scaling state in froths deduced from a corrected von neumann s law abstract a corrected and generalized von neumann s law is proposed so that its statistical consequences agree with all experiments reported in the literature it is shown that a froth s scaling state concerning the surface area distribution may be deduced from the stochastical independence between the number of sides distribution and the bubbles surface area and on the simple change of von neumann s law from da dt k n 6 to da dt ka n 6

statistical properties and shell analysis in random cellular structures we investigate the statistical properties of two dimensional random cellular systems froths in terms of their shell structure the froth is analyzed as a system of concentric layers of cells around a given central cell we derive exact analytical relations for the topological properties of the sets of cells belonging to these layers experimental observations of the shell structure of two dimensional soap froth are made and compared with the results on two kinds of voronoi constructions it is found that there are specific differences between soap froths and purely geometrical constructions in particular these systems differ in the topological charge of clusters as a function of shell number in the asymptotic values of defect concentrations and in the number of cells in a given layer we derive approximate expressions with no free parameters which correctly explain these different behaviors s1063 651x 96 13111 1

commutative discrete filtering on unstructured grids based on least squares techniques the present work is concerned with the development of commutative discrete filters for unstructured grids and contains two main contributions first building on the work of marsden et al j comp phys 175 2002 584 a new commutative discrete filter based on least squares techniques is constructed second a new analysis of the discrete commutation error is carried out the analysis indicates that the discrete commutation error is not only dependent on the number of vanishing moments of the filter weights but also on the order of accuracy of the discrete gradient operator the results of the analysis are confirmed by grid refinement studies

the use of explicit filters in large eddy simulation abstract explicit filtering is considered as a means of controlling the numerical errors that result when finite difference methods are used in large eddy simulation les the notion that the finite difference expressions themselves act as an effective filter is shown to be false for three dimensional simulations performed on nonuniform meshes for consistency the nonlinear terms in the navier stokes equations should be filtered explicitly at each time step in order to insure that the spectral content of the solution remains fixed at the desired filter level the explicit filtering operation allows a separation between the filter size and the mesh spacing and can be used to control the impact of the numerical errors numerical tests of the explicit filtering approach in turbulent channel flow are used to investigate the effectiveness of the explicit filtering approach and to assess its associated cost explicit filtering is shown to improve the computed results but this improvement comes at a rather high computational cost the explicitly filtered approach is also compared with straightforward mesh refinement as an alternative means of improving the computed results mesh refinement is also seen to increase the accuracy of the simulation but some traces of numerical error appear to persist in the solution

a measure for the decentralized assignability of eigenvalues abstract the results of 7 are generalized to produce a continuous measure of how close a mode is to being a decentralized fixed mode 13 implications of this measure on controller design are also explored

construction of commutative filters for les on unstructured meshes a method of constructing discrete filters for large eddy simulation of turbulent flows on unstructured meshes is presented the commutation error between differentiation and filtering can be made arbitrarily small with these filters the filtering method is applied to various test cases to demonstrate commutation an extension to three dimensions and implementation into an unstructured solver for les are discussed

decentralized stabilization and pole assignment for general proper systems considered is the problem of finding existence conditions and a controller synthesis procedure using decentralized control for assigning the poles of a linear time invariant proper system described by a state space model c a b d where no assumption is made regarding the structure of d this problem has direct application to the decentralized stabilization problem decentralized robust servomechanism problem etc and is a nontrivial extension to the standard decentralized problem where it is assumed that the direct feedthrough terms either are absent or have a block diagonal structure

pole placement and compensator design of generalized systems abstract the system considered is a generalized system e ax bu y cx with matrix e singular when the impulsive modes of the system are both controllable and observable it is shown in this paper that these modes can be eliminated by almost any constant output feedback for a strongly controllable and observable generalized system after its impulsive modes are eliminated the poles of the system can be assigned arbitrarily by state feedback even if the states are not available the paper adopts an efficient method to design a compensator for the system

brief bezout identity related to reduced order observer based controllers for singular systems a design method of causal reduced order observer based controllers for singular systems is presented a new state space representation of the bezout identity for singular systems is developed a parameterization of all causal reduced order controllers is also given the general results given here can be extended to various cases including minimal and full order observer based controllers

