the regular spaces with countably based models the regular spaces which may be realized as the set of maximal elements in an continuous dcpo are the polish spaces in addition we give a new and conceptually simple model for complete metric spaces these results enable us to prove that the probabilistic powerdomain of a countably based model of a metric space always contains a copy of the normalized borel measures in their weak topology and to establish the hierarchy for countably based models

numerical solutions of the modified burgers equation by petrov galerkin method abstract the modified burgers equation mbe is solved numerically by the petrov galerkin method using a linear hat function as the trial function and a cubic b spline function as the test function product approximation has been used in this method a linear stability analysis of the scheme shows it to be unconditionally stable the accuracy of the presented method is demonstrated by two test problems the numerical results are found in good agreement with the exact solutions

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

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

the asymptotic relative efficiency of the mantel haenszel estimator in the increasing number of strata case the asymptotic relative efficiency are of the mantel haenszel estimator of a common odds ratio at is determined for the case in which the number of strata increases indefinitely for fixed withinstratum sample sizes the are remains above 90 over a very wide range of cases and above 93 for 2 a 5 these results support consideration of the relatively easily calculated mantel haenszel estimator rather than the conditional maximum likelihood estimator in these increasing strata cases

lattice boltzmann method for the generalized kuramoto sivashinsky equation abstract in this paper a lattice boltzmann model with an amending function is proposed for the generalized kuramoto sivashinsky equation that has the form u t u u x u x x u x x x u x x x x 0 with the chapman enskog expansion the governing evolution equation is recovered correctly from the continuous boltzmann equation it is found that the numerical results agree well with the analytical solutions

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 study of moving mesh methods applied to a thin flame propagating in a detonator delay element we study the application of moving mesh methods to a one dimensional time dependent detonator delay element problem we consider moving mesh methods based on the equidistribution principle derived by huang et al 1 adaptive mesh methods have been widely used recently to solve time dependent partial differential equations having large solution gradients significant improvements in accuracy and efficiency are achieved by adapting the nodes mesh points so that they are concentrated about areas of large solution variations each system of equations for the moving mesh methods is solved in conjunction with the detonator problem in this paper the system of ordinary differential equations that results after discretising in space is solved using the double precision version of the stiff ordinary differential equation solver dassl the numerical results clearly demonstrate that the moving mesh methods are capable of tracking the deflagration wave as it travels down the detonator delay element more accurately and more efficiently than a fixed mesh method

on the numerical solution of one dimensional pdes using adaptive methods based on equidistribution numerical experiments are described that illustrate some important features of the performance of moving mesh methods for solving one dimensional partial differential equations pdes the particular method considered here is an adaptive finite difference method based on the equidistribution of a monitor function and it is one of the moving mesh methods proposed by w huang y ren and r d russell 1994 siam j numer anal 31 709 we show how the accuracy of the computations is strongly dependent on the choice of monitor function and we present a monitor function that yields an optimal rate of convergence motivated by efficiency considerations for problems in two or more space dimensions we demonstrate a robust and efficient algorithm in which the mesh equations are uncoupled from the physical pde the accuracy and efficiency of the various formulations of the algorithm are considered and a novel automatic time step control mechanism is integrated into the scheme

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

numerical solution of burgers equation by lattice boltzmann method in this paper a lattice boltzmann model for burgers equation is proposed through selecting equilibrium distribution function properly the model has been verified by three test examples the numerical results are found in good agreement with analytical solutions and numerical solutions reported in previous studies the advantages of the resulting method are algorithmic simplicity parallel computation easy handling of complicated boundary conditions so it is very easy to implement and deal with more complex problems

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

a computational model for metric spaces for every metric space x we define a continuous poset bx such that x is homeomorphic to the set of maximal elements of bx with the relative scott topology the poset bx is a dcpo iff x is complete and continuous iff x is separable the computational model bx is used to give domain theoretic proofs of banach s fixed point theorem and of two classical results of hutchinson on a complete metric space every hyperbolic iterated function system has a unique non empty compact attractor and every iterated function system with probabilities has a unique invariant measure with bounded support we also show that the probabilistic power domain of bx provides an continuous computational model for measure theory on a separable complete metric space x

