Showing papers in "Physical Review E in 1997"

Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation

Abstract: In this paper, the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. Various approximations for the discretization of the Boltzmann equation in both time and phase space are discussed in detail. A general procedure to derive the lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly. The lattice Boltzmann models derived include the two-dimensional 6-bit, 7-bit, and 9-bit, and three-dimensional 27-bit models.

Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach

Abstract: In has recently been shown that the Helmholtz free-energy difference between two equilibrium configurations of a system may be obtained from an ensemble of finite-time (nonequilibrium) measurements of the work performed in switching an external parameter of the system. Here this result is established, as an identity, within the master equation formalism. Examples are discussed and numerical illustrations provided.

Dynamics and thermodynamics of complex fluids. I. Development of a general formalism

Abstract: We recognize some universal features of macroscopic dynamics describing the approach of a well-established level of description (that is, successfully tested by experimental observations) to equilibrium. The universal features are collected in a general equation for the nonequilibrium reversible-irreversible coupling (abbreviated as GENERIC). In this paper we formulate a GENERIC, derive properties of its solutions, and discuss their physical interpretation. The relation of the GENERIC with thermodynamics is most clearly displayed in a formulation that uses contact structures. The GENERIC is also discussed in the presence of noise. In applications we either search for new governing equations expressing our insight into a particular complex fluid or take well-established governing equations and cast them into the form of a GENERIC. In the former case we obtain the governing equations as particular realizations of the GENERIC structure; in the latter case we justify the universality of the GENERIC and derive some properties of solutions. Both types of applications are discussed mainly in the following paper [Phys. Rev. E 56, 6633 (1997)].

A priori derivation of the lattice Boltzmann equation

Abstract: The lattice Boltzmann equation (LBE) is directly derived from the Boltzmann equation by discretization in both time and phase space. A procedure to systematically derive discrete velocity models is presented. A LBE algorithm with arbitrary mesh grids is proposed and a numerical simulation of the backward-facing step is conducted. The numerical result agrees well with experimental and previous numerical results. Various improvements on the LBE models are discussed, and an explanation of the instability of the existing LBE thermal models is also provided.

Interface and chain confinement effects on the glass transition temperature of thin polymer films

Abstract: We have used Brillouin light scattering and ellipsometry to measure the glass transition temperature ${T}_{g}$ of thin polystyrene (PS) films as a function of the film thickness $h$ for two different molecular weights ${M}_{w}.$ Three different film geometries were studied: freely standing films, films supported on a ${\mathrm{SiO}}_{x}$ surface with the other film surface free (uncapped supported), and films supported on a ${\mathrm{SiO}}_{x}$ surface and covered with a ${\mathrm{SiO}}_{x}$ layer (capped supported). For freely standing films ${T}_{g}$ is reduced dramatically from the bulk value by an amount that depends on both $h$ and ${M}_{w}.$ For $h\ensuremath{\lesssim}{R}_{\mathrm{EE}}$ (the average end-to-end distance of the unperturbed polymer molecules), ${T}_{g}$ decreases linearly with decreasing $h$ with reductions as large as 60 K for both ${M}_{w}$ values. We observe a large ${M}_{w}$ dependence of the ${T}_{g}$ reductions for freely standing films which provides the first strong evidence of the importance of chain confinement effects on the glass transition temperature of thin polymer films. For both the uncapped and capped supported films, ${T}_{g}$ is reduced only slightly $(l10\mathrm{K})$ from the bulk value, with only small differences in ${T}_{g}$ $(l4\mathrm{K})$ observed between uncapped and capped supported films of the same thickness. The results of our experiments demonstrate that the polymer-substrate interaction is the dominant effect in determining the glass transition temperature of PS films supported on ${\mathrm{SiO}}_{x}.$

Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism

Abstract: For a number of well-known time-evolution equations for nonequilibrium systems we extract a common structure from these equations, referred to as a general equation for the nonequilibrium reversible-irreversible coupling (GENERIC). This fundamental structure is determined by four building blocks, two ``potentials'' (total energy and entropy) and two ``matrices.'' We illustrate for various examples how three of the four building blocks can be determined in a rather straightforward manner so that, within our GENERIC approach to nonequilibrium dynamics, understanding of a given nonequilibrium system is reduced to determining a single ``metric matrix,'' or friction matrix, either empirically or by more microscopic considerations. In formulating nonisothermal polymer kinetic theories, we show how the general structure provides a clear distinction between spring potentials of energetic and entropic origins in the various time-evolution equations.

