lattice boltzmann model for two dimensional unsteady burgers equation in this paper a special lattice boltzmann model is proposed to simulate two dimensional unsteady burgers equation the maximum principle and the stability are proved the model has been verified by several test examples excellent agreement is obtained between numerical predictions and exact solutions the cases of steep oblique shock waves are solved and compared with the two point compact scheme results the study indicates that lattice boltzmann model is highly stable and efficient even for the problems with severe gradients

a modified multiple relaxation time lattice boltzmann model for convection diffusion equation a modified lattice boltzmann model with multiple relaxation times mrt for the convection diffusion equation cde is proposed by modifying the relaxation matrix as well as choosing the corresponding equilibrium distribution function properly the present model can recover the cde with anisotropic diffusion coefficient with no deviation term even when the velocity vector varies generally with space or time through the chapman enskog analysis this model is firstly validated by simulating the diffusion of a gaussian hill which demonstrates it can handle the anisotropic diffusion problem correctly then it is adopted to calculate the longitudinal dispersion coefficient of the taylor aris dispersion numerical results show that the present model can further reduce the numerical error under the condition of non zero velocity vector especially when the dimensionless relaxation time is relatively large

introducing a new kinetic model which admits an h theorem for simulating the nearly incompressible fluid flows we present a new kinetic model for simulating the nearly incompressible fluid flows the model uses constant speed particles which are free to move in all directions in the new model the maxwellian is replaced by a fractional form while the navier stokes and continuity equations are recovered it is known that the conventional lattice boltzmann model lbm with polynomial equilibrium distribution function cannot admit an h theorem wagner 1998 9 in the present work we show that the new model admits an h theorem and the numerical schemes which stem from the new model are more stable than the conventional lbm for the streaming stage two different approaches namely the lattice based and the discontinuous galerkin based schemes are introduced the former is more cost effective than the conventional lattice boltzmann models while it maintains their simplicity the latter is a higher order spectral element method using which one can employ non uniform triangular elements with high accuracy and geometrical flexibility unlike the conventional lbm the new model is derived from continuous relations hence it does not require a symmetric discrete velocity model the accuracy and stability of the model have been verified by simulating three benchmark problems the plane couette flow lid driven square cavity and flow around an impulsively started cylinder have been simulated the results of the present work are in excellent agreement with the exact solutions and with the results reported by others

invertible cellular automata a review abstract in the light of recent developments in the theory of invertible cellular automata we attempt to give a unified presentation of the subject and discuss its relevance to computer science and mathematical physics

a cellular automaton fluid model with simple rules in arbitrarily many dimensions a new cellular automaton model for fluid dynamics is introduced unlike the conventional fhp type models the model uses easily implementable deterministic pair interaction rules which work on arbitrary dimensional orthogonal lattices the statistical and hydrodynamic theory of the model is developed and the navier stokes like hydrodynamic equations that describe the macroscopic behavior of the model are derived it turns out that the unwanted anisotropic convection behavior can be eliminated in the incompressible limit by suitable choice of the mass density an explicit expression for the viscosity tensor is calculated from a boltzmann type approximation unfortunately the viscosity turns out to be anisotropic which is a drawback as against the conventional fhp and fchc models nevertheless the new model could become interesting for fluid dynamic problems with additional variables e g free surfaces especially in two dimensions since its simple rules could relatively easily be extended for such cases

a lattice boltzmann equation for diffusion the formulation of lattice gas automata lga for given partial differential equations is not straightforward and still requires some sort of magic lattice boltzmann equation lbe models are much more flexible than lga because of the freedom in choosing equilibrium distributions with free parameters which can be set after a multiscale expansion according to certain requirements here a lbe is presented for diffusion in an arbitrary number of dimensions the model is probably the simplest lbe which can be formulated it is shown that the resulting algorithm with relaxation parameter 1 is identical to an explicit finite difference efd formulation at its stability limit underrelaxation 0 1 allows stable integration beyond the stability limit of efd the time step of the explicit lbe integration is limited by accuracy and not by stability requirements

