finite size scaling properties of the damage distance and dynamical critical exponent for the ising model abstract with the damage spreading method scaling properties of the damage distance on the ising model with heat bath dynamics are studied numerically with the parallel flipping scheme the scaling curves fall on two curves which depend on the odd or even lattice sizes the both scaling curves give the consistent dynamical exponent as z 2 16 0 04 for d 2 and z 2 09 0 05 for d 3 respectively by shifting one of them two curves overlap each other perfectly meanwhile all the scaling curves obtained by single spin flipping processes with different odd or even lattice sizes fall on a single curve from which the consistent dynamical critical exponent with the parallel scheme is obtained z 2 18 0 02 for d 2 and z 2 08 0 04 for d 3

a stochastic projection method for fluid flow ii random process an uncertainty quantification scheme is developed for the simulation of stochastic thermofluid processes the scheme relies on spectral representation of uncertainty using the polynomial chaos pc system the solver combines a galerkin procedure for the determination of pc coefficients with a projection method for efficiently simulating the resulting system of coupled transport equations implementation of the numerical scheme is illustrated through simulations of natural convection in a 2d square cavity with stochastic temperature distribution at the cold wall the properties of the uncertainty representation scheme are analyzed and the predictions are contrasted with results obtained using a monte carlo approach

exact two cell correlations in random cellular structures generated from a 2d ising ferromagnet abstract random 2d cellular structures are generated from distributions of spins given by a ferromagnetic ising model with nearest neighbour couplings on a square lattice topological correlations between pairs of neighbouring cells are expressed as rational functions of even number spin correlations involving two four and six spins which are exactly known for the square ising model the latter correlations have been calculated numerically in the vicinity of the curie point they agree with computer simulation results

long range geometrical correlations in two dimensional foams the statistical properties of two dimensional space filling random cellular structures foams or their dual random triangulations in statistical equilibrium are obtained by maximum entropy inference and topological simulations we show by maximum entropy inference that for a broad class of foams shell structured including three sided cell inclusions all two cell topological correlators aj k n average number of pairs of k cell and n cell at a topological distance j are linear in n and k the numbers of neighbours of the cells this generalizes a correlation known for neighbouring cells j d 1 which implies the linearity of aboav s relation between the total number of neighbours of the cells adjacent to a n neighboured cell andn our results verified by simulations also build up gauss s theorem for cellular structures any additional restriction in exploring local cell configurations besides the constraints of filling space at random will manifest itself through a deviation from linearity of the correlators aj k n and the aboav relation notably foams made of feynman diagrams have additional context dependent restrictions and their aboav relation is slightly curved it is essential that the local random variablen denotes the number of neighbours of the cell and not that of its sides whenever the two are different

cellular automata as microcanonical simulators the deterministic q2r cellular automation has been tested by many authors as a fast algorithm to simulate the ising model in the microcanonical ensemble however the magnetic susceptibility curve measured from the fluctuations of the magnetization is found to be far below the expected results inside the ordered ising phase the non ergodicity degree of this automaton seems to be inadequate to simulate the ising dynamics in this work the authors introduce two modified automata and test their performance for the square lattice for the first one they found improved results concerning the ising transition for the second modified automaton the ising transition does not occur the magnetization vanishing even for energies far below the normal critical threshold on the other hand another transition appears at a different critical energy value that seems to be the same as that of the periodic chaotic transition already observed in the normal q2r dynamics the critical indices of this new transition are measured from finite size scaling the results indicating that it is at the same universality class as the ising transition

topological models of cellular structures a method for constructing topological models of cellular structures is described it is based on lattices with topologically unstable sites which belong to more than zs polygons zs 3 in 2d and on rules which allow removing this degeneracy for every value of the coordination number z and for a given rule there are q z stable configurations called states cellular models are associated with distributions of states on the lattice sites the distribution of cell sides as well as other characteristics such as the correlations among cells can be derived many models of statistical physics may be used ising potts cellular automata the case z 4 is discussed and observed to agree with some experimental or simulation results