a category of compositional domain models for separable stone spaces in this paper we introduce sfpm a category of sfp domains which provides very satisfactory domain models i e partializations of separable stone spaces 2 stone spaces more specifically sfpm is a subcategory of sfpep closed under direct limits as well as many constructors such as lifting sum product and plotkin powerdomain with the notable exception of the function space constructor sfpm is structurally well behaved in the sense that the functor max which associates to each object of sfpm the stone space of its maximal elements is compositional with respect to the constructors above and continuous a correspondence can be established between these constructors over sfpm and appropriate constructors on stone spaces whereby sfpm domain models of stone spaces defined as solutions of a vast class of recursive equations in sfpm can be obtained simply by solving the corresponding equations in sfpm moreover any continuous function between two 2 stone spaces can be extended to a continuous function between any two sfpm domain models of the original spaces the category sfpm does not include all the sfp s with a 2 stone space of maximal elements csfp s we show that the csfp s can be characterized precisely as suitable retracts of sfpm objects then the results proved for sfpm easily extends to the wider category having csfp s as objects using sfpm we can provide a plethora of partializations of the space of finitary hypersets the hyperuniverse n ann new york acad sci 806 1996 140 these includes the classical ones proposed in abramsky a cook s tour of the finitary non well founded sets unpublished manuscript 1988 inform comput 92 2 1991 161 and mislove et al inform comput 93 1 1991 16 which are also shown to be non isomorphic thus providing a negative answer to a problem raised in mislove et al

ideal models of spaces ideal domains have an elementary order theoretic structure every element is either compact or maximal despite this we establish that 1 they can model any space currently known to possess a countably based model and 2 the metric spaces with ideal models are exactly the completely metrizable spaces

dynamical systems measures and fractals via domain theory abstract we introduce domain theory in dynamical systems iterated function systems fractals and measure theory for a discrete dynamical system given by the action of a continuous map f x x on a metric space x we study the extended dynamical systems vx vf ux uf and lx lf where v u and l are respectively the vietoris hyperspace the upper hyperspace and the lower hyperspace functors we show that if x f is chaotic then so is ux uf when x is locally compact ux is a continuous bounded complete dcpo if x is second countable as well then ux will be continuous and can be given an effective structure we show how strange attractors attractors of iterated function systems fractals and julia sets are obtained effectively as fixed points of deterministic functions on ux or fixed points of non deterministic functions on cux where c is the convex plotkin power domain we also show that the set m x of finite borel measures on x can be embedded in pux where p is the probabilistic power domain this provides an effective framework for measure theory we then prove that the invariant measure of an hyperbolic iterated function system with probabilities can he obtained as the unique fixed point of an associated continuous function on pux

kappa coefficients in medical research kappa coefficients are measures of correlation between categorical variables often used as reliability or validity coefficients we recapitulate development and definitions of the k categories by m ratings kappas k x m discuss what they are well or ill designed to do and summarize where kappas now stand with regard to their application in medical research the 2 x m m 2 intraclass kappa seems the ideal measure of binary reliability a 2 x 2 weighted kappa is an excellent choice though not a unique one as a validity measure for both the intraclass and weighted kappas we address continuing problems with kappas there are serious problems with using the k x m intraclass k 2 or the various k x m weighted kappas for k 2 or m 2 in any context either because they convey incomplete and possibly misleading information or because other approaches are preferable to their use we illustrate the use of the recommended kappas with applications in medical research

a fourth order numerical scheme for solving the modified burgers equation a finite difference scheme based on fourth order rational approximants to the matrix exponential term in a two time level recurrence relation is proposed for the numerical solution of the modified burgers equation the resulting nonlinear system which is analyzed for stability is solved using an already known modified predictor corrector scheme the results arising from the experiments are compared with the corresponding ones known from the available literature

a steady state lattice boltzmann model for incompressible flows in this paper we propose a steady state lattice boltzmann equation which is independent of time for steady incompressible flows on the basis of the steady state lattice boltzmann equation we find a way of modeling some steady state problems using the lattice boltzmann model in further study we investigate steady state incompressible flows with the method of the higher order moment of equilibrium distribution functions and a series of partial differential equations for different space scales by assuming r constant we obtain the momentum equation for incompressible steady state flow the numerical results show that the new method is effective

