on cal h _ infty estimation of randomly occurring faults for a class of nonlinear time varying systems with fading channels this technical note is concerned with the finite horizon cal h infty fault estimation problem for a class of nonlinear stochastic time varying systems with both randomly occurring faults and fading channels the system model dynamical plant is subject to lipschitz like nonlinearities and the faults occur in a random way governed by a set of bernoulli distributed white sequences the system measurements are transmitted through fading channels described by a modified stochastic rice fading model the purpose of the addressed problem is to design a time varying fault estimator such that in the presence of channel fading and randomly occurring faults the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by a cal h infty norm in the mean square sense by utilizing the stochastic analysis techniques sufficient conditions are established to ensure that the dynamic system under consideration satisfies the prespecified performance constraint on the fault estimation and then a recursive linear matrix inequality approach is employed to design the desired fault estimator gains simulation results demonstrate the effectiveness of the developed fault estimation design scheme

critical probabilities for diversity and number of clusters in randomly occupied square lattices we report the occurrence of critical probabilities associated with the maximum of diversity and the maximum number of fragments clusters on a two dimensional square lattice some scaling relations of these two variables are observed in accordance with work on fragmentation processes

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

an improved unsteady unstructured artificial compressibility finite volume scheme for viscous incompressible flows part i theory and implementation a robust artificial compressibility scheme has been developed for modelling laminar steady state and transient incompressible flows over a wide range of reynolds and rayleigh numbers artificial compressibility is applied in a consistant manner resulting in a system of preconditioned governing equations a locally generalized preconditioner is introduced designed to be robust and offer good convergence rates free artificial compressibility parameters in the equations are automated to allow ease of use while facilitating improved or comparable convergence rates as compared with the standard artificial compressibility scheme memory efficiency is achieved through a multistage pseudo time explicit time marching solution procedure a node centred dual cell edge based finite volume discretization technique suitable for unstructured grids is used due to its computational efficiency and high resolution spatial accuracy in the interest of computational efficiency and ease of implementation stabilization is achieved via a scalar valued artificial dissipation scheme temporal accuracy is facilitated by employing a second order accurate dual time stepping method in this part of the paper the theory and implementation details are discussed in part 11 the scheme will be applied to a number of example problems to solve flows over a wide range of reynolds and rayleigh numbers

adaptive neural tracking control for a class of nonstrict feedback stochastic nonlinear systems with unknown backlash like hysteresis this paper considers the problem of adaptive neural control of stochastic nonlinear systems in nonstrict feedback form with unknown backlash like hysteresis nonlinearities to overcome the design difficulty of nonstrict feedback structure variable separation technique is used to decompose the unknown functions of all state variables into a sum of smooth functions of each error dynamic by combining radial basis function neural networks universal approximation capability with an adaptive backstepping technique an adaptive neural control algorithm is proposed it is shown that the proposed controller guarantees that all the signals in the closed loop system are four moment semiglobally uniformly ultimately bounded and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value simulation results further show the effectiveness of the presented control scheme

cluster size entropy in the axelrod model of social influence small world networks and mass media we study the axelrod s cultural adaptation model using the concept of cluster size entropy s c which gives information on the variability of the cultural cluster size present in the system using networks of different topologies from regular to random we find that the critical point of the well known nonequilibrium monocultural multicultural order disorder transition of the axelrod model is given by the maximum of the s c q distributions the width of the cluster entropy distributions can be used to qualitatively determine whether the transition is first or second order by scaling the cluster entropy distributions we were able to obtain a relationship between the critical cultural trait q c and the number f of cultural features in two dimensional regular networks we also analyze the effect of the mass media external field on social systems within the axelrod model in a square network we find a partially ordered phase whose largest cultural cluster is not aligned with the external field in contrast with a recent suggestion that this type of phase cannot be formed in regular networks we draw a q b phase diagram for the axelrod model in regular networks

on the simulation of flows with violent free surface motion abstract a volume of fluid vof technique has been developed and coupled with an incompressible euler navier stokes solver operating on adaptive unstructured grids to simulate the interactions of extreme waves and three dimensional structures the present implementation follows the classic vof implementation for the liquid gas system considering only the liquid phase extrapolation algorithms to obtain velocities and pressure in the gas region near the free surface have been implemented the vof technique is validated against the classic dam break problem as well as series of 2d sloshing experiments and results from smoothed particle hydrodynamics sph calculations these and a series of other examples demonstrate that the present cfd method is capable of simulating violent free surface flows with strong nonlinear behavior

