an anisotropic h type mesh refinement strategy abstract an anisotropic h type mesh refinement strategy for finite element approximations is presented the strategy consists of subsecting quadrilateral elements in one of two possible directions the decision which elements should be subsected and in which direction is based on minimization of interpolation errors the method is especially suitable for approximate solutions which in some regions display almost one dimensional behavior for instance solutions with boundary layers

on reliable stabilization via rectangular dilated lmis and dissipativity based certifications in this short note we consider the problem of reliable stabilization for multi channel systems where our main objective is to maintain the robust stability of the perturbed closed loop system when there is a single controller failure in any of the control channels specifically we present a less conservative result than results in the literature in terms of a set of dilated lmis for the reliable state feedback stabilization of the nominal system while a dissipativity based certification is used to extend the stability condition when there is an additive model perturbation in the system finally a numerical example is presented to illustrate the applicability of the proposed technique

asymptotic formation and orbital stability of phase locked states for the kuramoto model abstract we discuss the asymptotic formation and nonlinear orbital stability of phase locked states arising from the ensemble of non identical kuramoto oscillators we provide an explicit lower bound for a coupling strength on the formation of phase locked states which only depends on the diameters of natural frequencies and initial phase configurations we show that when the phases of non identical oscillators are distributed over the half circle and the coupling strength is sufficiently large the dynamics of kuramoto oscillators exhibits two stages transition and relaxation stages in a transition stage initial configurations shrink to configurations whose diameters are strictly less than 2 in a finite time and then the configurations tend to phase locked states asymptotically this improves previous results on the formation of phase locked states by chopra spong 2009 26 and ha ha kim 2010 27 where their attention were focused only on the latter relaxation stage we also show that the kuramoto model is l 1 contractive in the sense that the l 1 distance along two smooth kuramoto flows is less than or equal to that of initial configurations in particular when two initial configurations have the same averaged phases the l 1 distance between them decays to zero exponentially fast for the configurations with different phase averages we use the method of average adjustment and translation invariant of the kuramoto model to show that one solution converges to the translation of the other solution exponentially fast this establishes the orbital stability of the phase locked states our stability analysis does not employ any standard linearization technique around the given phase locked states but instead we use a robust l 1 metric functional as a lyapunov functional in the formation process of phase locked states we estimate the number of collisions between oscillators and lower upper bounds of the transversal phase differences

lyapunov function for the kuramoto model of nonlinearly coupled oscillators a lyapunov function for the phase locked state of the kuramoto model of non linearly coupled oscillators is presented it is also valid for finite range interactions and allows the introduction of thermodynamic formalism such as ground states and universality classes for the kuramoto model a minimum of the lyapunov function corresponds to a ground state of a system with frustration the interaction between the oscillators xy spins is ferromagnetic whereas the random frequencies induce random fields which try to break the ferromagnetic order i e global phase locking the ensuing arguments imply asymptotic stability of the phase locked state up to degeneracy and hold for any probability distribution of the frequencies special attention is given to discrete distribution functions we argue that in this case a perfect locking on each of the sublattices which correspond to the frequencies results but that a partial locking of some but not all sublattices is not to be expected the order parameter of the phase locked state is shown to have a strictly positive lower bound r 1 2 so that a continuous transition to a nonlocked state with vanishing order parameter is to be excluded

regulator problem with internal stability a frequency domain solution this paper considers the general regulator problem with internal stability where the measured outputs are not necessarily the same as the regulated outputs using polynomial matrix techniques necessary and sufficient conditions are obtained in terms of skew primeness of two polynomial matrices one of these polynomial matrices represents the disturbance modes whereas the other is the polynomial system matrix representing the system zeros various special cases considered in the literature are also analyzed in terms of these necessary and sufficient conditions