a high resolution differential filter for large eddy simulation a high resolution low pass differential filter for numerical simulations on unstructured grids is proposed the finite element discretization of the filter equation on a structured grid results in a discrete compact filter the proposed filter is significantly less dissipative than germano s differential filter while completely suppresses fluctuations at the grid cut off frequency manufactured solutions were used to verify the performance of the proposed filter the results suggest that the proposed filter will be very effective for explicit filtering and approximate deconvolution modeling in large eddy simulations

a note on stages of evolution in a 2d froth abstract the scaling properties of 2d froth have been extensively investigated via numerical simulations theory and experiment the evolutionary process as a whole however consists of two regions involving several distinct stages which are characterized by the froth structure in particular transient behaviour which reflects initial levels of froth disorder can be varied both in its nature and duration the final stage of froth evolution is associated with a few remaining bubbles which change relatively slowly unlike the many frequent changes originally associated with transience thus late configurations do not affect achievement of scaling but influence the rate at which it is attained recent studies of ordered 2d froths with single multiple defects provide some examples for length of transition period which appears to be related to concentration of defects and highly ordered systems with few defects exhibit an anomalous approach to the scaling state details are briefly discussed

modelling froth dynamics persistence measures the soap froth provides an idealised example of a cellular structure which evolves or coarsens over laboratory time scales and for which topological measures appear to provide an intuitive characterisation however froth is an intrinsically non equilibrium system and topological measures are not universally applicable to such processes recently persistence has been proposed as a more general probe of non equilibrium dynamics where the froth is viewed as a two phase system through construction of a virtual phase we use a direct simulation method to investigate persistence for random 2 d voronoi and hexagonal froths of size up to 2500 bubbles we find that simulation results are qualitatively similar to those of experiment with the normalised average area a t a 0 of persistent regions within a bubble at time t approaching an equilibrium value for a range of volume or sampling fraction values for the voronoi froth the case for the hexagonal is less clear since exclusion of the defect or defects from the virtual phase leads to rapid decline in the average area of persistent bubbles simulation times required are very long however and evolution is slow for long term survivors consequently persistent behaviour is not demonstrated satisfactorily for the fraction of survivors n t n t in a random system of this size although for the hexagonal with one or more seeded defects there is some indication that decay depends on for some colouring patterns however limiting slope values are probably not established

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

on algebraic properties of general proper decentralized abstract the new concepts of the decentralized output feedback variable polynomial the decentralized output feedback cycle index of general proper systems and the geometric multiplicities of decentralized fixed modes are introduced their computational methods and some algebraic properties are presented it is shown that the decentralized output feedback cycle index of a general proper system is equal to one when the system has no fixed modes or equal to the maximum of the geometric multiplicities of its decentralized fixed modes it is also shown that almost all decentralized output feedback can be used to make the zeros of the decentralized variable polynomial distinct and disjoint from any given finite set of points on the complex plane

a tutorial on the geometric analysis of linear time invariant implicit systems abstract a background of recent work in nonregular and regular implicit systems of the form e x ax bu is provided then the output nulling unknown input and composite subspaces are defined for singular systems with recursions given for their computation inner subspaces that is those in the domain of e and a are distinguished from outer subspaces those in the codomain of e and a the notions of composite preimage and composite image are introduced the result is a framework that unifies some of the recent work in the geometric theory of implicit systems system properties are discussed for both regular and nonregular systems and duality is investigated

high order variational multiscale model in finite elements applied to the leisa 2 configuration a variational multiscale sugbrid model including an explicit filtering is studied in the framework of an equal order finite element formulation for solving compressible navier stokes equations in e

algebraic properties of singular systems subject to decentralized output feedback this paper investigates algebraic properties of decentralized singular systems dsss under local static output feedback new concepts of the geometric multiplicity gm of the finite decentralized fixed mode dfm the decentralized output feedback variable polynomial dvp and the finite decentralized output feedback cycle index dci of the dss are defined the formulas for determining the gm and the dci are given in terms of the dfm and the system matrices it is shown that almost any decentralized output feedback can make the zeros of the dvp i e the closed loop poles that are variable distinct and away from any given finite set in the complex plane it is also shown that the finite dfm of the dss are those uncontrollable and or observable finite modes of the closed loop dss through any single channel finally the minimal number of the inputs and outputs that guarantee the finite modes of the closed loop dss controllable and observable is shown to be the finite dci of the dss an illustrative example is provided