universal properties of voronoi tessellations of hard discs the authors describe a 2d mosaic obtained by the voronoi tessellation of a monosize assembly of discs at different packing fractions the experimental device hard discs moving on an air table produces for every packing fraction a succession of mosaics in statistical equilibrium which constitutes a statistical ensemble this ensemble is large enough for fluctuations from the most probable distributions to be negligible they use the maximum entropy principle to get the distribution of the polygons in 2d mosaics generated from an assembly of hard discs steric exclusion yields an extra conservation law which is sufficient to give a good agreement with the experimental data a similar behaviour in the six fold parameter seems to hold for other mosaics

tessellation of a stripe this paper describes enumeration of a class of topologically distinct periodic divisions of a stripe optimization of the geometry of these periodic tilings optimization that yields minimum total perimeter of the tiles gives a set of physically plausible periodic structures of monodisperse two dimensional foams bounded by two parallel walls evaluation of the minimum total perimeters of the lattices that we enumerated suggests two possible lower bounds for the mean perimeter of tiles forming periodic coverings of a stripe

towards statistical mechanics of a 2d random cellular structure using the methods of statistical mechanics the authors construct the partition function of a system of a large number of 2d cells that covers without pores or overlaps a flat surface each cell is defined by its position area perimeter and number of sides besides topological and space filling constraints they impose new ones regarding the energy and maximum area of the cells the entropy and free energy of the system are calculated and the mean values of the macroscopic parameters are determined in the equilibrium configuration the results are compared with experimental ones for soap froths and metallurgical aggregates

the voronoi tessellation generated from eigenvalues of complex random matrices the voronoi froth generated from eigenvalues of asymmetric complex random matrices is studied by numerical simulation it is more regular than the random voronoi froth irvf generated from a poisson process the existence of a unique tessellation called here random matrix voronoi froth rmvf follows from the universality of the distribution of eigenvalues which is also briefly commented on the geometrical and topological properties of the rmvf have been characterised an empirical and accurate distribution function is also proposed for the cell side length of a rvf deviations from the aboav weaire law are discussed their magnitude may be interpreted as a measure ofthe departure from an equilibrium structure in the frame of the statistical crystallography theory of rivier

a comment on rivier s maximum entropy method of statistical crystallography in the literature rivier s maximum entropy method was used to prove lewis law and a linear aboav s law in this paper we show that the functional forms of these two laws for a statistically equilibrated cellular network even if such a network really exists cannot be derived or proved by this method for example within the maximum entropy method we demonstrate that a quadratic aboav s or lewis s law is as probable as a linear one

test of three dimensional q2r ising algorithm simulation results of q2r cellular automata on the simple cubic lattice are compared with usual monte carlo simulations of the ising model curie temperature spontaneous magnetisation and specific heat agree but at low temperatures the susceptibility and the distribution of local energies differ

an adaptive multi element generalized polynomial chaos method for stochastic differential equations we formulate a multi element generalized polynomial chaos me gpc method to deal with long term integration and discontinuities in stochastic differential equations we first present this method for legendre chaos corresponding to uniform random inputs and subsequently we generalize it to other random inputs the main idea of me gpc is to decompose the space of random inputs when the relative error in variance becomes greater than a threshold value in each subdomain or random element we then employ a generalized polynomial chaos expansion we develop a criterion to perform such a decomposition adaptively and demonstrate its effectiveness for odes including the kraichnan orszag three mode problem as well as advection diffusion problems the new method is similar to spectral element method for deterministic problems but with h p discretization of the random space

random cellular structures generated from a 2d ising ferromagnet topological models of 2d cellular structures are associated with distributions of spins given by a ferromagnetic ising model with nearest neighbour interactions on a square lattice every vertex of a square lattice is topologically unstable as it belongs to more than three polygons there are two ways associated with the spin states to remove this degeneracy by replacing every vertex by one side topological properties such as the distribution p n of the number n of cell sides the two cell correlation mk n p k akn which is the average number of k sided neighbours of a cell with n sides n cell the mean number m n of sides of the first neighbour cells of n cells are characterized as a function of t tc by direct calculations and by monte carlo and q2r simulations the correlations akn of a biological tissue are compared with the akn of a ferromagnetic ising cellular structure and with the akn expected from the maximum entropy model

