Colin Atkinson is an applied mathematician who combines physical insight, use of analytic function theory, asymptotic methods and invariant integrals. Though focused mostly towards problems in materials science and engineering, his versatility has enabled him to make substantial contributions in other areas.
His achievements include finding some of the first solutions for dynamically expanding cracks, and studies of crack propagation in the presence of a variety of dissipative mechanisms, including plasticity, viscoelasticity and poroelasticity. He has made major studies of cracks near interfaces and boundaries and contributed to dislocation theory. His work on diffusive processes in solids, including growth kinetics of ledges, has been incisive.
He has studied the existence of solutions of partial differential equations (particularly, some that model epidemics), stochastic processes (queuing theory), the solution of transcendental equations, the numerical analysis of boundary integral equations and the design of tissue expanders used in plastic surgery. His interests also include stochastic control and its applications to transaction costs in portfolio theory and option pricing; continuum theory liquid crystals; and sensors for oilfield service applications.
Applied mathematics, Mathematical and statistical techniques, Mathematical modeling, Continuum mechanics, Numerical analysis