bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Use of the Reverse Monte Carlo Technique to Generate Amorphous Carbon Structures
Authors: Rosato Vittorio , Lascovich Juan C. , Santoni Antonino , Colombo Luciano
Published: October 2003

The reverse Monte Carlo (RMC) technique has been used to generate atomic structures of amorphous carbon based on the radial distribution functions and the fraction of differently coordinated sites measured on experimental samples. The resulting structures have been subsequently relaxed via a Tight Binding Molecular Dynamics simulation (TBMD). The radial distribution function, the energy and the fraction of 2-, 3- and 4-fold coordinated sites, evaluated on the relaxed structures, have been compared to those calculated for atomic systems generated on the basis of the "conventional" numerical melt-quench technique. We thus suggest the possibility of using RMC modeling as a useful and convenient tool for generating amorphous structures to be used as initial configurations in Molecular Dynamics simulations.
Numerically Efficient Computation of Eigensolution Spectrum in One-Dimensional Heterostructures
Authors: Farrelly F. , Petri A.
Published: October 2003

We describe a method that allows an efficient determination of the density of states of one-dimensional heterostructures. We show that the propagation of an appropriate vector through the structure together with the use of the node theorem is much more effective than transfer matrix methods in those cases in which highly degenerate spectra are present. As a by-product, spatial behavior of solutions is also easily obtained. A case of elastic propagation is discussed in detail and application to Schrödinger's equation is presented.
Semelparous Penna Ageing Model with Parental Care
Authors: Fehsenfeld K. M. , Sá Martins J. S. , de Oliveira S. Moss , Bernardes A. T.
Published: October 2003

In this paper we study the importance of parental care for the survival of semelparous species, that reproduce only once in life. We perform our simulations for sexual and asexual reproductions and show that catastrophic senescence (death soon after reproduction) is delayed if parental care is considered.
Finite Size Scaling in the tt'-Hubbard Model and in BCS-Reduced Hubbard Models
Authors: Fettes W. , Morgenstern I.
Published: October 2003

With the projector quantum Monte Carlo algorithm and the stochastic diagonalization it is possible to calculate the ground state of the Hubbard model for small finite clusters. Nevertheless the usual finite size scaling of the Hubbard model has problems of deducing the behavior of the infinite system correctly from the numerical data of small system sizes. Therefore we study the finite size scaling of the superconducting correlation functions in superconducting BCS-reduced Hubbard models to analyze the finite size behavior in small finite clusters. The ground state of the BCS-reduced Hubbard models is calculated with the stochastic diagonalization without any approximations. As result of these analyses we propose a new finite size scaling ansatz for the Hubbard model, which is able describe the finite size effects in a consistent way taking the corrections to scaling into account, which are dominant for weak interaction strength and small clusters. With this new finite size scaling ansatz it is possible to give evidence for superconductivity for all interaction strengths for both the attractive tt'-Hubbard model (with s-wave symmetry) and the repulsive tt'-Hubbard model (with dx2-y2-wave symmetry).
Modular Transformations, Order-Chaos Transitions and Pseudo-Random Number Generation
Authors: Bonelli Antonio , Ruffo Stefano
Published: October 2003

Successive pairs of pseudo-random numbers generated by standard linear congruential transformations display ordered patterns of parallel lines. We study the "ordered" and "chaotic" distribution of such pairs by solving the eigenvalue problem for two-dimensional modular transformations over integers. We conjecture that the optimal uniformity for pair distribution is obtained when the slope of linear modular eigenspaces takes the value [Formula: see text], where p is a prime number. We then propose a new generator of pairs of independent pseudo-random numbers, which realizes an optimal uniform distribution (in the "statistical" sense) of points on the unit square (0, 1] × (0, 1]. The method can be easily generalized to the generation of k-tuples of random numbers (with k>2).
Eigen's Error Threshold and Mutational Meltdown in a Quasispecies Model
Authors: Bagnoli F. , Bezzi M.
Published: October 2003

We introduce a toy model for interacting populations connected by mutations and limited by a shared resource. We study the presence of Eigen's error threshold and mutational meltdown. The phase diagram of the system shows that the extinction of the whole population due to mutational meltdown can occur well before an eventual error threshold transition.
Finite-Size Effects in the φ4 Field and Lattice Theory Above the Upper Critical Dimension
Authors: Chen X. S. , Dohm V.
Published: October 2003

We demonstrate that the standard O(n) symmetric φ4 field theory does not correctly describe the leading finite-size effects near the critical point of spin systems with periodic boundary conditions on a d-dimensional lattice with d>4. We show that these finite-size effects require a description in terms of a lattice Hamiltonian. For n →∞ and n=1, explicit results are given for the susceptibility and for the Binder cumulant. They imply that these quantities do not have the universal properties predicted previously and that recent analyses of Monte Carlo results for the five-dimensional Ising model are not conclusive.
Phase Transition in Two-Dimensional Biased Diffusion
Authors: Kirsch Alexander
Published: October 2003

We investigate the long-time behavior of the drift velocity of two-dimensional biased diffusion with varying bias B and percentage p of allowed sites. A phase diagram for the drift/no-drift transition depending on B and p is presented.
A Simple Model of Large Scale Organization in Evolution
Authors: Manrubia S. C. , Paczuski M.
Published: October 2003

