Synchronization based system identification of an extended excitable system

A basic state and parameter estimation scheme for an extended excitable system is presented, where time series from a spatial grid of sampling points are used to drive and synchronize corresponding model equations. Model parameters are estimated by minimizing the synchronization error. This estimation scheme is demonstrated using data from generic models of excitable media exhibiting spiral wave dynamics and chaotic spiral break-up that are implemented on a graphics processing unit.     

Flow of an elastico-viscous fluid past an oscillating plate

An exact solution for the flow of an elastico-viscous fluid (Walters' liquid B') due to an oscillating infinite plate has been derived. It has been observed that forgwt=0, ( — frequency,t — time) the flow near the plate may become unstable with increasing whereas fort>0, the velocity increases with increasing. The shearing stress decreases with increasing.I wish to thank the referee for his useful comments which led to the improvement of this paper.     

Two-state system in an oscillating field

We consider two states connected by two channels, one of which is activated but the other has no potential barrier. The height of the barrier is oscillating together with an external ac-field. We find that an external field shifts the average populations of the states and tends to equalize them. The steady-state flux circulates along the close circuit formed by these channels.     

On flow of an elastico-viscous fluid past an oscillating porous plate

A solution for the flow problem of an elastico-viscous fluid (Walters liquid B) due to an oscillating infinite porous plate with constant suction has been obtained. It has been observed that the magnitude of velocity decreases with increase in suction velocity. The shearing stress increases with increase in suction.We thank the referee for his useful suggestions.     

Heat transfer of an oscillating cylinder in a viscous incompressible fluid flow

Unsteady flow and heat transfer of the heated cylinder with transverse and longitudinal oscillations in unbounded flow of viscous incompressible heat conducting fluid are considered. Influence of amplitude, frequency and direction of harmonic oscillations of the cylinder on the near-wake structure and heat transfer are investigated.     

Synchronization in networks of spatially extended systems

Synchronization processes in networks of spatially extended dynamical systems are analytically and numerically studied. We focus on the relevant case of networks whose elements (or nodes) are spatially extended dynamical systems, with the nodes being connected with each other by scalar signals. The stability of the synchronous spatio-temporal state for a generic network is analytically assessed by means of an extension of the master stability function approach. We find an excellent agreement between the theoretical predictions and the data obtained by means of numerical calculations. The efficiency and reliability of this method is illustrated numerically with networks of beam-plasma chaotic systems (Pierce diodes). We discuss also how the revealed regularities are expected to take place in other relevant physical and biological circumstances.     

Bistable and oscillating chemical reactions

In the last decade the number and the diversity of isothermal oscillating reactions in homogeneous aqueous solution have tremendously increased. We present an updated classified review of these chemical reactions.

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Résumé L'impossibilité d'isoler la nomenclature de la science et la science de la nomenclature tient à ce que toute science physique est nécessairement formée de trois choses: la série des faits qui constituent la science, les idées qui les rappellent, les mots qui les expriment. Le mot doit faire naître l'idée, l'idée doit peindre le fait; ce sont trois empreintes d'un même cachet; et comme ce sont les mots qui conservent les idées et qui les transmettent, il en résulte qu'on ne peut perfectionner le langage sans perfectionner la science, ni la science sans le langage, et que quelques certains que furent les faits, quelques justes que fussent les idées qu'ils auraient fait naître, ils ne transmettraient encore que des impressions fausses, si nous n'avions pas des expressions exactes pour les rendres.

     

Mixed convection of a conducting third-grade fluid past an oscillating porous plate

We study heat transfer in the incompressible flow of a conducting third-grade fluid subject to a uniform magnetic field past an oscillating porous vertical plate.We obtain the analytical form of the boundary-layer velocity profile, the temperature profile, and the skin friction coefficient for small deviations from the Newtonian rheology. We examine the dependence of these quantities on the Prandtl number, the mixed convection parameter, the Hartmann number, and the suction parameter.     

