solving second order initial value problems by a hybrid multistep method without predictors abstract a three step seventh order hybrid linear multistep method hlmm with three non step points is proposed for the direct solution of the special second order initial value problems ivps of the form y f x y with an extension to y f x y y the main method and additional methods are obtained from the same continuous scheme derived via interpolation and collocation procedures the stability properties of the methods are discussed by expressing them as a one step method in higher dimension the methods are then applied in block form as simultaneous numerical integrators over non overlapping intervals numerical results obtained using the proposed block form reveal that it is highly competitive with existing methods in the literature

voronoi delaunay analysis of voids in systems of nonspherical particles the voronoi network is known to be a useful tool for the structural description of voids in the packings of spheres produced by computer simulations in this article we extend the voronoi delaunay analysis to packings of nonspherical convex objects main properties of the voronoi network which are known for systems of spheres are valid for systems of any convex objects a general numerical algorithm for calculation of the voronoi network in three dimensions is proposed it is based on the calculation of the trajectory of the imaginary empty sphere of variable size moving inside a system the delaunay empty sphere method analysis of voids is presented for an ensemble of random straight lines and for a molecular dynamics model of liquid crystal the spatial distribution of voids and a simple percolation analysis are obtained the distributions of the bottleneck radii and the radii of spheres inscribed in the voids are calculated

a multigrid method with unstructured adaptive grids for steady euler equations the multigrid method based on multi stage jacobi relaxation earlier developed by the authors for structured grid calculations with euler equations is extended to unstructured grid applications the meshes are generated with delaunay triangulation algorithms and are adapted to the flow solution

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

the atomic strain tensor abstract a definition of the local atomic strain increments in three dimensions and an algorithm for computing them is presented an arbitrary arrangement of atoms is tessellated into delaunay tetrahedra identifying interstices and voronoi polyhedra identifying atomic domains the deformation gradient increment tensor for interstitial space is obtained from the displacement increments of the corner atoms of delaunay tetrahedra the atomic site strain increment tensor is then obtained by finding the intersection of the delaunay tetrahedra with the voronoi polyhedra accumulating the individual deformation gradient contributions of the intersected delaunay tetrahedra into the voronoi polyhedra an example application is discussed showing how the atomic strain clarifies the relative local atomic movement for a polymeric glass treated at the atomic level

a new algorithm for three dimensional voronoi tessellation abstract a new efficient algorithm for computing the voronoi tessellation in three dimensions is presented the voronoi tessellation is obtained by constructing delaunay tetrahedra the complete set of these tetrahedra corresponds to that of a single voronoi polyhedron

discrete system reduction via impulse response gramians and its relation to q markov covers a method for model reduction of linear discrete systems is proposed it is based on the impulse response gramian proposed by the authors 1989 for discrete systems this gramian is an extension of the one proposed for linear continuous systems and contains information on the input output behavior of the system the rth order reduced order models are made to retain the first r markov parameters and the first r r elements of the impulse response gramian of the original system the relation between this method and the q markov cover method is also discussed the method is illustrated by a numerical example

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

the fit of a sum of exponentials to noisy data abstract given a set of noisy data y0 ym measured at equidistant points on the time axis find n n 1 2 m exponents bi and coefficients ci such that i ci exp bit yields a good approximation of the data we study two algorithms for the reconstruction of the exponents and coefficients we show that the error in the reconstructed exponents is of the order of the gap n 1 n n 1 between the smallest accepted singular value n and the largest rejected singular value n 1 of a hankel matrix constructed from the data moreover we provide a statistical analysis which gives some insight in the optimal choice of the dimensions of the hankel matrix to be used given a fixed number of datapoints and we illuminate this by several clarifying examples

model reduction using balanced realizations with improved low frequency behaviour abstract model reduction using balanced realization techniques is known to give a better approximation of the high frequency behaviour than the low frequency one in this paper a simple modification to the technique is proposed to get a better approximation of the low frequency behaviour of the original system the proposed technique is illustrated by numerical examples

statistical geometry of particle packings i algorithm for exact determination of connectivity volume and surface areas of void space in monodisperse and polydisperse sphere packings packings of spheres serve as useful models of the geometry of many physical systems in particular the description of the void region in such packings the region not occupied by the spheres is crucial in many studies the void region is in general composed of disconnected cavities we present an algorithm for decomposing void space into cavities and determining the exact volumes and surface areas of such cavities in three dimensional packings of monodisperse and polydisperse spheres