A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age, confirming a general relation between Age and Area proposed by Willis. The ecology exhibits punctuated equilibrium. Analytic and numerical results show that the probability distribution of genera sizes, genera lifetimes, and extinction event sizes are the same power law P(x)~ 1/x2, consistent with paleontological data.
Cumulant Ratios of Eden Model Surfaces in 1+1 Dimensions
Authors: Stauffer Dietrich
Published: October 2003

Monte Carlo simulations suggest that dimensionless ratios of cumulants for the height of the surface depend on how randomness is used.
Bond Functions and Core Correlation Energy Contributions To HeBe Potential
Authors: Shalabi A. S. , Nour E. M. , Abdel Halim W. S.
Published: October 2003

An empirical scheme for implementation of bond functions in heteronuclear diatomics is suggested and applied to HeBe using universal even-tempered functions. The effects of bond functions and core-correlation energy on the interaction potential of HeBe calculated at the uncorrelated (SCF) and correlated (MBPT and CC) levels are examined. The results confirm that an accuracy of sub μ Hartree level can be obtained using even-tempered functions with s-, p-, and d- symmetry and that bond functions of size {4s2p} for He and {6s3p} for Be recovers 100% of energy lowering obtained from the addition of 10d atom-centered functions to He and 13d atom centred functions to Be. The various treatments of the electron correlation, conclude that the system is interacting weakly with a well depth from 14.5–24.7 μE h at a separation near 9.1a0 compared with 20.7–25.5 μE h previously reported with a rather limited basis set. The most reliable well depth corrected for BSSE (19.0 μE h ) was obtained at the CC-SD(T)level at separation of 8.71a0 taking into account the effects of bond functions and core correlation energy. Potential energy curves at the CC-SD(T) valence and CC-SD(T) valence + core correlation levels are analyzed in analytical forms in terms of exchange repulsion, induction and dispersion components.
High Algebraic Order Methods with Minimal Phase-Lag for Accurate Solution of the Schrödinger Equation
Authors: Simos T. E.
Published: October 2003

A family of new hybrid four-step tenth algebraic order methods with phase-lag of order fourteen is developed for accurate computations of the radial Schrödinger equation. Numerical results obtained for the integration of the phase shift problem for the well known case of the Lennard-Jones potential and for the numerical solution of the coupled equations arising from the Schrödinger equation show that these new methods are better than other finite difference methods.
Lattice φ4 Theory of Finite-Size Effects Above the Upper Critical Dimension
Authors: Chen X. S. , Dohm V.
Published: October 2003

We present a perturbative calculation of finite-size effects near Tc of the φ4 lattice model in a d-dimensional cubic geometry of size L with periodic boundary conditions for d>4. The structural differences between the φ4 lattice theory and the φ4 field theory found previously in the spherical limit are shown to exist also for a finite number of components of the order parameter. The two-variable finite-size scaling functions of the field theory are nonuniversal whereas those of the lattice theory are independent of the nonuniversal model parameters. One-loop results for finite-size scaling functions are derived. Their structure disagrees with the single-variable scaling form of the lowest-mode approximation for any finite ξ/L where ξ is the bulk correlation length. At Tc, the large-L behavior becomes lowest-mode like for the lattice model but not for the field-theoretic model. Characteristic temperatures close to Tc of the lattice model, such as T max (L) of the maximum of the susceptibility χ, are found to scale asymptotically as Tc-T max (L) ~L-d/2, in agreement with previous Monte Carlo (MC) data for the five-dimensional Ising model. We also predict χ max ~Ld/2 asymptotically. On a quantitative level, the asymptotic amplitudes of this large-L behavior close to Tc have not been observed in previous MC simulations at d=5 because of nonnegligible finite-size terms ~L(4-d)/2 caused by the inhomogeneous modes. These terms identify the possible origin of a significant discrepancy between the lowest-mode approximation and previous MC data. MC data of larger systems would be desirable for testing the magnitude of the L(4-d)/2 and L4-d terms predicted by our theory.
Monte Carlo Partitioning of Graphs with a Self-Organizing Map
Authors: Bonabeau Eric , Hénaux Florian
Published: October 2003

A Monte Carlo algorithm for partitioning graphs is presented. The algorithm is based on the self-organizing map, an unsupervised, competitive neural network. A mean-field analysis suggests that the complexity of the algorithm is at most is on the order of O(n3/|E|), where n is the number of vertices of the graph, and |E| the number of edges. This prediction is tested on a class of random graphs. Scaling laws that deviate from the mean-field prediction are obtained. Although the origin of these scaling laws is unclear, their consequences are discussed.
A Comparison Between Lattice-Boltzmann and Finite-Element Simulations of Fluid Flow in Static Mixer Reactors
Authors: Kandhai D. , Vidal D. J.-E. , Hoekstra A. G. , Hoefsloot H. , Iedema P. , Sloot P. M. A.
Published: October 2003

We present a comparison between the finite-element and the lattice-Boltzmann method for simulating fluid flow in a SMRX static mixer reactor. The SMRX static mixer is a piece of equipment with excellent mixing performance and it is used in highly efficient chemical reactors for viscous systems like polymers. The complex geometry of this mixer makes such 3D simulations nontrivial. An excellent agreement between the results of the two simulation methods and experimental data was found.
Simulation of a 2D Channel Flow Around a Square Obstacle with Lattice-Boltzmann (BGK) Automata
Authors: Bernsdorf J. , Zeiser Th. , Brenner G. , Durst F.
Published: October 2003

