singular perturbation analysis of competitive neural networks with different time scales the dynamics of complex neural networks must include the aspects of long and short term memory the behavior of the network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system the main idea of this paper is to apply a stability analysis method of fixed points of the combined activity and weight dynamics for a special class of competitive neural networks we present a quadratic type lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables as a global stability method and a modality of detecting the local stability behavior around individual equilibrium points

necessary and sufficient graphical conditions for formation control of unicycles the feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control the directed graph defined by the information flow plays a key role it is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node a similar result is given for formation stabilization to a line and to more general geometric arrangements

the jameson s numerical method for solving the incompressible viscous and inviscid flows by means of artificial compressibility and preconditioning method abstract a computational code is developed using cell centered finite volume method with a non uniform grid for solving the incompressible viscous and inviscid flows the method has been used to determine the steady incompressible inviscid flows past a cylinder in free stream the steady incompressible inviscid flows past a circular bump through a channel and also the steady incompressible viscous flows past a backward facing step in this method the 2d navier stokes equations or 2d incompressible euler equations for inviscid flow which are modified by artificial compressibility and preconditioning concepts are solved with the jameson s artificial dissipation and viscosity terms under the form of a fourth and second order x derivative respectively an explicit fourth order runge kutta integration algorithm is applied to find the steady state condition the effects of cfl number artificial viscosity coefficient and pseudo compressibility parameter in convergence of solution are investigated

abelian mathrm c ast subalgebras of mathrm c ast algebras of real rank zero and inductive limit mathrm c ast algebras

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

distributed exponential finite time coordination of multi agent systems containment control and consensus in this paper exponential finite time coordination problems of multi agent systems are investigated including containment control and consensus the theoretical basis is that a class of nonlinear systems has favourable finite time convergence characteristic for the objective of containment control the proposed protocol ensures that the boundary agents in the same strong component exponentially reach a consensus and the internal agents exponentially converge to the convex hull spanned by the boundary agents in a finite time for the objective of consensus a pinning control strategy is designed for a fraction of agents such that all the agents exponentially reach a consensus with the leader in a finite time the distinguished features of this paper lie in the following two points 1 a smaller settling time of the lyapunov function is obtained which manifests in a faster convergence rate than the traditional one and 2 the weakly connected topology considered in this paper is more general than the o

predictable dynamics of opinion forming for networks with antagonistic interactions for communities of agents which are not necessarily cooperating distributed processes of opinion forming are naturally represented by signed graphs with positive edges representing friendly and cooperative interactions and negative edges the corresponding antagonistic counterpart unlike for nonnegative graphs the outcome of a dynamical system evolving on a signed graph is not obvious and it is in general difficult to characterize even when the dynamics are linear in this paper we identify a significant class of signed graphs for which the linear dynamics are however predictable and show many analogies with positive dynamical systems these cases correspond to adjacency matrices that are eventually positive for which the perron frobenius property still holds and implies the existence of an invariant cone contained inside the positive orthant as examples of applications we determine cases in which it is possible to anticipate or impose unanimity of opinion in decision voting processes even in presence of stubborn agents and show how it is possible to extend the pagerank algorithm to include negative links

explicit and semi implicit cbs procedures for incompressible viscous flows this paper presents a numerical comparison of two different numerical procedures based on the characteristic based split cbs algorithm for the solution of incompressible flows the first procedure is based on the original semi implicit version of the cbs introduced in the early days of the scheme development the second was proposed more recently in order to have a fully explicit version of the scheme and is based on the introduction of an artificial compressibility type of formulation the interest in fully explicit schemes has increased because of the easy and efficient parallelization the main differences between the two versions of the schemes are highlighted in this work and a numerical comparison is presented on the basis of several benchmark solutions both steady and unsteady flows are considered with the explicit version of the scheme a dual time stepping procedure is needed to recover unsteady solutions copyright 2006 john wiley sons ltd

on the relation between an operator and its self commutator we show that a bounded operator a on a hilbert space belongs to a certain set associated with its self commutator a a provided that a zi can be approximated by invertible operators for all complex numbers z the theorem remains valid in a general c algebra of real rank zero under the assumption that a zi belong to the closure of the connected component of unity in the set of invertible elements this result implies the brown douglas fillmore theorem and huaxin lin s theorem on almost commuting matrices moreover it allows us to refine the former and to extend the latter to operators of infinite rank and other norms including the schatten norms on the space of matrices the proof is based on an abstract theorem which states that a normal element of a c algebra of real rank zero satisfying the above condition has a resolution of the identity associated with any open cover of its spectrum