a lattice boltzmann equation for waves we propose a lattice boltzmann model for the wave equation using a lattice boltzmann equation and the chapman enskog expansion we get 1d and 2d wave equations with truncation error of order two the numerical tests show the method can be used to simulate the wave motions

power spectrum scaling in anomalous kinetic roughening of surfaces in this paper we study kinetically rough surfaces which display anomalous scaling in their local properties such as roughness or height height correlation function by studying the power spectrum of the surface and its relation to the height height correlation we distinguish two independent causes for anomalous scaling one is super roughening global roughness exponent larger than or equal to one even if the spectrum behaves nonanamalously another cause is what we term an intrinsically anomalous spectrum in whose scaling an independent exponent exists which induces different scaling properties for small and large length scales that is the surface is not self affine in this case the surface does not need to be super rough in order to display anomalous scaling in both cases we show how to extract the independent exponents and scaling relations from the correlation functions and we illustrate our analysis with two exactly solvable examples one is the simplest linear equation for molecular beam epitaxy well known to display anomalous scaling due to super roughening the second example is a random diffusion equation which features anomalous scaling independent of the value of the global roughness exponent below or above one

lattice boltzmann model for the modified burgers equation abstract in this paper a special lattice boltzmann model is developed to solve the modified burgers equation the maximum principle and the stability are proved the model has been verified by several test examples excellent agreement is obtained between numerical predictions and the constructed asymptotic solutions or available numerical results the careful numerical study indicates the computational efficiency and stability of the lattice boltzmann method

visibility to discern local from nonlocal dynamic processes we compare using visibility the usual kardar parisi zhang kpz universality class and a fractional edward wilkinson ewf equation with correlated noise which share the same kinetic roughening exponents the kpz universality class is described by an equation in terms of the usual derivatives uncorrelated noise and therefore is intrinsically local the second model includes fractional powers of the laplace operator and correlated noise both of which are nonlocal from their scaling properties one could be tempted to conclude that both dynamics belong to the same universality class specifically to the kpz universality class however this is a wrong conclusion that calls the attention against the indiscriminate application of this approach in real systems without taking into consideration basic physical assumptions e g locality these examples reveal the necessity of finding new algorithms for detecting characteristics that remain unnoticed to classical scaling analysis where only the two first moments of the interface distribution mean and variance are used to classify the dynamics we show that visibility and in particular the kinetic roughening exponents of the visibility interface are able to distinguish between these two dynamics which are confused by standard techniques

cellular automaton fluids a model for flow in porous media numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties the large scale viewpoint is perhaps the most prevalent darcy s law relates the chief macroscopic parameters of interest flow rate permeability viscosity and pressure gradient and may be invoked to solve for any of these parameters when the others are known in practical situations however this solution may not be possible attention is then typically focused on the estimation of permeability and numerous numerical methods based on knowledge of the microscopic pore space geometry have been proposed because the intrinsic inhomogeneity of porous media makes the application of proper boundary conditions difficult microscopic flow calculations have typically been achieved with idealized arrays of geometrically simple pores throats and cracks i propose here an attractive alternative which can freely and accurately model fluid flow in grossly irregular geometries this new method s

a new scheme for source term in lbgk model for convection diffusion equation a new scheme for source term in the lattice bgk lbgk model for convection diffusion equation is proposed unlike the models proposed previously the present scheme only requires the source term in order of the knudsen number by adding a differential operator of the source term to the evolution equation the scheme can be applied to reaction diffusion systems directly numerical results are found to be in excellent agreement with the analytical solutions it is also found that the numerical accuracy of the present scheme is generally much better than that of the existing models

dynamic output integral sliding mode control with disturbance attenuation this technical note proposes a dynamic output feedback sliding mode control algorithm for linear mimo systems with mismatched norm bounded uncertainties along with disturbances and matched nonlinear perturbations a control law is first designed to ensure that the system behavior can satisfy the reaching and sliding condition a scheme designed to combine the output dependent integral sliding surface with a full order compensator is then proposed through utilizing h infin control analytical technique once the system is in the sliding mode the proposed algorithm can guarantee robust stabilization and sustain the nature of performing disturbance attenuation when the solutions to two algebraic riccati inequalities can be found finally the feasibility of our proposed algorithm is illustrated using a numerical example