fast multigrid method for solving incompressible hydrodynamic problems with free surfaces we develop of a finite volume multigrid euler scheme for solving three dimensional fully nonlinear ship wave problems the flowfield and the a priori unknown free surface location are calculated by coupling the free surface kinematic and dynamic equations with the equations of motion for the bulk flow the evolution of the free surface boundary condition is linked to the evolution of the bulk flow via a novel iteration strategy that allows temporary leakage through the surface before the solution is converged the method of artificial compressibility is used to enforce the incompressibility constraint for the bulk flow a multigrid algorithm is used to accelerate convergence to a steady state

a new result on h_ infty state estimation of delayed static neural networks this brief presents a new guaranteed h infty performance state estimation criterion for delayed static neural networks to facilitate the use of the slope information about activation function the estimation error of activation function is separated into two parts for the first time then a novel lyapunov krasovskii functional lkf is constructed which has fully captured the slope information of the activation based on the new lkf a less conservative design criterion of estimator is derived to ensure the asymptotic stability of estimation error system with h infty performance the desired estimator gain matrices and the performance index are obtained by solving a convex optimization problem the simulation results show that the proposed method has much better performance than the most recent results

an efficient artificial compressibility ac scheme based on the characteristic based split cbs method for incompressible flows in this paper an artificial compressibility scheme using the finite element method is introduced 2002 zienkiewicz silver medal and prize winning paper the multi purpose cbs scheme is implemented in its fully explicit form to solve incompressible fluid dynamics problems it is important to note that the scheme developed here includes split and velocity correction the proposed method takes advantage of good features from both velocity correction and standard artificial compressibility schemes unlike many other artificial compressibility schemes the proposed one works on a variety of grids and gives results for a wide range of reynold s numbers the paper presents some bench mark two and three dimensional steady and unsteady incompressible flow solutions obtained from the proposed scheme copyright 2003 john wiley sons ltd

a high order characteristics upwind fv method for incompressible flow and heat transfer simulation on unstructured grids abstract this paper presents a new unstructured grid upwind finite volume algorithm for accurate numerical simulation of incompressible flows and convection heat transfer on unstructured grids it is an upwind method at both the differential equation level and discretized equation level based on the method of characteristics this is made possible with the introduction of chorin s j comput phys 2 1967 12 26 artificial compressibility formulation to the incompressible flow equations flow variables are calculated along characteristics and their initial values are interpolated based on the signs of the corresponding characteristic speed in addition an upwind biased interpolation method of third order accuracy is used for interpolating flow variables on unstructured grids with these inherent upwinding techniques for evaluating convection fluxes at control volume surfaces no artificial viscosity is required and the method is accurate and less sensitive to the grid orientation thus suitable for unstructured grid application the use of the finite volume method combined with unstructured grids makes the scheme very flexible in dealing with very complex boundary geometries while remaining to be fully conservative at the cell as well as global level the discretized equations are solved by an explicit multistage runge kutta time stepping scheme which is found to be efficient in terms of cpu and memory overheads a computer code has been developed which uses the numerical methods presented and a highly efficient edge based data structure for flux calculation and data storage a number of well documented test cases including 2d laminar flow in a channel with a backward facing step forced and natural convection flows have been calculated in order to validate the code and evaluate the performance of the numerical algorithm good agreement between the computed and measured results have been obtained for all the cases to demonstrate the accuracy of the third order scheme flow in another channel with a backward facing step studied by gartling int j numer meth fluids 1990 11 is simulated with both the third order and first order schemes it is shown that the third order scheme can produce a velocity profile across the channel that has perfect agreement with that of gartling local citation whilst the first order scheme cannot even predict the separation near the upper wall the proposed numerical methods are also used to calculate 3d incompressible inviscid flows and results show that the method is accurate and robust for general 3d simulation the 3d navier stokes code is later used to study a lid driven cavity flow at a reynolds number of 400 the unstructured grid used has 97 336 nodes and 455 625 tetrahedral elements with strong grid clustering near the walls the convergence rate is found to be satisfactory which shows that the method is also robust for 3d navier stokes simulation the results obtained agree well with those reported by jiang et al comput meth appl mech eng 114 109 1994 results obtained using the second order central scheme with artificial viscosity are also presented for comparison it is observed that the third order characteristics scheme is more accurate than the latter thus confirming its third order accuracy