the generalized berg theorem and bdf theorem let a be a separable simple af algebra with finitely many extreme traces we give a necessary and sufficient condition for an essentially normal element x e m a i e ir x is normal r m a m a a is the quotient map having the form y a for some normal element y c m a and a e a we also show that a normal element x e m a can be quasidiagonalized if and only if the fredholm index ind a x 0 for all a 0 sp 7r x in the case that a is a simple c algebra of real rank zero with stable rank one and with continuous scale k1 a 0 and ko a has countable rank we show that a normal element x e m a with zero fredholm index can be written as

modulus consensus in a network of singularly perturbed systems with collaborative and antagonistic interactions abstractthis paper addresses the modulus consensus in a network of singularly perturbed systems all of which own multi time scales characteristics the interactions among the agents are collaborat

non conservative and conservative formulations of characteristics based numerical reconstructions for incompressible flows summary an investigation of characteristics based cb schemes for solving the incompressible navierstokes equations in conjunction with the artiflcial compressibility approach is presented both nonconservative and conservative characteristics based numerical reconstructions are derived and their accuracy and convergence properties are assessed analytically and numerically we demonstrate by means of eigenvalue analysis that there are difierences in the spectral characteristics of these formulations that result in difierent convergence properties numerical tests for two and threedimensional ows reveal that the two formulations provide similar accuracy but the non conservative formulation converges faster copyright c 2000 john wiley sons ltd

nonlinear finite time bipartite consensus protocol for multi agent systems associated with signed graphs in this paper finite time multi agent consensus problems are considered under networks associated with signed graphs whose edge weights can be not only positive but also negative a nonlinear consensus protocol is proposed to guarantee the states of all agents to converge in a finite time if the signed graph is structurally balanced then the final consensus states of all agents are the same in modulus but not in sign otherwise if the signed graph is structurally unbalanced then the states of all agents converge to zero moreover the final consensus states of agents can be provided uniformly regarding a signed average quantity that depends on both the initial states of agents and the topology structure of the whole multi agent network numerical simulations illustrate that the protocol is effective in achieving the finite time consensus of agents under signed graphs and can particularly solve the finite time average consensus problem of agents when their associated graph has all positive edge weights

composite control of non linear singularly perturbed systems a geometric approach using a geometric approach a composite control the sum of a slow control and a fast control is derived for a general class of non linear singularly perturbed systems a new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset the slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of e accuracy

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 matrix free implicit incompressible fractional step algorithm for fluid structure interaction applications in this paper we detail a fast fully coupled partitioned fluid structure interaction fsi scheme for the incompressible fluid new fractional step algorithms are proposed which make possible the fully implicit but matrix free parallel solution of the entire coupled fluid solid system these algorithms include artificial compressibility pressure poisson solution in conjunction with upwind velocity stabilisation as well as simplified pressure stabilisation for improved computational efficiency a dual timestepping approach is proposed where a jacobi method is employed for the momentum equations while the pressures are concurrently solved via a matrix free preconditioned gmres methodology this enables efficient sub iteration level coupling between the fluid and solid domains parallelisation is effected for distributed memory systems the accuracy and efficiency of the developed technology is evaluated by application to benchmark problems from the literature the new schemes are shown to be efficient and robust with the developed preconditioned gmres solver furnishing speed ups ranging between 50 and 80

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

petrov galerkin solutions of the incompressible navier stokes equations in primitive variables with adaptive remeshing the solution of the incompressible navier stokes equations in primitive variables is addressed in this paper a petrov galerkin formulation which automatically introduces streamline upwinding and allows equal order interpolation for all flow variables is presented the solution algorithm is segregated involving a series of updatings of the velocity and pressure fields error estimation and adaptive remeshing strategies for both steady and unsteady problems are demonstrated in some representative numerical examples

exponentials in simple z stable c algebras abstract let a be a unital separable simple z stable c algebra which has rational tracial rank at most one and let u u 0 a where u 0 a is the connected component of the unitary group of a containing the identity we show that for any 0 there exists a self adjoint element h a such that 0 1 u exp i h but there is no control of h in general let cu a be the closure of the commutator subgroup of the unitary group of a and let u cu a we prove that there exists a self adjoint element h a such that 0 2 u exp i h and h 2 examples are given that the bound 2 for h is optimal in general for the jiang su algebra z we show that if u u 0 z and 0 there exists a real number t and a self adjoint element h z with h 2 such that e i t u exp i h