Mechanics with fractional derivatives

Abstract: Lagrangian and Hamiltonian mechanics can be formulated to include derivatives of fractional order [F. Riewe, Phys. Rev. 53, 1890 (1996)]. Lagrangians with fractional derivatives lead directly to equations of motion with nonconservative classical forces such as friction. The present work continues the development of fractional-derivative mechanics by deriving a modified Hamilton's principle, introducing two types of canonical transformations, and deriving the Hamilton-Jacobi equation using generalized mechanics with fractional and higher-order derivatives. The method is illustrated with a frictional force proportional to velocity. In contrast to conventional mechanics with integer-order derivatives, quantization of a fractional-derivative Hamiltonian cannot generally be achieved by the traditional replacement of momenta with coordinate derivatives. Instead, a quantum-mechanical wave equation is proposed that follows from the Hamilton-Jacobi equation by application of the correspondence principle.

Energy flow, partial equilibration, and effective temperatures in systems with slow dynamics

Abstract: We show that, in nonequilibrium systems with small heat flows, there is a time-scale-dependent effective temperature that plays the same role as the thermodynamical temperature in that it controls the direction of heat flows and acts as a criterion for thermalization. We simultaneously treat the case of stationary systems with weak stirring and of glassy systems that age after cooling and show that they exhibit very similar behavior provided that time dependences are expressed in terms of the correlations of the system. We substantiate our claims with examples taken from solvable models with nontrivial low-temperature dynamics, but argue that they have a much wider range of validity. We suggest experimental checks of these ideas.

Metastable states in a microscopic model of traffic flow

Abstract: It is a well known fact that metastable states of very high throughput and hysteresis effects exist in traffic flow, which the simple cellular automaton model of traffic flow and its continuous generalization fail to reproduce. It is shown that the model can be generalized to give a one-parametric family of models, a part of which reproduces the metastable states and the hysteresis. The models that have that property and those that do not that are separated by a transition that can be clearly identified.

Pruned-enriched Rosenbluth method: Simulations of θ polymers of chain length up to 1 000 000

Abstract: We present an algorithm for simulating flexible chain polymers. It combines the Rosenbluth-Rosenbluth method with recursive enrichment. Although it can be applied also in more general situations, it is most efficient for three-dimensional {theta} polymers on the simple-cubic lattice. There it allows high statistics simulations of chains of length up to N=10{sup 6}. For storage reasons, this is feasable only for polymers in a finite volume. For free {theta} polymers in infinite volume, we present very high statistics runs with N=10000. These simulations fully agree with previous simulations made by Hegger and Grassberger [J. Chem. Phys. {bold 102}, 6681 (1995)] with a similar but less efficient algorithm, showing that logarithmic corrections to mean field behavior are much stronger than predicted by field theory. But the finite volume simulations show that the density inside a collapsed globule scales with the distance from the {theta} point as predicted by mean field theory, in contrast to claims in the work mentioned above. In addition to the simple-cubic lattice, we also studied two versions of the bond fluctuation model, but with much shorter chains. Finally, we show that our method can be applied also to off-lattice models, and illustrate this with simulations of amore » model studied in detail by Freire {ital et al.} [Macromolecules {bold 19}, 452 (1986) and later work]. {copyright} {ital 1997} {ital The American Physical Society}« less

Simulation of rayleigh-benard convection using a lattice boltzmann method

Abstract: Rayleigh-B\'enard convection is numerically simulated in two and three dimensions using a recently developed two-component lattice Boltzmann equation (LBE) method. The density field of the second component, which evolves according to the advection-diffusion equation of a passive scalar, is used to simulate the temperature field. A body force proportional to the temperature is applied, and the system satisfies the Boussinesq equation except for a slight compressibility. A no-slip, isothermal boundary condition is imposed in the vertical direction, and periodic boundary conditions are used in horizontal directions. The critical Rayleigh number for the onset of the Rayleigh-B\'enard convection agrees with the theoretical prediction. As the Rayleigh number is increased higher, the steady two-dimensional convection rolls become unstable. The wavy instability and aperiodic motion observed, as well as the Nusselt number as a function of the Rayleigh number, are in good agreement with experimental observations and theoretical predictions. The LBE model is found to be efficient, accurate, and numerically stable for the simulation of fluid flows with heat and mass transfer.

