stability analysis of lattice boltzmann methods the lattice boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered although the equation is a derivative of lattice gas automata it may be interpreted as a lagrangian finite difference method for the numerical simulation of the discrete velocity boltzmann equation that makes use of a bgk collision operator as a result it is not surprising that numerical instability of lattice boltzmann methods have been frequently encountered by researchers we present an analysis of the stability of perturbations of the particle populations linearized about equilibrium values corresponding to a constant density uniform mean flow the linear stability depends on the following parameters the distribution of the mass at a site between the different discrete speeds the bgk relaxation time the mean velocity and the wavenumber of the perturbations this parameter space is too large to compute the complete stability characteristics we report some stability results for a subset of the parameter space for a 7 velocity hexagonal lattice a 9 velocity square lattice and a 15 velocity cubic lattice results common to all three lattices are 1 the bgk relaxation time must be greater than 12 corresponding to positive shear viscosity 2 there exists a maximum stable mean velocity for fixed values of the other parameters and 3 as is increased from 12 the maximum stable velocity increases monotonically until some fixed velocity is reached which does not change for larger

comparisons of lattice boltzmann and finite difference methods for a two dimensional viscous burgers equation lattice boltzmann methods have been proposed as a computational means for solving various partial differential equations we look at three lattice boltzmann methods and an analogous finite difference method for solving a two dimensional scalar viscous burgers equation with periodic boundary conditions first using monotonicity arguments we prove that in the ell 1 norm the lattice boltzmann methods converge first order temporally and second order spatially then we provide some computational results which substantiate the theoretical results finally we compare the lattice boltzmann and finite difference methods the basis of comparison includes numerical results with regard to accuracy order of convergence performance and timing measurements memory requirements and conservations laws

memory effects in a nonequilibrium growth model we study memory effects in a kinetic roughening model for d 1 a different dynamic scaling is uncovered in the memory dominated phases the kardar parisi zhang scaling is restored in the absence of noise dc 2 represents the critical dimension where memory is shown to smoothen the roughening front a 0 studies on a discrete atomistic model in the same universality class reconfirm the analytical results in the large time limit while a different scaling behavior shows up for t t with t being the memory characteristic of the atomistic model results can be generalized for other nonconservative systems

an algorithm for decomposing the parametric space in multiobjective dynamic programming problems abstract this paper presents an algorithm for decomposing the parametric space in multiobjective dynamic programming modp problems by using the weighted norm approach also the basic notions of stability in convex programming problems with parameters in the objective functions are redefined and analyzed qualitatively for modp problems a numerical example is given to clarify the developed algorithm

multiple objective fuzzy dynamic programming problems a survey and some applications many real world problems involve sequential or multistage decision making dynamic programming dp is a powerful optimization technique that is particularly applicable to many complex problems requiring a sequence of interrelated decisions a new methodology multiobjective dynamic programming modp which relies heavily on conventional dynamic programming is developed as a technique for solving problems that involve conflicting objectives that obey dp characteristics in the past two decades a major development of multiobjective dynamic optimization has been made modp one of the most provocative topics within the broader subject a natural extension of dp is its use in conjumction with fuzzy sets this involves the perturbation of its components in a manner that admits of systematic fuzzification fuzzy dynamic programming fdp represents an advance on the theory of dp this paper reviews the major concepts used in modp and fmodp and examins the current progress made in the development of the corresponding theory and methodology

scaling behaviour of the time fractional kardar parisi zhang equation the scaling behaviour of the time fractional kardar parisi zhang tfkpz equation in 1 1 dimensions is investigated by scaling analysis and numerical simulations the surface morphology and critical exponents with different fractional orders are obtained the analytical results are consistent with the corresponding numerical solutions based on a caputo type fractional derivative we find that similar to the normal kardar parisi zhang equation anomalous behaviour does not appear in the tfkpz model according to the scaling idea of local slope and numerical evidence however there exists significant finite time effect of local scaling exponents in the tfkpz system our results also imply that memory effects can affect the scaling behaviour of evolving fractional surface growth