Results for time-dependent, viscous, incompressible flows were investigated using the lattice-Boltzmann (BGK) automata. The decay of a synthetic turbulent flow field and the time evolution of an initial vortex were simulated for validation purposes. The focal point was the investigation of the instationary flow around a square obstacle in a two-dimensional channel for a range of Reynolds numbers between 80 and 300 and a blockage ratio of 0.125. The Strouhal number was measured for this case and found to be in the range of data given in the literature.
Implicit discretization and nonuniform mesh refinement approaches for FD discretizations of LBGK Models
Authors: Tölke Jonas , Krafczyk Manfred , Schulz Manuel , Rank Ernst , Berrios Rodolfo
Published: October 2003

After a short discussion of recent discretization techniques for the lattice-Boltzmann equations we motivate and discuss some alternative approaches using implicit, nonuniform FD discretization and mesh refinement techniques. After presenting results of a stability analysis we use an implicit approach to simulate a boundary layer test problem. The numerical results compare well to the reference solution when using strongly refined meshes. Some basic ideas for a nonuniform mesh refinement (with non-cartesian mesh topology) are introduced using the standard discretization procedure of alternating collision and propagation.
Incorporating Turbulence Models into the Lattice-Boltzmann Method
Authors: Teixeira Christopher M.
Published: October 2003

The Lattice-Boltzmann method (LBM) is extended to allow incorporation of traditional turbulence models. Implementation of a two-layer mixing-length algebraic model and two versions of the k-ε two-equation model, Standard and RNG, in conjunction with a wall model, are presented. Validation studies are done for turbulent flows in a straight pipe at three Re numbers and over a backwards facing step of expansion ratio 1.5 and Re H=44 000. All models produce good agreement with experiment for the straight pipes but the RNG k-ε model is best able to capture both the recirculation length, within 2% of experiment, and the detailed structure of the mean fluid flow for the backwards facing step.
Connection Between Lattice-Boltzmann Equation and Beam Scheme
Authors: Xu Kun , Luo Li-Shi
Published: October 2003

In this paper we analyze and compare the lattice-Boltzmann equation with the beam scheme in detail. We notice the similarity and differences between the lattice Boltzmann equation and the beam scheme. We show that the accuracy of the lattice-Boltzmann equation is indeed second order in space. We discuss the advantages and limitations of the lattice-Boltzmann equation and the beam scheme. Based on our analysis, we propose an improved multi-dimensional beam scheme.
A Lattice-Boltzmann Method for Partially Saturated Computational Cells
Authors: Noble D. R. , Torczynski J. R.
Published: October 2003

The lattice-Boltzmann (LB) method is applied to complex, moving geometries in which computational cells are partially filled with fluid. The LB algorithm is modified to include a term that depends on the percentage of the cell saturated with fluid. The method is useful for modeling suspended obstacles that do not conform to the grid. Another application is to simulations of flow through reconstructed media that are not easily segmented into solid and liquid regions. A detailed comparison is made with FIDAP simulation results for the flow about a periodic line of cylinders in a channel at a non-zero Reynolds number. Two cases are examined. In the first simulation, the cylinders are given a constant velocity along the axis of the channel, and the steady solution is acquired. The transient behavior of the system is then studied by giving the cylinders an oscillatory velocity. For both steady and oscillatory flows, the method provides excellent agreement with FIDAP simulation results, even at locations close to the surface of a cylinder. In contrast to step-like solutions produced using the "bounce-back" condition, the proposed condition gives close agreement with the smooth FIDAP predictions. Computed drag forces with the proposed condition exhibit apparent quadratic convergence with grid refinement rather than the linear convergence exhibited by other LB boundary conditions.
Development of LGA & LBE 2D Parallel Programs
Authors: Ujita Hiroshi , Nagata Satoru , Akiyama Minoru , Naitoh Masanori , Ohashi Hirotada
Published: October 2003

A lattice-gas Automata two-dimensional program was developed for analysis of single and two-phase flow behaviors, to support the development of integrated software modules for Nuclear Power Plant mechanistic simulations. The program has single-color, which includes FHP I, II, and III models, two-color (Immiscible lattice gas), and two-velocity methods including a gravity effect model. Parameter surveys have been performed for Karman vortex street, two-phase separation for understanding flow regimes, and natural circulation flow for demonstrating passive reactor safety due to the chimney structure vessel. In addition, lattice-Boltzmann Equation two-dimensional programs were also developed. For analyzing single-phase flow behavior, a lattice-Boltzmann-BGK program was developed, which has multi-block treatments. A Finite Differential lattice-Boltzmann Equation program of parallelized version was introduced to analyze boiling two-phase flow behaviors. Parameter surveys have been performed for backward facing flow, Karman vortex street, bent piping flow with/without obstacles for piping system applications, flow in the porous media for demonstrating porous debris coolability, Couette flow, and spinodal decomposition to understand basic phase separation mechanisms. Parallelization was completed by using a domain decomposition method for all of the programs. An increase in calculation speed of at least 25 times, by parallel processing on 32 processors, demonstrated high parallelization efficiency. Application fields for microscopic model simulation to hypothetical severe conditions in large plants were also discussed.
A Multiparticle Lattice-Gas Model for Hydrodynamics
Authors: Masselot A. , Chopard B.
Published: October 2003