cellular automation model of reaction transport processes abstract the transport and chemical reactions of solutes are modelled as a cellular automation in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule the model describes advection and diffusion in a simple way and as no restriction is placed on the number of particles at a lattice site it is also able to describe a wide variety of chemical reactions assuming molecular chaos and a smooth density function we obtain the standard reaction transport equations in the continuum limit simulations on one an two dimensional lattices show that the discrete model can be used to approximate the solutions of the continuum equations we discuss discrepancies which arise from correlations between molecules and how these disappear as the continuum limit is approached of particular interest are simulations displaying long time behaviour which depends on long wavelength statistical fluctuations not accounted for by the standard equations the model is applied to the reactions a b c and a b c with homogenous and inhomogenous initial conditions as well as to systems subject to autocatalytic reactions and displaying spontaneous formation of spatial concentration patterns

a lattice boltzmann model for elliptic equations with variable coefficient abstract a lattice boltzmann model is proposed to solve elliptic equations with variable coefficient compared with the previous model the present model is a more effective solver to the ellipse equation with variable coefficient and the ellipse equation is exactly recovered to order o e 2 the relaxation time is not fixed and is determined by the coefficient of the equation the limited numerical results show that the present model is valid for ellipse equations

lattice boltzmann model for free surface flow for modeling foaming we present a 2d and 3d lattice boltzmann model for the treatment of free surface flows including gas diffusion interface advection and related boundary conditions are based on the idea of the lattice boltzmann equation the fluid dynamic boundary conditions are approximated by using the mass and momentum fluxes across the interface which do not require explicit calculation of gradients a similar procedure is applied to fulfill the diffusion boundary condition simple verification tests demonstrate the correctness of the algorithms 2d and 3d foam evolution examples demonstrate the potential of the method

brief variable structure output feedback control design for a class of uncertain dynamic systems in this paper we consider the problem of designing a variable structure output feedback control vsofc law for a class of uncertain systems with mismatched uncertainty in the state matrix we derive existence conditions of linear sliding surfaces in terms of constrained linear matrix inequalities lmis and we give vsofc strategies we also give a simple design procedure and parameterizations of the linear switching surfaces together with solvability conditions for the given constrained lmis finally we give a design example in order to show the effectiveness of our method

simulation of cavity flow by the lattice boltzmann method a detailed analysis is presented to demonstrate the capabilities of the lattice boltzmann method thorough comparisons with other numerical solutions for the two dimensional driven cavity flow show that the lattice boltzmann method gives accurate results over a wide range of reynolds numbers studies of errors and convergence rates are carried out compressibility effects are quantified for different maximum velocities and parameter ranges are found for stable simulations the paper s objective is to stimulate further work using this relatively new approach for applied engineering problems in transport phenomena utilizing parallel computers

a lattice boltzmann model for the generalized burgers huxley equation abstract in this paper we develop a lattice boltzmann model for the generalized burgers huxley equation gbhe by choosing the proper time and space scales and applying the chapman enskog expansion the governing equation is recovered correctly from the lattice boltzmann equation and the local equilibrium distribution functions are obtained excellent agreement with the exact solution is observed and better numerical accuracy is obtained than the available numerical result the results indicate the present model is satisfactory and efficient the method can also be applied to the generalized burgers fisher equation and be extended to multidimensional cases

on variable structure output feedback controllers for uncertain dynamic systems a class of variable structure output feedback controllers for uncertain dynamic systems with bounded uncertainties is proposed no statistical information about the uncertain elements is assumed a variable structure systems approach and a geometric approach to the analysis and synthesis of system zeros are employed in the synthesis of the proposed controllers

output feedback variable structure control design this paper describes a procedure for variable structure output feedback control vsofc for a class of multivariable linear time invariant systems the equivalent control method of utkin in the output feedback mode yields a reduced order system exhibiting output feedback equivalent dynamics using the kimura davison sufficient conditions for pole placement using output feedback a sufficient condition is derived to assign the eigenvalues of the reduced order system the observability and controllability of the reduced system is discussed two switching surface design algorithms are introduced based on both a static output feedback and on an eigenstructure assignment techniques a control design is discussed as well