Propagation and stability of waves of electrical activity in the cerebral cortex

Abstract: Nonlinear equations are introduced to model the behavior of the waves of cortical electrical activity that are responsible for signals observed in electroencephalography. These equations incorporate nonlinearities, axonal and dendritic lags, excitatory and inhibitory neuronal populations, and the two-dimensional nature of the cortex, while rendering nonlinear features far more tractable than previous formulations, both analytically and numerically. The model equations are first used to calculate steady-state levels of cortical activity for various levels of stimulation. Dispersion equations for linear waves are then derived analytically and an analytic expression is found for the linear stability boundary beyond which a seizure will occur. The effects of boundary conditions in determining global eigenmodes are also studied in various geometries and the corresponding eigenfrequencies are found. Numerical results confirm the analytic ones, which are also found to reproduce existing results in the relevant limits, thereby elucidating the limits of validity of previous approximations.

Shift in the velocity of a front due to a cutoff

Abstract: We consider the effect of a small cutoff $\ensuremath{\varepsilon}$ on the velocity of a traveling wave in one dimension. Simulations done over more than ten orders of magnitude as well as a simple theoretical argument indicate that the effect of the cutoff $\ensuremath{\varepsilon}$ is to select a single velocity that converges when $\ensuremath{\varepsilon}\ensuremath{\rightarrow}0$ to the one predicted by the marginal stability argument. For small $\ensuremath{\varepsilon}$, the shift in velocity has the form $K(\mathrm{ln}\ensuremath{\varepsilon}{)}^{\ensuremath{-}2}$ and our prediction for the constant $K$ agrees very well with the results of our simulations. A very similar logarithmic shift appears in more complicated situations, in particular in finite-size effects of some microscopic stochastic systems. Our theoretical approach can also be extended to give a simple way of deriving the shift in position due to initial conditions in the Fisher-Kolmogorov or similar equations.

Solitary waves in a chain of beads under Hertz contact

Abstract: We study experimentally the propagation of high-amplitude compressional waves in a chain of beads in contact, submitted or not to a small static force. In such a system, solitary waves have been theoretically predicted by Nesterenko J. Appl. Mech. Tech. Phys. USSR 5, 733 1984. We have built an impact generator in order to create high-amplitude waves in the chain. We observe the propagation of isolated nonlinear pulses, measure their velocity as a function of their maximum amplitude, for different applied static forces, and record their shape. In all experiments, we find good agreement between our observations and the theoretical predictions of the above reference, without using any adjustable parameter in the data analysis. We also show that the velocity measurements taken at three different nonzero applied static forces all lie on a single curve, when expressed in rescaled variables. The size of the pulses is typically one-tenth the total length of the chain. All the measurements support the identification of these isolated nonlinear pulses with the solitary waves predicted by Nesterenko. S1063-651X9704211-6

Triple point of Yukawa systems

Abstract: The molecular dynamics simulations of Yukawa (i.e., screened-Coulomb) systems that were applied to the regime of weak screening in an earlier study [S. Hamaguchi, R. T. Farouki, and D. H. E. Dubin, J. Chem. Phys. 105, 7641 (1996)] are extended to the strong screening regime. Transition temperatures at the fluid-solid phase boundary and the solid-solid phase boundary are obtained as functions of the screening parameter $\ensuremath{\kappa}=a/{\ensuremath{\lambda}}_{D}$ (i.e., the ratio of the Wigner-Seitz radius $a$ to the Debye length ${\ensuremath{\lambda}}_{D}$). The resulting phase diagram also covers the triple point\char22{}the intersection of the fluid-solid and solid-solid phase boundaries\char22{}at $\ensuremath{\kappa}=4.28$ and $\ensuremath{\Gamma}=5.6\ifmmode\times\else\texttimes\fi{}{10}^{3},$ where \ensuremath{\Gamma} is the ratio of the Coulomb potential energy to the kinetic energy per particle (i.e., $\ensuremath{\Gamma}{=Q}^{2}/4\ensuremath{\pi}{\ensuremath{\epsilon}}_{0}akT,$ where $Q$ is the charge of each Yukawa particle and $T$ is the system temperature). Yukawa systems serve as models for plasmas and colloidal suspensions of charged particulates.