estimation of operating characteristics for dependent diagnostic tests based on latent markov models we describe a method for making inferences about the joint operating characteristics of multiple diagnostic tests applied longitudinally and in the absence of a definitive reference test log linear models are adopted for the classification distributions conditional on the latent state where inclusion of appropriate interaction terms accommodates conditional dependencies among the tests a marginal likelihood is constructed by marginalizing over a latent two state markov process specific latent processes we consider include a first order markov model a second order markov model and a time nonhomogeneous markov model although the method is described in full generality adaptations to handle missing data are described model diagnostics are considered based on the bootstrap distribution of conditional residuals the methods are illustrated by application to a study of diffuse bilateral infiltrates among patients in intensive care wards in which the objective was to assess aspects of validity and clinical agreement

a self adaptive moving mesh method for the camassa holm equation a self adaptive moving mesh method is proposed for the numerical simulations of the camassa holm equation it is an integrable scheme in the sense that it possesses the exact n soliton solution it is named a self adaptive moving mesh method because the non uniform mesh is driven and adapted automatically by the solution once the non uniform mesh is evolved the solution is determined by solving a tridiagonal linear system due to these two superior features of the method several test problems give very satisfactory results even if by using a small number of grid points

an efficient adaptive mesh redistribution method for a non linear dirac equation this paper presents an efficient adaptive mesh redistribution method to solve a non linear dirac nld equation our algorithm is formed by three parts the nld evolution the iterative mesh redistribution of the coarse mesh and the local uniform refinement of the final coarse mesh at each time level the equidistribution principle is first employed to iteratively redistribute coarse mesh points and the scalar monitor function is subsequently interpolated on the coarse mesh in order to do one new iteration and improve the grid adaptivity after an adaptive coarse mesh is generated ideally and finally each coarse mesh interval is equally divided into some fine cells to give an adaptive fine mesh of the physical domain and then the solution vector is remapped on the resulting new fine mesh by an affine method the nld equation is finally solved by using a high resolution shock capturing method on the fixed non uniform fine mesh extensive numerical experiments demonstrate that the proposed adaptive mesh method gives the third order rate of convergence and yields an efficient and fast nld solver that tracks and resolves both small local and large solution gradients automatically

an adaptive mesh refinement strategy for finite element solution of the elliptic problem abstract in this paper we develop an adaptive finite element method for elliptic problems first we assume that in each subdomain the norm of the approximation error at the current mesh configuration is bounded by the norm of the approximation error obtained at the previous mesh configuration for some norm h s then an a posteriori error estimator is designed based on the approximate solution correction between the solution on the last two mesh configurations based on this new error estimator the element wise refinement strategy in each subdomain is provided for a given tolerance a discussion on the choice of the coefficients in the assumption is given for different norm spaces and for different degrees of finite element family four 2d numerical benchmark examples of different domains and two 3d numerical benchmark examples are tested to demonstrate the robustness of our method when possible our numerical results are also compared to corresponding results from existing methods all the results show that the proposed method is robust and efficient in terms of the number of degrees of freedom

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

error estimates for discontinuous galerkin approximations of implicit parabolic equations we analyze the classical discontinuous galerkin method for implicit parabolic equations symmetric error estimates for schemes of arbitrary order are presented the ideas developed allow certain assumptions frequently required in previous work to be relaxed for example different discrete spaces are allowed at each time step and the spatial operator is not required to be self adjoint or independent of time error estimates are posed in terms of projections of the exact solution onto the discrete spaces and are valid under the minimal regularity guaranteed by the natural energy estimate these projections are local and enjoy optimal approximation properties when the solution is sufficiently regular

an application of a representation theorem for fuzzy metrics to domain theory in this paper we study the interplay between fuzzy metric spaces and domain theory using the representation theorem established in mardones perez and de prada vicente 2012 12 we will prove that suitable restrictions of completeness in fuzzy metric spaces correspond to a structure of domain in the poset of formal balls endowed with appropriate orders

solution of parabolic equations by backward euler mixed finite element methods on a dynamically changing mesh we develop and analyze methods based on combining the lowest order mixed finite element method with backward euler time discretization for the solution of diffusion problems on dynamically changing meshes the methods developed are shown to preserve the optimal rate error estimates that are well known for static meshes the novel aspect of the scheme is the construction of a linear approximation to the solution which is used in projecting the solution from one mesh to another extensions to advection diffusion equations are discussed where the advection is handled by upwinding numerical results validating the theory are also presented

on assessing interrater agreement for multiple attribute responses new methods are developed for assessing the extent of interrater agreement when each unit to be rated is characterized by a possibly empty subset of a specified set of distinct nominal attributes for such multiple attribute response data a two rater concordance statistic is derived and associated statistical inference making procedures are provided this concordance statistic is corrected for chance agreement by using an underlying hypergeometric model numerical examples are given to illustrate the proposed methodology and comparisons to other agreement statistics e g kappa are made