an a posteriori error estimate for finite element approximations of the navier stokes equations abstract in this paper an a posteriori error estimate for the steady state navier stokes equations based on element residual methods is developed here a special norm is designed to measure the error in velocity and pressure for incompressible flow problems we prove that under mild assumptions the new norm is asymptotically equivalent to the product space norm for the navier stokes equations moreover by summing the solutions of local elliptic residual problems the computed global error is shown to be always bounded below by the true global error when measured in the new norm a numerical experiment on the backstep channel problem is given to demonstrate the effectiveness of the error estimate

a connection between state space and doubly coprime fractional representations explicit formulas for a doubly coprime fractional representation of the transfer function of a lumped lti system are given in terms of a stabilizable and detectable state space realization of the transfer function these formulas allow existing computational algorithms to be utilized for the purpose of computing doubly coprime factorizations several additional implications of this result are briefly discussed as are some immediate extensions and future research directions

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

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

mesh generation and adaptivity for the solution of compressible viscous high speed flows an implicit explicit procedure for the solution of the compressible navier stokes equations on unstructured triangular and tetrahedral meshes is outlined a procedure for constructing continuous lines made up of edges in the mesh is employed and the implicit equation system is solved via line relaxation the problem of generating and adapting unstructured meshes for viscous flow simulations is addressed a number of examples are included which demonstrate the numerical performance of the proposed procedures

an adaptive finite element procedure for compressible high speed flows abstract a two step explicit finite element procedure for obtaining time accurate solutions to the compressible euler equations is described the method is coupled with an adaptive mesh refinement process which enables steady state solutions of improved quality to be obtained

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

synchronization and transient stability in power networks and nonuniform kuramoto oscillators motivated by recent interest for multiagent systems and smart grid architectures we discuss the synchronization problem for the network reduced model of a power system with nontrivial transfer conductances our key insight is to exploit the relationship between the power network model and a first order model of coupled oscillators assuming overdamped generators possibly due to local excitation controllers a singular perturbation analysis shows the equivalence between the classic swing equations and a nonuniform kuramoto model here nonuniform kuramoto oscillators are characterized by multiple time constants nonhomogeneous coupling and nonuniform phase shifts extending methods from transient stability synchronization theory and consensus protocols we establish sufficient conditions for synchronization of nonuniform kuramoto oscillators these conditions reduce to necessary and sufficient tests for the standard kuramoto model combining our singular perturbation and kuramoto analyses we derive

a posteriori error estimation of steady state finite element solutions of the navier stokes equations by a subdomain residual method abstract we present a subdomain residual method as well as its mathematical basis for estimating errors in steady state finite element solutions of the incompressible navier stokes equations the estimated errors are obtained by solving a series of local problems in which velocity boundary condition is used wherever the exact traction boundary condition is not available an iterative procedure similar to the newton method is employed to improve the error estimates the performance of the method is demonstrated in two numerical examples i e the channel flow over a backward facing step and past a circular cylinder at low reynolds numbers

linear control theory with an h 0e optimality criterion this expository paper sets out the principal results in bf h infty control theory in the context of continuous time linear systems the focus is on the mathematical theory rather than computational methods

a new approach to synthesis problems in linear system theory we consider a rational nonlinear equation which is involved in the general synthesis design problem of linear multivariable systems the complete solution of this equation subject to causality stability and minimality constraints is provided formal power series and in particular the theory of partial realizations prove of central importance for the design problem

algebraic aspects of linear control system stability after formulating the problem of linear control system stability in very general terms the problem is resolved by 1 establishing a necessary and sufficient condition for stability 2 exploring in some detail the nature of this condition and 3 developing a parametric characterization of all controllers which stabilize a given plant the problem formulation is based on a ring theoretic setting for linear systems and is distinguished by the use of a novel control system configuration any interconnection of two distinct systems can be represented in terms of this configuration while preserving the distinction between the two systems furthermore no other configuration has this property several benefits and extensions are accrued as a result of using this configuration first a completely general yet physically meaningful problem formulation results consequently state space and operator theoretic approaches to linear control system stability are thoroughly reconciled this reconciliation embraces continuous time as well as discrete time systems lumped as well as distributed systems and 1 d as well as n d systems second the controller parametrization affords four degrees of freedom two more than any existing parametrization the additional degrees of freedom make explicit the design opportunity associated with controller implementation and thus determine several important control system characteristics this result is expected to provide a theoretical basis for the development of comprehensive control system design methodologies wherein design considerations related to controller implementation are addressed

