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At least 811 records · Page 45Linked to original sources
PubMed2005

Twist of cholesteric liquid crystal cells: stability of helical structures and anchoring energy effects.

We consider helical configurations of a cholesteric liquid crystal (CLC) sandwiched between two substrates with homogeneous director orientation favored at both confining plates. We study the CLC twist wave number q characterizing the helical structures in relation to the free twisting number q(0) which determines the equilibrium value of CLC pitch P(0) = 2 pi/ q(0) . We investigate the instability mechanism underlying transitions between helical structures with different spiral half-turn numbers. Stability analysis shows that for equal finite anchoring strengths this mechanism can be dominated by in-plane director fluctuations. In this case the metastable helical configurations are separated by the energy barriers and the transitions can be described as the director slippage through these barriers. We extend our analysis to the case of an asymmetric CLC cell in which the anchoring strengths at the two substrates are different. The asymmetry introduces two qualitatively different effects: (a) the intervals of twist wave numbers representing locally stable configurations with adjacent helix half-turn numbers are now separated by instability gaps; and (b) sufficiently large asymmetry, when the difference between azimuthal anchoring extrapolation lengths exceeds the thickness of the cell, will suppress the jumplike behavior of the twist wave number.

Journal Article↗
PubMed2005

Nonequilibrium patterns and shape fluctuations in reactive membranes.

A simple kinetic model of a two-component deformable and reactive bilayer is presented. The two differently shaped components are interconverted by a nonequilibrium reaction, and a phenomenological coupling between local composition and curvature is proposed. When the two components are not miscible, linear stability analysis predicts, and numerical simulations show, the formation of stationary nonequilibrium composition/curvature patterns whose typical size is determined by the reactive process. For miscible components, a linearization of the dynamic equations is performed in order to evaluate the correlation function for shape fluctuations from which the behavior of these systems in micropipet aspiration experiments can be predicted.

Computer Simulation↗
PubMed2005

Stiff stability of the hydrogen atom in dissipative Fokker electrodynamics.

We introduce an ad hoc electrodynamics with advanced and retarded Liénard-Wiechert interactions plus the dissipative Lorentz-Dirac self-interaction force. We study the covariant dynamical system of the electromagnetic two-body problem, i.e., the hydrogen atom. We perform the linear stability analysis of circular orbits for oscillations perpendicular to the orbital plane. In particular, we study the normal modes of the linearized dynamics that have an arbitrarily large imaginary eigenvalue. These large eigenvalues are fast frequencies that introduce a fast (stiff) time scale into the dynamics. As an application, we study the phenomenon of resonant dissipation, i.e., a motion where both particles recoil together in a drifting circular orbit (a bound state), while the atom dissipates center-of-mass energy only. This balancing of the stiff dynamics is established by the existence of a quartic resonant constant that locks the dynamics to the neighborhood of the recoiling circular orbit. The resonance condition quantizes the angular momenta in reasonable agreement with the Bohr atom. The principal result is that the emission lines of quantum electrodynamics agree with the prediction of our resonance condition within 1% average deviation.

Journal Article↗
PubMed2005

Marangoni-driven instabilities of an evaporating liquid-vapor interface.

Marangoni-driven instabilities of a liquid-vapor interface of ethanol formed in a horizontally oriented capillary tube of 600 microm diameter are described. Instabilities of the interface are reported as well as instabilities of the liquid flow underneath the meniscus. The experimental results consist of visual observation of the interface, microscale particle image velocimetry measurements of the liquid flow and ir temperature measurements of the interface. The instabilities are found in both the flow structure and the interfacial temperature which present a periodic oscillatory pattern with a characteristic frequency of about 5 Hz. The interface also oscillates periodically, having a characteristic frequency of about 1.4 Hz. The differential evaporative cooling along the extended meniscus in the triple-line region produces a temperature difference which sustains the liquid-thermocapillary Marangoni-driven convection. A linear stability analysis based on a one-sided model, modified to take into account evaporation, is used to show that the self-induced temperature difference at the triple-line region is responsible for the observed interfacial instabilities. The instabilities in the flow pattern are due to competition between the surface tension driving force and gravity and are also found to be influenced by the meniscus instabilities.

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PubMed2005

Maxwell and very-hard-particle models for probabilistic ballistic annihilation: hydrodynamic description.

The hydrodynamic description of probabilistic ballistic annihilation, for which no conservation laws hold, is an intricate problem with hard spherelike dynamics for which no exact solution exists. We consequently focus on simplified approaches, the Maxwell and very-hard-particle (VHP) models, which allows us to compute analytically upper and lower bounds for several quantities. The purpose is to test the possibility of describing such a far from equilibrium dynamics with simplified kinetic models. The motivation is also in turn to assess the relevance of some singular features appearing within the original model and the approximations invoked to study it. The scaling exponents are first obtained from the (simplified) Boltzmann equation, and are confronted against direct Monte Carlo simulations. Then, the Chapman-Enskog method is used to obtain constitutive relations and transport coefficients. The corresponding Navier-Stokes equations for the hydrodynamic fields are derived for both Maxwell and VHP models. We finally perform a linear stability analysis around the homogeneous solution, which illustrates the importance of dissipation in the possible development of spatial inhomogeneities.

