Showing papers in "Physical Review E in 1993"

Lattice Boltzmann model for simulating flows with multiple phases and components

Abstract: A lattice Boltzmann model is developed which has the ability to simulate flows containing multiple phases and components. Each of the components can be immiscible with the others and can have different mass values. The equilibrium state of each component can have a nonideal gas equation of state at a prescribed temperature exhibiting thermodynamic phase transitions. The scheme incorporated in this model is the introduction of an interparticle potential. The dynamical rules in this model are local so it is highly efficient to compute on massively parallel computers. This model has many applications in large-scale numerical simulations of various types of fluid flows.

Extended self-similarity in turbulent flows

Abstract: We report on the existence of a hitherto undetected form of self-similarity, which we call extended self-similarity (ESS). ESS holds at high as well as at low Reynolds number, and it is characterized by the same scaling exponents of the velocity differences of fully developed turbulence.

Simulation of the differential adhesion driven rearrangement of biological cells

Abstract: We show that differential adhesion with fluctuations is sufficient to explain a wide variety of cell re- arrangement, by using the extended large-Q Potts model with differential adhesivity to simulate different biological phenomena. Different values of relative surface energies correspond to different biological cases, including complete and partial cell sorting, checkerboard, position reversal, and dispersal. We examine the convergence and temperature dependence of the simulation and distinguish spontaneous, neutral, and activated processes by performing simulations at different temperatures. We discuss the biological and physical implications of our quantitative results.

Cluster effect in initially homogeneous traffic flow.

Abstract: This paper presents the nonlinear cluster effect in initially homogeneous traffic flow. It is shown that, in an initially homogeneous traffic flow, a region of high density and low average velocity of cars can spontaneously appear, if the density of cars in the flow exceeds some critical value. This region, a cluster of cars, can move with constant velocity in the opposite direction or in the direction of the flow, depending on the selected parameters and the initial conditions of the traffic flow. Based on numerical simulations, the kinetics of cluster formation and the shape of stationary moving clusters are found. These results can explain the spontaneous appearance of a traffic congestion, or phantom traffic jam, that appears in real traffic flow without obvious reasons.

Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method

Abstract: Several attempts have been made recently to generalize the multifractal formalism, originally introduced for singular measures, to fractal signals. We report on a systematic comparison between the structure-function approach, pioneered by Parisi and Frisch [in 2 Proceedings of the International School on Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, edited by M. Ghil, R. Benzi, and G. Parisi (North-Holland, Amsterdam, 1985), p. 84] to account for the multifractal nature of fully developed turbulent signals, and an alternative method we have developed within the framework of the wavelet-transform analysis. We comment on the intrinsic limitations of the structure-function approach; this technique has fundamental drawbacks and does not provide a full characterization of the singularities of a signal in many cases. We demonstrate that our method, based on the wavelet-transform modulus-maxima representation, works in most situations and is likely to be the ground of a unified multifractal description of self-affine distributions. Our theoretical considerations are both illustrated on pedagogical examples and supported by numerical simulations.

Asynchronous states in networks of pulse-coupled oscillators.

Abstract: We use a mean-field approach to analyze the stability of the asynchronous state in a population of all-to-all, pulse-coupled, nonlinear oscillators. We determine the conditions that must be satisfied by the time constants and phase dependence characterizing the coupling between the oscillators in order for the asynchronous state to be stable. We also consider the effects of noise. This work complements results on synchronous states in similar models and allows us to study the validity of firing-rate models commonly used for neural networks.

Initial and boundary conditions for the lattice Boltzmann method.

Abstract: An alternative approach of implementing initial and boundary conditions for the lattice Boltzmann method is presented. The basic idea is to calculate the lattice Boltzmann populations at a boundary node from the fluid variables that are specified at this node using the gradients of the fluid velocity. The numerical performance of the lattice Boltzmann method is tested on several problems with exact solutions and is also compared to an explicit finite-difference projection method. The discretization error of the lattice Boltzmann method decreases quadratically with finer resolution both in space and in time. The roundoff error of the lattice Boltzmann method creates problems unless double-precision arithmetic is used.

Entropy-driven DNA denaturation.

Abstract: We present a nonlinear dynamical model for DNA denaturation which includes cooperativity effects through anharmonic nearest-neighbor stacking interactions. Transfer-integral calculations show that this one-dimensional model, without including long-range interactions, exhibits a sharp denaturation reminiscent of a first-order transition at a temperature lower than a similar model with harmonic coupling. Self-consistent phonon calculations point out the essential role of nonlinear effects in the mechanism.