complete synchronization of kuramoto oscillators with finite inertia abstract we present an approach based on gronwall s inequalities for the asymptotic complete phase frequency synchronization of kuramoto oscillators with finite inertia for given finite inertia and coupling strength we present admissible classes of initial configurations and natural frequency distributions which lead to the complete phase frequency synchronization asymptotically for this we explicitly identify invariant regions for the kuramoto flow and derive second order gronwall s inequalities for the evolution of phase and frequency diameters our detailed time decay estimates for phase and frequency diameters are independent of the number of oscillators we also compare our analytical results with numerical simulations

reliable decentralized stabilization of linear systems reliable stabilization of linear time invariant multi input multi output plants is considered using a two channel decentralized controller configuration necessary and sufficient conditions are obtained for existence of reliable controllers that maintain stability under the possible failure of either one of the two controllers all decentralized controllers that achieve reliable stabilization are characterized

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

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

toward a universal h p adaptive finite element strategy part 2 a posteriori error estimation abstract in this second paper of the series on h p adaptive finite element methods we present five different techniques for a posteriori error estimation of h p methods for linear elliptic boundary value problems the techniques are referred to as the residual estimation method the duality method the subdomain residual method a method based on interpolation theory and a post processing method the present study examines the theory and behavior of such techniques applied specifically to h p adaptive finite element methods several numerical examples illustrate the efficiency of the methods

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner

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

an anisotropic h adaptive finite element method for compressible navier stokes equations abstract application of the finite element method with significantly stretched elements to solve compressible navier stokes equations is presented stretched elements are introduced in an adaptive process as a result of selective directional subsecting of elements an adaptive strategy of such anisotropic h type refinements was developed it is based on minimization of the interpolation errors reduction of the residual error indicators and an adaptive recovery of the viscous fluxes with the possibility to control their accuracy an iterative solver with the convergence characteristics independent of the aspect ratio of elements is presented the solver is the gmres algorithm with the domain decomposition schwarz type preconditioner the proposed techniques are used to solve a benchmark problem a hypersonic high reynolds number flow with strong shock boundary layer interaction

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

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

adaptative remeshing for viscous incompressible flows this paper presents an adaptive finite element procedure for solving viscous incompressible flows the methodology is based on adaptive remeshing for steady state problems the navier stokes equations for an incompressible fluid are solved in primitive variables by an uzawa algorithm using a highly accurate element the efficiency and convergence rate of the adaptive strategy are evaluated by solving problems with known analytical solutions finally the methodology is applied to the flow over a backward facing step and predictions are compared with experimental measurements the use of the proposed adaptive procedure is shown to lead to improved accuracy of the finite element predictions nomenclature c a constant e error in the solution h element size dissipation energy n number of elements in the mesh p pressure 5 step and fence height u velocity vector u v velocity components x y coordinates v gradient operator 6 element size predicted by adaptation module e strain rate tensor 1a v u v ut a stress tensor 2 e similarity variable in a boundary layer t relative error on a mesh h absolute viscosity of the fluid v kinematic viscosity of the fluid

a feedback theory of two degree of freedom optimal wiener hopf design the design of linear two degree of freedom stabilizing controllers is treated in a quadratic cost setting the class of all such controllers which give finite cost is established and the tradeoff possible between optimum performance tracking cost sensitivity and stability margins is discussed