Journal Article↗
PubMed2005

Layered synchronous propagation of noise-induced chaotic spikes in linear arrays.

Stable propagation of noise-induced synchronous spiking in uncoupled linear neuron arrays is studied numerically. The chaotic neurons in the unidirectionally coupled linear array are modeled by Hindmarsh-Rose neurons. Stability analysis shows that the synchronous chaotic spiking can be successfully transmitted to cortical areas through layered synchronization in the neural network under certain conditions of the network structure.

Action Potentials↗
PubMed2005

Turing pattern formation in fractional activator-inhibitor systems.

Activator-inhibitor systems of reaction-diffusion equations have been used to describe pattern formation in numerous applications in biology, chemistry, and physics. The rate of diffusion in these applications is manifest in the single parameter of the diffusion constant, and stationary Turing patterns occur above a critical value of d representing the ratio of the diffusion constants of the inhibitor to the activator. Here we consider activator-inhibitor systems in which the diffusion is anomalous subdiffusion; the diffusion rates are manifest in both a diffusion constant and a diffusion exponent. A consideration of this problem in terms of continuous-time random walks with sources and sinks leads to a reaction-diffusion system with fractional order temporal derivatives operating on the spatial Laplacian. We have carried out an algebraic stability analysis of the homogeneous steady-state solution in fractional activator-inhibitor systems, with Gierer-Meinhardt reaction kinetics and with Brusselator reaction kinetics. For each class of reaction kinetics we identify a Turing instability bifurcation curve in the two-dimensional diffusion parameter space. The critical value of d , for Turing instabilities, decreases monotonically with the anomalous diffusion exponent between unity (standard diffusion) and zero (extreme subdiffusion). We have also carried out numerical simulations of the governing fractional activator-inhibitor equations and we show that the Turing instability precipitates the formation of complex spatiotemporal patterns. If the diffusion of the activator and inhibitor have the same anomalous scaling properties, then the surface profiles of these patterns for values of d slightly above the critical value varies from smooth stationary patterns to increasingly rough and nonstationary patterns as the anomalous diffusion exponent varies from unity towards zero. If the diffusion of the activator is anomalous subdiffusion but the diffusion of the inhibitor is standard diffusion, we find stable stationary Turing patterns for values of d well below the threshold values for pattern formation in standard activator-inhibitor systems.

Journal Article↗
PubMed2005

Dispersion curves in the diffusional instability of autocatalytic reaction fronts.

A (linear) stability analysis of planar reaction fronts to transverse perturbations is considered for systems based on cubic autocatalysis and a model for the chlorite-tetrathionate reaction. Dispersion curves (plots of the growth rate sigma against a transverse wave-number k) are obtained. In both cases it is seen that there is a nonzero value D0 of D (the ratio of the diffusion coefficients of autocatalyst and substrate) at which sigma(max), the maximum value of sigma for a given value of D, achieves its largest value, with sigma(max) being less for other values of D and becoming small as D decreases to zero. The existence of the optimum value D0 for initiating a diffusional instability is confirmed, in the cubic autocatalysis case, by an asymptotic analysis for small wave numbers.

Journal Article↗
PubMed2005

Pattern-forming instabilities in nematic liquid crystals under oscillatory Couette flow.

We consider instabilities, either homogeneous or periodic in space, which develop in a nematic liquid crystal layer under rectilinear oscillatory Couette flow for planar surface alignment of the director perpendicular to the flow plane. On the basis of a numerical and analytical linear stability analysis we determine the critical amplitude of the oscillatory flow, the wave number, and the symmetry of the destabilizing mode and present a comprehensive phase diagram of the flow instabilities. In particular it is found that by varying the frequency of the Couette flow the instability changes its temporal symmetry. This transition is shown to be related to the inertia effects of the nematic fluid, which become more important with increasing flow frequency. We also show that an electric field applied perpendicularly to the nematic layer can induce an exchange of instabilities with different spatial and temporal symmetries. The theoretical results are compared with experiments, when available.

Journal Article↗
PubMed2005

Galerkin model for Turing patterns on a sphere.

We carry out a Lorenz-like truncation of reaction diffusion systems to investigate pattern formation on a spherical surface. Stability analysis suggests spots to be favored more than stripes in general. Numerical calculations on the truncated model are in agreement with the theoretical predictions.

Journal Article↗
PubMed2005

Spatiotemporal characterization of interfacial Faraday waves by means of a light absorption technique.