ring correlations in random networks we examine the correlations between rings in random network glasses in two dimensions as a function of their separation initially we use the topological separation measured by the number of intervening rings but this leads to pseudo long range correlations due to a lack of topological charge neutrality in the shells surrounding a central ring this effect is associated with the noncircular nature of the shells it is therefore necessary to use the geometrical distance between ring centers hence we find a generalization of the aboav weaire law out to larger distances with the correlations between rings decaying away when two rings are more than about three rings apart

boundary conditions for a divergence free velocity pressure formulation of the navier stokes equations new sets of boundary conditions for the velocity pressure formulation of the incompressible navier stokes equations are derived the boundary conditions have the same form on both inflow and outflow boundaries and lead to a divergence free solution moreover the specific form of the boundary condition makes it possible derive a symmetric positive definite equation system for the internal pressure numerical experiments support the theoretical conclusions

topological models of 2d cellular structure ii z 5 for pt i see ibid vol 24 p 1307 1991 topological models of 2d cellular structures are associated with planar tessellations with topologically unstable sites which belong to z 3 polygons this degeneracy is removed by replacing every z vertex by z 3 added sides a method which uses the diagonal triangulation of the dual tiling is also described the number of stable configurations called states is calculated as a function of z topological properties of the associated cellular structures are derived for a distribution of equiprobable and independent states on the various sites and for z ranging from 5 to infinity the distributions p n of the number n of cell sides for the latter distribution of states are typical of the p n of planar cuts of polycrystals and differ from the p n of soap froths deviations from the aboav weaire relation which describes the correlations between nearest neighbour cells occur mainly for n 3 and n 9

a fourth order accurate method for the incompressible navier stokes equations on overlapping grids a method is described to solve the time dependent incompressible navier stokes equations with finite differences on curvilinear overlapping grids in two or three space dimensions the scheme is fourth order accurate in space and uses the momentum equations for the velocity coupled to a poisson equation for the pressure the boundary condition for the pressure is taken as u 0 extra numerical boundary conditions are chosen to make the scheme accurate and stable the velocity is advanced explicitly in time any standard time stepping scheme such as runge kutta can be used the poisson equation is solved using direct or iterative sparse matrix solvers or by the multigrid algorithm computational results in two and three space dimensions are given

stability of pressure boundary conditions for stokes and navier stokes equations abstract the stability of a finite difference discretization of the time dependent incompressible navier stokes equations in velocity pressure formulation is studied in paticular we compare the stability for different pressure boundary conditions in a semiimplicit time integration scheme where only the viscous term is treated implicitly the stability is studied in three different ways by a normal mode analysis by numerical computation of the amplification factors and by direct numerical simulation of the governing equations all three approaches identify the same pressure boundary condition as the best alternative this condition implicitly enforces the normal derivative of the divergence to be zero on the boundary by coupling the normal derivative of the pressure to the normal component of the curl of the vorticity using this boundary condition we demonstrate that the time step is determined only by the convective term

robust boundary conditions for stochastic incompletely parabolic systems of equations we study an incompletely parabolic system in three space dimensions with stochastic boundary and initial data we show how the variance of the solution can be manipulated by the boundary conditions

the effects of regularity on the geometrical properties of voronoi tessellations this study comprehensively quantifies the effects of regularity on the geometrical properties of a random three dimensional voronoi tessellation vt where regularity was defined as the ratio of the minimum seed distance to the seed distance of the correlated body centred cubic lattice a scheme to generate voronoi tessellations with controlled regularity is proposed which was used to simulate 106 cells for a series of regularities the results were used to derive probability distributions for the properties of the tessellation including faces and edges per cell vertex and dihedral cell angles cell areas and volumes etc an understanding of the relation between a simple measurable parameter characterizing the degree of regularity of a voronoi tessellation and its geometrical properties is essential in generating virtual microstructures that are statistically representative of reality the statistical results are also relevant to all other applications involving random voronoi tessellations finally an application is presented of the proposed voronoi tessellation generation scheme applied to micromechanical modelling of grain structures with defined regularities for crystal plasticity finite element analysis