Permeability and effective porosity of porous media

Abstract: The concept of permeability of porous media is discussed, and a modification of Kozeny's permeability equation to include the effect of effective porosity is introduced. An analytical expression for the specific surface area of a system constructed of randomly placed identical obstacles with unrestricted overlap is derived, and a lattice-gas cellular automaton method is then used to simulate the dependence on porosity of permeability, tortuosity, and effective porosity for a flow of Newtonian uncompressible fluid in this two-dimensional porous substance. The simulated permeabilities can well be explained by the concept of effective porosity, and the exact form of the specific surface area. The critical exponent of the permeability near the percolation threshold is also determined from the simulations.

Geometrical and transport properties of random packings of spheres and aspherical particles

Abstract: Random packings of grains of arbitrary shape are built with an algorithm that is mostly applied to spheres, ellipsoids, cylinders, and parallelepipeds. A systematic account of the main geometrical properties such as the porosity, the reduced specific area, etc. is given. The conductivity, the permeability, and the dispersion are also systematically determined and they are shown not to depend upon their mode of construction.

Fundamental-measure free-energy density functional for hard spheres: Dimensional crossover and freezing

Abstract: A geometrically based fundamental-measure free-energy density functional unified the scaled-particle and Percus-Yevick theories for the hard-sphere fluid mixture. It has been successfully applied to the description of simple ~‘‘atomic’’ ! three-dimensional ~3D! fluids in the bulk and in slitlike pores, and has been extended to molecular fluids. However, this functional was unsuitable for fluids in narrow cylindrical pores, and was inadequate for describing the solid. In this work we analyze the reason for these deficiencies, and show that, in fact, the fundamental-measure geometrically based theory provides a free-energy functional for 3D hard spheres with the correct properties of dimensional crossover and freezing. After a simple modification of the functional, as we propose, it retains all the favorable D53 properties of the original functional, yet gives reliable results even for situations of extreme confinements that reduce the effective dimensionality D drastically. The modified functional is accurate for hard spheres between narrow plates (D52), and inside narrow cylindrical pores ( D51), and it gives the exact excess free energy in the D50 limit ~a cavity that cannot hold more than one particle!. It predicts the ~vanishingly small! vacancy concentration of the solid, provides the fcc hard-sphere solid equation of state from closest packing to melting, and predicts the hard-sphere fluid-solid transition, all in excellent agreement with the simulations. @S1063-651X~97!07404-7#

Bjerknes forces between small cavitation bubbles in a strong acoustic field

Abstract: The mutual interaction between small oscillating cavitation bubbles ${(R}_{0}l10\ensuremath{\mu}\mathrm{m})$ in a strong acoustic field (${P}_{a}g1\mathrm{bar},$ $f=20\mathrm{kHz}$) is investigated numerically. We assume spherical symmetry and a coupling of the bubble oscillations. Our results show that the strength and even the directions of the resulting secondary Bjerknes forces differ considerably from predictions of the well-known linear theory. This is of immediate consequence for understanding and modeling structure formation processes in acoustic cavitation and multibubble sonoluminescence.

Departure from navier-stokes hydrodynamics in confined liquids

Abstract: In this work we use nonequilibrium molecular dynamics (NEMD) to simulate an atomic liquid undergoing gravity-fed flow down a narrow channel. We compare the simulation results against the predictions of classical Navier-Stokes theory for two different channel widths. For a channel width of 5.1 molecular diameters, we find that the velocity profile deviates significantly from the hydrodynamic prediction. The shape of this velocity profile is found to be independent of the applied field (pressure gradient). We find that the heat flux profile does not agree with the cubic profile predicted by Navier-Stokes hydrodynamics, but shows significant oscillations located about one molecular diameter from the walls. This result differs from the earlier work of Todd and Evans [B. D. Todd and D. J. Evans, J. Chem. Phys. 103, 9804 (1995)], in which an assumption of a purely quadratic velocity profile resulted in very weak oscillations in the heat flux. We find that in narrow channels the viscosity cannot be described by a linear, local constitutive relation. However, classical Navier-Stokes behavior is approached for a channel width of g\ensuremath{\sim}10 molecular diameters.

