical Systems, 10:31--52, 2004.

J.M. Ball and A. Majumdar.  Nematic Liquid Crystals : from Maier-Saupe to a Continuum Theory, Mol. Cryst. Liq. Cryst. 525 (2010) 1-11. 

J.M. Ball and A. Zarnescu.  Orientability and energy minimization in liquid crystal models, Arch. Ration. Mech. Anal. 202 (2011), no 2, 493-535.

J. M. Ball, K. Koumatos, Quasiconvexity at the boundary and the nucleation of austenite, Archive for Rational Mechanics and Analysis, to appear.