an improved unsteady unstructured artificial compressibility finite volume scheme for viscous incompressible flows part ii application in part i of this paper a preconditioned artificial compressibility scheme was developed for modelling laminar steady state and transient incompressible flows for a wide range of reynolds and rayleigh numbers in this part several examples of laminar incompressible problems are solved and discussed the influence of various ac parameters on robustness and convergence rates are assessed for a complex category of problems it is shown that the scheme developed in part i is an accurate robust and easy to use method for solving incompressible laminar flow problems over a wide range of flow regimes copyright 2002 john wiley sons ltd

classification of simple c algebras with unique traces we classify certain almost multiplicative morphisms up to approximate unitary equivalence and use this result to prove the following let a and b be two unital separable simple c algebras of real rank zero stable rank one with weakly unperforated k 0 groups and with unique normalized quasi traces suppose that both a and b are locally ah and k a k a 1 a k b k b 1 b then a is isomorphic to b

on the consensus and bipartite consensus in high order multi agent dynamical systems with antagonistic interactions abstract the aim of this paper is to address consensus and bipartite consensus for a group of homogeneous agents under the assumption that their mutual interactions can be described by a weighted signed connected and structurally balanced communication graph this amounts to assuming that the agents can be split into two antagonistic groups such that interactions between agents belonging to the same group are cooperative and hence represented by nonnegative weights while interactions between agents belonging to opposite groups are antagonistic and hence represented by nonpositive weights in this framework bipartite consensus can always be reached under the stabilizability assumption on the state space model describing the dynamics of each agent on the other hand nontrivial standard consensus may be achieved only under very demanding requirements both on the laplacian associated with the communication graph and on the agents description in particular consensus may be achieved only if there is a sort of equilibrium between the two groups both in terms of cardinality and in terms of the weights of the conflicting interactions amongst agents

steady and unsteady incompressible flow in a double driven cavity using the artificial compressibility ac based characteristic based split cbs scheme in this paper the explicit characteristic based split cbs scheme has been employed to solve both steady and unsteady flows inside a non rectangular double driven cavity this problem is recently suggested as a benchmark problem for incompressible flows both unstructured and structured meshes have been employed in the present study to make sure that the predicted results are as close to reality as possible the results obtained show the existence of steady state at lower reynolds numbers 1000 and transient states at higher reynolds numbers the flow approaches a turbulent state as the reynolds number is increased to 10 000 copyright 2005 john wiley sons ltd

computation of natural convection in two dimensional cavities with chebyshev polynomials abstract a semi implicit spectral method for the computation of buoyancy induced two dimensional flow of a viscous incompressible fluid is presented the incompressible navier stokes equations expressed in terms of the primitive variables velocity and pressure and an additional equation for the temperature are considered all the variables are expanded in double truncated series of chebyshev polynomials the pressure distribution at the boundary of the computational domain is determined by means of an influence matrix technique in order to satisfy the incompressibility condition everywhere in the field the algorithm is applied to the classical problem of natural convection of a boussinesq fluid within a differentially heated vertical square cavity results show that for a prandtl number of 0 71 corresponding to air and up to rayleigh numbers of 106 very accurate solutions are obtained with a spatial resolution of 33 polynomials in each direction new interesting phenomena are shown for higher values of the rayleigh number

exponential rank of c algebras with real rank zero and the brown pedersen conjectures abstract we show that every c algebra with real rank zero has exponential rank 1 consequently c algebras with real rank zero have the property weak fu we also show that if a is a unital c algebra with real rank zero stable rank one and trivial k1 group then its multiplier algebra has real rank zero if a is a unital stable c algebra with stable rank one we show that its multiplier algebra has real rank zero if and only if a has real rank zero and k1 a 0

an accelerated fully coupled parallel 3d hybrid finite volume fluid structure interaction scheme abstract in this paper we propose a fast parallel 3d fully coupled partitioned hybrid unstructured finite volume fluid structure interaction fsi scheme spatial discretisation is effected via a vertex centred finite volume method where a hybrid nodal elemental strain procedure is employed for the solid in the interest of accuracy for the incompressible fluid a split step algorithm is presented which allows the entire fluid solid system to be solved in a fully implicit yet matrix free manner the algorithm combines a preconditioned gmres solver for implicit integration of pressures with dual timestepping on the momentum equations thereby allowing strong coupling of the system to occur through the inner solver iterations further acceleration is provided at little additional cost by applying lu sgs relaxation to the viscous and advective terms the solver is parallelised for distributed memory systems using mpi and its scaling efficiency evaluated the developed modelling technology is evaluated by application to two 3d fsi problems the advanced matrix free solvers achieve reductions in overall cpu time of up to 50 times while preserving close to linear parallel computing scaling using up to 128 cpus for the problems considered