Surface freezing in chain molecules: Normal alkanes

Abstract: A rare surface freezing phenomenon is observed in molten normal alkanes, using x-ray and surface tension measurements. An ordered monolayer forms on the surface of the liquid alkane at temperatures up to 3 \ifmmode^\circ\else\textdegree\fi{}C above the bulk freezing temperature ${\mathrm{T}}_{\mathrm{f}}$. The structure of the monolayer was studied in detail for a wide range of molecular lengths and temperatures. The single layer formed persists down to ${\mathrm{T}}_{\mathrm{f}}$. The rare surface phase exists only for carbon numbers of 16\ensuremath{\leqslant}n\ensuremath{\leqslant}50. The molecules in the layer are hexagonally packed and show three distinct ordered phases: two rotator phases, with molecules oriented vertically (16\ensuremath{\leqslant}n\ensuremath{\leqslant}30) and tilted towards nearest neighbors (3044) and one crystalline phase with molecules tilted towards next-nearest neighbors (n\ensuremath{\geqslant}44). The temperature dependence of the surface tension and the range of existence vs carbon number are satisfactorily accounted for within a simple theory based on surface energy considerations.

Ion charge state distributions of vacuum arc plasmas: The origin of species

Abstract: Vacuum arc plasmas are produced at micrometer-size, nonstationary cathode spots. Ion charge state distributions (CSD{close_quote}s) are experimentally known for 50 elements, but the theoretical understanding is unsatisfactory. In this paper, CSD{close_quote}s of vacuum arc plasmas are calculated under the assumption that the spot plasma experiences an instantaneous transition from equilibrium to nonequilibrium while expanding. Observable charge state distributions are the result of a freezing process at this transition. {open_quotes}Frozen{close_quotes} CSD{close_quote}s have been calculated using Saha equations in the Debye-H{umlt u}ckel approximation of the nonideal plasma for all metals of the Periodic Table and for boron, carbon, silicon, and germanium. The results are presented in a {open_quotes}periodic table of CSD.{close_quotes} The table contains also the mean ion charge state, the neutral vapor fraction, and the effective plasma temperature and density at the freezing point for each element. The validity of the concepts of {open_quotes}instantaneous freezing{close_quotes} and {open_quotes}effective temperature and density{close_quotes} is discussed for low and high currents and for the presence of a magnetic field. Temperature fluctuations have been identified to cause broadening of CSD{close_quote}s. {copyright} {ital 1997} {ital The American Physical Society}

Simulating the rheology of dense colloidal suspensions using dissipative particle dynamics

Abstract: The rheological properties of colloidal suspensions of spheres, rods, and disks have been studied using a mesoscopic simulation technique, known as dissipative particle dynamics (DPD). In DPD, a suspension is modeled as a system of large colloidal particles in a liquid of interacting point particles. For the calculation of hydrodynamic interactions, this method is computationally more efficient than conventional techniques using a continuum model for the solvent. Applying a steady-shear rate to the particulate suspensions, we have measured the viscosity as a function of shear rate and volume fraction of the suspended particles. The viscosity of a 30 vol % suspension of spheres displays characteristic shear-thinning behavior as a function of increasing shear rate. The values for the high- and low-shear viscosity are in good agreement with experimental data. For higher particulate densities good results are obtained for the high-shear viscosity, although the viscosity at low-shear rates shows a dependence on the size of the suspended spheres that we attribute to finite size effects. Dilute suspensions of rods and disks show intrinsic viscosities which are in excellent agreement with theoretical predictions. For concentrated suspensions of both rods and disks, the viscosity increases with the third power of the volume fraction. We find the same scaling behavior as predicted by Doi and Edwards [M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, New York, 1986)] for rod suspensions in the semidilute regime. The DPD simulation technique emerges as a useful tool for studying the rheology of particulate suspensions.