Theory of continuum random walks and application to chemotaxis

Abstract: We formulate the general theory of random walks in continuum, essential for treating a collision rate which depends smoothly upon direction of motion We also consider a smooth probability distribution of correlations between the directions of motion before and after collisions, as well as orientational Brownian motion between collisions These features lead to an effective Smoluchowski equation Such random walks involving an infinite number of distinct directions of motion cannot be treated on a lattice, which permits only a finite number of directions of motion, nor by Langevin methods, which make no reference to individual collisions The effective Smoluchowski equation enables a description of the biased random walk of the bacterium Escherichia coli during chemotaxis, its search for food The chemotactic responses of cells which perform temporal comparisons of the concentration of a chemical attractant are predicted to be strongly positive, whereas those of cells which measure averages of the ambient attractant concentration are predicted to be negative The former prediction explains the observed behavior of wild-type (naturally occurring) cells; however, the latter behavior has yet to be observed, even in cells defective in adaption

Nonlinear Thomson scattering of intense laser pulses from beams and plasmas

Abstract: A comprehensive theory is developed to describe the nonlinear Thomson scattering of intense laser fields from beams and plasmas. This theory is valid for linearly or circularly polarized incident laser fields of arbitrary intensities and for electrons of arbitrary energies. Explicit expressions for the intensity distributions of the scattered radiation are calculated and numerically evaluated. The space-charge electrostatic potential, which is important in high-density plasmas and prevents the axial drift of electrons, is included self-consistently. Various properties of the scattered radiation are examined, including the linewidth, angular distribution, and the behavior of the radiation spectra at ultrahigh intensities. Nonideal effects, such as electron-energy spread and beam emittance, are discussed. A laser synchrotron source (LSS), based on nonlinear Thomson scattering, may provide a practical method for generating tunable, near-monochromatic, well-collimated, short-pulse x rays in a compact, relatively inexpensive source. Two examples of possible LSS configurations are presented: an electron-beam LSS generating hard (30-keV, 0.4-\AA{}) x rays and a plasma LSS generating soft (0.3-keV, 40-\AA{}) x rays. These LSS configurations are capable of generating ultrashort (\ensuremath{\sim}1-ps) x-ray pulses with high peak flux (\ensuremath{\gtrsim}${10}^{21}$ photons/s) and brightness [\ensuremath{\gtrsim}${10}^{19}$ photons /(s ${\mathrm{mm}}^{2}$ ${\mathrm{mrad}}^{2}$), 0.1% bandwidth].

Lattice Boltzmann thermohydrodynamics.

Abstract: We introduce a lattice Boltzmann computational scheme capable of modeling thermohydrodynamic flows of monatomic gases. The parallel nature of this approach provides a numerically efficient alternative to traditional methods of computational fluid dynamics. The scheme uses a small number of discrete velocity states and a linear, single-time relaxation collision operator. Numerical simulations in two dimensions agree well with exact solutions for adiabatic sound propagation and Couette flow with heat transfer.

Structural changes accompanying densification of random hard-sphere packings

Abstract: Local icosahedral order is found to increase as random hard-sphere packings (one- and two-component) generated on the computer are densified from the (recently established) ``loose random-packing'' limit to the ``dense random-packing'' limit. While icosahedral ordering in ``atomic'' systems is frequently ascribed to the energetic stability of icosahedral clusters, the present results show that icosahedral ordering can arise from packing constraints alone. However, the icosahedra are often distorted, partly due to the lack of preferred distance between hard spheres. At high density one-third to one-half of the pairs in the first peak of the radial distribution function (RDF) are icosahedral fragments. The splitting of the second peak, which is characteristic of packings of spherical particles, was studied by decomposing the RDF into components according to the local environment of the pairs. Linear trimers of spheres are responsible for the second subpeak while the first subpeak arises roughly equally from tetrahedra sharing a face and triangles with adjacent sides. The hard-sphere packings were compared with packings of soft, attracting spheres by relaxing the configurations under a Lennard-Jones potential. The fraction of pairs characteristic of local crystalline order in the first peak of the RDF was found to increase. The reversal of the relative height of the two parts of the split second peak results from a broadening of the distribution of distances within the linear trimers, while the distribution sharpens for the face sharing tetrahedra and adjacent triangles.

Dynamics and thermodynamics of a nonlinear model for DNA denaturation.

