Deterministic patterns of random motion: fundamentals, electronics, lasers and the human cardiovascular system

Random fluctuations play a crucially important role in many processes in physics, biology and other branches of science and technology. The dawning understanding that random process can not only disturb a system, but also induce totally new kinds of behaviour, has led to sharply increased interest in noise-induced phenomena. Recently discovered examples include: (i) stochastic resonance, which manifests in e.g. geophysics, optical bistability and neural dynamics) stochastic ratchets, which provide the basis for nanoscale machinery within biological cells; resonant activation; and coherence resonance. The importance of fluctuation theory to industry is becoming apparent. It is now generally appreciated that thermal fluctuations are critical for most nanotechnologies, and especially to the paradigms of quantum computation.The fluctuational dynamics of a nonlinear system is usually rich and complex. In many cases, however, it can be divided into two parts, corresponding to different manifestations of the fluctuations. One part is diffusional motion in the vicinity of metastable states of system; the other is large f uctuation events, in which the system moves far away from the initial state in phase space. Large fluctuations, although infrequent, play a fundamental role in a wide range of processes, from earthquakes and nucleation at phase transitions to processes in nanowires, mutations in DNA sequences, failures of electronic devices, and transitions between states of the human cardiovascular systems. A mathematical basis to describe large fluctuations is the rigorous large deviations theory, applicable in the asymptotic zero-noise limit. The theory predicted, and it was shown experimentally, that during a large fluctuation event the system moves along a well-defined most probable (optimal) path, and moreover that fluctuations generate that specific optimal force in a deterministic way. The optimal path and force result in a deterministic pattern of fluctuational motion that significantly simplifies understanding of random dynamics. The use of the rigorous (zero noise intensity) theory of large fluctuations clarified many fundamental problems of statistical physics and also suggested several approaches to control of fluctuations, e.g. finding an energy-minimal deterministic force for inducing the transition from one state to another, and for the inference (reconstruction) of the system dynamics in terms of a mathematical model through the analysis of random motion.However, for real practical applications of these approaches, we have to go beyond the rigorous (but asymptotic) theory and take into account a finite value of fluctuational intensity. The project is directed to exactly this aim: to develop the formalism and numerical tools needed for the description of large fluctuations at finite noise intensity; and, on this basis, to develop new applied methods and approaches which are ready for use by experimentalists; then to use these methods for characterization of state of the human cardiovascular system.The proposed investigations will be developed in sequential stages: the formulation of the theoretical background - developing numerical methods - testing the methods in analogue experiments - the application of inference methods to reveal cardiovascular dysfunctions. The combination and iterations between numerical methods and experiments will provide robust practical methods which can be used in laser physics, biophysics, and electronics. The developed control methods have a potential application in communication devices for increasing stability to fluctuations and/or for decreasing power consumption. An especially important benefice will be received by the medical community in form of tools to improved early diagnosis of a range of pathologies and better assessment of the effect of treatment. The cardiovascular part of the project will be undertaken in collaboration with cardiologists at the Royal Lancaster Infirmary who are already close collaborators of the Lancaster Nonlinear Group.