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

a second order projection method for variable density flows this paper describes a second order projection method for variabledensity incompressible flows the method is suitable for both finite amplitude density variations and for fluids that are modeled using a boussinesq approximation it is based on a second order fractional step scheme in which diffusion convection terms are advanced without enforcing the incompressibility condition and the resulting intermediate velocity field is then projected onto the space of discretely divergencefree vector fields the nonlinear convection terms are treated using a godunov type procedure that is second order for smooth flow and remain stable and non oscillatory for nonsmooth flows with low fluid viscosities the method is described for finite amplitude density variation and the simplifications for a boussinesq approximation are sketched numerical results are presented that validate the convergence properties of the method and demonstrate its performance on more realistic problems

state feedback h_ infty control for a class of nonlinear stochastic systems this paper discusses the h infty control problem for a class of nonlinear stochastic systems with both state and disturbance dependent noise by means of hamilton jacobi equations both infinite and finite horizon nonlinear stochastic h infty control designs are developed some results on nonlinear h infty control of deterministic systems are generalized to a stochastic setting we introduce some useful concepts such as zero state observability and zero state detectability which together with the stochastic lasalle invariance principle yield some valuable consequences in infinite horizon nonlinear stochastic h infty control

modelling non linear heat conduction via a fast matrix free implicit unstructured hybrid algorithm abstract a matrix free implicit algorithm is developed for the fast and efficient solution of the non linear diffusion equation on unstructured hybrid meshes the aforementioned captures the physics prevalent in plasticity structural mechanics moisture transport in porous materials and non linear heat conduction this paper will be restricted to the latter the boundary condition types supported are prescribed temperature convection and radiation type neumann conditions a compact edge based vertex centered finite volume technique is employed for spatial discretisation purposes while implicit temporal discretisation is effected the resulting system of equations is newton linearized where approximate analytical expressions for the jacobian terms are developed the discrete system is solved via a preconditioned generalised minimal residual gmres algorithm where lower upper symmetric gauss seidel lu sgs is used as preconditioner the computational performance of the developed algorithm is demonstrated by application to the modelling of steady 2d non linear heat conduction problems the calculated jacobian terms are stored in the interest of computational speed with an associated additional overall memory cost of less than 10 even for small problems the developed solver outperforms jacobi with local time stepping in terms of computational time by a factor ranging between 30 and 1000 while having a total memory requirement of 1 9 times the aforementioned further as compared to the lu sgs and gmres methods the proposed solver methodology offers a speed up in solution time of between one and two orders of magnitude

scaling and critical probabilities for cluster size and la diversity on randomly occupied square lattices using monte carlo simulations we report the behaviour of the total number of clusters the cluster size diversity and the lattice animals la diversity on randomly occupied square lattices the critical probability associated with the maximum of these variables is determined in comparison with the percolation probability pc our simulations indicate that pc and the critical probability of the maximum cluster size diversity pc d s max occur at the same point as indicated in a previous paper tsang i r and tsang i j 1997 j phys a math gen 30 l239 the probability for the maximum number of clusters is obtained at a lower value pc n max 0 27 0 01 we describe the cluster identification algorithm used to count the different la and determined the critical probability for the maximum la diversity pc d f max 0 45 0 02 we derive the exponents characterizing the relation between d s max d f max and n max and several scaling relations between the variables measured the lattice size and the probability of occupation p in addition we show the scaling behaviour of la diversity versus cluster size diversity for each value of p