reliability of self affine measurements reliability and accuracy of the determination of self affine exponents are studied and quantified from the analysis of synthetic self affine profiles and surfaces the self affine exponent is measured using different methods either relying on the determination of a fractal dimension i e box counting and divider methods or directly analyzing the self affine exponent the second group of methods includes the variable bandwidth the first return and the multireturn probability distribution and the power spectrum the accuracy of all these methods is assessed in terms of the difference between an input self affine exponent used for the synthetic construction and the output exponent measured by those different methods the statistical results of this study provide a quantitative estimate of the dependence of the accuracy with the system size and the value of the self affine exponent artifacts in the measurement of self affine profiles or surfaces misorientation signal amplification and local geometric filtering which lead to biased estimates of the self affine exponent are also discussed

lattice boltzmann model for generalized nonlinear wave equations in this paper a lattice boltzmann model is developed to solve a class of the nonlinear wave equations through selecting equilibrium distribution function and an amending function properly the governing evolution equation can be recovered correctly according to our proposed scheme in which the chapman enskog expansion is employed we validate the algorithm on some problems where analytic solutions are available including the second order telegraph equation the nonlinear klein gordon equation and the damped driven sine gordon equation it is found that the numerical results agree well with the analytic solutions which indicates that the present algorithm is very effective and can be used to solve more general nonlinear problems

technical communique static output feedback stabilization an ilmi approach in this note the static output feedback stabilization problem is addressed using the linear matrix inequality technique a necessary and sufficient condition for static output feedback stabilizability for linear time invariant systems is derived in the form of a matrix inequality the extension of the result to h control is studied an iterative lmi ilmi algorithm is proposed to compute the feedback gain numerical examples are employed to demonstrate the effectiveness and the convergence of the algorithm

a convergent algorithm for computing stabilizing static output feedback gains we revisit the approach by cao et al that uses a fixed structure control law to find stabilizing static output feedback gains for linear time invariant systems by performing singular value decomposition on the output matrix together with similarity transformations we present a new stabilization method unlike their results that involve a difficult modified riccati equation whose solution is coupled with other two intermediate matrices that are difficult to find we obtain lyapunov equations we present a convergent algorithm to solve the new design equations for the gains we will show that our new approach like theirs is a dual optimal output feedback linear quadratic regulator theory numerical examples are given to illustrate the effectiveness of the algorithm and validate the new method

relaxation and transport in fchc lattice gases fchc lattice gases are the basic models for studying flow problems in three dimensional systems this paper presents a self contained theoretical analysis and some computer simulations of such lattice gases extended to include an arbitrary number of rest particles with special emphasis on non semi detailed balance nsdb models the special fchc lattice symmetry guarantees isotropy of the navier stokes equations and enumerates the 12 spurious conservation laws staggered momenta the kinetic theory is based on the mean field approximation or the nonlinear boltzmann equation it is shown how calculation of the eigenvalues of the linearized boltzmann equation offers a simple alternative to the chapman enskog method or the multi time scale methods for calculating transport coefficients and relaxation rates the simulated values for the speed of sound in nsdb models slightly disagree with the boltzmann prediction

a new lattice boltzmann model for solving the coupled viscous burgers equation abstract in this paper a new lattice boltzmann model for the coupled nonlinear system of viscous burgers equation is proposed by using the double evolutionary equations through selecting equilibrium distribution functions and amending functions properly the governing evolution system can be recovered correctly according to our proposed scheme in which the chapman enskog expansion is employed the effects of space and time resolutions on the accuracy and stability of the model are numerically investigated in detail the numerical solutions for various initial and boundary conditions are calculated and validated against analytic solutions or other numerical solutions reported in previous studies it is found that the numerical results agree well with the analytic solutions which indicates the potential of the present algorithm for solving the coupled nonlinear system of viscous burgers equation