semi implicit and explicit finite element schemes for coupled fluid thermal problems a comparative investigation based on a series of numerical tests of two purely explicit and one semi implicit finite element methods used for incompressible flow computation is presented the segregated approach is followed and the equations of motion are considered sequentially the fundamental concepts and characteristics of the formulations and the solution methodology used are described in technical detail various modifications to chorin s projection algorithm are investigated particularly with respect to their effects on stability and accuracy the stability of the semi implicit method is shown to be less restrictive when compared to the explicit methods as the reynolds number increases at large time steps the artificial viscosity is also reduced and higher accuracy is obtained the performance of the methods discussed in this paper is illustrated by the numerical solutions obtained for the cavity flow and flow past a rearward facing step problems at high reynolds numbers and free convection flow problem at high rayleigh numbers it is shown that the semi implicit method needs fewer iterations than the explicit methods and the accuracy of the present methods is guaranteed by comparison with the existing methods

automatic directional refinement in adaptive analysis of compressible flows in such local phenomena as shocks and boundary layers etc the discretization errors are directional and the use of elongated elements is obvious if economy is to be achieved although facilities for local mesh elongation have been incorporated into earlier codes in generating unstructured meshes these do not permit the use of very high stretch ratios required for the analysis of such problems as boundary layers here the use of locally introduced structured meshes has been practised involving much manual interaction and loss of error control in the paper we present a procedure which achieves the combination of such locally structured meshes with a general unstructured mesh generator in an automatic and fully adaptive manner the procedure is illustrated in the context of compressible viscous and inviscid flows but has obvious applications in other solid mechanics problems involving localization

an algebraic theory for design of controllers for linear multivariable systems part i structure matrices and feedforward design in this two part paper a theory is presented in which several control problems can be solved the theory is applicable to a general class of linear multivariable systems where the measured output does not have to be equal to the controlled output or the state the system may be affected by nonmeasurable disturbances only controllers which stabilize the system and have proper transfer functions are allowed i e the controllers have to be physically realizable it is shown that the solutions to control problems of servo type e g problems of model matching decoupling and invertibility are special cases of the solution to a more general problem analogously the solutions to problems of regulator type e g disturbance decoupling output regulation and pole placement are also speclal cases of the solution to a more general problem it is shown that problems of servo type and regulator type can be solved independently of each other in part i generalized polynomials are introduced as a mathematical framework structue matrices which describe how well a system can be controlled are defined finally problems of servo type are solved part ii mainly deals with problems of regulator type

dynamical analysis of neural networks of subgradient system in this technical note we consider a class of neural network which is a generalization of neural network models considered in the optimization context under some mild assumptions this neural network can be translated into a negative subgradient dynamical system at first we study the existence and uniqueness of solution of this neural network then by nonsmooth ojasiewicz inequality we prove the convergence of the trajectories of this neural network in the end a constrained minimization problem is studied which can be associated with this neural network it is proved that the local constrained minimum of the cost function coincides with the stable equilibria point of this neural network

local phase synchronization and clustering for the delayed phase coupled oscillators with plastic coupling abstract in this paper we investigate the local synchronization problem for delayed phase coupled oscillators with plastic coupling also referred as a generalized kuramoto model by linearizing the phase coupled oscillators system at a special solution an approximation phase coupled system with delay effects is deduced moreover we find the multiplicity of semisimple zero eigenvalue for coupling strength coefficients matrix and the rank of vandermonde matrix associated initial values are two sensitive factors the former is closely related to the maximum number of clusters phase of linear coupled system and the latter determines clusters phase synchronization as results both frequency synchronization criteria and phase synchronization criteria are established in this literature also the final synchronization frequency and phase are formulated in terms of coupling strength initial values and time delay

technical communique tracking with sensor failures this paper studies the reliability with sensor failures of the asymptotic tracking problem for linear time invariant systems using the factorization approach the plant is two output and the compensator is two degree of freedom necessary and sufficient conditions are presented for the general problem and a simple solution is given for problems with stable plants