detecting structure in two dimensions combining voronoi tessellation and percolation conventional source detection algorithms in high energy astrophysics and other fields mostly use spherical or quadratic sliding windows of varying size on two dimensionally binned representations of spatial event distributions in order to detect statistically significant event enhancements sources within a given field while this is a reasonably reliable technique for nearly pointlike sources with good statistics poor and extended sources are likely to be incorrectly assessed or even missed at all as the calculations are governed by nonphysical parameters like the bin size and the window geometry rather than by the actual data the approach presented here does not introduce any artificial bias but makes full use of the unbinned two dimensional event distribution a voronoi tessellation on a finite plane surface yields individual densities or fluxes for every single event the distribution of which allows the determination of the contribution from a random poissonian background field noise the application of a nonparametric percolation to the tessellation cells exceeding this noise level leads directly to a source list which is free of any assumptions about the source geometry high density fluctuations from the random background field will still be included in this tentative source list but can be easily eliminated in most cases by setting a lower threshold to the required number of events per source since no finite size detection windows or the like have been used this analysis yields automatically straightforward fluxes for every source finally accepted the main disadvantage of this approach is the considerable cpu time required for the construction of the voronoi tessellation it is thus applicable only to either small fields or low event density regions

about the delaunay voronoi tesselation abstract the topological description of the neighborhood of the constituing atoms in a dense random material liquids glasses is of a major importance for their characterization we discuss an algorithm for the delaunay construction which is global and independent of the dimension of the space and derive from it the full dual voronoi tesselation by an original realization of duality

fitting distribution like data to exponential sums with genetic algorithms conventional derivative based algorithms of fitting distribution like data to exponential sum functions can be easily trapped in some local minima this paper is concerned with the development of algorithms of fitting distribution like data to exponential sums with genetic algorithms both binary coding scheme and real valued coding scheme have been investigated in this research experimental results have shown that real valued coding scheme is more appropriate to the problem of fitting distribution like data to exponential sums testing with real engineering data it has been demonstrated that the fitting algorithm derived in this paper is quite promising the fitted exponential sum models using genetic algorithm can very well describe the measured data however for the data with wavy trends pure exponential sum functions may not be the best candidate models more generalized exponential sum models need to be studied

triangle distribution and equation of state for classical rigid disks the triangle distribution function f 3 for three mutual near neighbors in the plane describes basic aspects of short range order and statistical thermodynamics in two dimensional many particle systems this paper examines prospects for constructing a self consistent calculation for the rigid disk system f 3 we present several identities obeyed by f 3 a rudimentary closure suggested by scaled particle theory is introduced in conjunction with three of the basic identities this closure leads to an unique f 3 over the entire density range the pressure equation of state exhibits qualitatively correct behaviors in both the low density and the close packed limits but no intervening phase transition appears we discuss extensions to improved disk closures and to the three dimensional rigid sphere system

model reduction via balanced state space representations a model reduction procedure based on balanced state space representations is studied in this paper the reduced order model is examined from the point of view of stability controllability and observability both continuous time and discrete time systems are considered

the generation of discrete time q markov covers via inverse solution of the lyapunov equation a method for generating q markov covers for siso discrete time systems is proposed the method is based on computing first the impulse response gramian from the markov parameters and covariances and then solving the lyapunov equation inversely to get the system matrices in controllability canonical form the conditions for existence of q markov covers are also derived the method is illustrated by a numerical example and is shown to be computationally simple

a generalized approach to q markov covariance equivalent realizations for discrete systems abstract a new algorithm is developed which constructs q markov covariance equivalent realizations q markov covers of multivariable linear discrete time systems a q markov cover is a state realization which matches exactly a finite portion of the impulse response sequence markov parameters and output autocorrelation sequence covariance parameters of a linear system the algorithm generates the q markov covers starting with only the basic data namely the q markov parameters and the q covariance parameters the algorithm leads to a parameterization of all minimal stable q markov covers which can be constructed since the data are easily computed from a given state space model the algorithm presented will be useful for both realization and model reduction of multivariable linear discrete time systems an example is presented to demonstrate the algorithm