determining exponents in models of kinetic surface roughening one of the central objectives when simulating models of kinetic surface roughening is the calculation of the scaling exponents that describe the roughness of the surface and its temporal evolution this can generally be done by studying various correlation functions in this paper it is shown that in models that exhibit a crossover at large length scales the choice of the correlation function is crucial using the two dimensional wolf villain model as an example it is shown that the exponents obtained from the scaling behavior of the width or the height height correlation function can be almost twice as large as the correct values reliable estimates are obtained using the structure factor or the time time autocorrelation function

intrinsic versus superrough anomalous scaling in spontaneous imbibition we study spontaneous imbibition using a phase field model in a two dimensional system with a dichotomic quenched noise by imposing a constant pressure mu a 0 at the origin we study the case when the interface advances at low velocities obtaining the scaling exponents z 3 0 0 1 alpha 1 50 0 02 and alpha loc 0 95 0 03 within the intrinsic anomalous scaling scenario these results are in quite good agreement with experimental data recently published likewise when we increase the interface velocity the resulting scaling exponents are z 4 0 0 1 alpha 1 25 0 02 and alpha loc 0 95 0 03 moreover we observe that the local properties of the interface change from a superrough to an intrinsic anomalous description when the contrast between the two values of the dichotomic noise is increased from a linearized interface equation we can compute analytically the global scaling exponents which are comparable to the numerical results introducing some properties of the quenched noise

on variable structure output feedback controllers in a recent work by zak hui 1993 a sliding mode controller for mimo systems using static output feedback was proposed very nice geometric conditions for how to design sliding surfaces were given however there are two restrictive assumptions in it one is that the uncertainties in the system must be bounded by a known function of outputs which excludes some possible uncertainties in the a matrix if the system is described by the triple a b c the other one requires a matrix equality to be held which may also be very difficult to satisfy in many systems in this paper we propose a modification of the sliding mode controller for a class of single input single output siso systems which can eliminate the above mentioned limitations and under certain conditions guarantee global closed loop stability hence the range of applicability of zak hui s method can be greatly broadened

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

a new lattice boltzmann model for the laplace equation in this paper a new lattice boltzmann equation which is independent of time is proposed based on the new lattice boltzmann equation some steady problems can be modeled by the lattice boltzmann method in the further study the laplace equation is investigated with the method of the higher order moment of equilibrium distribution functions and a series of partial differential equations in different space scales the numerical results show that the new method is effective

magnetohydrodynamics computations with lattice gas automata lattice gas automata have received considerable interest for the last several years and possibly may become a powerful numerical method for solving various partial differential equations and modeling different physical phenomena because of their discrete and parallel nature and the capability of handling complicated boundaries in this paper we present recent studies on the lattice gas model for magnetohydrodynamics the fhp type lattice gas model has been extended to include a bidirectional random walk process which allows well defined statistical quantities such as velocity and magnetic field to be computed from the microscopic particle representation the model incorporates a new sequential particle collision method to increase the range of useful reynolds numbers in the model an improvement that may also be of use in other lattice gas models in the context of a chapman enskog expansion the model approximates the incompressible magnetic hydrodynamic equations in the limit of low mach number and high simulation results presented here demonstrate the validity of the model for several basic problems including sound wave and alfven wave propagation and diffusive kolmogoroff type flows

macroscopic model and truncation error of discrete boltzmann method a derivation procedure to secure the macroscopically equivalent equation and its truncation error for discrete boltzmann method is proffered in this paper essential presumptions of two time scales and a small parameter in the chapman enskog expansion are disposed of in the present formulation equilibrium particle distribution function instead of its original non equilibrium form is chosen as key variable in the derivation route taylor series expansion encompassing fundamental algebraic manipulations is adequate to realize the macroscopically differential counterpart a self contained and comprehensive practice for the linear one dimensional convection diffusion equation is illustrated in details numerical validations on the incurred truncation error in one and two dimensional cases with various distribution functions are conducted to verify present formulation as shown in the computational results excellent agreement between numerical result and theoretical prediction are found in the test problems straightforward extensions to more complicated systems including convection diffusion reaction multi relaxation times in collision operator as well as multi dimensional navier stokes equations are also exposed in the appendix to point out its expediency in solving complicated flow problems