cluster diversity and entropy on the percolation model the lattice animal identification algorithm we present an algorithm to identify and count different lattice animals la s in the site percolation model this algorithm allows a definition of clusters based on the distinction of cluster shapes in contrast with the well known hoshen kopelman algorithm in which the clusters are differentiated by their sizes it consists in coding each unit cell of a cluster according to the nearest neighbors nn and ordering the codes in a proper sequence in this manner a la is represented by a specific code sequence in addition with some modification the algorithm is capable of differentiating between fixed and free la s the enhanced hoshen kopelman algorithm j hoshen m w berry and k s minser phys rev e 56 1455 1997 is used to compose the set of nn code sequences of each cluster using monte carlo simulations on planar square lattices up to 2000x2000 we apply this algorithm to the percolation model we calculate the cluster diversity and cluster entropy of the system which leads to the determination of probabilities associated with the maximum of these functions we show that these critical probabilities are associated with the percolation transition and with the complexity of the system

a five equation reduced model for compressible two phase flow problems this paper studies an eulerian diffuse interface model for the simulation of compressible multifluid and two phase flow problems we first show how to derive this model from a seven equation two pressure two velocity model of baer nunziato type using an asymptotic analysis in the limit of zero relaxation time we then study the mathematical properties of the system the structure of the waves the expression of the riemann s invariants and the existence of a mathematical entropy we also describe two different numerical approximation schemes for this system the first one relies on a linearized riemann solver while the second uses more heavily the mathematical structure of the system and relies on a linearization of the characteristic relations finally we present some numerical experiments and comparisons with the results obtained by the two pressure two velocity model as well as some test cases and comparisons with another five equation model recently proposed for interface computations between compressible fluids

formation and maintenance of complex systems a complex system is often identified by the absence of a characteristic length e g as in a fractal a very large system subject to a fragmentation and or aggregation dynamics passes through such complex configurations we study statistically creation and maintenance of such configurations in space dimensions d 1 to 5 and find that they are easily created maintained for small large d an intermediate d such as d 3 seems to be ideal for the creation and maintenance of complex systems this has consequences in a statistical description of the universe

how to solve compressible multifluid equations a simple robust and accurate method solving multifluid equations of compressible multiphase flows has proven to be extremely demanding because of some peculiar mathematical properties such as nonhyperbolicity nonconservative form and stiffness due to disparity in fluid properties and flow scales occurring typically in this paper we first consider the mathematical issues concerning nonhyperbolicity and nonconservative form their effects on the stability and convergence of numerical solutions are the theme of our presentation we shall present solutions for a range of problems selected to illuminate these numerical issues to this end we present a new numerical method that is simple to implement for a general class of fluids and yet is capable of robustly and accurately calculating phenomena involving material and shock discontinuities and interactions between them additionally the paper is completed with a new information for ensuring hyperbolicity under an interfacial pressure representation

on the game of life population and its diversity abstract one of the most important features of biological life in all levels is its astounding diversity in this work we study the well known game life due to conway analysing the statistics of cluster population n t and cluster diversity d t we have performed simulations on life for dimensions d 1 and 2 starting with an uncorrelated distribution of live and dead sites at t 0 for d 2 we study the effect of different neighbourhood relations in identifying and counting clusters an interesting scaling relation connecting the maxima of n t and d t is found

finite element solution of the unsteady navier stokes equations by a fractional step method abstract a finite element method is presented for the numerical simulation of time dependent incompressible viscous flows the method is based on a fractional step approach to the time integration of the navier stokes equations in which only the incompressibility condition is treated implicitly this leads to a computational scheme of extremely simple algorithmic structure that is particularly attractive for cost effective solutions of large scale problems numerical results indicate the versatility and effectiveness of the proposed method

numerical simulations for fragmentation dynamics a geometrical model for the study of fragmentation dynamics is introduced detailed statistical analysis of the fragment distribution for percolation clusters sierpinski carpets and menger sponges on square and cubic lattices is given and static and dynamic critical exponents are calculated

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

robust integral sliding mode control for uncertain stochastic systems with time varying delay this paper is concerned with sliding mode control for uncertain stochastic systems with time varying delay both time varying parameter uncertainties and an unknown nonlinear function may appear in the controlled system an integral sliding surface is first constructed then by means of linear matrix inequalities lmis a sufficient condition is derived to guarantee the global stochastic stability of the stochastic dynamics in the specified switching surface for all admissible uncertainties the synthesized sliding mode controller guarantees the reachability of the specified sliding surface finally a simulation example is presented to illustrate the proposed method