formation of phase locked states in a population of locally interacting kuramoto oscillators abstract in this paper we present an asymptotic formation of phase locked states from the ensemble of kuramoto oscillators with a symmetric and connected interaction topology for a limited interaction topology that does not have an all to all interaction lyapunov type approaches based on phase and frequency diameters do not work due to the lack of completeness thus we employ an energy method together with the connectedness of underlying interaction topologies to determine the complete synchronization estimates our synchronization estimation method consists of two parts first we establish that the uniform boundedness of fluctuations yields the asymptotic formation of phase locked states using ojasiewicz gradient inequality second we show that for the initial configurations lying in the half circle the uniform boundedness of fluctuations can be derived by a comparison with solutions to the linear gronwall s differential inequality for the total phase variance

fast adaptive finite element scheme for viscous incompressible flows this paper presents an adaptive finite element procedure for solving viscous incompressible flows the methodology is based on adaptive remeshing for the solution of the steady state navier stokes equations for an incompressible fluid solutions are obtained in primitive variables by an uzawa algorithm using a highly accurate element two error estimators are presented and compared for a problem with a known analytical solution the methodology is then applied to a problem of practical interest and predictions are compared with experimental measurements the proposed adaptive scheme is shown to lead to improved accuracy of the finite element predictions c e e h l n p q q 5 u u v x y 6 v a v v nomenclature constant velocity error error in the solution element size dissipation energy plate length number of elements in the mesh pressure pressure error test function for pressure error step and fence height velocity vector velocity components test function for velocity error coordinates element size predicted by adaptation module strain rate tension vi vu vf 7 relative error on a mesh similarity variable in a boundary layer absolute viscosity of the fluid kinematic viscosity of the fluid deviatoric stress sensor 2pe gradient operator

comparison of mesh adaptation using the adjoint methodology and truncation error estimates mesh adaptation based on error estimation has become a key technique to improve th eaccuracy o fcomputational fluid dynamics computations the adjoint based approach for error estimation is one of the most promising techniques for computational fluid dynamics applications nevertheless the level of implementation of this technique in the aeronautical industrial environment is still low because it is a computationally expensive method in the present investigation a new mesh refinement method based on estimation of truncation error is presented in the context of finite volume discretization the estimation method uses auxiliary coarser meshes to estimate the local truncation error which can be used for driving an adaptation algorithm the method is demonstrated in the context of two dimensional naca0012 and three dimensional onera m6 wing inviscid flows and the results are compared against the adjoint based approach and physical sensors based on features of the flow field

a constructive algorithm for the complete set of compensators for two dimensional feedback system design in the recent factorization approach to linear feedback system design it has been found that in order to completely solve a generalized stabilization problem a coprime condition in the ring of stable transfer functions must be solved in this note two dimensional 2 d systems are considered and this stable coprime condition is solved for stable rings a well known 2 d zero coprime condition is a special case of this condition this is the first constructive method for obtaining the complete set of solutions or compensators for 2 d feedback system design some examples of systems treated as 2 d systems are temporal spatial spatial spatial delay differential multipass etc

the superconvergent patch recovery and a posteriori error estimates part 2 error estimates and adaptivity in this second part of the paper the issue of a posteriori error estimation is discussed in particular we derive a theorem showing the dependence of the effectivity index for the zienkiewicz zhu error estimator on the convergence rate of the recovered solution this shows that with superconvergent recovery the effectivity index tends asymptotically to unity the superconvergent recovery technique developed in the first part of the paper1 is the used in the computation of the zienkiewicz zhu error estimator to demonstrate accurate estimation of the exact error attainable numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient stress error estimation several examples of the performance of the error estimator in adaptive mesh refinement are also presented