Osmotic pressure and viscoelastic shear moduli of concentrated emulsions

Abstract: We present an experimental study of the frequency \ensuremath{\omega} dependence and volume fraction \ensuremath{\varphi} dependence of the complex shear modulus ${G}^{*}(\ensuremath{\omega},\ensuremath{\varphi})$ of monodisperse emulsions which have been concentrated by an osmotic pressure \ensuremath{\Pi}. At a given \ensuremath{\varphi}, the elastic storage modulus ${G}^{\ensuremath{'}}(\ensuremath{\omega})=\mathrm{Re}[{G}^{*}(\ensuremath{\omega})]$ exhibits a low-frequency plateau ${G}_{p}^{\ensuremath{'}},$ dominating the dissipative loss modulus ${G}^{\ensuremath{'}\ensuremath{'}}(\ensuremath{\omega})=\mathrm{Im}[{G}^{*}(\ensuremath{\omega})]$ which exhibits a minimum. Above a critical packing fraction ${\ensuremath{\varphi}}_{c},$ we find that both \ensuremath{\Pi}(\ensuremath{\varphi}) and ${G}_{p}^{\ensuremath{'}}(\ensuremath{\varphi})$ increase quasilinearly, scaling as $(\ensuremath{\varphi}\ensuremath{-}{\ensuremath{\varphi}}_{c}{)}^{\ensuremath{\mu}},$ where ${\ensuremath{\varphi}}_{c}\ensuremath{\approx}{\ensuremath{\varphi}}_{c}^{\mathrm{rcp}},$ the volume fraction of a random close packing of spheres, and \ensuremath{\mu} is an exponent close to unity. To explain this result, we develop a model of disordered droplets which interact through an effective repulsive anharmonic potential, based on results obtained for a compressed droplet. A simulation based on this model yields a calculated static shear modulus $G$ and osmotic pressure \ensuremath{\Pi} that are in excellent agreement with the experimental values of ${G}_{p}^{\ensuremath{'}}$ and \ensuremath{\Pi}.

Autonomous stochastic resonance in bursting neurons

Abstract: Noise-induced firing is studied in two major classes of bursting neuron models in the absence of periodic input. In the biologically relevant subthreshold regime where no deterministic firing occurs, additive noise induces spiking limit cycles. This noise makes the output firing patterns sensitive to the characteristics of autonomous subthreshold oscillations, which can change in response to various physicochemical stimuli. The nonmonotonic behavior with increasing noise of the phase locking between spikes and subthreshold oscillations, measured using spectral signal-to-noise ratios and line shape characteristics, are a manifestation of autonomous stochastic resonance in these systems. The type of bifurcation giving rise to bursting activity determines the behavior with noise of the mean firing frequency, interspike interval histogram, spike train power spectrum, and phase locking. In particular, it is shown that a saddle-node bifurcation is not required to see stochastic resonance ~SR! without periodic input when there exists a stable deterministic subthreshold oscillation. This paper also studies SR in a detailed ionic neuron model, an approach that leads to tests of hypotheses regarding the nature of noise in real neurons. @S1063-651X~97!12001-3#

Envelope analysis of intense relativistic quasilaminar beams in rf photoinjectors:mA theory of emittance compensation

Abstract: In this paper we provide an analytical description for the transverse dynamics of relativistic, space-chargedominated beams undergoing strong acceleration, such as those typically produced by rf photoinjectors. These beams are chiefly characterized by a fast transition, due to strong acceleration, from the nonrelativistic to the relativistic regime in which the initially strong collective plasma effects are greatly diminished. However, plasma oscillations in the transverse plane are still effective in significantly perturbing the evolution of the transverse phase space distribution, introducing distortions and longitudinal-transverse correlations that cause an increase in the rms transverse emittance of the beam as a whole. The beam envelope evolution is dominated by such effects and not by the thermal emittance, and so the beam flow can be considered quasilaminar. The model adopted is based on the rms envelope equation, for which we find an exact particular analytical solution taking into account the effects of linear space-charge forces, external focusing due to applied as well as ponderomotive RF forces, acceleration, and adiabatic damping, in the limit that the weak nonlaminarity due to the thermal emittance may be neglected. This solution represents a special mode for beam propagation that assures a secularly diminishing normalized rms emittance and it represents the fundamental operating condition of a space-charge-compensated RF photoinjector. The conditions for obtaining emittance compensation in a long, integrated photoinjector, in which the gun and linac sections are joined, as well as in the case of a short gun followed by a drift and a booster linac, are examined. @S1063-651X~97!10706-1#