Cellular automata (CA) and lattice-Boltzmann (LB) models are two possible approaches to simulate fluid-like systems. CA models keep track of the many-body correlations and provide a description of the fluctuations. However, they lead to a noisy dynamics and impose strong restrictions on the possible viscosity values. On the other hand, LB models are numerically more efficient and offer much more flexibility to adjust the fluid parameters, but they neglect fluctuations. Here we discuss a multiparticle lattice model which reconciles both approaches. Our method is tested on Poiseuille flows and on the problem of ballistic annihilation in two dimensions for which the fluctuations are known to play an important role.
Inverse Chapman–Enskog Derivation of the Thermohydrodynamic Lattice-BGK Model for the Ideal Gas
Authors: Boghosian B. M. , Coveney P. V.
Published: October 2003

A thermohydrodynamic lattice-BGK model for the ideal gas was derived by Alexander et al. in 1993, and generalized by McNamara et al. in the same year. In these works, particular forms for the equilibrium distribution function and the transport coefficients were posited and shown to work, thereby establishing the sufficiency of the model. In this paper, we rederive the model from a minimal set of assumptions, and thereby show that the forms assumed for the shear and bulk viscosities are also necessary, but that the form assumed for the thermal conductivity is not. We derive the most general form allowable for the thermal conductivity, and the concomitant generalization of the equilibrium distribution. In this way, we show that it is possible to achieve variable (albeit density-dependent) Prandtl number even within a single-relaxation-time lattice-BGK model. We accomplish this by demanding analyticity of the third moments and traces of the fourth moments of the equilibrium distribution function. The method of derivation demonstrates that certain undesirable features of the model — such as the unphysical dependence of the viscosity coefficients on temperature — cannot be corrected within the scope of lattice-BGK models with constant relaxation time.
Thermal Lattice-Boltzmann Models (TLBM) for Compressible Flows
Authors: Vahala George , Pavlo Pavol , Vahala Linda , Martys Nicos S.
Published: October 2003

The progress and challenges in thermal lattice-Boltzmann modeling are discussed. In particular, momentum and energy closures schemes are contrasted. Higher order symmetric (but no longer space filling) velocity lattices are constructed for both 2D and 3D flows and shown to have superior stability properties to the standard (but lower) symmetry lattices. While this decouples the velocity lattice from the spatial grid, the interpolation required following free-streaming is just 1D. The connection between fixed lattice vectors and temperature-dependent lattice vectors (obtained in the Gauss–Hermite quadrature approach) is discussed. Some (compressible) Rayleigh–Benard simulations on the 2D octagonal lattice are presented for extended BGK collision operators that allow for arbitrary Prandtl numbers.
Boundary Conditions in Lattice Gas with Continuous Velocity
Authors: Hashimoto Yasuhiro , Chen Yu , Ohashi Hirotada
Published: October 2003

The model we have adopted is called "Hydrodynamic Lattice Gases", that is, a kind of lattice gas with continuous velocity. This model describes the conservation of energy naturally, using innovative collision and propagation schemes. As a result, operations of particles on the boundary become more flexible and complicated as compared with those of the FHP model. And we need to pay attention to the way of treating individual particles. Focusing on the velocity and the coordinates of particles that will return from the boundary to the system, we introduce a reasonable operation that can set temperature and flow velocity of any value required as boundary conditions. Numerical calculations show that those parameters are well controlled using a new boundary scheme.
Boundary-Fitting and Local Grid Refinement for Lattice-BGK Models
Authors: Filippova O. , Hänel D.
Published: October 2003

Lattice-Boltzmann models, proposed at the end of the 1980s as the noise-free version of lattice-gas models are based on gas-kinetical-like representation of fluid flow. Their recent modifications, the lattice-BGK models, provide especially simple, effective and stable algorithms for the solution of incompressible flows. The boundary-fitting concept and local grid refinement proposed for the lattice-BGK model conserve the second order accuracy of the original algorithm for flows around complicated geometries in regions of small and moderate Reynolds numbers.
Realization of Fluid Boundary Conditions via Discrete Boltzmann Dynamics
Authors: Chen Hudong , Teixeira Chris , Molvig Kim
Published: October 2003

We describe a novel way based on lattice-Boltzmann representation for realizing hydrodynamic boundary conditions at a solid surface. It is shown that using this approach the resulting physics properties are independent of the position and the orientation of the surface with respect to the lattice mesh. The fluxes of mass, energy as well as both normal and tangential momenta can be accurately controlled to correspond to various fluid dynamics situations.
Entropy Functionals for Dense Fluids, Mixtures and Suspensions
Authors: Romero-Salazar L. , Mayorga M.
Published: October 2003

In this work we present the entropy functionals for dense gases that results from a maximum entropy procedure, for two levels of description. In analogy to this work, we review the case of dense mixtures. The resulting entropy functionals serve as a starting point to derive in a systematic manner, Fokker–Planck equations to model interacting Brownian particles.
Upper Bound for the Entropy Production and Dissipative Particle Dynamics
Authors: Mayorga M.
Published: October 2003