algebraic theory of linear multivariable feedback systems this paper presents an algebraic theory for analysis and design of linear multivariable feedback systems the theory is developed in an algebraic setting sufficiently general to include as special cases continuous and discrete time systems both lumped and distributed designs are implemented by construction of a controller with two vector inputs and one vector output use of controllers of this type is shown to generate convenient stability results and convenient global parametrizations of all i o maps and all disturbance to output maps achievable for a given plant by a stabilizing compensator these parametrizations are then used to show that any such i o map and any such disturbance to output map may be simultaneously realized by choice of an appropriate controller in the special case of lumped systems it is shown that the design theory can be reduced to manipulations involving polynomial matrices only the resulting design procedure is thus shown to be more efficient computationally finally the problem of asymptotically tracking a class of input signals is considered in the general algebraic setting it is shown that the classical results on asymptotic tracking can be generalized to this setting additionally sufficient conditions for robustness of asymptotic tracking and robustness of stability are developed

on the complete synchronization of the kuramoto phase model abstract we discuss the asymptotic complete phase frequency synchronization for the kuramoto phase model with a finite size n we present sufficient conditions for initial configurations leading to the exponential decay toward the completely synchronized states our new sufficient conditions and decay rate depend only on the coupling strength and the diameter of initial phase and natural frequency configurations but they are independent of the system size n hence they can be used for the mean field limit for the complete synchronization estimates we estimate the time evolution of the phase and frequency diameters for configurations the initial phase configurations for identical oscillators located on the half circle will converge to the complete synchronized states exponentially fast in contrast for the non identical oscillators the complete frequency synchronization will occur exponentially fast for some restricted class of initial phase configurations our estimates are based on the monotonicity arguments of extremal phase and frequencies which do not employ any linearization procedure of nonlinear coupling terms and detailed information on the eigenvalue of the linearized system around the complete synchronized states we compare our analytical results with numerical simulations

on stabilization and the existence of coprime factorizations let k be an integral domain and f its quotient field we show there are plants over f which have no stable coprime factorizations but can be stabilized in a stable closed loop this answers a question posed by vidyasagar schneider and francis

on exponential synchronization of kuramoto oscillators in this technical note we study the problem of exponential synchronization for one of the most popular models of coupled phase oscillators the kuramoto model we consider the special case of finite oscillators with distinct bounded natural frequencies our first result derives a lower bound on the coupling gain which is necessary for the onset of synchronization this bound improves the one derived by jadbabaie we then calculate a lower bound on the coupling gain that is sufficient to guarantee oscillator synchronization and derive further sufficient conditions to ensure exponential synchronization of the angular frequencies of all oscillators to the mean natural frequency of the group we also characterize the coupling gain that is sufficient for the oscillator phase differences to approach any desired compact set in finite time

adaptive refinement for least squares finite elements with element by element conjugate gradient solution an error analysis and an adaptive refinement scheme are developed for use with a class of least squares finite element methods the error indicators for the refinement procedure are based on element residuals which are calculated as part of the least squares method the solution scheme used in the supporting numerical studies employs an elment by element conjugate gradient algorithm consequently storage and computation are not influenced by nodal numbering

synthesis of linear multivariable regulators this paper generalizes the results obtained by the authors in 1 and presents new results on the construction of proper controllers for linear multivariable regulators these results may lead to efficient computation methods that do not involve smith forms or the order relations used in 1 to construct proper controllers the methods are based on the recently developed theory of generalized polynomials 2 we discuss several numerical algorithms and how they can be applied to the regulator problem we also point out an important computational problem in need of an efficient numerical algorithm

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

on the łojasiewicz exponent of kuramoto model the ojasiewicz inequality and ojasiewicz exponent reveal a fundamental relation between a potential function and its gradient in this paper we explore the ojasiewicz exponent of kuramoto model and prove that the exponent is exactly 12 for equilibria located inside a quarter of circle this implies that the convergence towards such a phase locked state must be exponentially fast in contrast we give an example to see the exponent can be less than 12 for other equilibriums more precisely we prove that the exponent for the bi cluster equilibrium which is located on the boundary of a quarter of circle is 13 this gives an insight for the occurrence of exponential and algebraic convergence of kuramoto model we also present a general theorem for exponential convergence of second order gradient like system by which a criterion for the kuramoto model with inertia is established