interactive decision making for multiobjective nonlinear programming problems with fuzzy parameters this paper presents interactive decision making methods for multiobjective linear linear fractional and nonlinear programming problems with fuzzy parameters on the basis of the level sets of the fuzzy numbers the concept of multiobjective programming and local m pareto optimality is introduced through the interaction with the decision maker dm the fuzzy goals of the dm for each of the objective functions in multiobjective programming are quantified by eliciting the corresponding membership functions after determining the membership functions in order to generate a candidate for the local satisficing solution which is also local m pareto optimal if the dm specifies the degree of the level sets and the reference membership values the augmented minimax problem is solved and the dm is supplied with the corresponding local m pareto optimal solution together with the trade off rates among the values of the membership functions and the degree then by considering the current values of the membership functions and as well as the trade off rates the dm responds by updating his her reference membership values and or the degree in this way the local satisficing solution for the dm can be derived efficiently from among an m pareto optimal solution set based on the proposed methods for multiobjective linear linear fractional and nonlinear programming problems with fuzzy parameters interactive computer programs are developed and an illustrative numerical example for nonlinear case is demonstrated

analysis of lattice boltzmann initialization routines lb simulations can be affected by the arising of initial layers due to an inconsistent initialization of the discrete lb populations we present some previously proposed initialization routines built to overcome that problem using the asymptotic expansion technique we show how their features can be analyzed and in some cases how accuracy and computational efficiency can be improved

a fuzzy dynamic approach to the multicriterion resource allocation problem abstract in this paper a new approach using fuzzy dynamic programming is proposed for solving the multiple criteria resource allocation problems it has been concluded that solutions obtained by this approach are always efficient hence an optimal compromise solution can be introduced a characteristic feature of the presented approach is that the objective function scalarization can be taken into account by using fuzzy set notations a numerical example is given to clarify the developed approach

convergence of convective diffusive lattice boltzmann methods lattice boltzmann methods are numerical schemes derived as a kinetic approximation of an underlying lattice gas a numerical convergence theory for nonlinear convective diffusive lattice boltzmann methods is established convergence consistency and stability are defined through truncated hilbert expansions in this setting it is shown that consistency and stability imply convergence monotone lattice boltzmann methods are defined and shown to be stable and hence convergent when consistent examples of diffusive and convective diffusive lattice boltzmann methods that are both consistent and monotone are presented

scaling analysis of the conservation growth equation with temporally correlated noise the effects of temporally correlated noise on the conservation growth are studied via the flory type approach introduced by hentschel and family phys rev lett 66 1991 1982 this phenomenological equation contains the kardar parisi zhang sun guo grant and molecular beam epitaxy growth equations as special cases and allows for a unified investigation of growth equations the scaling exponents obtained here can be in good agreement with the corresponding results derived by previous scaling approach

kardar parisi zhang equation with temporally correlated noise a self consistent approach in this paper we discuss the well known kardar parisi zhang kpz equation driven by temporally correlated noise we use a self consistent approach to derive the scaling exponents of this system we also draw general conclusions about the behavior of the dynamic structure factor ensuremath phi q t as a function of time the approach we use here generalizes the well known self consistent expansion sce that was used successfully in the case of the kpz equation driven by white noise but unlike sce it is not based on a fokker planck form of the kpz equation but rather on its langevin form a comparison to two other analytical methods as well as to the only numerical study of this problem is made and a need for an updated extensive numerical study is identified we also show that a generalization of this method to any spatiotemporal correlations in the noise is possible and two examples of this kind are considered

self consistent mode coupling approach to the nonlocal kardar parisi zhang equation the dynamic scaling of the nonlocal kardar parisi zhang equation in the strong coupling regime is investigated by a self consistent mode coupling approximation the values of the dynamic exponent depending on nonlocal parameter p are calculated numerically for the substrate dimension d 1 d 2 and d 3 respectively

an interactive fuzzy satisficing method for generalized multiobjective linear programming problems with fuzzy parameters abstract a new interactive fuzzy satisficing method for multiobjective linear programming problems with fuzzy parameters is proposed in general two types of fuzziness of human judgements should be incorporated in multiobjective programming problems one is the experts ambiguous understanding of the nature of the parameters in the problem formulation process and the other is the fuzzy goals of the decision maker for each of the objective functions in order to cope with both types of fuzziness multiobjective linear programming problems with fuzzy parameters which reflect the experts ambiguous understanding in the problem formulation are formulated and the concept of generalized multiobjective linear programming and m pareto optimality is introduced in our interactive fuzzy satisficing method the satisficing solution of the decision maker is derived efficiently from among m pareto optimal solutions on the basis of the proposed method an interactive computer program is written to implement man machine interactive procedures finally an illustrative numerical example for multiobjective linear programming problems with fuzzy parameters is demonstrated along with the corresponding computer outputs