The upper bound for the entropy production of a dense gas is presented and its connection with the so-called Fisher information measure is revised. The relation with dissipative particle dynamics is analyzed, which serve to identify the thermostat for the fluid system. The analogy with a turbulence approach, a probabilistic approach to dynamical sytems, detailed balance for dissipative particle dynamics and fluctuation dissipation theorems for relaxing systems is presented.
Resolution Effects in Dissipative Particle Dynamics Simulations
Authors: Boek Edo S. , Van Der Schoot Paul
Published: October 2003

Dissipative Particle Dynamics (DPD) simulations were performed to investigate resolution or "coarse graining" effects on the simulation results. Fluid flow through a periodic array of spheres has been studied as a model for fluid filtration into a porous medium. In our model system, it appears that quantitatively correct results for the dimensionless drag can be obtained for relatively small system sizes. For higher solid volume fractions, it is necessary to increase the system size to avoid finite size and resolution effects. Simulations of colloidal spheres suspended in a DPD fluid show effective attraction between the large colloid particles, causing depletion aggregation. This effect may be expected as a consequence of the coarse-grained nature of the DPD fluid. By imposing a steady shear rate the aggregation can be suppressed. The results show that for dilute suspensions, the Brownian noise in the particle interactions causes an effective colloid polydispersity, which suppresses aggregation effects.
Boundary Models in DPD
Authors: Revenga M. , Zúñiga I. , Español P. , Pagonabarraga I.
Published: October 2003

We present a model for treating solid boundaries of a DPD fluid. The basic idea is to model the stick boundary conditions by assuming that a layer of DPD particles is stuck on the boundary. By taking a continuum limit of this layer effective dissipative and stochastic forces on the fluid DPD particles are obtained. The boundary model is tested by a simulation of planar Couette flow which allows the performance of vicosimetric measurements. We analyze the conditions that ensure a proper stick boundary condition for an impenetrable wall, comparing with previous methods used.
Dissipative Particle Dynamics with Energy Conservation: Heat Conduction
Authors: Ripoll M. , Español P. , Ernst M. H.
Published: October 2003

We study, by means of numerical simulations, the model of dissipative particle dynamics with energy conservation for the simple case of thermal conduction. It is shown that the model displays correct equilibrium fluctuations and reproduces Fourier law. The connection between "mesoscopic coarse-graining" and "resolution" is clarified.
Noise Reduction and Pattern Formation in Rapid Granular Flows
Authors: Brito R. , Ernst M. H.
Published: October 2003

Spatial fluctuations in dissipative systems, such as rapid granular flows, behave very differently from those in elastic fluids. Fluctuations in the flow field drive the linear and nonlinear instability in the density field (clustering), while vortex structures appear and grow through the mechanism of noise reduction. The dynamics of the flow field on the largest space and time scales is described by diffusion equations with different diffusivities for the transverse and longitudinal flow fields. The results are obtained from analytic and simulation methods.
Coupling Particles and Fields for Gas–Grain Flow
Authors: Flekkøy Eirik G.
Published: October 2003

A model for the flow of fluids with particles in them is introduced. It relies on the coupling of discretely represented particles and a fluid pressure field that is given by a continuum description — a local Darcy law. In order to validate the qualitative behavior of the model, it is applied to simulate two different sedimentation processes. These processes include an initially homogeneous sedimenting bed of particles and a fluid bubble rising through a sedimenting field of particles. Agreement with experiments is observed on the qualitative level.
Local Drag Law for Suspensions from Particle-Scale Simulations
Authors: Wachmann B. , Schwarzer S. , Höfler K.
Published: October 2003

Two-phase continuum descriptions of the dynamical behavior of particulate suspensions require, among others, the formulation of a "local drag law". Such a "law" specifies the mean force fl on particles as a function of averaged local properties, most notably, the mean difference velocity [Formula: see text] of particles and fluid and the local volume fraction Φl. The subscript l shall indicate the dependence of these quantities on the size l of the averaging cell. We study fl by direct numerical simulation, solving the incompressible Navier–Stokes equation on a fixed, regular grid on a scale much smaller than the particle diameter. The particle–fluid interaction is computed by a method similar to the one proposed in [Fogelson and Peskin J. Comp. Phys.79, 50 (1988)]. We find a relation similar to the law of Richardson & Zaki, [Formula: see text], which relates the local phase difference velocity to the local volume fraction of the particles.
Spinodal Decomposition in Two-Dimensional Binary Fluids
Authors: Wagner Alexander J. , Yeomans J. M.
Published: October 2003

We use lattice-Boltzmann simulations to examine late stage spinodal decomposition in binary fluids, showing that the scaling hypothesis for phase ordering does not hold in all cases. We also examine the effects of an applied shear on the coarsening of the spinodal pattern.
Lattice-Boltzmann Simulation of Two-Phase Fluid Flows
Authors: Chen Yu , Teng Shulong , Shukuwa Takauki , Ohashi Hirotada
Published: October 2003