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

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

an adaptive moving grid method for one dimensional systems of partial differential equations we describe a fully adaptive moving grid method for solving initial boundary value problems for systems of one space dimensional partial differential equations whose solutions exhibit rapid variations in space and time the method based on finite differences is of the lagrangian type and has been derived through a co ordinate transformation which leads to equidistribution in space of the second derivative our technique is intermediate between static regridding methods where nodes remain fixed for intervals of time and continuously moving grid methods where the node movement and the pde integration are fully coupled in our approach the computation of the moving grids and the solution on these grids are carried out separately while the nodes are moved at each time step two error monitors have been implemented one to govern the time step selection and the other to eventually adapt the number of moving nodes the method allows the use of different moving grids for different components in the pde system numerical experiments are presented for a set of five sample problems from the literature including two problems from combustion

a mixed variable continuously deforming finite element method for parabolic evolution problems part ii the coupled problem of phase change in porous media the conceptual framework of a least squares rate variational approach to the formulation of continuously deforming mixed variable finite element computational scheme for a single evolution equation was presented in part i 1 in this paper part ii we extend these concepts and present an adaptively deforming mixed variable finite element method for solving general two dimensional transport problems governed by a system of coupled non linear partial differential evolution equations in particular we consider porous media problems that involve coupled heat and mass transport processes that yield steep continuous moving fronts and abrupt discontinuous moving phase change interfaces in this method the potentials such as the temperature pressure and species concentration and the corresponding fluxes are permitted to jump in value across the phase change interfaces the equations and the jump conditions governing the physical phenomena which were specialized from a general multiphase multiconstituent mixture theory provided the basis for the development and implementation of a two dimensional numerical simulator this simulator can effectively resolve steep continuous fronts i e shock capturing without oscillations or numerical dispersion and can accurately represent and track discontinuous fronts i e shock fitting through adaptive grid deformation and redistribution the numerical implementation of this simulator and numerical examples that demonstrate the performance of the computational method are presented in part iii2 of this paper

evaluating interrater agreement through case control sampling an approach to evaluating interrater agreement is presented that is based on case control sampling scheme in which individuals are classified by one rating method and stratified prior to being classified by a second rating method a new estimate of the kappa interrater agreement index that is based on the case control scheme is also presented power and other economic considerations are discussed indicating that the new approach may be useful in practice

convex power domain and vietoris space abstract in this paper the maximal point spaces mp space in short of convex power domains are investigated some characterizations of the maximal points of convex power domains are obtained it is proved that for a scott compact continuous domain d convex power domain c d is a domain hull of its maximal points max c d if each element of max c d is generated by a compact subset of max d in this case the space max c d can be identified with the compact subsets com max d of max d and the vietoris topology on com max d is the topology inherited from the convex power domain finally an example is given to show that even for a weakly compact continuous domain its convex power domain need not be a domain hull of the maximal points

moving finite elements i we present new and general numerical methods for dealing with problems whose solutions develop sharp transition layers or near shocks these methods allow many nodes automatically to concentrate in the critical regions and move with them for clarity of exposition we concentrate on the space of piecewise linear functions with movable nodes with burgers equation as our test equation but the generalization to much more general spaces and equations including even certain previous moving vorticity blobs of the first author and s doss for the navier stokes equations becomes clear in this paper we present the theoretical and computational details of our scheme along with computational trial runs for burgers equation showing that the nodes do concentrate sharply and move with the shocks as desired the conclusiveness of these preliminary numerical trials is marred somewhat by the fact that we never successfully debugged a newton s method for our implicit stiff ode solver and were thus limited to ver

effectively given spaces abstract the theory of domains has been presented in various formalisms the purpose of this paper is to show how to use the ideas in effectively given domains to formalize a theory of effectively given t0 spaces in an effectively given space there are two equivalent formulations of the notion of a computable object an operational one and a topological one the operational notion may be viewed as an implementation of the topological notion