convergence of lattice boltzmann methods for stokes flows in periodic and bounded domains combining an asymptotic analysis of the lattice boltzmann method m junk z yang asymptotic analysis of lattice boltzmann boundary conditions j stat phys 121 2005 3 35 with the stability estimate presented in m junk w a yong weighted l 2 stability of the lattice boltzmann equation preprint we are able to prove some strict convergence results the proof applies to the lattice boltzmann method with linear collision operator both in the case of periodic domains and bounded domains if the dirichlet boundary condition is realized with the bounce back rule

asymptotic analysis of lattice boltzmann boundary conditions in this article we use a general method for the analysis of finite difference schemes to investigate lattice boltzmann algorithms for navier stokes problems with dirichlet boundary conditions several link based boundary conditions for commonly used lattice boltzmann bgk models are considered with our method the accuracy of the algorithms can be exactly predicted moreover the analytical results can be used to construct new algorithms which is demonstrated with a corrected bounce back rule that requires only local evaluations but still yields second order accuracy for the velocity the analysis is applicable to general geometries and instationary flows

asymptotic analysis of the lattice boltzmann equation in this article we analyze the lattice boltzmann equation lbe by using the asymptotic expansion technique we first relate the lbe to the finite discrete velocity model fdvm of the boltzmann equation with the diffusive scaling the analysis of this model directly leads to the incompressible navier stokes equations as opposed to the compressible navier stokes equations obtained by the chapman enskog analysis with convective scaling we also apply the asymptotic analysis directly to the fully discrete lbe as opposed to the usual practice of analyzing a continuous equation obtained through the taylor expansion of the lbe this leads to a consistency analysis which provides order by order information about the numerical solution of the lbe the asymptotic technique enables us to analyze the structure of the leading order errors and the accuracy of numerically derived quantities such as vorticity it also justifies the use of richardson s extrapolation method as an example a two dimensional taylor vortex flow is used to validate our analysis the numerical results agree very well with our analytic predictions

an interactive algorithm for decomposing the parametric space in fuzzy multiobjective dynamic programming problem the aim of this chapter is to study the stability of multi objective dynamic programming modp problems with fuzzy parameters in the objective functions and in the constraints these fuzzy parameters are characterized by fuzzy numbers for such problems the concept and notion of the stability set of the first kind in parametric nonlinear programming problems are redefined and analyzed qualitatively under the concept of pareto optimality an interactive fuzzy decision making algorithm for the determination of any subset of the parametric space that has the same corresponding pareto optimal solution is proposed a numerical example is given to illustrate the method developed in the chapter

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

reproduction time statistics and segregation patterns in growing populations pattern formation in microbial colonies of competing strains under purely space limited population growth has recently attracted considerable research interest we show that the reproduction time statistics of individuals has a significant impact on the sectoring patterns generalizing the standard eden growth model we introduce a simple one parameter family of reproduction time distributions indexed by the variation coefficient d 0 1 which includes deterministic d 0 and memory less exponential distribution d 1 as extreme cases we present convincing numerical evidence and heuristic arguments that the generalized model is still in the kpz universality class and the changes in patterns are due to changing prefactors in the scaling relations which we are able to predict quantitatively at the example of saccharomyces cerevisiae we show that our approach using the variation coefficient also works for more realistic reproduction time distributions

a new approach to some possibilistic linear programming problems abstract in practice the unit costs profits of new products or new projects the lending and borrowing interest rates and cash flows are always imprecise we provide an auxiliary multiple objective linear programming model to solve a linear programming problem with imprecise objective and or constraint coefficients our strategy is to maximize the most possible value of the imprecise profit at the same time we would like to minimize the risk of obtaining lower profit and maximize the possibility of obtaining higher profit this strategy is equivalent to the practical considerations of financial problems in this paper a numeric investment problem is solved for illustrating the new approach

a stability notion for lattice boltzmann equations lattice boltzmann equations are usually constructed to satisfy some physical requirements such as galilean invariance and isotropy to possess a velocity independent pressure and no compressible effects and so on in this paper a stability requirement is introduced as a new criterion for the constructions with this requirement we derive some relations of parameters for several lattice boltzmann models interestingly these relations are satisfied by many choices of parameters used in the literature

