one dimensional lattices topologically equivalent to two dimensional lattices within the context of the lattice gas model ii the triangular lattice abstract continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non markovian and markovian processes and applied to the diffusion within the context of the lattice gas model a procedure allowing to construct one dimensional lattices that are topologically equivalent to two dimensional lattices is described in detail in the case of a hexagonal lattice which has the particular feature that need four types of dynamical variables this example shows additional features to the general procedure and some extensions are also suggested in order to provide a wider insight in the present approach

fuzzy stage characteristic preserving product life cycle modeling abstract stage concerns have been important in product life cycles plc such concerns are stage identification stage related strategies and here newly introduced stage modeling stage modeling is concerned with not only modeling but also aggregation of individual stages in an overall influencing manner it not only preserves the respective characteristics of the stages but also may be explored for the stage related strategy issue later to date this aspect of plc modeling has not yet been explored in this paper a fuzzy plc modeling capable of preserving the fuzzy individual characteristics of the stages is proposed the various concepts such as boundary identification fuzzy stages modeling and stages inter influence functions are introduced and discussed finally to illustrate and support the approach a numerical example and a comparison with classical data analytic procedures segmented polynomial regression and autoregressive integrated moving average is provided

regular article on a class of pade finite volume methods a class of pade finite volume methods providing an improved spectral resolution is presented and compared with well known methods the formulation is based on the sliding averages of the variables and allows the computation of derivatives of all orders using the fourier analysis these methods are examined with respect to i order of accuracy ii spectral resolution iii boundary conditions and iv stability

one dimensional lattices topologically equivalent to two dimensional lattices within the context of the lattice gas model continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non markovian and markovian processes and applied to the diffusion within the context of the lattice gas model a procedure allowing to construct one dimensional lattices that are topologically equivalent to two dimensional lattices is described in detail in the case of a rectangular lattice this example shows the general features that possess the procedure and extensions are also suggested in order to provide a wider insight in the present approach

discrete stochastic evolution rules and continuum evolution equations abstract the continuum evolution equations are derived from updating rules for three classes of stochastic models the first class corresponds to models whose stochastic continuum equations are of the langevin type obtained after carrying out a local average known as coarse graining the second class consists of a hierarchy of continuum equations for the correlations of the dynamical variables obtained after making an average over realizations this average generates a hierarchy of deterministic partial differential equations except when the dynamical variables do not depend on the values of the neighboring dynamical variables in which case a hierarchy of ordinary differential equations is obtained the third class of evolution equations for the correlations of the dynamical variable constitutes another hierarchy after calculating an average over both realizations and all the sites of the lattice this double average generates a hierarchy of deterministic ordinary differential equations the second and third classes of equations are truncated using a mean field m n closure approximation in order to obtain a finite set of equations illustrative examples of every class are given

an analysis of finite volume finite element and finite difference methods using some concepts from algebraic topology in this paper we apply the ideas of algebraic topology to the analysis of the finite volume and finite element methods illuminating the similarity between the discretization strategies adopted by the two methods in the light of a geometric interpretation proposed for the role played by the weighting functions in finite elements we discuss the intrinsic discrete nature of some of the factors appearing in the field equations underlining the exception represented by the constitutive term the discretization of which is maintained as the key issue for numerical methods devoted to field problems we propose a systematic technique to perform this task present a rationale for the adoption of two dual discretization grids and point out some optimization opportunities in the combined selection of interpolation functions and cell geometry for the finite volume method finally we suggest an explanation for the intrinsic limitations of the classical finite difference method in the construction of accurate high order formulas for field problems

an analysis of finite difference and finite volume formulations of conservation laws abstract finite difference and finite volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws a new coordinate free formulation of systems of conservation laws is developed which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system the analysis considers general types of equations potential euler and navier stokes three dimensional unsteady flows with time varying grids are described using a single consistent nomenclature for both formulations grid motion due to a non inertial reference frame as well as flow adaptation is covered in comparing the two formulations it is found useful to distinguish between differences in numerical methods and differences in grid definition the former plays a role for non cartesian grids and results in only cosmetic differences in the manner in which geometric terms are handled the differences in grid definition for the two formulations is found to be more important since it affects the manner in which boundary conditions zonal procedures and grid singularities are handled at computational boundaries the proper interpretation of strong and weak conservation law forms for quasi one dimensional and axisymmetric flows is brought out