We present measurements of the complete spatiotemporal Fourier spectrum of Faraday waves. The Faraday waves are generated at the interface of two immiscible index matched liquids of different density. By use of a light absorption technique we are able to determine the bifurcation scenario from the flat surface to the patterned state for each complex spatial and temporal Fourier component separately. The surface spectra at onset are found to be in good agreement with the predictions from the linear stability analysis. For the nonlinear state our measurements show in a direct manner how energy is transferred from lower to higher harmonics and we quantify the nonlinear coupling coefficients. Furthermore we find that the nonlinear coupling generates static components in the temporal Fourier spectrum leading thus to a contribution of a nonoscillating permanent sinusoidal deformed surface state. A comparison of hexagonal and rectangular patterns reveals that spatial resonance can give rise to a spectrum that violates the temporal resonance conditions given by the weakly nonlinear theory.

Journal Article↗
PubMed2005

Modulational instability and unstable patterns in the discrete complex cubic Ginzburg-Landau equation with first and second neighbor couplings.

The generation of nonlinear modulated waves is investigated in the framework of hydrodynamics using a model of coupled oscillators. In this model, the separatrices between each pair of vortices may be viewed as individual oscillators and are described by a phenomenological one-dimensional discrete complex Ginzburg-Landau equation involving first- and second-nearest neighbor couplings. A theoretical approach based on the linear stability analysis predicts regions of modulational instability, governed by both the first and second-nearest neighbor couplings. From numerical investigations of different wave patterns that may be driven by the modulational instability, it appears that analytical predictions are correctly verified. For wave number in the unstable regions, an initial condition whose amplitude is slightly modulated breaks into a train of unstable patterns. This phenomenon agrees with the description of amplification of the spectral component of the perturbation and its harmonics, as well.

Journal Article↗
PubMed2005

Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh.

A numerical model of the lattice Boltzmann method (LBM) utilizing least-squares finite-element method in space and the Crank-Nicolson method in time is developed. This method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite-element method, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow, and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility.

Journal Article↗
PubMed2005

Generation of dynamic structures in nonequilibrium reactive bilayers.

We present a nonequlibrium approach for the study of a flexible bilayer whose two components induce distinct curvatures. In turn, the two components are interconverted by an externally promoted reaction. Phase separation of the two species in the surface results in the growth of domains characterized by different local composition and curvature modulations. This domain growth is limited by the effective mixing due to the interconversion reaction, leading to a finite characteristic domain size. In addition to these effects, first introduced in our earlier work [Phys. Rev. E 71, 051906 (2005)], the important new feature is the assumption that the reactive process actively affects the local curvature of the bilayer. Specifically, we suggest that a force energetically activated by external sources causes a modification of the shape of the membrane at the reaction site. Our results show the appearance of a rich and robust dynamical phenomenology that includes the generation of traveling and/or oscillatory patterns. Linear stability analysis, amplitude equations, and numerical simulations of the model kinetic equations confirm the occurrence of these spatiotemporal behaviors in nonequilibrium reactive bilayers.

Computer Simulation↗
PubMed2005

Fine structure generation in a double-diffusive system.

Double-diffusive convection in a horizontally infinite layer of a unit height in a large-Rayleigh-number limit is considered. From linear stability analysis it is shown that the convection tends to have a form of traveling tall thin rolls with width about 30 times less than height. Amplitude equations of type for vertical variations of the amplitude of these rolls and mean values of diffusive components are derived. As a result of its numerical simulation it is shown that for a wide variety of parameters considered system have solutions, known as diffusive chaos, which can be useful for the explanation of fine structure generation in some important oceanographical systems like thermohaline staircases.

Journal Article↗
PubMed2005

MRI measurements of an acoustically cavitated fluid in a standing wave.

Double-diffusive convection in a horizontally infinite layer of a unit height in a large-Rayleigh-number limit is considered. From linear stability analysis it is shown that the convection tends to have a form of traveling tall thin rolls with width about 30 times less than height. Amplitude equations of ABC type for vertical variations of the amplitude of these rolls and mean values of diffusive components are derived. As a result of its numerical simulation it is shown that for a wide variety of parameters considered ABC system have solutions, known as diffusive chaos, which can be useful for the explanation of fine structure generation in some important oceanographical systems like thermohaline staircases.

Journal Article↗
PubMed2005

Partial amplitude death in coupled chaotic oscillators.

We have investigated the dynamics of the coupled Lorenz oscillators numerically and theoretically. We find the partial amplitude death when the interaction is strong enough. The linear stability analysis of the partial amplitude death is proposed.

Journal Article↗
PubMed2005

Bulk electroconvection in electrolyte.

Bulk electroconvection pertains to flow induced by the action of the mean electric field upon the residual space charge in the macroscopic regions of a locally quasielectroneutral strong electrolyte. There existed a long time controversy in the literature as to whether quiescent electric conduction from such an electrolyte into a uniform charge selective solid, such as a metal electrode or an ion exchange membrane, is stable with respect to bulk electroconvection and whether bulk electroconvection at a nonuniform solid of this type may develop into a fully fledged flow. Numerical results reported in this paper confirm previous conclusions of a linear stability analysis concerning the nonexistence of bulk electroconvective instability, while we suggest that bulk electroconvection at a nonuniform charge selective solid results in a fully fledge flow on the length scale of nonuniformity of the surface.

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