spin dynamics confinement in q2r for low concentrations the occupied sites in q2r cellular automata on the square lattice are known to be confined to the smallest rectangles surrounding them however they do not necessarily fill out the whole rectangle allowed for them the effective confinement transition is found numerically to agree well with that of bootstrap percolation

applicability of the lewis and aboav weaire laws to 2d and 3d cellular structures based on poisson partitions two and three dimensional networks of a columnar type are described which result from partitions based on poisson point distributions the metric and topological properties of such laminated poisson networks are derived and the applicability of the lewis and aboav weaire laws to them is tested the 2d poisson network contains cells with i or 4 i is the number of sides and both laws are obeyed the 3d poisson networks are of various types and have f or 6 f is the number of faces in a cell and f 14 in one particular type of 3d poisson network the two laws are again exactly obeyed in another type the laws show large deviations at low f but are asymptotically obeyed when f tends to infinite

l estimates for the bar partial problem in a half planeproblem in a half plane l approche de dualite pour trouver des solutions de f est suffisante pour plusieurs problemes apparaissant en theorie h p on donne des operateurs solution qui permettent de resoudre des problemes non resolubles par la dualite

stochastic geometry of polygonal networks an alternative approach to the hexagon square transition in benard convection we apply stochastic geometry to the transition from hexagonal to square cells recently observed in surface tension driven benard convection in particular we study the metric and topological evolution of benard patterns as a function of the temperature difference dt across the layer the preference of square benard cells at higher dt is a consequence of both a higher efficiency in heat transfer and more favorable metric properties most notably the perimeter area ratio of a square cell exceeds that of a hexagonal cell by an unexpectedly high value from a topological point of view the benard pattern obeys the aboav weaire law at all times even in the presence of threefold and fourfold vertices the regimes above and below the transition are characterized by different topological correlations between neighboring cells with the appearance of fourfold vertices the topological correlation changes from negative to positive s1063 651x 98 14709 8

on stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity on stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity

multifractal behaviour of the estimated natural measure for colloidal cluster cluster aggregation in 2 d abstract the cluster morphology and the aggregation dynamics in 2 d cluster cluster aggregation experiments is characterized by examining the scaling of the natural measure the calculated f spectra display a typical multifractal behaviour as expected the order of the particles upon aggregation is reflected in the decrease of entropy of the system

some results on q p spaces 0lpl1 for p is an element of 0 1 let q p be a proper subspace of bmoa defined by means of a modified garcia norm we give a boundary value criterion for a function to be in q p and a necessary and sufficient condition in terms of p carleson measure for an

on the correlation between sizes and shapes of cells in epithelial mosaics it is shown that lewis s empirical linear relationship between the average area of a cell and the number of its sides in two dimensional mosaics corresponds to maximal arbitrariness in the cellular distribution an expression for the distribution is given in the general case

scaling properties of three dimensional foams we obtain the scaling states of three dimensional soap foams by using equilibrium statistical mechanics techniques we consider a phase space where each bubble is characterized by its center of mass position volume surface and number of faces a gibbs entropy function is then defined and as done in standard statistical mechanics we obtain the probability density function defined in the phase space by maximizing the entropy subject to convenient constraints the froth is supposed to completely fill the available volume and we consider energy terms accounting for surface tension and the thermal energy of the gas inside the bubbles we find that the volume distribution presents an exponential decay with cell size and the correlation between cell volume and number of faces fits very well the available numerical data additional distribution functions and average values are also in good agreement with numerical simulations