higher order accurate numerical solution of unsteady burgers equation abstract higher order accurate finite difference schemes for solving the unsteady burgers equation which often arises in mathematical modeling used to solve problems in fluid dynamics are presented the unsteady burgers equation belongs to a few nonlinear partial differential equations which has an exact solution and it allows one to compare the numerical solution with the exact one and the properties of different numerical methods we propose an explicit finite difference scheme for a numerical solution of the heat equation with robin boundary conditions it has a sixth order approximation in the space variable and a third order approximation in the time variable as an application we developed numerical schemes for solving a numerical solution of burgers equation using the relationship between the heat and burgers equations this scheme has up to sixth order approximation in the space variables the main advantage of our approach is transition to one dimensional equation which essentially reduces the computation costs compared to other direct methods for solving the unsteady burgers equation the numerical results of test examples are found in good agreement with exact solutions for a wide range of reynolds number and confirm the approximation orders of the schemes proposed

truncation error analysis of lattice boltzmann methods a truncation error analysis is performed for models based on the lattice boltzmann lb equation this analysis involves two steps the recursive application of the lb equation and a taylor series expansion unlike previous analytical studies of lb methods the present work does not assume an asymptotic relationship between the temporal and spatial discretization parameters or between the probability distribution function f and its equilibrium distribution feq effective finite difference stencils are derived for both the distribution function and the primitive variables i e density and velocity the governing partial differential equations are also recovered the associated truncation errors are derived and the results are validated by numerical simulation of analytic flows analysis of the truncation errors elucidates the roles of the kinetic theory relaxation parameter and the discretization parameters x and t the effects of initial and boundary conditions are also addressed and are shown to significantly affect the overall accuracy of the 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

on the mass matrix spectrum bounds of wathen and the local moving finite elements of baines andrew wathen has shown that the eigenvalues of the diagonally preconditioned piecewise linear moving finite element mfe or finite element fe mass matrix in n dimensions lie in frac 1 2 1 frac 1 2 n baines using similar considerations has designed very local mfe methods with block diagonal mass matrices in this paper a simplified proof of wathen s basic spectrum bound is given it results from a simple comparison bound between the l 2 norm and a certain diagonal norm for discontinuous piecewise linear functions on an arbitrary triangular grid the simplicity of our comparison lets us extend wathen s result to other situations such as miller s gradient weighted mfe method gwmfe it also lets us design very local mfe and fe and gwmfe methods which minimize the pde residual dot u l u not in l 2 norm but in a comparable norm these methods turn out to be equivalent to those of baines these methods retain the desired conservation properties for pde s in conservation l

numerical stability analysis of fdlbm we analyze the numerical stability of finite difference lattice boltzmann method fdlbm by means of von neumann stability analysis the stability boundary of the fdlbm depends on the bgk relaxation time the cfl number the mean flow velocity and the wavenumber as the bgk relaxation time is increased at constant cfl number the stability of the central difference lb scheme may not be ensured the limits of maximum stable velocity are obtained around 0 39 0 43 and 0 43 for the central difference for the explicit upwind difference and for the semi implicit upwind difference schemes respectively we derive artificial viscosities for every difference scheme and investigate their influence on numerical stability the requirements for artificial viscosity is consistent with the conditions derived from von neumann stability analysis this analysis elucidates that the upwind difference schemes are suitable for simulation of high reynolds number flows

a moving mesh finite element method for the two dimensional stefan problems an r adaptive moving mesh method is developed for the numerical solution of an enthalpy formulation of two dimensional heat conduction problems with a phase change the grid is obtained from a global mapping of the physical to the computational domain which is designed to cluster mesh points around the interface between the two phases of the material the enthalpy equation is discretised using a semiimplicit galerkin finite element method using linear basis functions the moving finite element method is applied to problems where the phase front is cusp shaped and where the interface changes topology

on computational environments of topological spaces as has been disclosed by k martin a large number of important topological spaces do not have any continuous domain as their computational model so it is of interest to study new kinds of pragmatic computational environments so as to model more topological spaces in this paper we focus on bounded complete continuous posets with enough maximal points which are shown to be a good choice for computational environments of tychonoff spaces with no directed complete model it is proved that the maximal point space of a choquet complete weak domain is also choquet complete furthermore it is proved that x is a tychonoff space iff x has a bounded complete weak domain environment and it is also shown that hausdorff compactifications of tychonoff spaces can be realized via some of their computational environments

moving mesh partial differential equations mmpdes based on the equidistribution principle this paper considers several moving mesh partial differential equations that are related to the equidistribution principle several of these are new and some correspond to discrete moving mesh equations that have been used by others their stability is analyzed and it is seen that a key term for most of these moving mesh pdes is a source like term that measures the level of equidistribution it is shown that under weak assumptions mesh crossing cannot occur for most of them finally numerical experiments for these various moving mesh pdes are performed to study their relative properties