Abstract: We present a model for the dynamical structure of DNA that can be considered as an extension of the usual Ising-like statistical approach to the melting curves. The model uses the stretching of the hydrogen bonds in a base pair as its main variable. Numerical simulations at constrained temperature show that it provides a good qualitative description of the collective motions of the base pairs, including their large-amplitude fluctuational openings and the emergence of the denaturation bubbles from the thermal fluctuations. The results are in good agreement with a statistical-mechanics analysis of the denaturation and specific-heat curves, performed with the transfer-integral method, provided that discreteness effects are treated exactly by a numerical solution of the transfer-integral operator. Second-order self-consistent phonon theory agrees with the exact transfer-integral results in the low- and intermediate-temperature ranges and explains the phonon softening observed in the molecular-dynamics simulations. When the temperature approaches the denaturation temperature, the second-order self-consistent phonon results deviate significantly from the exact ones, pointing to the fundamental role of nonlinear processes in DNA denaturation.

Phase-field models for anisotropic interfaces.

Abstract: The inclusion of anisotropic surface free energy and anisotropic linear interface kinetics in phase-field models is studied for the solidification of a pure material. The formulation is described for a two-dimensional system with a smooth crystal-melt interface and for a surface free energy that varies smoothly with orientation, in which case a quite general dependence of the surface free energy and kinetic coefficient on orientation can be treated; it is assumed that the anisotropy is mild enough that missing orientations do not occur. The method of matched asymptotic expansions is used to recover the appropriate anisotropic form of the Gibbs-Thomson equation in the sharp-interface limit in which the width of the diffuse interface is thin compared to its local radius of curvature. It is found that the surface free energy and the thickness of the diffuse interface have the same anisotropy, whereas the kinetic coefficient has an anisotropy characterized by the product of the interface thickness with the intrinsic mobility of the phase field.

Collective effects due to charge-fluctuation dynamics in a dusty plasma.

Abstract: Highly charged dust grains immersed in a plasma can exhibit charge fluctuations in response to oscillations in the plasma currents flowing into them. This introduces a new physical effect, namely, the electric charge on the dust particles becomes time dependent and a self-consistent dynamical variable. The consequent modifications in the collective properties of a dusty plasma are investigated. It is shown that these effects lead to dissipative and instability mechanisms for ion waves in the plasma and can lead to interesting applications to many laboratory and astrophysical situations.

Electrostatic oscillations in the presence of grain-charge perturbations in dusty plasmas

Abstract: The properties of electrostatic oscillations and instability phenomena are studied, accounting for the time-dependent variation of the grain electric charge due to wave motions in an unmagnetized dusty plasma. It is found that charge fluctuations on the dust grains give rise to two purely damped modes, in addition to causing a collisionless damping of the existing normal modes. Furthermore, some interesting electrostatic instabilities arise in the presence of an equilibrium drift of charged fluids.

Scale-invariant motion in intermittent chaotic systems

Abstract: We investigate the dynamics generated from iterated maps and analyze the motion in terms of the probabilistic continuous-time random-walk (CTRW) approach. Two different CTRW models are considered: (i) Particles jump between sites (turning points) or (ii) particles move at a constant velocity between sites and choose a new direction at random. For both models we study the mean-squared displacement 〈${\mathit{r}}^{2}$(t)〉 and the propagator P(r,t), the probability to be at location r at time t having started at the origin at t=0. Iterated maps are used to generate both dispersive and enhanced diffusion and the results are analyzed using the CTRW framework and scaling arguments. For the case of dispersive motion we discuss the problem of the stationary state and point out its relevance.

RNA folding and combinatory landscapes.

Abstract: In this paper we view the folding of polynucleotide (RNA) sequences as a map that assigns to each sequence a minimum-free-energy pattern of base pairings, known as secondary structure. Considering only the free energy leads to an energy landscape over the sequence space. Taking into account structure generates a less visualizable nonscalar landscape,'' where a sequence space is mapped into a space of discrete shapes.'' We investigate the statistical features of both types of landscapes by computing autocorrelation functions, as well as distributions of energy and structure distances, as a function of distance in sequence space. RNA folding is characterized by very short structure correlation lengths compared to the diameter of the sequence space. The correlation lengths depend strongly on the size and the pairing rules of the underlying nucleotide alphabet. Our data suggest that almost every minimum-free-energy structure is found within a small neighborhood of any random sequence. The interest in such landscapes results from the fact that they govern natural and artificial processes of optimization by mutation and selection. Simple statistical model landscapes, like Kauffman and Levin's [ital n]-[ital k] model [J. Theor. Biol. 128, 11 (1987)], are often used as a proxy for understanding realistic landscapes, likemore » those induced by RNA folding. We make a detailed comparison between the energy landscapes derived from RNA folding and those obtained from the [ital n]-[ital k] model. We derive autocorrelation functions for several variants of the [ital n]-[ital k] model, and briefly summarize work on its fine structure. The comparison leads to an estimate for [ital k]=7--8, independent of [ital n], where [ital n] is the chain length. While the scaling behaviors agree, the fine structure is considerably different in the two cases.« less