weighted mathbb l 2 stability of the lattice boltzmann method this article is concerned with the linearized stability of the lattice boltzmann method both on periodic domains and on bounded domains with the bounce back rule used at the boundaries under a structural hypothesis we prove that a weighted mathbb l 2 norm of the solutions to the linearized lattice boltzmann method is decreasing with time moreover we show that the structural hypothesis holds true for many lattice boltzmann models

vector valued dynamic programming dynamic programming models with vector valued returns are investigated the sets of pareto maximal returns and pareto maximal policies are defined monotonicity conditions are shown to be sufficient for the set of maximal policies to include a stationary policy and for the set of maximal returns to be in the convex hull of returns of stationary policies in particular it is shown that these results hold for markov decision processes

nonlocal kardar parisi zhang equation with spatially correlated noise the effects of spatially correlated noise on a phenomenological equation equivalent to a nonlocal version of the kardar parisi zhang kpz equation are studied via the dynamic renormalization group drg techniques the correlated noise coupled with the long ranged nature of interactions prove the existence of different phases in different regimes giving rise to a range of roughness exponents defined by their corresponding critical dimensions finally self consistent mode analysis is employed to compare the non kpz exponents obtained as a result of the long range interactions with the drg results

decomposition of the parametric space in multiobjective convex programs using the generalized tchebycheff norm abstract a method for decomposing the parametric space in multiobjective convex programs with or without parameters in the constraints using the generalized tchebycheff norm is presented this approach is rather simpler than the corresponding one using the nonnegative weighted sum of objectives also several results are introduced which relate two convex programs with each other one with parameters in the constraints and the other with parameters in the objective function such results make the study of the first type of problems rather simple

stability on multiobjective dynamic programming problems with fuzzy parameters in the objective functions and in the constraints abstract the purpose of the paper is to investigate the stability on multiobjective dynamic programming problems with fuzzy parameters in the objective functions and in the constraints these fuzzy parameters are characterized by fuzzy numbers for such problems concept and notion of the stability set of the first kind in parametric nonlinear programming problems are redefined and analyzed qualitatively under the concept of pareto optimality an algorithm for the determination of any subset of the parametric space which has the same corresponding pareto optimal solution is proposed a numerical example is given to illustrate the method developed in the paper

generalized dynamic programming for multicriteria optimization abstract applications of dynamic programming dp to multicriteria sequential decision problems involving the optimization of a multicriteria preference function have been rare this is due to the ease with which dp s monotonicity assumption can be violated in such situations generalized dp avoids the potential pitfalls created by this absence of monotonicity thereby guaranteeing optimality the methodology is applied to a prototypical multicriteria dp problem namely a multicriteria version of the shortest path problem

elephants can always remember exact long range memory effects in a non markovian random walk we consider a discrete time random walk where the random increment at time step t depends on the full history of the process we calculate exactly the mean and variance of the position and discuss its dependence on the initial condition and on the memory parameter p at a critical value p 1 c 1 2 where memory effects vanish there is a transition from a weakly localized regime where the walker elephant returns to its starting point to an escape regime inside the escape regime there is a second critical value where the random walk becomes superdiffusive the probability distribution is shown to be governed by a non markovian fokker planck equation with hopping rates that depend both on time and on the starting position of the walk on large scales the memory organizes itself into an effective harmonic oscillator potential for the random walker with a time dependent spring constant k 2p 1 t the solution of this problem is a gaussian distribution with time dependent mean and variance which both depend on the initiation of the process

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

exact result vs dynamic renormalization group analysis for the non local kardar parisi zhang equation abstract in this paper i discuss a generalization of the well known kardar parisi zhang kpz equation that includes long range interactions this non local kardar parisi zhang nkpz equation has been suggested in the past to describe physical phenomena such as burning paper or deposition of colloids i show that the steady state strong coupling solution for a subfamily of the nkpz models can be solved exactly in one dimension using the fokker planck form of the equation and yields a gaussian distribution this exact result does not agree with a previous result obtained by dynamic renormalization group drg analysis the reasons for this disagreement are not yet clear