percolation on disordered mosaics abstract to assess the effect of randomness on the permeability of topologically disordered structures we study the percolation properties of a bond model on various random mosaics the networks are efficiently generated by topological models which reproduce a wide range of naturally observed structures the percolation properties are obtained by monte carlo calculations on the corresponding site model for which we have developed a novel algorithm to create moderate lattice disorder our numerical results exhibit that the percolation threshold grows with increasing disorder on ordinary random mosaics due to the increased variation in the number of cell edges however in binary structures where randomness reduces the number of large and small cells we observe an unexpected threshold decrease

a well posed and stable stochastic galerkin formulation of the incompressible navier stokes equations with random data we present a well posed stochastic galerkin formulation of the incompressible navier stokes equations with uncertainty in model parameters or the initial and boundary conditions the stochastic galerkin method involves representation of the solution through generalized polynomial chaos expansion and projection of the governing equations onto stochastic basis functions resulting in an extended system of equations a relatively low order generalized polynomial chaos expansion is sufficient to capture the stochastic solution for the problem considered we derive boundary conditions for the continuous form of the stochastic galerkin formulation of the velocity and pressure equations the resulting problem formulation leads to an energy estimate for the divergence with suitable boundary data on the pressure and velocity the energy estimate implies zero divergence of the velocity field based on the analysis of the continuous equations we present a semi discretized system where the spatial derivatives are approximated using finite difference operators with a summation by parts property with a suitable choice of dissipative boundary conditions imposed weakly through penalty terms the semi discrete scheme is shown to be stable numerical experiments in the laminar flow regime corroborate the theoretical results and we obtain high order accurate results for the solution variables and the velocity divergence converges to zero as the mesh is refined

simulations of aggregation in 2d a study of kinetics structure and topological properties abstract colloidal aggregation in 2d has been studied using off lattice simulations structural kinetic and topological properties these last using the voronoi construction have been analysed in diffusion limited cluster aggregation dlca and reaction limited cluster aggregation rlca the simulations show dynamic scaling of the cluster size distribution for large sizes and times it has been observed that when the system reaches dynamic scaling some topological properties become stationary furthermore kinetic and topological aspects are related among them

modeling uncertainty in flow simulations via generalized polynomial chaos we present a new algorithm to model the input uncertainty and its propagation in incompressible flow simulations the stochastic input is represented spectrally by employing orthogonal polynomial functionals from the askey scheme as trial basis to represent the random space a standard galerkin projection is applied in the random dimension to obtain the equations in the weak form the resulting system of deterministic equations is then solved with standard methods to obtain the solution for each random mode this approach can be considered as a generalization of the original polynomial chaos expansion first introduced by wiener am j math 60 1938 897 the original method employs the hermite polynomials one of the 13 members of the askey scheme as the basis in random space the algorithm is applied to micro channel flows with random wall boundary conditions and to external flows with random freestream efficiency and convergence are studied by comparing with exact solutions as well as numerical solutions obtained by monte carlo simulations it is shown that the generalized polynomial chaos method promises a substantial speed up compared with the monte carlo method the utilization of different type orthogonal polynomials from the askey scheme also provides a more efficient way to represent general non gaussian processes compared with the original wiener hermite expansions

analytical results for size topology correlations in 2d disk and cellular packings random tilings or packings in the plane are characterized by a size distribution of individual elements domains and by the statistics of neighbor relations between the domains most systems occurring in nature or technology have a unimodal distribution of both areas and number of neighbors empirically strong correlations between these distributions have been observed and formulated as universal laws using only the local correlation free granocentric model approach with no free parameters we construct accurate analytical descriptions for disk crystallization size topology correlations and lemaitre s law

the wiener askey polynomial chaos for stochastic differential equations we present a new method for solving stochastic differential equations based on galerkin projections and extensions of wiener s polynomial chaos specifically we represent the stochastic processes with an optimum trial basis from the askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error several continuous and discrete processes are treated and numerical examples show substantial speed up compared to monte carlo simulations for low dimensional stochastic inputs