support operator finite difference algorithms for general elliptic problems abstract an algorithm is developed for discretizing boundary value problems given by a general linear elliptic second order partial differential equation with general mixed or robin boundary conditions in general logically rectangular grids the continuum problem can be written as an operator equation where the operator is self adjoint and positive definite the discrete approximations have the same property consequently the matrices for the discrete problem are symmetric and positive definite also the scheme has a nearest neighbor stencil consequently the most powerful linear solvers can be applied in smooth grids the algorithm produces second order accurate solutions it is the generality of the problem general matrix coefficients general boundary conditions general logically rectangular grids that makes finding such an algorithm difficult the algorithm which is a combination of the method of support operators and the mapping method overcomes certain difficulties of the individual methods producing a high quality algorithm for solving general elliptic problems

a theorem allowing the derivation of deterministic evolution equations from stochastic evolution equations iii the markovian non markovian mix abstract the proof of a theorem that allows one to construct deterministic evolution equations from a set with two subsets containing two types of discrete stochastic evolution equation is developed one subset evolves markovianly and the other non markovianly as an illustrative example the deterministic evolution equations of quantum electrodynamics are derived from two sets of markovian and non markovian stochastic evolution equations of different type after an average over realization using the theorem this example shows that deterministic differential equations that contain both first order and second order time derivatives can be derived after a taylor series expansion of the dynamical variables it is shown that the derivation of such deterministic differential equations can be done by solving a set of linear equations two explicit examples the first containing updating rules that depend on one previous time step and the second containing updating rules that depend on two previous time steps are given in detail in order to show step by step the linear transformations that allow one to obtain the deterministic differential equations

one dimensional diffusion validity of various expressions for jump rates the coverage dependence of the one dimensional collective diffusion coefficient is analyzed by using the gradient expansion of the local density the transition probabilities are written as an expansion of the probabilities of the occupation configurations since the detail balance principle determines only a part of the diffusion terms in the expansion different functional relations are proposed for these terms the diffusion coefficient is obtained for various choices of these relations however some of them seem to be not physically sound and the diffusion coefficient does not behave properly the range of validity of various expressions for the jump rates is determined and phase diagrams are shown besides that it is shown that the transition state theory guarantees physically suitable behavior of the coefficient of one dimensional diffusion

a global approach for solving evolutive heat transfer for image denoising and inpainting this paper proposes an alternative to partial differential equations pdes for solving problems in computer vision based on evolutive heat transfer traditionally the method for solving such physics based problems is to discretize and solve a pde by a purely mathematical process instead of using the pde we propose to use the global heat principle and to decompose it into basic laws we show that some of these laws admit an exact global version since they arise from conservative principles we also show that the assumptions made about the other basic laws can be made wisely taking into account knowledge about the problem and the domain the numerical scheme is derived in a straightforward way from the modeled problem thus providing a physical explanation for each step in the solution the advantage of such an approach is that it minimizes the approximations made during the whole process and it modularizes it allowing changing the application to a great number of problems we apply the scheme to two applications image denoising and inpainting which are modeled with heat transfer for denoising we propose a new approximation for the conductivity coefficient and we add thin lines to the features in order to block diffusion

non markovian stochastic evolution equations abstract non markovian continuum stochastic and deterministic equations are derived from a set of discrete stochastic and deterministic evolution equations examples are given of discrete evolution equations whose updating rules depend on two or more previous time steps among them the continuum stochastic evolution equation of the newton second law the stochastic evolution equation of a wave equation the stochastic evolution equation for the scalar meson field etc are obtained as special cases extension to systems of evolution equations and other extensions are considered and examples are given the concept of isomorphism and almost isomorphism are introduced in order to compare the coefficients of the continuum evolution equations of two different smoothing procedures that arise from two different approaches usually these discrepancies arising from two sources on the one hand the use of different representations of the generalized functions appearing in the models and on the other hand the different approaches used to describe the models these new concept allows to overcome controversies that were appearing during decades in the literature

high order finite volume approximations of differential operators on nonuniform grids abstract when computing numerical solutions to partial differential equations difference operators that mimic the crucial properties of the differential operators are usually more accurate than those that do not properties such as symmetry conservation stability and the duality relationships and identities between the gradient curl and divergence operators are all important using the finite volume method we have derived local accurate reliable and efficient difference methods t divergence gradient and curl operators are defined using a discrete versions of the divergence theorem and stokes theorem these methods are especially powerful on coarse nonuniform grids and in calculations where the mesh moves to track interfaces or shocks numerical examples comparing local second and fourth order finite volume approximations to conservation laws on very rough grids are used to demonstrate the advantages of the higher order methods