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

the large sample relative efficiency of the mantel haenszel estimator in the fixed strata case the large sample relative efficiency of the mantel haenszel estimator psi mh of an odds ratio is investigated for the case in which the number of strata is fixed and the sample sizes within each stratum increase indefinitely the results show that psi mh is very efficient over a wide range of designs likely to occur in practice however conditions are identified under which the relative efficiency of this widely used estimator can be unusually low

finite element methods for nonlinear flows in porous media abstract a model problem is presented for fluid flow in porous media which has numerical difficulties common with many other areas of nonlinear mechanics special finite element techniques are described which have proved useful in alleviating many of these difficulties a modified method of characteristics mixed finite element methods for fluid velocities singularity removal and self adaptive local grid refinement techniques are presented both theoretical and computational results are described together with an indication of the present and future uses of finite element methods in large scale reservoir simulation

conditional inference for predictive agreement we introduce the concept and a measure of predictive agreement tau for two raters classifying items into q categories the measure is based on the linear combination of log odds ratios from 2 x 2 subtables of a q x q cross classification table we show that analysis procedures for this measure and transforms of it can be based on conditional likelihood procedures these procedures are exact which is particularly helpful because of the small tabular cell frequencies which can typically arise with agreement data to illustrate the advantages of the methodology examples of typical agreement data arising from medical studies are considered we demonstrate that the conditional likelihood function portrays the available sample information about tau often more appropriately than the maximum likelihood estimate and an associated standard error we highlight the value of combining information via likelihoods in an example involving 24 2 x 2 tables an example involving three categories is used to illustrate that the methodology for the overall agreement measure can be adapted to examine relative agreement between pairs of categories

optimal discretizations in adaptive finite element electromagnetics one of the primary objectives of adaptive finite element analysis research is to determine how to effectively discretize a problem in order to obtain a sufficiently accurate solution efficiently therefore the characterization of optimal finite element solution properties could have significant implications on the development of improved adaptive solver technologies ultimately the analysis of optimally discretized systems in order to learn about ideal solution characteristics can lead to the design of better feedback refinement criteria for guiding practical adaptive solvers towards optimal solutions efficiently and reliably a theoretical framework for the qualitative and numerical study of optimal finite element solutions to differential equations of macroscopic electromagnetics is presented in this study for one two and three dimensional systems the formulation is based on variational aspects of optimal discretizations for helmholtz systems that are closely related to the underlying stationarity principle used in computing finite element solutions to continuum problems in addition the theory is adequately general and appropriate for the study of a range of electromagnetics problems including static and time harmonic phenomena moreover finite element discretizations with arbitrary distributions of element sizes and degrees of approximating functions are assumed so that the implications of the theory for practical h p hp and r type finite element adaption in multidimensional analyses may be examined copyright 2001 john wiley sons ltd

a novel lattice boltzmann model for the coupled viscous burgers equations abstract in this work a new lattice boltzmann model for coupled burgers equations is proposed through selecting proper distribution functions unlike the previous models the present model can exactly recover the coupled equations without any assumptions a detailed numerical study on several coupled burgers equations is performed to validate the present model and the results show that the present model not only has a second order convergence rate in space but also is more accurate than the previous model

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

lattice boltzmann models for two dimensional coupled burgers equations abstract in this paper two lattice boltzmann models for two dimensional coupled burgers equations are proposed through treating the part or all of convection items as the source term where the spatial gradient can be calculated by the distribution function the models can exactly recover the burgers equations without any assumptions some numerical tests are also performed to validate the present models it is found that the proposed models are more accurate and efficient in solving two dimensional coupled burgers equations