spin models on random lattices under certain conditions phase transitions in systems with quenched disorder are expected to exhibit a dierent behaviour than in the corresponding pure system here we discuss a series of monte carlo studies of a special type of such disordered systems namely spin models dened on quenched random lattices exhibiting geometrical disorder in the connectivity of the lattice sites in two dimensions we present results for the q state potts model on random tri valent 3 planar graphs which appear quite naturally in the dynamically triangulated random surface dtrs approach to quantum gravity as well as on poissonian random lattices of voronoi delaunay type both cases q64 and 4 are discussed which in the pure model without disorder give rise to second and rst order phase transitions respectively in three dimensions results for the ising model on poissonian random lattices are briey described we conclude with a comparison of the two types of connectivity disorder with the more standard case of bond disorder and a discussion of the distinguishing dierences c 2000 elsevier science b v all rights reserved

voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids voronoi cells and the notion of natural neighbours are used to develop a finite difference method for the diffusion operator on arbitrary unstructured grids natural neighbours are based on the voronoi diagram which partitions space into closest point regions the sibson and the laplace non sibsonian interpolants which are based on natural neighbours have shown promise within a galerkin framework for the solution of partial differential equations in this paper we focus on the laplace interpolant with a two fold objective first to unify the previous developments related to the laplace interpolant and to indicate its ties to some well known numerical methods and secondly to propose a voronoi cell finite difference scheme for the diffusion operator on arbitrary unstructured grids a conservation law in integral form is discretized on voronoi cells to derive a finite difference scheme for the diffusion operator on irregular grids the proposed scheme can also be viewed as a point collocation technique a detailed study on consistency is conducted and the satisfaction of the discrete maximum principle stability is established owing to symmetry of the laplace weight a symmetric positive definite stiffness matrix is realized which permits the use of efficient linear solvers on a regular rectangular or hexagonal grid the difference scheme reduces to the classical finite difference method numerical examples for the poisson equation with dirichlet boundary conditions are presented to demonstrate the accuracy and convergence of the finite difference scheme copyright 2003 john wiley sons ltd

on the statistics of area size in two dimensional thick voronoi diagrams cells of voronoi diagrams in two dimensions are usually considered as having edges of zero width however this is not the case in several experimental situations in which the thickness of the edges of the cells is relatively large in this paper the concept of a thick voronoi tessellation that is with edges of non zero width is introduced and the statistics of cell areas as thickness changes are analyzed

geometrical ambiguity of pair statistics point configurations point configurations have been widely used as model systems in condensed matter physics materials science and biology statistical descriptors such as the n body distribution function g n are usually employed to characterize point configurations among which the most extensively used is the pair distribution function g 2 an intriguing inverse problem of practical importance that has been receiving considerable attention is the degree to which a point configuration can be reconstructed from the pair distribution function of a target configuration although it is known that the pair distance information contained in g 2 is in general insufficient to uniquely determine a point configuration this concept does not seem to be widely appreciated and general claims of uniqueness of the reconstructions using pair information have been made based on numerical studies in this paper we present the idea of the distance space called the mathbb d space the pair distances of a specific point configuration are then represented by a single point in the mathbb d space we derive the conditions on the pair distances that can be associated with a point configuration which are equivalent to the realizability conditions of the pair distribution function g 2 moreover we derive the conditions on the pair distances that can be assembled into distinct configurations i e with structural degeneracy these conditions define a bounded region in the mathbb d space by explicitly constructing a variety of degenerate point configurations using the mathbb d space we show that pair information is indeed insufficient to uniquely determine the configuration in general we also discuss several important problems in statistical physics based on the mathbb d space including the reconstruction of atomic structures from experimentally obtained g 2 and a recently proposed decorrelation principle the degenerate configurations have relevance to open questions involving the famous traveling salesman problem

on the generalized q markov cover models for discrete time systems a new method for obtaining generalized q markov cover models for discrete time siso systems is proposed and is based on the inverse solution of the lyapunov equation the reduced order models not only match the markov parameters and high frequency power moments like the conventional q markov cover techniques but also match time moments and low frequency power moments of the original system

on the construction of the voronoi mesh on a sphere abstract a new construction of the voronoi mesh on the sphere is presented the main feature is that the algorithm adds points one at a time until the final voronoi mesh is built up by adding one point to an existing voronoi mesh of k points only local changes are needed to construct a voronoi mesh of k 1 points this construction is particularly well suited to time dependent problems since using information from the voronoi mesh at the previous time step allows us to reduce the construction to o n operations when the two configurations are close while the algorithm does not break down when they are far apart numerical experiments are presented to substantiate the o n operation count for a typical case