lattice boltzmann method for one and two dimensional burgers equation abstract in this paper a new method higher order moment lattice boltzmann method for one and two dimensional burgers equation is proposed the lattice boltzmann models presented here are based on a series of lattice boltzmann equations in different time scales in order to achieve higher order accuracy we use seven and four moments of the equilibrium distribution function in one and two dimensional models respectively we find two kinds of strategy to seek equilibrium distribution functions for the two dimensional model with second order accuracy these two are equivalent when a scale factor k 2 3 lastly we provide a fine numerical result of a one dimensional burgers equation numerical examples show the method can be used to simulate one and two dimensional burgers equation

a lattice boltzmann model for the nonlinear schrodinger equation the lattice boltzmann model for the nonlinear schrodinger equation is proposed the new model is based on the technique of the higher order moment of equilibrium distribution functions and a series of lattice boltzmann equations in different time scales the euler equations are derived from the nonlinear schrodinger equation by removing non physical pressure we have simulated two irrotational flows these numerical results agree well with classical ones

further results on variable output feedback controllers zak and hui 1993 proposed a sliding mode controller for linear multiple input multiple output mimo systems using static output feedback the author s previous paper 1996 provides an improvement of the output feedback controller of zak hui for a class of linear single input single output siso systems that eliminated two important limitations 1 system uncertainties must be bounded by the system output and 2 a requirement of a matrix inequality the controller developed previously can guarantee global closed loop stability this paper extends the previous results to linear mimo systems it is emphasized that the proposed mimo controller yields global closed loop stability whereas the one in zak hui can only guarantee local stability an application of the proposed mimo controller to an aircraft model is included to show the effectiveness of the method

morphology and dynamic scaling analysis of cell colonies with linear growth fronts the growth of linear cell colony fronts is investigated from the morphology of cell monolayer colonies the cell size and shape distribution the front displacement velocity and the dynamic scaling analysis of front roughness fluctuations at the early growth stages colony patterns consist of rather ordered compact domains of small cells whereas at advanced stages an uneven distribution of cells sets in and some large cells and cells exhibiting large filopodia are produced colony front profiles exhibit overhangs and behave as fractals with the dimension d f 1 25 0 05 the colony fronts shift at 0 22 0 02 m min 1 average constant linear velocity and their roughness w increases with time t dynamic scaling analysis of experimental and overhang corrected growth profile data shows that w versus system width l log log plots collapse to a single curve when l exceeds a certain threshold value l o a width corresponding to the average diameter of few cells then the influence of overhangs on the roughness dynamics becomes negligible and a growth exponent 0 33 0 02 is derived from the structure factor analysis of overhang corrected profiles a global roughness exponent s 0 50 0 05 is obtained for l 200 m this set of exponents fulfills the family vicsek relationship it is consistent with the predictions of the continuous kardar parisi zhang model

numerical simulation for solitary wave of klein gordon zakharov equation based on the lattice boltzmann model abstract this work reports a study of klein gordon zakharov equation by using the lattice boltzmann method the klein gordon zakharov equation describes the interaction of the langmuir wave and the ion acoustic wave in plasma numerical simulations of the constructed lattice boltzmann model for the klein gordon zakharov equation show the propagation and the interaction of the 1 1 and 2 1 dimensional solitary waves these simulation results are examined and compared by using different parameters and different schemes this work indicates that the lattice boltzmann method can be a very effective tool for the simulation of klein gordon zakharov equation

an ilmi approach to robust static output feedback sliding mode control this paper proposes a systematic methodology for designing robust static output feedback sliding mode control sofsmc for a class of systems with mismatched uncertainties this methodology consists of two parts one is a new sufficient and necessary condition for the existence problem in terms of two matrix inequalities the other is a direct solving method using the iterative linear matrix inequality ilmi technique the main advantages of this method are that only original system parameters are involved without any extra coordinate changes and that appealing to solving the static output feedback stabilization sofs problem is no longer required in addition the ilmi algorithm includes an optimal part to avoid high control efforts a numerical example also demonstrates the efficacy of the proposed approach