Noise reduction in chaotic time-series data: A survey of common methods.

Abstract: This paper surveys some of the methods that have been suggested for reducing noise in time-series data whose underlying dynamical behavior can be characterized as low-dimensional chaos. Although the procedures differ in details, all of them must solve three basic problems: how to reconstruct an attractor from the data, how to approximate the dynamics in various regions on the attractor, and how to adjust the observations to satisfy better the approximations to the dynamics. All current noise-reduction methods have similar limitations, but the basic problems are reasonably well understood. The methods are an important tool in the experimentalist's repertoire for data analysis. In our view, they should be used more widely, particularly in studies of attractor dimension, Lyapunov exponents, prediction, and control.

Measurement of the persistence length of polymerized actin using fluorescence microscopy

Abstract: Single actin filaments were confined between bovine-serum-albumine-coated glass plates, with a separation of about 1 \ensuremath{\mu}m, and their flickering Brownian movement was observed by fluorescence microscopy. The rigidity of the filaments was measured by extracting the correlation function given by the mean dot product between unit tangent vectors of an isolated filament. The result is consistent with current rigidity values found in the literature.

Finite-size effects on long-range correlations: Implications for analyzing DNA sequences

Abstract: We analyze the fluctuations in the correlation exponents obtained for noncoding DNA sequences We find prominent sample-to-sample variations as well as variations within a single sample in the scaling exponent To determine if these fluctuations may result from finite system size, we generate correlated random sequences of comparable length and study the fluctuations in this control system We find that the DNA exponent fluctuations are consistent with those obtained from the control sequences having long-range power-law correlations Finally, we compare our exponents for the DNA sequences with the exponents obtained from power-spectrum analysis and correlation-function techniques, and demonstrate that the original "DNA-walk" method is intrinsically more accurate due to reduced noise

Filtered Noise Can Mimic Low-Dimensional Chaotic Attractors

Abstract: This contribution presents four results. First, calculations indicate that when examined by the Grassberger-Procaccia algorithm alone, filtered noise can mimic low-dimensional chaotic attractors. Given the ubiquity of signal filtering in experimental investigations, this is potentially important. Second, a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor. Third, it is shown that a criterion derived by Eckmann and Ruelle [Physica D 56, 185 (1992)] to estimate the minimum number of data points required in a Grassberger-Procaccia calculation can be used to provide a further check on these dimension estimates. Fourth, it is shown that surrogate data techniques recently published by Theiler and his colleagues [in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubanks (Addison Wesley, Reading, MA, 1992)] can successfully distinguish between linearly correlated noise and nonlinear structure. These results, and most particularly the first, indicate that Grassberger-Procaccia results must be interpreted with far greater circumspection than has previously been the case, and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data. When filtered signals are examined by this algorithm alone, a finite noninteger value of ${\mathit{D}}_{2}$ is consistent with low-dimensional chaotic behavior, but it is certainly not a definitive diagnostic of chaos.

Clustering and slow switching in globally coupled phase oscillators

Abstract: We consider a network of globally coupled phase oscillators. The interaction between any two of them is derived from a simple model of weakly coupled biological neurons and is a periodic function of the phase difference with two Fourier components. The collective dynamics of this network is studied with emphasis on the existence and the stability of clustering states. Depending on a control parameter, three typical types of dynamics can be observed at large time: a fully synchronized state of the network (one-cluster state), a totally incoherent state, and a pair of two-cluster states connected by heteroclinic orbits. This last regime is particularly sensitive to noise. Indeed, adding a small noise gives rise, in large networks, to a slow periodic oscillation between the two two-cluster states. The frequency of this oscillation is proportional to the logarithm of the noise intensity. These switching states should occur frequently in networks of globally coupled oscillators.

Extremely simple nonlinear noise-reduction method.

