Ralph WILLOX
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Title

Professor 
Field

Applied Mathematics 
Research interests

Integrable systems, discrete (nonlinear) dynamical systems, cellular automata. 
Current research

A major part of my research activity focuses on the study of nonlinear integrable systems and their algebraic properties, and especially on the construction of particular classes of solutions for integrable systems and on the algebraic methods required for this purpose. I am particularly interested in socalled discrete integrable systems (discrete in space and time) as these systems often encompass a multitude of integrable systems in certain limits. A special limiting procedure that can be performed on such discrete systems, the ultradiscrete limit, allows one to obtain cellular automata that exhibit solitonlike behaviour. As it turns out, these solitonic cellular automata are related to (quantum) solvable lattice models, at their zero temperature limit. The role socalled YangBaxter maps play in this connection is a particularly important research topic. I also study the possible applications of discretization and ultradiscretization techniques, originally developed in the context of integrable systems, to nonintegrable dynamical systems. The aim is to obtain discretizations that exhibit the same dynamics as the original continuous systems, over a vast range of the discretization parameters. In many cases, going to the ultradiscrete limit allows one to obtain cellular automata that preserve the essential dynamics of the original continuous systems. 
Selected publications


Memberships and activities

Mathematical Society of Japan Japan Society of Industrial and Applied Mathematics (JSIAM) Member of the General Assembly of the "Instituts Internationaux de Chimie et Physique, fondés par E. Solvay" Journal of Physics A : Mathematical and Theoretical, Advisory Board member 