A model with a volumetric stress tensor added to the Navier–Stokes Equation is used to study two-phase fluid flows. The implementation of such an interface model into the lattice-Boltzmann equation is derived from the continuous Boltzmann BGK equation with an external force term, by using the discrete coordinate method. Numerical simulations are carried out for phase separation and "dam breaking" phenomena.
An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann Models
Authors: Holdych D. J. , Rovas D. , Georgiadis J. G. , Buckius R. O.
Published: October 2003

Lattice-Boltzmann (LB) models provide a systematic formulation of effective-field computational approaches to the calculation of multiphase flow by replacing the mathematical surface of separation between the vapor and liquid with a thin transition region, across which all magnitudes change continuously. Many existing multiphase models of this sort do not satisfy the rigorous hydrodynamic constitutive laws. Here, we extend the two-dimensional, seven-speed Swift et al. LB model1 to rectangular grids (nine speeds) by using symbolic manipulation (MathematicaTM) and compare the LB model predictions with benchmark problems, in order to evaluate its merits. Particular emphasis is placed on the stress tensor formulation. Comparison with the two-phase analogue of the Couette flow and with a flow involving shear and advection of a droplet surrounded by its vapor reveals that additional terms have to be introduced in the definition of the stress tensor in order to satisfy the Navier–Stokes equation in regions of high density gradients. The use of Mathematica obviates many of the difficulties with the calculations "by-hand," allowing at the same time more flexibility to the computational analyst to experiment with geometrical and physical parameters of the formulation.
Mesoscopic Models of Liquid/Solid Phase Transitions
Authors: de Fabritiis G. , Mancini A. , Mansutti D. , Succi S.
Published: October 2003

A generalization of mesoscopic Lattice-Boltzmann models aimed at describing flows with solid/liquid phase transitions is presented. It exhibits lower computational costs with respect to the numerical schemes resulting from differential models. Moreover it is suitable to describe chaotic motions in the mushy zone.
Surface of Dense Phase in Lattice-Gas Fluid with Long-Range Interaction
Authors: Ebihara Kenichi , Watanabe Tadashi , Kaburaki Hideo
Published: October 2003

A lattice gas with long-range interaction can simulate phase separation in the system consisting of one kind of component particle like the liquid-vapor theory of van der Waals. The generated phases are distinguished from each other by their particle density. In lattice-gas fluid with long-range interaction, the phase with high density can be observed in the phase with low density like the droplet in vapor. In this paper, the surface of the droplet in lattice-gas fluid with the long-range interaction is determined from the local density and its position is compared with that of Gibbs's dividing surface. The inside region and the outside region of the droplet are defined on the basis of the mean free path in each region. The surface tension is calculated through Laplace's formula using the droplet radius and the pressures in both regions. It is shown that the surface thickness becomes 4r where r is the distance of the long-range interaction.
Lattice-Boltzmann Simulation of Polymer-Solvent Systems
Authors: Ahlrichs Patrick , Dünweg Burkhard
Published: October 2003

We investigate a new method for simulating polymer-solvent systems which combines a lattice-Boltzmann approach for the fluid with a continuum molecular dynamics (MD) model for the polymer chain. The two parts are coupled by a friction force which is proportional to the difference of the monomer velocity and the fluid velocity at the monomer's position. The strength of the coupling can be tuned by a friction coefficient. Using this approach we examine the dynamics of one monomer immersed in the fluid, and by adding fluctuations to the fluid and the monomer, also the velocity autocorrelation function of one monomer. This results in the definition of an effective friction coefficient for the dynamics of the monomer. Furthermore we analyze the mapping of the model to an MD simulation, allowing us to compare results obtained using the new method with MD.
Lattice-BGK Model for Low Mach Number Combustion
Authors: Filippova O. , Hänel D.
Published: October 2003

For the simulation of low Mach number reactive flows with significant density changes a modified lattice-BGK model in combination with the conventional convective-diffusion solvers for equations of temperature and species is proposed. Together with boundary-fitting conditions and local grid refinement the scheme enables the accurate consideration of low Mach number combustion in complex geometry as the flows around porous burners or droplets combustion.
Electrorheological Fluids of Coated Microspheres
Authors: Yu K. W. , Wan Jones T. K. , Law M. F. , Leung K. K.
Published: October 2003

We study model electrorheological (ER) fluids which consist of three material components in an attempt to explain recent experimental results, in which the ER effects can be promoted by adding some water. At low water concentration, the droplets tend to aggregate on the surfaces of the dispersed particles, forming coated microspheres. The ER effects are analyzed via spectral representation, and the experimental conditions for optimal ER responses are obtained. At low frequencies, it is found that by tuning the thickness and dielectric properties of the coating materials, it is possible to enhance the effective dielectric constant, thereby increasing the applicability of the ER fluids.
Phase Transitions of a Two-Dimensional Periodic Hydrophilic Hydrophobic Chain
Authors: Orlandini Enzo , Garel Thomas
Published: October 2003