bounded mobius invariant q k spaces abstract we prove the corona theorem for the banach algebra q k h under some assumptions of the weight k and a fefferman stein type decomposition of the boundary values of q k is obtained

planar voronoi cells the violation of aboav s law explained in planar cellular systems mn denotes the average sidedness of a cell neighbouring an n sided cell aboav s empirical law states that nmn is linear in n a downward curvature is nevertheless observed in the numerical nmn data of the random voronoi froth the exact large n expansion of mn obtained in the present work namely explains this curvature its inverse square root dependence on n sets a new theoretical paradigm similar curved behaviour may be expected and must indeed be looked for in experimental data of sufficiently high resolution we argue that it occurs in particular in diffusion limited colloidal aggregation on the basis of recent simulation data due to fernandez toledano et al 2005 phys rev e 71 041401 and earlier experimental results by earnshaw and robinson 1994 phys rev lett 72 3682

importance of starting configurations in q2r temperature measurement the incorrect local energy distribution given by q2r at low temperatures is show to be due to the non microcanonical character of the starting states correct measurements are obtained with microcanonically distributed starting configurations the probable behaviour of the dynamics for large lattices is also discussed

structure factors from cluster cluster aggregation simulation at high concentration aggregation of particles in two dimensions at high concentration is simulated using the diffusion limited cluster cluster aggregation model static structure factors are calculated from particle configurations a simple model in which clusters diffuse at rates inversely proportional to their radii of gyration reproduces qualitatively the behaviour observed in experiments a peak in the structure factor s q is observed at small scattering vectors q the intensity of the peak increases and its q value decreases as the aggregation proceeds finally all particles belong to a single system spanning cluster the gel state and the scattering peak is frozen at a given q the gel structure is formed from a random close packed collection of smaller ramified clusters

structure of random cellular networks and their evolution abstract the methods of statistical mechanics are applied to the structure of random space filling cellular structures foams metallurgical grain aggregates biological tissues microreversibility of the structural properties under elementary transformations is demonstrated maximum entropy inference under a few constraints yields structural equations of state relating the size of cells to their topological shape these equations of state classify the structures and are criteria for their randomness quasistatic evolution is obtained if the structure remains in statistical equilibrium at all times in 2d it is governed by von neumann s law

bounded functions in mobius invariant dirichlet spaces abstract for p 0 1 let q p q p 0 be the space of analytic functions f on the unit disk with sup w f w d p w 1 f w d p 0 where d p means the weighted dirichlet norm and w is the mobius map of onto itself with w 0 w in this paper we prove the corona theorem for the algebra q p h q p 0 h then we provide a fefferman stein type decomposition for q p q p 0 and finally we describe the interpolating sequences for q p h q p 0 h

invariant in cellular automata for a subclass of the set of reversible cellular automata the author gives the form of an exact time invariant quantity which can be seen as a kind of energy with the ergodic assumption this is a model of two interacting ising spin systems

damage spreading in the q2r ising model abstract we find evidence of metastability in the spreading of damage in the q2r cellular automaton approximation for a 2d ising system which is first equilibrated with a standard metropolis simulation a subsequent study of both single site and whole line damage spreading in metropolis q2r systems as well as in pure q2r systems shows a logarithmic dependence of the damage spreading threshold on time and saturation effects in single site damage suggest a transition in the damage spreading threshold at low initial energy values examination of the magnetization as a function of energy in pure q2r shows extremely long relaxation times for p

scaling behavior of two dimensional domain growth computer simulation of vertex models computer simulations are performed for vertex models which are coarse grained models for dynamical cellular patterns in two dimensions by simulating large systems we obtain conclusive evidence of scaling behavior that is a power law for the growth of the average cell size and the scaling properties for the distribution functions of edge number and size of cells several versions of the vertex models are obtained by making some approximations for the equation of motion of a vertex and we compare the statistical properties of the patterns in the scaling regime