lattice boltzmann method for 3 d flows with curved boundary in this work we investigate two issues that are important to computational efficiency and reliability in fluid dynamic applications of the lattice boltzmann equation lbe 1 computational stability and accuracy of different lattice boltzmann models and 2 the treatment of the boundary conditions on curved solid boundaries and their 3 d implementations three athermal 3 d lbe models q15d3 q19d3 and q27d3 are studied and compared in terms of efficiency accuracy and robustness the boundary treatment recently developed by filippova and hanel 1998 j comp phys 147 219 and mei et al 1999 j comp phys 155 307 in 2 d is extended to and implemented for 3 d the convergence stability and computational efficiency of the 3 d lbe models with the boundary treatment for curved boundaries were tested in simulations of four 3 d flows 1 fully developed flows in a square duct 2 flow in a 3 d lid driven cavity 3 fully developed flows in a circular pipe and 4 a uniform flow over a sphere we found that while the 15 velocity 3 d q15d3 model is more prone to numerical instability and the q27d3 is more computationally intensive the q19d3 model provides a balance between computational reliability and efficiency through numerical simulations we demonstrated that the boundary treatment for 3 d arbitrary curved geometry has second order accuracy and possesses satisfactory stability characteristics

an interactive satisfying method based on alternative tolerance for multiple objective optimization with fuzzy parameters an interactive satisfying method based on alternative tolerance is presented for the multiple objective optimization problem with fuzzy parameters using the alpha level sets of the fuzzy numbers all the objectives are modeled as the fuzzy goals and the tolerances of the objectives are iteratively changed according to a decision maker for a satisfying solution via a specific attainable point programming model the membership functions can be modified and then a lexicographic two phase programming procedure is constructed correspondingly to find the final solution in a special case the objective constraint is added instead of changing the membership functions therefore the dissatisfying objectives for the decision maker can be improved step by step the presented method not only acquires the alpha pareto optimal or weak alpha pareto optimal solution of the fuzzy multiple objective optimization but also satisfies the progressive preference of the decision maker a numerical example shows its power

an algorithm for generating efficient solutions of multiobjective dynamic programming problems abstract this paper presents an algorithm for generating efficient solutions of multiobjective mathematical programming problem the generation of efficient solutions is based on the principle of optimality in dynamic programming a generalized functional equation of dynamic programming is derived from the constraint method assuming the separability and monotonicity of the problem the basic notion of stability in convex programming problems with parameters in the constraints is redefined and analyzed quantitatively for the problem a numerical example is given for the sake of illustration

self consistent expansion results for the nonlocal kardar parisi zhang equation in this paper various predictions for the scaling exponents of the nonlocal kardar parisi zhang nkpz equation are discussed i use the self consistent expansion sce and obtain results that are quite different from the result obtained in the past using dynamic renormalization group analysis a scaling approach and a self consistent mode coupling approach it is shown that the results obtained using sce recover an exact result for a subfamily of the nkpz models in one dimension while all the other methods fail to do so it is also shown that the sce result is the only one that is compatible with simple observations on the dependence of the dynamic exponent z in the nkpz model on the exponent rho characterizing the decay of the nonlinear interaction the reasons for the failure of other methods to deal with nkpz are also discussed

stability on multiobjective linear programming problems with fuzzy parameters this paper deals with multiobjective linear programming problems with fuzzy parameters fmolp for such problems some stability notions as the solvability set and the stability set of the first kind ssk1 are defined and characterized two algorithms for the determination of the set ssk1 are proposed one of these algorithms is applied when the fuzzy multiobjective problem remains linear after introducing the so called level set of the fuzzy numbers while the other algorithm is applied when the fuzzy multiobjective problem becomes nonlinear finally a numerical example is given to illustrate the theory developed in the paper

fuzzy linear programming problems with fuzzy numbers abstract linear programming problems with fuzzy parameters are formulated by fuzzy functions the ambiguity considered here is not randomness but fuzziness which is associated with the lack of a sharp transition from membership to nonmembership parameters on constraint and objective functions are given by fuzzy numbers in this paper our object is the formulation of a fuzzy linear programming problem to obtain a reasonable solution under consideration of the ambiguity of parameters this fuzzy linear programming problem with fuzzy numbers can be regarded as a model of decision problems where human estimation is influential

topsis for modm abstract in this study we extend topsis to solve a multiple objective decision making problem the principle of compromise of topsis for multiple criteria decision making is that the chosen solution should have the shortest distance from the positive ideal solution as well as the longest distance from the negative ideal solution thus we reduce a k dimensional objective space to a two dimensional objective space by a first order compromise procedure we then use membership functions of fuzzy set theory to represent the satisfaction level for both criteria we obtain a single objective programming problem by using the max min operator for the second order compromise operation to illustrate the procedure the bow river valley water quality management problem is solved by use of topsis