Abstract: A very simple method to reduce noise in experimental data with nonlinear time evolution is presented. Locally constant fits are used to obtain a less noisy trajectory consistent with the dynamics as well as with the measured data. Neighborhoods are defined by coordinates both from the past and from the future. The method is applied to the H\'enon map and to a discretized form of the Mackey-Glass equation.

Lattice Bhatnagar-Gross-Krook models for miscible fluids

Abstract: Lattice Bhatnagar-Gross-Krook models for miscible fluid flow in two (2D) and three (3D) dimensions are introduced. The convection-diffusion (CD) equation and the Navier-Stokes (NS) equation describing the macroscopic behavior of the models are derived using the Chapman-Enskog expansion technique. Corrections to the CD equation of higher order in the flow velocity are obtained, and it is shown how the present models are linked with the existing Boltzmann model. It is also shown how the Navier-Stokes dynamics is explicitly decoupled from the diffusive behavior of the model. The results obtained from both 2D and 3D simulations are observed to be in excellent agrement with the analytic predictions. In particular it is shown that the models are well described by theory for high-P\'eclet-number flows. We also present simulation results confirming the anomalous (but small) velocity dependence of the CD equation, and we investigate the models' sensitivity to large gradients in the concentration profile.

Self-similar transport in incomplete chaos.

Abstract: Particle chaotic dynamics along a stochastic web is studied for three-dimensional Hamiltonian flow with hexagonal symmetry in a plane. Two different classes of dynamical motion, obtained by different values of a control parameter, and corresponding to normal and anomalous diffusion, have been considered and compared. It is shown that the anomalous transport can be characterized by powerlike wings of the distribution function of displacement, flights which are similar to L\'evy flights, approximate trappings of orbits near the boundary layer of islands, and anomalous behavior of the moments of a distribution function considered as a function of the number of the moment. The main result is related to the self-similar properties of different topological and dynamical characteristics of the particle motion. This self-similarity appears in the Weierstrass-like random-walk process that is responsible for the anomalous transport exponent in the mean-moment dependence on t. This exponent can be expressed as a ratio of fractal dimensions of space and time sets in the Weierstrass-like process. An explicit form for the expression of the anomalous transport exponent through the local topological properties of orbits has been given.

Volume-fraction dependence of elastic moduli and transition temperatures for colloidal silica gels.

Abstract: Colloidal silica spheres bearing grafted octadecyl chains dispersed in hexadecane undergo a sol-gel transition with decreasing temperature. The gelation temperature depends on the volume fraction \ensuremath{\varphi} and, perhaps, the particle size. For \ensuremath{\varphi}g${\mathrm{\ensuremath{\varphi}}}_{gel}$(T), the value at the transition, the elastic modulus varies as (\ensuremath{\varphi}-${\mathrm{\ensuremath{\varphi}}}_{gel}$${)}^{\mathit{s}}$ with the prefactor and exponent independent of temperature. This form resembles prediction from static percolation theories, but the exponent s=3.0\ifmmode\pm\else\textpm\fi{}0.5 lies significantly below those expected and the transition volume fraction varies with temperature. The relationship of the gelation transition to dynamic percolation and phase transitions predicted by equilibrium statistical mechanics has also been addressed. Matching the calculated structure factor for adhesive spheres with that measured by static light scattering yields the unknown strength of the interparticle attraction as a function of temperature. Though an imperfect fit introduces considerable uncertainty, this empirical relationship distinguishes the gel transition from both the dynamic percolation threshold and the spinodal associated with the fluid-fluid transition for adhesive spheres. Thus we conclude that gelation in this colloidal dispersion corresponds to a metastable state lying between the fluid-solid phase boundary and the spinodal.

Local false nearest neighbors and dynamical dimensions from observed chaotic data.

Abstract: The time delay reconstruction of the state space of a system from observed scalar data requires a time lag and an integer embedding dimension. The minimum necessary global embedding dimension ${\mathit{d}}_{\mathit{E}}$ may still be larger than the actual dimension of the underlying dynamics ${\mathit{d}}_{\mathit{L}}$. The embedding theorem only guarantees that the attractor of the system is fully unfolded using ${\mathit{d}}_{\mathit{E}}$ greater than 2${\mathit{d}}_{\mathit{A}}$, with ${\mathit{d}}_{\mathit{A}}$ the fractal attractor dimension. Using the idea of local false nearest neighbors, we discuss methods for determining the integer-valued ${\mathit{d}}_{\mathit{L}}$.