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

an iterative grid redistribution method for singular problems in multiple dimensions we introduce an iterative grid redistribution method based on the variational approach the iterative procedure enables us to gain more precise control of the grid distribution near the regions of large solution variations the method is particularly effective for solving partial differential equations with singular solutions e g blowup solutions our method requires little prior information of the singular solutions and can handle multiple singularities the method is successfully applied to the nonlinear schrodinger equation and the keller segal equations where solutions with multiple blowup points can be solved up to times very close to the blowup time

unified approach to simulation on deforming elements with application to phase change problems abstract several different approaches to simulation on deforming finite elements are shown to generate the same weighted residuals formulation for the evolution of the dependent variables control of node motion by means of mesh stretching in two dimensions is illustrated in the context of phase change problems simulation of problems with large phase boundary excursions shows good agreement with analytic solutions

a new adaptive mesh refinement strategy for numerically solving evolutionary pde s a graph based implementation of quadtree meshes for dealing with adaptive mesh refinement amr in the numerical solution of evolutionary partial differential equations is discussed using finite volume methods the technique displays a plug in feature that allows replacement of a group of cells in any region of interest for another one with arbitrary refinement and with only local changes occurring in the data structure the data structure is also specially designed to minimize the number of operations needed in the amr implementation of the new scheme allows flexibility in the levels of refinement of adjacent regions moreover storage requirements and computational cost compare competitively with mesh refinement schemes based on hierarchical trees low storage is achieved for only the children nodes are stored when a refinement takes place these nodes become part of a graph structure thus motivating the denomination autonomous leaves graph alg for the new scheme neighbors can then be reached without accessing their parent nodes additionally linear system solvers based on the minimization of functionals can be easily employed alg was not conceived with any particular problem or geometry in mind and can thus be applied to the study of several phenomena some test problems are used to illustrate the effectiveness of the technique

the kappa coefficient of agreement for multiple observers when the number of subjects is small published results on the use of the kappa coefficient of agreement have traditionally been concerned with situations where a large number of subjects is classified by a small group of raters the coefficient is then used to assess the degree of agreement among the raters through hypothesis testing or confidence intervals a modified kappa coefficient of agreement for multiple categories is proposed and a parameter free distribution for testing null agreement is provided for use when the number of raters is large relative to the number of categories and subjects the large sample distribution of kappa is shown to be normal in the nonnull case and confidence intervals for kappa are provided the results are extended to allow for an unequal number of raters per subject

total objects of domains abstract the main result of this paper is a characterization of the space induced by scott topology on the set of total objects of a bounded complete cpo this characterization is simple with bounded complete algebraic cpo s where a family of clopen sets plays an essential role in the characterization in the more general case of continuity one can only produce distinct families of open sets and closed sets to axiomatize the essential properties of a total space besides the main characterization we also discuss its relation to continuous spaces studied in our earlier paper and the relation between compact t spaces and total spaces under the lower topology

convergence of lattice boltzmann methods for navier stokes flows in periodic and bounded domains combining an asymptotic analysis of the lattice boltzmann method with a stability estimate we are able to prove some convergence results which establish a strict relation to the incompressible navier stokes equation the proof applies to the lattice boltzmann method in the case of periodic domains and for specific bounded domains if the dirichlet boundary condition is realized with the bounce back rule

computational solution of two dimensional unsteady pdes using moving mesh methods numerical experiments are described which illustrate some important features of the performance of moving mesh methods for solving two dimensional partial differential equations pdes here we are concerned with algorithms based on moving mesh methods proposed by w huang and r d russell siam j sci comput 20 998 1999 we show that the accuracy of the computations is strongly influenced by the choice of monitor function and we present a monitor function which yields a higher rate of convergence than those that are commonly used in an earlier paper g beckett j a mackenzie a ramage and d m sloan j comput phys 167 372 2001 we demonstrated a robust and efficient algorithm for problems in one space dimension in which the mesh equation is decoupled from the physical pde and the time step is controlled automatically the present work extends this algorithm to deal with problems in two space dimensions

a space time fully decoupled wavelet galerkin method for solving two dimensional burgers equations abstract a space time fully decoupled formulation for solving two dimensional burgers equations is proposed based on the coiflet type wavelet sampling approximation for a function defined on a bounded interval by applying a wavelet galerkin approach for spatial discretization nonlinear partial differential equations are first transformed into a system of ordinary differential equations in which all matrices are completely independent of time and never need to be updated in the time integration finally the mixed explicit implicit scheme is employed to solve the resulting semi discretization system by numerically studying three widely considered test problems results demonstrate that the proposed method has a much better accuracy and a faster convergence rate than many existing numerical methods most importantly the study also indicates that the present wavelet method is capable of solving the two dimensional burgers equation at high reynolds numbers

