Synchronization of a large number of continuous one-dimensional stochastic elements with time-delayed mean-field coupling

We study synchronization as a means of control of collective behavior of an ensemble of coupled stochastic units in which oscillations are induced merely by external noise. For a large number of one-dimensional continuous stochastic elements coupled non-homogeneously through the mean field with delay we developed an approach to find a boundary of synchronization domain and the frequency of the mean-field oscillations on it. Namely, the exact location of the synchronization threshold is shown to be a solution of the boundary value problem (BVP) which was derived from the linearized Fokker-Planck equation. Here the synchronization threshold is found by solving this BVP numerically. Approximate analytics is obtained by expanding the solution of the linearized Fokker-Planck equation into a series of eigenfunctions of the stationary Fokker-Planck operator. Bistable systems with a polynomial and piece-wise linear potential are considered as examples. Multistability and hysteresis in the mean-field behavior are observed in the stochastic network at finite noise intensities. In the limit of small noise intensities the critical coupling strength is shown to remain finite, provided that the delay in the coupling function is not infinitely small. Delay in the coupling term can be used as a control parameter that manipulates the location of the synchronization threshold.     

On the role of the definition of potential models in Gibbs ensemble phase equilibria simulations of the H2S-pentane mixture

The effect of treating explicitly the coulombic and polarization interactions is investigated through the calculation of the coexistence curve of the pentane-H₂S binary mixture. In this work, potential models have been developed for hydrogen sulphide and pentane, which include electrostatic sites—estimated from ab initio calculations—and polarizable sites—estimated from experimental data—in addition to Lennard-Jones sites. Compared to existing models, these new models have the same number of fitting parameters to experimental thermodynamic data. They are shown to correctly describe the coexistence curve of the pure compounds. When applied to the case of mixtures, together with Lorentz-Berthelot combining rules, they allow one to obtain a more accurate prediction of the coexisting compositions of the mixture. Furthermore, it is shown that the interaction energy in this kind of mixture cannot be properly described by using effective potential models usually considered for pure compounds.     

Rotational viscosity of uniaxial molecules

Non-equilibrium molecular dynamics (NEMD) are used to calculate the vortex or rotational viscosity of fluids composed of uniaxial molecules. It is shown that the NEMD homogeneous spin flow algorithm proposed by Edberg, R., Evans, D. J., and Moriss, G. P., 1987, Molec. Phys., 62, 1357 considerably underestimates the vortex viscosity. A modified version of this algorithm is proposed and applied to liquid chlorine and nitrogen. The results are in good agreement with previous work using equilibrium or other NEMD methods, and also show that at high spin rates the vortex viscosity decreases with increase in magnitude of the external torque used to drive the spin flow.     

Delayed feedback applied to breathing in humans

We studied the response of healthy volunteers to the delayed feedback generated from the breathing signals. Namely, in the freely-breathing volunteers the breathing signal was recorded, delayed by τ seconds and fed back to the same volunteer in real time in the form of a visual and auditory stimulus of low intensity, i.e. the stimulus was crucially non-intrusive. In each case volunteers were instructed to breathe in the way which was most comfortable for them, and no explanation about the kind of applied stimulus was provided to them. Each volunteer experienced 10 different delay times ranging between 10% and 100% of the average breathing period without external stimulus. It was observed that in a significant proportion of subjects (11 out of 24) breathing was slowed down in the presence of delayed feedback with moderate delay. Also, in 6 objects out of 24 the delayed feedback was able to induce transition from nearly periodic to irregular breathing. These observations are consistent with the phenomena observed in numerical simulation of the models of periodic and chaotic self-oscillations with delays, and also in experiments with simpler self-oscillating systems.     

Force generation by polymerizing microtubules

Polymerization ratchets formed by the assembly of actin filaments and microtubules are possibly the simplest realizations of biological thermal ratchets. A variety of experimental evidence exists that significant forces are generated by these processes, but quantitative studies lag far behind similar studies for molecular motors such as kinesin and myosin. Here we present a discussion of the theory of polymerization ratchets as well as experimental techniques used in our laboratory for the study of forces generated by single growing microtubules. Data obtained with these techniques provide us with valuable information that may eventually allow us to distinguish between different models for the growth of microtubules. Received: 15 January 2002 / Accepted: 11 February 2002 / Published online: 22 April 2002     

Invariance principles for stochastic area and related stochastic integrals

Given an antisymmetric kernel K (K(z, z′) = ?K(z′, z)) and i.i.d. random variates Z_n, n?1, such that EK²(Z₁, Z₂)<∞, set A_n = ∑₁?i?j?nK(Z_i,Z_j), n?1. If the Z_n's are two-dimensional and K is the determinant function, A_n is a discrete analogue of Paul Lévy's so-called stochastic area. Using a general functional central limit theorem for stochastic integrals, we obtain limit theorems for the A_n's which mirror the corresponding results for the symmetric kernels that figure in theory of U-statistics.