algebraic properties of decentralized control systems the new concepts of the decentralized output feedback cycle index the geometric multiplicities of decentralized fixed modes dfm and the decentralized output feedback variable polynomial dvp of a decentralized control system dcs are introduced their computational methods and some properties are given it is shown that the decentralized output feedback cycle index is equal to one when the dcs has no decentralized fixed modes dfm or equal to the maximum of the geometric multiplicities of dfm otherwise almost every decentralized output feedback law can be used to make the zeros of the dvp distinct it is also shown that almost any decentralized output feedback law will make the zeros of the dvp disjoint from any given finite set of points on the complex plane it is then shown that if a dcs has no dfm then it can be made both controllable and observable with respect to any non trivial input and output by applying almost any decentralized output feedback law

stable spins in the zero temperature spinodal decomposition of 2d potts models we present the results of zero temperature monte carlo simulations of the q state potts model on a square lattice with either four or eight neighbors and for the triangular lattice with six neighbors in agreement with previous works we observe that the domain growth process gets blocked for the nearest neighbor square lattice when q is large enough whereas for the eight neighbor square lattice and for the triangular lattice no blocking is observed our simulations indicate that the number of spins which never flipped from the beginning of the simulation up to time t follows a power law as a function of the energy even in the case of blocking the exponent of this power law varies from less than 1 2 for the ising case q 2 to 2 for q o0 and seems to be universal the effect of blocking on this exponent is invisible at least up to q 7

a general class of commutative filters for les in complex geometries a class of filters for large eddy simulations of turbulent inhomogeneous flows is presented a general set of rules for constructing discrete filters in complex geometry is given and examples of such filters are presented with these filters the commutation error between numerical differentiation and filtering can be made arbitrarily small allowing for derivation of a consistent set of equations for the large scale field the application of such filters for explicit filtering in large eddy simulations and the issue of boundary conditions for the filtered field are also discussed

doubly coprime fractional representations of generalized dynamical systems explicit formulas for doubly coprime fractional representations of the transfer matrix of a generalized dynamical system are given in terms of a stabilizable and detectable state space realization of the transfer matrix these formulas establish a possible way to use the fractional representation approach in the synthesis of generalized dynamical systems

structurally fixed modes a notion of structurally fixed modes is introduced in the framework of decentralized control systems to identify the modes that cannot be shifted by decentralized feedback regardless of the numerical values of system parameters in this way a qualitative characterization of decentralized fixed modes is provided which is suitable for delineating decentrally stabilizable systems the characterization leads naturally to the notion of fixed modes with respect to arbitrary feedback structure constraints

a family of low dispersive and low dissipative explicit schemes for flow and noise computations explicit numerical methods for spatial derivation filtering and time integration are proposed they are developed with the aim of computing flow and noise with high accuracy and fidelity all the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to k x 2 corresponding to four points per wavelength they are shown to be more accurate and also more efficient numerically than most of the standard explicit high order methods for uniform and slowly non uniform grids two problems involving long range sound propagation are resolved to illustrate their respective precisions remarks about their practical applications are then made especially about the connection with the boundary conditions finally their relevance for the simulation of turbulent flows is emphasized

a subgrid scale deconvolution approach for shock capturing we develop a method for the modeling of flow discontinuities which can arise as weak solutions of inviscid conservation laws due to its similarity with recently proposed approximate deconvolution models for large eddy simulation the method potentially allows for a unified treatment of flow discontinuities and turbulent subgrid scales a filtering approach is employed since for the filtered evolution equations the solution is smooth and can be solved for by standard central finite difference schemes without special consideration of discontinuities a sufficiently accurate representation of the filtered nonlinear combination of discontinuous solution components which arise from the convection term can be obtained by a regularized deconvolution applied to the filtered solution for stable integration the evolution equations are supplemented by a relaxation regularization based on a secondary filter operation and a relaxation parameter an estimate for the relaxation parameter is provided the method is related to the spectral vanishing viscosity method and the regularized chapman enskog expansion method for conservation laws we detail the approach and demonstrate its efficiency with the inviscid and viscous burgers equations the isothermal shock problem and the one dimensional euler equations