We study a single self-avoiding hydrophilic hydrophobic polymer chain, through Monte Carlo lattice simulations. The affinity of monomer i for water is characterized by a (scalar) charge λi, and the monomer-water interaction is short-ranged. Assuming incompressibility yields an effective short ranged interaction between monomer pairs (i,j), proportional to (λi + λj). In this article, we take λi=+1 (resp. (λi=-1)) for hydrophilic (resp. hydrophobic) monomers and consider a chain with (i) an equal number of hydrophilic and -phobic monomers (ii) a periodic distribution of the λi along the chain, with periodicity 2p. This model may be of interest in various situations (protein folding, polysoaps, …) The simulations are done on the square lattice (d=2), for various chain lengths N. There is a critical value (pc(N)~0.07N) of the periodicity, which distinguishes between different low temperature structures. For p>pc, the ground state corresponds to a macroscopic phase separation between a dense hydrophobic core and hydrophilic loops. For p<pc (but not too small), one gets a microscopic (finite scale) phase separation, and the ground state corresponds to a chain or network of hydrophobic droplets, coated by hydrophilic monomers. These different cases will be explored through a Multiple Markov chain method. The results for the d=3 case (where pc(N)~N1/3) are similar.
Modeling the Dynamics of Amphiphilic Fluids
Authors: Lamura A. , Gonnella G. , Yeomans J. M.
Published: October 2003

We show how a lattice-Boltzmann approach can be extended to ternary fluid mixtures with the aim of modeling the diverse behavior of oil–water-surfactant systems. We model the mixture using a Ginzburg–Landau free energy with two scalar order parameters which allows us to define a lattice-Boltzmann scheme in the spirit of the Cahn–Hilliard approach to nonequilibrium dynamics. Results are presented for the spontaneous emulsification of an oil–water droplet and for spinodal decomposition in the presence of a surfactant.
Lattice-Gas Simulations of Ternary Amphiphilic Fluid Flow in Porous Media
Authors: Coveney P. V. , Maillet J.-B. , Wilson J. L. , Fowler P. W. , Al-Mushadani O. , Boghosian B. M.
Published: October 2003

We develop our existing two-dimensional lattice-gas model to simulate the flow of single phase, binary immiscible and ternary amphiphilic fluids. This involves the inclusion of fixed obstacles on the lattice, together with the inclusion of "no-slip" boundary conditions. Here we report on preliminary applications of this model to the flow of such fluids within model porous media. We also construct fluid invasion boundary conditions, and the effects of invading aqueous solutions of surfactant on oil-saturated rock during imbibition and drainage are described.
Lattice-Boltzmann Method for Macroscopic Porous Media Modeling
Authors: Freed David M.
Published: October 2003

An extension to the basic lattice-BGK algorithm is presented for modeling a simulation region as a porous medium. The method recovers flow through a resistance field with arbitrary values of the resistance tensor components. Corrections to a previous algorithm are identified. Simple validation tests are performed which verify the accuracy of the method, and demonstrate that inertial effects give a deviation from Darcy's law for nominal simulation velocities.
Simulations of Single-Fluid Flow in Porous Media
Authors: Koponen A. , Kataja M. , Timonen J. , Kandhai D.
Published: October 2003

Several results of lattice-gas and lattice-Boltzmann simulations of single-fluid flow in 2D and 3D porous media are discussed. Simulation results for the tortuosity, effective porosity and permeability of a 2D random porous medium are reported. A modified Kozeny–Carman law is suggested, which includes the concept of effective porosity. This law is found to fit well the simulated 2D permeabilities. The results for fluid flow through large 3D random fibre webs are also presented. The simulated permeabilities of these webs are found to be in good agreement with experimental data. The simulations also confirm that, for this kind of materials, permeability depends exponentially on porosity over a large porosity range.
Pore-Scale Flow and Dispersion
Authors: Maier Robert S. , Kroll D. M. , Davis H. Ted , Bernard Robert S.
Published: October 2003

Pore-scale simulations of fluid flow and mass transport offer a direct means to reproduce and verify laboratory measurements in porous media. We have compared lattice-Boltzmann (LB) flow simulations with the results of NMR spectroscopy from several published flow experiments. Although there is qualitative agreement, the differences highlight numerical and experimental issues, including the rate of spatial convergence, and the effect of signal attenuation near solid surfaces. For the range of Reynolds numbers relevant to groundwater investigations, the normalized distribution of fluid velocities in random sphere packings collapse onto a single curve, when scaled with the mean velocity. Random-walk particle simulations in the LB flow fields have also been performed to study the dispersion of an ideal tracer. These simulations show an encouraging degree of quantitative agreement with published NMR measurements of hydrodynamic and molecular dispersion, and the simulated dispersivities scale in accordance with published experimental and theoretical results for the Peclet number rangek 1 ≤ Pe ≤1500. Experience with the random-walk method indicates that the mean properties of conservative transport, such as the first and second moments of the particle displacement distribution, can be estimated with a number of particles comparable to the spatial discretization of the velocity field. However, the accurate approximation of local concentrations, at a resolution comparable to that of the velocity field, requires significantly more particles. This requirement presents a significant computational burden and hence a numerical challenge to the simulation of non-conservative transport processes.
Gradient and Percolative Clogging in Depth Filtration
Authors: Datta Somalee , Redner Sidney
Published: October 2003

The phenomenon of clogging in depth filtration is investigated, in which a dirty fluid is "cleaned" by the trapping of dirt particles within the pore space during flow through a porous medium. This gives rise to a self-generated gradient percolation process which exhibits a power law distribution for the density of trapped particles at downstream distance x from the input, both in idealized and lattice networks. Implications for efficient filter design are also mentioned.
Accuracy and Computational Efficiency in 3D Dispersion via Lattice-Boltzmann: Models for Dispersion in Rough Fractures and Double-Diffusive Fingering
Authors: Stockman Harlan W. , Glass Robert J. , Cooper Clay , Rajaram Harihar
Published: October 2003