Inelastic Collision and Switching of Coupled Bright Solitons in Optical Fibers

Abstract: By constructing the general six-parameter bright two-soliton solution of the integrable coupled nonlinear Schr\"odinger equation (Manakov model) using the Hirota method, we find that the solitons exhibit certain novel inelastic collision properties, which have not been observed in any other $(1+1)$-dimensional soliton system so far In particular, we identify the exciting possibility of switching solitons between modes by changing the phase However, the standard elastic collision property of solitons is regained with specific choices of parameters

Active Walker Model for the Formation of Human and Animal Trail Systems

Abstract: Active walker models have recently proved their great value for describing the formation of clusters, periodic patterns, and spiral waves as well as the development of rivers, dielectric breakdown patterns, and many other structures. It is shown that they also allow one to simulate the formation of trail systems by pedestrians and ants, yielding a better understanding of human and animal behavior. A comparison with empirical material shows a good agreement between model and reality. Our trail formation model includes an equation of motion, an equation for environmental changes, and an orientation relation. It contains some model functions, which are specified according to the characteristics of the considered animals or pedestrians. Not only the kind of environmental changes differs: Whereas pedestrians leave footprints on the ground, ants produce chemical markings for their orientation. Nevertheless, it is more important that pedestrians steer towards a certain destination, while ants usually find their food sources by chance, i.e., they reach their destination in a stochastic way. As a consequence, the typical structure of the evolving trail systems depends on the respective species. Some ant species produce a dendritic trail system, whereas pedestrians generate a minimal detour system. The trail formation model can be used as a tool for the optimization of pedestrian facilities: It allows urban planners to design convenient way systems which actually meet the route choice habits of pedestrians.

Physical symmetry and lattice symmetry in the lattice Boltzmann method

Abstract: The lattice Boltzmann method (LBM) is regarded as a specific finite difference discretization for the kinetic equation of the discrete velocity distribution function. We argue that for finite sets of discrete velocity models, such as LBM, the physical symmetry is necessary for obtaining the correct macroscopic Navier-Stokes equations. In contrast, the lattice symmetry and the Lagrangian nature of the scheme, which is often used in the lattice gas automaton method and the existing lattice Boltzmann methods and directly associated with the property of particle dynamics, is not necessary for recovering the correct macroscopic dynamics. By relaxing the lattice symmetry constraint and introducing other numerical discretization, one can also obtain correct hydrodynamics. In addition, numerical simulations for applications, such as nonuniform meshes and thermohydrodynamics can be easily carried out and numerical stability can be ensured by the Courant-Friedricks-Lewey condition and using the semi-implicit collision scheme. {copyright} {ital 1997} {ital The American Physical Society}

On the Universality of the Kolmogorov Constant in Numerical Simulations of Turbulence

Abstract: Motivated by a recent survey of experimental data [K.R. Sreenivasan, Phys. Fluids, 2778 (1995)], we examine data on the Kolmogorov spectrum constant in numerical simulations of isotropic turbulence, using results both from previous studies and from new direct numerical simulations over a range of Reynolds numbers (up to 240 on the Taylor scale) at grid resolutions up to 5123. It is noted that in addition to k-5/3 scaling, identification of a true inertial range requires spectral isotropy in the same wavenumber range. We found that a plateau in the compensated three-dimensional energy spectrum at k eta ~ 0.1--0.2 , commonly used to infer the Kolmogorov constant from the compensated three-dimensional energy spectrum, actually does not represent proper inertial range behavior. Rather, a proper, if still approximate, inertial range emerges at k eta ~ 0.02-0.05 when R>sub /sub sub /sub sub /sub sub /sub< ~ 0.53 for C =1.62, in excellent agreement with experiments. However the one- and three-dimensional estimates are not fully consistent, because of departures (due to numerical and statistical limitations) from isotropy of the computed spectra at low wavenumbers. The inertial scaling of structure functions in physical space is briefly addressed. Since DNS is still restricted to moderate Reynolds numbers, an accurate evaluation of the Kolmogorov constant is very difficult. We focus on providing new insights on the interpretation of Kolmogorov 1941 similarity in the DNS literature and do not consider issues pertaining to the refined similarity hypotheses of Kolmogorov.