c algebras with weak fn letabe a simplec algebra of real rank zero and stable rank one we show that for any normal elementx awith x inv0 a forall sp x there is a sequence of normal elementsxn awith finite spectra such thatx limn xn we show this for more generalc algebras we also point out that the condition thatais simple cannot be removed

unconditional stability and long term behavior of transient algorithms for the incompressible navier stokes and euler equations abstract this paper examines the long term behavior dissipativity and unconditional nonlinear stability properties of time integration algorithms for the incompressible navier stokes equations including both direct schemes and fractional step projection methods the algorithms are termed nonlinear unconditionally stable if in the absence of a forcing term but for arbitrary initial conditions the computed kinetic energy decreases for arbitrary step sizes i e l 2 stability such an a priori stability estimate is a characteristic feature of the navier stokes system similarly the algorithms are said to exhibit asymptotic t independent long term dissipative behavior if as the continuum flow generated by the navier stokes equations the algorithmic flow also exhibits an absorbing set and a maximal attractor both direct and fractional step methods are described which inherit these fundamental properties of the navier stokes system for any time step size moreover a subclass of algorithms which retain these strong notions of nonlinear stability and long term dissipative behavior is identified which in addition has the remarkable property of being linear within the time step the key implication is that no iterations are required to compute the solution within a time step a specific member of this class is shown to possess the same absorbing set as the continuum navier stokes system a second order accurate unconditionally stable method is also identified which retains the property of linearity within a time step numerical analysis and computational aspects involved in the implementation of these methods are addressed in detail and illustrated in representative numerical simulations

homotopy classification of homogeneous projections in the corona algebra of c x b for a graph x abstract in this paper we consider certain projections in the corona algebra of c x b for x a directed graph and b a stable c algebra of which the multiplier algebra has real rank zero assuming a kind of homogeneity on the projections we characterize when two such projections are homotopy equivalent as a result for a simple graph we show that such projections are always homotopic

on inductive limits of matrix algebras over the two torus it will be shown in this paper that certain real rank zero c algebras which are inductive limits of c algebras of the form i m k i c inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i can be expressed as inductive limits of c algebras of the form i m k i c s 1 in particular if both a and b are of real rank zero and are inductive limits of c algebras of the form i m k i c s 1 then also a b is an inductive limit of c algebras of the form i m k i c s 1 hence a b can be classified by its k theory this is a key step in the general classification theory of inductive limit c algebras

adaptive mesh generation for fluid mechanics problems in this study we give an in depth investigation of the adaptive procedures for compressible and incompressible flow problems many tests have been carried out with different error indicators for different problems these refinement procedures show that the interpolation error indicators are adequate to predict an accurate solution comparison between the gradient and curvature based error indicators show that the former yields better performance in most situations however we found that the latter indicators predict better motion in the recirculatory and unstable regions than the gradient based method many test cases have been presented for both compressible and incompressible flow problems in the later part of the paper we suggest a simple way of combining the curvature gradient indicators of different key variables and present an appropriate problem where it is applicable a wide coverage of relevant literature has also been presented in this paper copyright 2000 john wiley sons ltd

consensus problems on networks with antagonistic interactions in a consensus protocol an agreement among agents is achieved thanks to the collaborative efforts of all agents expresses by a communication graph with nonnegative weights the question we ask in this paper is the following is it possible to achieve a form of agreement also in presence of antagonistic interactions modeled as negative weights on the communication graph the answer to this question is affirmative on signed networks all agents can converge to a consensus value which is the same for all agents except for the sign necessary and sufficient conditions are obtained to describe cases in which this is possible these conditions have strong analogies with the theory of monotone systems linear and nonlinear laplacian feedback designs are proposed

preconditioning applied to variable and constant density flows a time derivative preconditioning of the navier stokes equations suitable for both variable and constant density fluids is developed the ideas of low mach number preconditioning and artificial compressibility are combined into a unified approach designed to enhance convergence rates of density based time marching schemes for solving flows of incompressible and variable density fluids at all speeds the preconditioning is coupled with a dual time stepping scheme implemented within an explicit multistage algorithm for solving time accurate flows the resultant time integration scheme is used in conjunction with a finite volume discretization designed for unstructured solution adaptive mesh topologies this method is shown to provide accurate steady state solutions for transonic and low speed flow of variable density fluids the time accurate solution of unsteady incompressible flow is also demonstrated