In the presence of buoyancy, multiple diffusion coefficients, and porous media, the dispersion of solutes can be remarkably complex. The lattice-Boltzmann (LB) method is ideal for modeling dispersion in flow through complex geometries; yet, LB models of solute fingers or slugs can suffer from peculiar numerical conditions (e.g., denormal generation) that degrade computational performance by factors of 6 or more. Simple code optimizations recover performance and yield simulation rates up to ~3 million site updates per second on inexpensive, single-CPU systems. Two examples illustrate limits of the methods: (1) Dispersion of solute in a thin duct is often approximated with dispersion between infinite parallel plates. However, Doshi, Daiya and Gill (DDG) showed that for a smooth-walled duct, this approximation is in error by a factor of ~8. But in the presence of wall roughness (found in all real fractures), the DDG phenomenon can be diminished. (2) Double-diffusive convection drives "salt-fingering", a process for mixing of fresh-cold and warm-salty waters in many coastal regions. Fingering experiments are typically performed in Hele-Shaw cells, and can be modeled with the 2D (pseudo-3D) LB method with velocity-proportional drag forces. However, the 2D models cannot capture Taylor–Aris dispersion from the cell walls. We compare 2D and true 3D fingering models against observations from laboratory experiments.
Class of Cellular Automata for the Formation of Surface Aggregates
Authors: Boon Jean Pierre , Bodenstein Christopher , Hanon David
Published: October 2003

A class of cellular automata is constructed on the basis of a set of simple rules: virtual particles obeying a full exclusion principle are subject to probabilistic dynamics with nonlocal (attractive and repulsive) interactions, and with momentum transfer memory effects. Boundary conditions can be periodic or can be set to simulate open systems, with various geometries. This model system possesses the essential elements to simulate the formation of surface aggregates. A specific application is presented for the formation and the dynamics of islands of hydroxyl groups in the catalytic reduction of NO on a Pt surface. The comparison between the simulation results and the experimental observations by Field Ion Microscopy suggests possible mechanisms for the so-far unexplained formation and dynamics of hydroxyl islands during the NO reduction processes.
Numerical Study of Flow and Temperature Patterns During the Growth of GaPO4 Crystals Using the Lattice-Boltzmann Method
Authors: Miller Wolfram , Böttcher Klaus
Published: October 2003

The lattice-Boltzmann method (LBM) with enhanced collisions is used to calculate the flow and the temperature in an equipment used for growing GaPO 4 crystals from solution. For this purpose the lattice-Boltzmann method is extended to handle blocks with different physical properties. The results of our numerical calculations for the velocities and the temperatures in the solution are in reasonable agreement with recent experimental results.
Lattice Quantum Mechanics: An Application to Bose–Einstein Condensation
Authors: Succi Sauro
Published: October 2003

A lattice formulation of nonrelativistic quantum mechanics is presented, based on a formal analogy with discrete kinetic theory. The method is applied to the Gross–Pitaevski equation, a specific form of self-interacting nonlinear Schrödinger equation relevant to the study of Bose–Einstein condensation.
Lattice-Gas Quantum Computation
Authors: Yepez Jeffrey
Published: October 2003

We present a quantum lattice-gas model for a quantum computer operating with continual wavefunction collapse; entanglement of the wavefunction occurs locally over small spatial regions between nearby qubits for only a short time period. The quantum lattice-gas is a noiseless method that directly models the lattice-gas particle dynamics at the mesoscopic scale. The system behaves like a viscous Navier–Stokes fluid. Numerical simulations indicate the viscosity of the quantum lattice-gas fluid is lower than its classical lattice-gas counterpart's.
Modeling Dynamical Geometry with Lattice-Gas Automata
Authors: Hasslacher Brosl , Meyer David A.
Published: October 2003

Conventional lattice-gas automata consist of particles moving discretely on a fixed lattice. While such models have been quite successful for a variety of fluid flow problems, there are other systems, e.g., flow in a flexible membrane or chemical self-assembly, in which the geometry is dynamical and coupled to the particle flow. Systems of this type seem to call for lattice gas models with dynamical geometry. We construct such a model on one-dimensional (periodic) lattices and describe some simulations illustrating its nonequilibrium dynamics.
A Simple Optimal Parallel Algorithm for Reporting Paths in a Tree
Authors: Lingas Andrzej , Maheshwari Anil
Published: October 2003

We present optimal parallel solutions to reporting paths between pairs of nodes in an n-node tree. Our algorithms are deterministic and designed to run on an exclusive read exclusive write parallel random-access machine (EREW PRAM). In particular, we provide a simple optimal parallel algorithm for preprocessing the input tree such that the path queries can be answered efficiently. Our algorithm for preprocessing runs in O( log n) time using O(n/ log n) processors. Using the preprocessing, we can report paths between k node pairs in O( log n + log k) time using O(k + (n + S)/ log n) processors on an EREW PRAM, where S is the size of the output. In particular, we can report the path between a single pair of distinct nodes in O( log n) time using O(L/ log n) processors, where L denotes the length of the path.