Objective
It has recently become possible (by the efforts of the members of the proposed consortium) to find exact analytic solutions for several problems involving the Brownian motion in external potentials. This enabled us to develop a rigorous linear response theory of the Brownian dynamics of stochastic non-linear systems under the influence of a small external force. In particular, it has been shown using examples in physics, chemistry and electrical engineering that the relaxation times for the appropriate linear response after-effect functions may be calculated exactly in terms of hypergeometric functions.
The aim of the present project is to extend the study to the non-linear case, where the same theoretical approach can be used. In particular we are going to undertake a comprehensive study of relaxation dynamics in stochastic physical systems under the influence of a strong external force with particular reference to non-linear Kerr effect and non-linear dielectric relaxation of liquid crystals and liquids, non- linear magnetic relaxation of single domain ferromagnetic particles from a theoretical viewpoint. Although describing diverse non-linear physical phenomena, these problems are mathematically united by the fact that they all involve the three dimensional rotational Brownian motion in potentials.
Theoretical progress is mainly to be made through the application of the exact analytic approach of solution of non-linear Langevin equations based on the continued fraction method which has been developed in our previous publications.
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Programme(s)
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Funding Scheme
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Coordinator
2 Dublin
Ireland
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.