In modern telecommunications
the development of all-optical
equivalents for electronic signal processing devices has been the
topic of much on-going research and development effort. This research
area is focused on the development of optical signal switching
using liquid crystals.
This figure shows two nematicons interacting.
They are out of phase and form a dipole
Two-dimensional, spatial, optical solitary waves, termed nematicons, can form in liquid crystals due to a balance of the non-local response of the nematic with the diffractive spreading of the light. Liquid crystals have the potential for the development of compact photonic devices and could be the basis of optical switches in devices which do not need to operate at the large GHz telecommunication repetition rates. An advantage of photonic devices based on liquid crystals is that a nematicon can form a waveguide through which another nematicon can propagate, thus forming a light ``circuit'' which is easily re-configurable. It is anticipated that these re-configurable light circuits could form the basis for a wide variety of photonic devices.
Some of the projects I am working on include the development of analytical techniques to describe the evolution and interaction of nematicons, and efficient numerical techniques to solve the nematicon equations
Waves are ubiquitous, occuring throughout the natural world. Describing their propagation and interaction is of prime importance. My research in this area has focussed on the Korteweg-de Vries (KdV) equation, which describes waves of small amplitude on shallow water. The KdV equation has a travelling wave solution called a soliton, which is a single humped wave. This nonlinear equation has the very special property that the collision of two solitons leaves them unchanged in shape. Of interest is the solitons home page at Heriot-Watt University, which has movies of soliton interactions, historical information and links to many other sites devoted to this topic.
I have been working on solitary wave interaction and evolutions for higher-order extensions to integrable models such as the KdV, NLS and Hirota equations. Listed below are some recent papers of mine on this topic
I am also interested in semi-analytical solutions for combustion problems. On problem considered the cubic-autocatalytic scheme in a reaction-diffusion cell while another looked at the classical pellet problem. The basic idea was to approximate the governing partial differential equations by ordinary differential equations, which are amenable to the usual methods of combustion theory. Below are two papers of mine on this topic. Dr. Mark Nelson and myself have submitted a current ARC Discovery grant application on this topic. A new collaborator of ours is Prof. Venkat Subramanian , Tennessee Technical University, USA who is a expert on batteries, fuel cells and electrochemical systems.