Optimal fluctuations and the control of chaos.

The energy-optimal migration of a chaotic oscillator from one attractor to another coexisting attractor is investigated via an analogy between the Hamiltonian theory of fluctuations and Hamiltonian formulation of the control problem. We demonstrate both on physical grounds and rigorously that the Wentzel-Freidlin Hamiltonian arising in the analysis of fluctuations is equivalent to Pontryagin's Hamiltonian in the control problem with an additive linear unrestricted control. The deterministic optimal control function is identied with the optimal fluctuational force. Numerical and analogue experiments undertaken to verify these ideas demonstrate that, in the limit of small noise intensity, fluctuational escape from the chaotic attractor occurs via a unique (optimal) path corresponding to a unique (optimal) fluctuational force. Initial conditions on the chaotic attractor are identified. The solution of the boundary value control problem for the Pontryagin Hamiltonian is found numerically. It is shown that this solution is approximated very accurately by the optimal fluctuational force found using statistical analysis of the escape trajectories. A second series of numerical experiments on the deterministic system (i.e. in the absence of noise) show that a control function of precisely the same shape and magnitude is indeed able to instigate escape. It is demonstrated that this control function minimizes the cost functional and the corresponding energy is found to be smaller than that obtained with some earlier adaptive control algorithms

Noise robustness of communications provided by coupling-function-encryption and dynamical Bayesian inference

In addition to the need for security, everyday information exchange must be able to cope with noise and interference. We discuss the noise robustness of a recently-introduced communications protocol inspired by the human cardiorespiratory interaction, based on analysis methods originally developed for reconstructing coupling functions between oscillatory processes underlying the biological signals. Security is assured by use of multiple, time-varying, coupling functions between two or more dynamical systems, and the protocol allows for multiplexing of the information transfer. We focus on the exceptional noise-robustness that arises from the application of dynamical Bayesian inference to the stochastic differential equations. A particular advantage of the protocol is that it facilitates an effective separation between the deterministic information signals and the dynamical (channel) noise perturbations. We define reliability in terms of the bit-error-rate (BER) as a function of noise strength, expressed as the signal-to-noise ratio (SNR). We present results confirming that the coupling function protocol is highly noise robust, and that it outperforms other known communications protocols. In the broader context, we point out that this use of coupling functions between dynamical systems is a modular construct that can be extended to implement a range of different encryption concepts. Similarly, the method of dynamical Bayesian inference carries wider implications for future applications to noise reduction in communications using other protocols

Monitoring the ageing of the cardiovascular system

This research developed a way of measuring blood flow through the capillaries and thereby monitoring the health of the endothelium, the inner lining of the blood vessels

Dynamics of cardiovascular ageing

We gain wrinkles and lose hair, as we age, but our bodies also change in less obvious but much more important ways. This project studied the age-related alterations that occur in the cardiovascular system – the heart, lungs and network of arteries and veins that carry oxygenated blood and nutrients to every cell of the body and remove the waste products of metabolism. It was already known that the phase of breathing affects the rate at which the heart beats, but that this effect decreases as we age. The research has associated this reduction in heart-lung interaction with changes in the endothelium, the inner lining of all the blood vessels. It involved making non-invasive measurements of blood flow in the skin of 200 healthy subjects of all ages. The analysis focused on very low frequency oscillations in blood flow that can give a measure of the state of the endothelium. The main conclusions are, first, that to age healthily, you should look after your endothelium and, secondly, that it should be feasible to design an instrument for assessing endothelial health – an endotheliometer

On Resolution of the Selectivity/Conductivity Paradox for the Potassium Ion Channel

The ability of the potassium channel to conduct K+ at almost the rate of free diffusion, while discriminating strongly against the (smaller) Na+ ion, is of enormous biological importance [1]. Yet its function remains at the center of a “many-voiced debate” [2,3]. In this presentation, a first-principles explanation is provided for the seemingly paradoxical coexistence of high conductivity with high selectivity between monovalent ions within the channel. It is shown that the conductivity of the selectivity filter is described by the generalized Einstein relation. A novel analytic approach to the analysis of the conductivity is proposed, based on the derivation of an effective grand canonical ensemble for ions within the filter. The conditions for barrier-less diffusion-limited conduction through the KcsA filter are introduced, and the relationships between system parameters required to satisfy these conditions are derived. It is shown that the Eisenman selectivity equation is one of these, and that it follows directly from the condition for barrier-less conduction. The proposed theory provides analytical insight into the “knock-on” [1] and Coulomb blockade [4] mechanisms of K+ conduction through the KcsA filter. It confirms and illuminates an earlier argument [3] that the “snug-fit" model cannot describe the fast diffusion-limited conduction seen in experiments. Numerical examples are provided illustrating agreement of the theory with experimentally-measured I-V curves. The results are not restricted to biological systems, but also carry implications for the design of artificial nanopores

Atomistic model of reptation at polymer interfaces

We study a molecular dynamics model of a polymer-polymer interface for a polyetherimide/polycarbonate blend, including its thermodynamic properties, its chain reptation, and its corresponding welding characteristics. The strength of the sample is analyzed by measuring strain-stress curves in simulations of uni-axial elongation. The work is motivated by potential applications to 3D manufacturing in space

Prehistory probability distribution of ionic transitions through a graphene nanopore

We analyze selective ionic conduction through an artificial nanopore in a single graphene sheet, using molecular dynamics simulations and the prehistory probability distribution. We assess position-dependent changes in the number and orientation of water molecules in the first and second hydration shells of the ion as it crosses the nanopore. We reveal coupling between an ionic double layer near the sheet to the statistical properties of the hydration shells

The dynamics of quasiparticles in a toy model of the KcsA biological ion channel

We study the highly-concerted motion of ions in a narrow biological ion channel (KcsA) by considering the notion of a quasiparticle, with specific focus on the transition process. Namely, we show that the ion entering or exiting the channel is correlated with the position of the quasiparticle. This result is of importance in the rate theories of ion conduction through narrow channels and artificial nanopores

Comment on "Nonlinear resonance and chaos in the relativistic phase space for driven nonlinear systems".

Kim and Lee (Phys. Rev. E 52, 473; 1995) report relativity-induced resonances in periodically driven oscillators. We comment that zero-dispersion nonlinear resonance (ZDNR) will occur in some of the systems considered, outline the physical origins of the ZDNR, and propose an explanation of a discrepancy noted by Kim and Lee between their theoretical and numerical values of the energy at the stationary stable points of Poincare sections