numerical method for analyzing surface fluctuations abstract a new method for measuring the width of an interface in the presence of overhangs and holes is presented using a local gibbs dividing surface it is compared with the conventional method based on the order parameter profile dynamics and size dependence of an interface are studied numerically in the two dimensional q2r cellular automaton two types of interface fluctuations can be distinguished the capillary waves dominate on length scales larger than the bulk correlation length whereas order parameter fluctuations on small scales give rise to an intrinsic interface width the scaling behavior of the capillary waves is shown to be the same as for the ising model the divergence of the intrinsic width at the critical point and its critical slowing down are investigated

integrable structure of ginibre s ensemble of real random matrices and a pfaffian integration theorem in the recent publication e kanzieper and g akemann in phys rev lett 95 230201 2005 an exact solution was reported for the probability pn k to find exactly k real eigenvalues in the spectrum of an n n real asymmetric matrix drawn at random from ginibre s orthogonal ensemble ginoe in the present paper we offer a detailed derivation of the above result by concentrating on the proof of the pfaffian integration theorem the key ingredient of our analysis of the statistics of real eigenvalues in the ginoe we also initiate a study of the correlations of complex eigenvalues and derive a formula for the joint probability density function of all complex eigenvalues of a ginoe matrix restricted to have exactly k real eigenvalues in the particular case of k 0 all correlation functions of complex eigenvalues are determined

a geometric formulation of the law of aboav weaire in two and three dimensions the law of aboav weaire is a simple mathematical expression deriving from empirical observations that the number of sides of a grain is related to the average number of sides of the neighboring grains and is usually restricted to natural two dimensional microstructures numerous attempts have been made to justify this relationship theoretically or to derive an analogous relation in three dimensions this paper provides several exact geometric results with expressions similar to that of the usual law of aboav weaire though with additional terms that may be used to establish when the law of abaov weaire is a suitable approximation specifically we derive several local relations that apply to individual grain clusters and a corresponding global relation that is identical in two and three dimensions except for a single parameter the derivation requires the definition and investigation of the average excess curvature a previously unconsidered physical quantity an approximation to our exact result is compared to the results of extensive simulations in two and three dimensions and we provide a compact expression that strikes a balance between complexity and accuracy

a stochastic projection method for fluid flow i basic formulation we describe the construction and implementation of a stochastic navier stokes solver the solver combines a spectral stochastic uncertainty representation scheme with a finite difference projection method for flow simulation the uncertainty quantification scheme is adapted from the spectral stochastic finite element method ssfem which is based on regarding uncertainty as generating a new dimension and the solution as being dependent on this dimension in the ssfem formalism the stochastic dependence is represented in terms of the polynomial chaos system and the coefficients in the corresponding spectral representation are obtained using a galerkin approach it is shown that incorporation of the spectral uncertainty representation scheme into the projection method results in a coupled system of advection diffusion equations for the various uncertainty fields and in a decoupled system of pressure projection steps this leads to a very efficient stochastic solver whose advantages are illustrated using steady and transient simulations of transport and mixing in a microchannel

combinatorial tools for the analysis of ramified patterns tree like patterns appear in many domains of physics and the quantitative description of their morphology raises an interesting problem to analyze their topological structure we introduce combinatorial concepts the bifurcation and length ratios and the ramification matrix which generalize ideas originating in hydrogeology two dimensional diffusion limited aggregation dla patterns are studied along these lines and their statistical combinatorial properties are compared to those of random and growing binary trees and to experimental data for injection of water in clay

obtaining critical point and shift exponent for the anisotropic two layer ising and potts models cellular automata approach abstract using probabilistic cellular automata with the glauber algorithm we have precisely calculated the critical points for the anisotropic two layer ising and potts models k x k y k z of the square lattice where k x and k y are the nearest neighbor interactions within each layer in the x and y directions respectively and k z is the inter layer coupling a general equation is obtained as a function of the inter and intra layer interactions for both the two layer ising and potts models separately where k z k x and k y k x furthermore the shift exponent for the two layer ising and potts models is calculated it was demonstrated that in the case of 1 for the two layer ising model the value of 1 756 0 0078 supports the scaling theories prediction that however for the unequal intra layer couplings for the two layer ising model and also in the case of both equal and unequal intra layer interactions for the two layer potts model our results are different from those obtained from the scaling theories finally an equation is obtained for the shift exponent as a function of intra layer couplings for the two layer ising and potts models