complementary geometric formulations for electrostatics summary the simultaneous use of a pair of complementary discrete formulations for electrostatic boundary value problems bvps allows to accurately compute electromagnetic quantities such as capacitance or electrostatic force with a minimum computational effort in fact the two formulations provide the upper and lower bounds for these quantities and their averages result quite close to the exact solution even for extremely coarse meshes despite the potential benefit to the many three dimensional large scale applications taking advantage of this feature is not exploited in practice due to theoretical difficulties in the potential design the aim of this paper is to fill this gap by rigorously introducing a pair of three dimensional complementary geometric formulations to solve electrostatic bvps on domains covered by conformal polyhedral meshes in particular an original formulation based on a vector potential is introduced by using cohomology theory with integer coefficients it is shown how the so called thick links are needed which are representatives of the second cohomology group generators of the dielectric region two easy to implement graph theoretic algorithms to automatically find such a basis with optimal computational complexity are described some benchmark problems are presented to show how the simultaneous use of both formulations yields to a sensible computational advantage therefore solvers based on complementary formulations should be embedded in the next generation of electromagnetic computer aided engineering cae softwares copyright 2010 john wiley sons ltd

multigrid preconditioning for krylov methods for time harmonic maxwell s equations in three dimensions we consider the rapid simulation of three dimensional electromagnetic problems in geophysical parameter regimes where the conductivity may vary significantly and the range of frequencies is moderate toward developing a multigrid preconditioner we present a fourier analysis based on a finite volume discretization of a vector potential formulation of time harmonic maxwell s equations on a staggered grid in three dimensions we prove grid independent bounds on the eigenvalue and singular value ranges of the system obtained using a preconditioner based on exact inversion of the dominant diagonal blocks of the non hermitian coefficient matrix this result implies that a preconditioner that uses single multigrid cycles to effect inversion of the diagonal blocks also yields a preconditioned system with an ell 2 condition number bounded independent of the grid size we then present numerical examples for more realistic situations involving large variations in conductivity i e jump discontinuities block preconditioning with one multigrid cycle using dendy s boxmg solver is found to yield convergence in very few iterations apparently independent of the grid size the experiments show that the somewhat restrictive assumptions of the fourier analysis do not prohibit it from describing the essential local behavior of the preconditioned operator under consideration a very efficient practical solver is obtained

a theorem allowing to derive deterministic evolution equations from stochastic evolution equations ii the non markovian extension abstract deterministic evolution equations of classical as well as quantum mechanical models are derived from a set of non markovian stochastic evolution equations after an average over realization using a theorem examples are given show that deterministic differential equations that contain derivatives with respect to time higher than or equal to two can be derived after a taylor series expansion of the dynamical variables it is shown that the derivation of such deterministic differential equations can be done by solving a set of linear equations that increase in number after increasing the number of previous time steps in the updating rules that define a given model two explicit examples the first containing updating rules that depend on two previous time steps and the second on three are worked in some detail in order to show some features of the linear transformation that allow one to obtain the deterministic differential equations

divergence preserving discrete surface integral methods for maxwell s curl equations using non orthogonal unstructured grids abstract several new discrete surface integral methods for solving maxwell s equations in the time domain are presented these methods which allow the use of general non orthogonal mixed polyhedral unstructured grids are direct generalizations of the canonical staggered grid finite difference method these methods are conservative in that they locally preserve divergence or charge employing mixed polyhedral cells hexahedral tetrahedral etc these methods allow more accurate modeling of non rectangular structures and objects because the traditional stair stepped boundary approximations associated with the orthogonal grid based finite difference methods can be avoided numerical results demonstrating the accuracy of these new methods are presented

a topological theorem and correlations within the context of stochastic evolution abstract a topological theorem that proves that any d dimensional lattice is equivalent to a one dimensional one allows to write the evolution equations as a function of only one spatial coordinate stochastic and continuum deterministic evolution equations are derived from a set of discrete stochastic evolution equations the evolution equations of the dynamical variables and correlations are obtained for processes that evolve non markovianly some relatively simple examples are given in order to illustrate the procedures

a theorem allowing to derive deterministic evolution equations from stochastic evolution equations abstract the deterministic evolution equations of classical as well as quantum mechanical models are derived from a set of stochastic evolution equations after taking an average over realizations using a theorem examples are given that show that deterministic quantum mechanical evolution equations obtained initially by r p feynman and subsequently studied by boghosian and taylor iv b m boghosian w taylor iv phys rev e 57 1998 54 see also arxiv quant ph 9904035 and meyer d a meyer phys rev e 55 1997 5261 among others are derived from a set of stochastic evolution equations in addition a deterministic classical evolution equation for the diffusion of monomers similar to the second fick law is also obtained