Stability criterions of an oscillating tip-cantilever system in dynamic force microscopy

This work is a theoretical investigation of the stability of the non-linear behavior of an oscillating tip-cantilever system used in dynamic force microscopy. Stability criterions are derived that may help to a better understanding of the instabilities that may appear in the dynamic modes, Tapping and NC-AFM, when the tip is close to a surface. A variational principle allows to get the temporal dependence of the equations of motion of the oscillator as a function of the non-linear coupling term. These equations are the basis for the analysis of the stability. One find that the branch associated to frequencies larger than the resonance is always stable whereas the branch associated to frequencies smaller than the resonance exhibits two stable domains and one unstable. This feature allows to re-interpret the instabilities appearing in Tapping mode and may help to understand the reason why the NC-AFM mode is stable. Received 12 April 2001     

Electrogravitational stability of oscillating streaming fluid cylinder

The electrogravitational instability of on oscillating streaming fluid cylinder under the action of the selfgravitating, capillary and electrodynamic forces has been discussed. The model is governed by the Mathieu second order integro-differential equation. Some limiting cases are recovering from the present general one. The capillary force is destabilizing in a small axisymmetric domain 0<x<1 and stabilizing otherwise. In the absence of electric fields, we found that the model is unstable in a small domain while it is selfgravitating stable in all other domains. The presence of the electric field led to the presence of a great number of stable waves. The electric field has a strong stabilizing influence on the selfgravitating instability of the model. The capillary force has a strong destabilizing influence on the selfgravitating instability of the model.Generally, the uniform stream supports the unstable waves, while the oscillating streaming has stability tendency.     

Synchronization and parameter estimations of an uncertain Rikitake system

In this Letter we address the synchronization and parameter estimation of the uncertain Rikitake system, under the assumption the state is partially known. To this end we use the master/slave scheme in conjunction with the adaptive control technique. Our control approach consists of proposing a slave system which has to follow asymptotically the uncertain Rikitake system, refereed as the master system. The gains of the slave system are adjusted continually according to a convenient adaptation control law, until the measurable output errors converge to zero. The convergence analysis is carried out by using the Barbalat's Lemma. Under this context, uncertainty means that although the system structure is known, only a partial knowledge of the corresponding parameter values is available.     

Entangling two oscillating mirrors in an optomechanical system via a flying atom

We propose a novel scheme for generating the entanglement of two oscillating mirrors in an optomechanical system via a flying atom. In this scheme, a two-level atom, in an arbitrary superposition state, passes through an optomechanical system with two oscillating cavity-mirrors, and then its states are detected. In this way, we can generate the entangled states of the two oscillating mirrors. We derive the analytical expressions of the entangled states and make numerical calculations. We find that the entanglement of the two oscillating mirrors can be controlled by the initial state of the atom,the optomechanical coupling strength, and the coupling strength between the atom and the cavity field. We investigate the dynamics of the system with dissipations and discuss the experimental feasibility.     

Pattern of flow around a sphere oscillating an neutrally buoyancy horizon in a continuously stratified fluid

The flow pattern produced by a sphere freely sinking to the neutral buoyancy horizon in a continuously stratified liquid is visualized with different schlieren methods. Dispersion of light in the brine produces colouring of conventional schlieren images when cutting diaphragm is at the edge of blade or thread and is used to form “natural rainbow” colour schlieren image. With sensitive schlieren methods a new structural element is distinguished in the flow pattern. That is a narrow jet covered with a high gradient envelope forming in the neighbourhood of the turning points on the trajectory of the oscillating body. Due to the interaction of the body with the emitted internal waves, and also with the wake and secondary jets, the rate of amplitude damping decreases with time     

Coincidence problem in an oscillating universe

We analyze an oscillating universe model in brane world cenario. The oscillating universe cycles through a series of expansions and contractions and its energy density is dominated by dust matter at early-time expansion phase and by phantom dark energy at late-time expansion phase. We find that the period of the oscillating universe is not sensitive to the tension of the brane, but sensitive to the equation-of-state parameter w of the phantom dark energy, and the ratio of the period to the current Hubble age approximately varies from 3 to 9 when the parameter w changes from −1.4 to −1.1. The fraction of time that the oscillating universe spends in the coincidence state is also comparable to the period of the oscillating universe. This result indicates that the coincidence problem can be significantly ameliorated in the oscillating universe without singularity.     

Time's arrow in an oscillating universe

In view of the time-symmetric nature of the laws of physics, time asymmetry in the universe must arise from “initial” conditions. A fully time-symmetric oscillating model is presented which exists in a highly compressed, highly ordered state att=0 and evolves forward, in the thermodynamic sense, as ∣t ∣ increases. This model offers the possibility of accounting for several fundamental and puzzling aspects of our universe, including matter-antimatter asymmetry, the large entropy per baryon, primordial density enhancements sufficient to form galaxies, and large-scale homogeneity.