stable lattice boltzmann schemes with a dual entropy approach for monodimensional nonlinear waves we follow the mathematical framework proposed by bouchut 2003 22 and present in this contribution a dual entropy approach for determining equilibrium states of a lattice boltzmann scheme this method is expressed in terms of the dual of the mathematical entropy relative to the underlying conservation law it appears as a good mathematical framework for establishing a h theorem for the system of equations with discrete velocities the dual entropy approach is used with d1q3 lattice boltzmann schemes for the burgers equation it conducts to the explicitation of three different equilibrium distributions of particles and induces naturally a nonlinear stability condition satisfactory numerical results for strong nonlinear shocks and rarefactions are presented we prove also that the dual entropy approach can be applied with a d1q3 lattice boltzmann scheme for systems of linear and nonlinear acoustics and we present a numerical result with strong nonlinear waves for nonlinear acoustics we establish also a negative result with the present framework the dual entropy approach cannot be used for the shallow water equations

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

transition models for multivariate longitudinal binary data in many settings with longitudinal binary data interest lies in modeling covariate effects on transition probabilities of an underlying stochastic process when data from two or more processes are available the scientific focus may be on the degree to which changes in one process are associated with changes in another process analysis based on independent markov models permits separate examination of covariate effects on the transition probabilities for each process but no insight into between process associations is obtained we propose a method of estimation and inference based on joint transitional models for multivariate longitudinal binary data using gee2 or alternating logistic regression that allows modeling of covariate effects on marginal transition probabilities as well as the association parameters consistent estimates of regression coefficients and association parameters are obtained and efficiency gains for the parameters governing the marginal transition probabilities are realized when

a three dimensional adaptive method based on the iterative grid redistribution in this paper we develop a three dimensional adaptive method based on iterative grid redistribution technique introduced in j comput phys 159 2000 246 the key step for the successful implementation is a fast algorithm for grid generation which is composed of solving the linear grid equation systems and an efficient method for inverting a map by computing iso surface intersections to carry out the three dimensional calculations the whole procedure is also parallelized on a pc cluster the improved and extended three dimensional adaptive method is applied to solve pdes with singular solutions that have three dimensional structures numerical experiments have demonstrated the method s effectiveness

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

2n order compact finite difference scheme with collocation method for solving the generalized burger s huxley and burger s fisher equations the generalized burger s huxley and burger s fisher equations are solved by fully different numerical scheme the equations are discretized in time by a new linear approximation scheme and in space by 2n order compact finite difference scheme after that a collocation method is applied also the two dimensional unsteady burger s equation is described by our proposed scheme numerical experiments and numerical comparisons are presented to show the efficiency and the accuracy of the proposed scheme

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

the modified local crank nicolson method for one and two dimensional burgers equations the modified local crank nicolson method is applied to solve one and two dimensional burgers equations new difference schemes that are explicit unconditionally stable and easy to compute are obtained numerical solutions obtained by the present method are compared with exact solutions and it is seen that they are in excellent agreement

exact solution of kauffman s model with connectivity one kauffman s model is a randomly assembled network of boolean automata each automaton receives inputs from at most k other automata its state at discrete time t 1 is determined by a randomly chosen but fixed boolean function of the k inputs at time t the resulting quenched random dynamics of the network demonstrates two phases a frozen and a chaotic phase the authors give an exact solution of the model for connectivity k 1 valid everywhere in the frozen phase and at a critical point valid for finite as well as for infinite networks they discuss the network s critical behaviour and finite size effects the results for the frozen phase presented complement recent exact results for the chaotic phase obtained for k infinity

the finite element method for parabolic equations in this first of two papers computable a posteriori estimates of the space discretization error in the finite element method of lines solution of parabolic equations are analyzed for time independent space meshes the effectiveness of the error estimator is related to conditions on the solution regularity mesh family type and asymptotic range for the mesh size for clarity the results are limited to a model problem in which piecewise linear elements in one space dimension are used the results extend straight forwardly to systems of equations and higher order elements in one space dimension while the higher dimensional case requires additional considerations the theory presented here provides the basis for the analysis and adaptive construction of time dependent space meshes which is the subject of the second paper computational results show that the approach is practically very effective and suggest that it can be used for solving more general problems

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