a weakly compressible free surface flow solver for liquid gas systems using the volume of fluid approach this paper presents a weakly compressible volume of fluid formulation for modelling immiscible high density ratio two fluid flow under low mach number conditions this follows findings of experimental analyses that concluded the compressibility of the gas has a noteworthy effect on predicted pressure loads in liquid gas flow in certain instances with the aim of providing a more accurate numerical representation of dynamic two fluid flow the solver is subsequently extended to account for variations in gas densities a set of governing equations is proposed which accounts for the compressible properties of the gas phase in a manner which allows for a computationally efficient numerical simulation furthermore the governing equations are numerically expressed so that they allow for large variations in the material properties without introducing notable non physical oscillations over the interface for the discretisation of the governing equations an edge based vertex centred finite volume approach is followed the developed solver is applied to various test cases and demonstrated to be efficient and accurate

neural network based dobc for a class of nonlinear systems with unmatched disturbances in this brief the problem of composite anti disturbance tracking control for a class of strict feedback systems with unmatched unknown nonlinear functions and external disturbances is investigated a disturbance observer based control dobc in combination with a neural network scheme and back stepping method is developed to achieve a composite anti disturbance controller design that provides guaranteed performance in the proposed method a conventional disturbance observer and a radial basis function neural network rbfnn are combined into a new disturbance observer to estimate the unmatched disturbances as compared with conventional dobc methods the primary merit of the proposed method is that the unknown nonlinear functions are approximated using the rbfnn technique and not regarded as part of the disturbances or estimated by a conventional disturbance observer hence the proposed method can obtain higher control accuracy than the conventional dobc methods this advantage is validated by simulation studies

a front tracking method for viscous incompressible multi fluid flows abstract a method to simulate unsteady multi fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described the flow field is discretized by a conservative finite difference approximation on a stationary grid and the interface is explicitly represented by a separate unstructured grid that moves through the stationary grid since the interface deforms continuously it is necessary to restructure its grid as the calculations proceed in addition to keeping the density and viscosity stratification sharp the tracked interface provides a natural way to include surface tension effects both two and three dimensional full numerical simulations of bubble motion are presented

a coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows we present a coupled level set volume of fluid clsvof method for computing 3d and axisymmetric incompressible two phase flows this method combines some of the advantages of the volume of fluid method with the level set method to obtain a method which is generally superior to either method alone we present direct comparisons between computations made with the clsvof method and computations made with the level set method the volume of fluid method and the boundary integral method we also compare our computations to the exact solution for an oscillating ellipse due to lamb and experimental results obtained for a rising gas bubble in liquid obtained by hnat and buckmaster our computational examples focus on flows in which surface tension forces and changes in topology are dominant features of the flow

adaptive neural network prescribed performance bounded h_ infty tracking control for a class of stochastic nonlinear systems this paper aims to give a design strategy on the prescribed performance h infty tracking control problem for a class of strict feedback stochastic nonlinear systems based on the backstepping technique generally by using the backstepping design method the stochastic nonlinear systems can only be made to be bounded in probability and it is difficult to achieve the h infty performance criterion due to the positive constant term appeared in the stability analysis thus a novel concept with regard to the bounded h infty performance is proposed in this paper to overcome the design difficulty by using the new concept and the adaptive neural network technique as well as gronwall inequality an adaptive neural network prescribed performance bounded h infty tracking controller is designed therein neural networks are used to approximate the unknown packaged nonlinear functions the assumption that the approximation errors of neural networks are square integrable in some literature is eliminated the designed controller guarantees that all the signals in the closed loop stochastic nonlinear systems are bounded in probability the tracking error is constrained into an adjustable neighborhood of the origin with the prescribed performance bounds and the controlled system has a given h infty disturbance attenuation performance for external disturbances finally the simulation results are provided to illustrate the effectiveness and feasibility of the proposed approach

a high resolution characteristics based implicit dual time stepping vof method for free surface flow simulation on unstructured grids in this paper a new unstructured grid finite volume incompressible navier stokes solver based on a high order characteristics based method the artificial compressibility method and a matrix free implicit dual time stepping scheme has been developed to study unsteady free surface flows the free surface effects are calculated using the volume of fluid vof method and continuum surface force the transport equation for the vof is numerically solved using exactly the same method for the flow solver a number of test cases have been studied to validate the proposed method and demonstrate its capability by comparison with other schemes and published results