new monte carlo method for planar poisson voronoi cells by a new monte carlo algorithm we evaluate the sidedness probability pn of a planar poisson voronoi cell in the range 3 n 1600 the algorithm is developed on the basis of earlier theoretical work it exploits in particular the known asymptotic behaviour of pn as n our pn values all have between four and six significant digits accurate n dependent averages second moments and variances are obtained for the cell area and the cell perimeter the numerical large n behaviour of these quantities is analysed in terms of an asymptotic power series in n 1 snapshots are shown of typical occurrences of extremely rare events implicating cells of up to n 1600 sides embedded in an ordinary poisson voronoi diagram we reveal and discuss the characteristic features of such many sided cells and their immediate environment their relevance for observable properties is stressed

characterizations of qt spaces abstract we introduce a new space qt space of analytic functions on the unit disk in terms of a nondecreasing function t the relation between qt and qp spaces which have attracted considerable attention is given by studying the growth order of t the counterpart q t of qt for the meromorphic case is also considered and investigated we note that some characterizations of q t and qt are different moreover our results answer a question raised by p wu 1998 complex variables35 157 170 in the negative

bubble size topology correlations in two dimensional foams derived from surface energy minimization we obtain the number fractions xi the average areas a i and the average perimeters p i of i sided bubbles in a two dimensional foam by minimizing the total surface energy and assuming a simple relation between p i and a i calculations for linear and weibull distributions of the square root of the bubble area yield large deviations particularly at small i from lewis s and desch s laws which linearly relate a i and p i respectively to i nevertheless we find good agreement with experimental results for xi p i and a i in foams

correlations in topological models of 2d random cellular structures general relations and constraints which must be satisfied by the topological correlations in 2d space filling random cellular structures are discussed and a topological short range order coefficient is defined topological models of 2d structures are associated with planar tessellations with topologically unstable sites which belong to z 3 polygons the stable configurations called states are obtained by replacing every vertex by z 3 added sides the topological properties of the latter models are calculated exactly for a distribution of independent and equiprobable states on the various sites and for any value of z the case of the structures associated with tilings by triangles is thoroughly considered the calculated correlations are compared with the correlations in alumina cuts and in random voronoi froths the variability of the topological properties of 2d random cellular structures is discussed

inter cluster scaling in two dimensional colloidal aggregation abstract cluster cluster aggregation has been studied experimentally in two dimensional colloidal systems of moderately high area fraction in the diffusion limited regime the system spontaneously exhibits ordering beyond the scale of the fractal aggregates which persists into the gelled state this ordering arises from an effective inter cluster repulsion due to the mutually exclusive depletion zones surrounding each cluster various metrical and topological properties of the system indicate that this long range order is stationary apart from the inherent change of scale as the clusters grow topological correlations show that the inter cluster self organization is compatible with maximum entropy the non equilibrium system behaves as if it were in statistical equilibrium and no physical forces are involved in the long range order for the reaction limited case no such inter cluster ordering is evident at any stage the system is nonstationary and the aggregation is governed by specific physical forces

time dependent thermodynamic properties of the ising model from damage spreading the relationship between damage spreading and static thermodynamic properties in the ising model developed by coniglioet al is here extended to include time dependent thermodynamic quantities we exploit this new result to measure the time dependent spin correlation function from damage spreading in the ising model with heat bath and glauber dynamics until now only static thermodynamic quantities have been correctly determined from damage spreading and even then only with heat bath dynamics we also show that there are significant differences between the kinetics of damage spreading as found in heat bath and glauber dynamics

several function theoretic characterizations of mobius invariant q k spaces this paper characterizes the so called mobius invariant qk spaces in terms of carleson type measures boundary values inner factors and absolute values of analytic functions on the unit disk