synchronization in general complex dynamical networks with coupling delays abstract complex networks have attracted increasing attention from various fields of science and engineering today due to the finite speeds of transmission and spreading as well as traffic congestions a signal or influence travelling through a complex network often is associated with time delays and this is very common in biological and physical networks in this paper we introduce complex dynamical network models with coupling delays for both continuous and discrete time cases and then investigate their synchronization phenomena and criteria based on these new complex network models we derive synchronization conditions for both delay independent and delay dependent asymptotical stabilities in terms of linear matrix inequalities lmi we finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results

a note on existence of anti periodic and heteroclinic solutions for a class of second order odes abstract we discuss the existence of anti periodic solutions to the following second order differential equation q u t q by using fixed point theory together with the green s function for the anti periodic boundary value problem in the first part section 2 of the paper then in the next part section 3 we construct a kind of heteroclinic solution to some special cases of the equation above our method is variational in nature and is inspired by the ideas of rabinowitz and stredulinsky in p rabinowitz e stredulinsky on some results of moser and of bangert aihp anal nonlin 21 2004 673 688

zero lag synchronization and multiple time delays in two coupled chaotic systems zero lag synchronization zls between two chaotic systems coupled by a portion of their signal is achieved for restricted ratios between the delays of the self feedback and the mutual coupling we extend this scenario to the case of a set of multiple self feedbacks n d i and a set of multiple mutual couplings n c j we demonstrate both analytically and numerically that zls can be achieved when ensuremath sum l i n d i ensuremath sum m j n c j 0 where l i m j mathbb z results which were mainly derived for bernoulli maps and exemplified with simulations of the lang kobayashi differential equations indicate that zls can be achieved for a continuous range of mutual coupling delay this phenomenon has an important implication in the possible use of zls in communication networks

guiding functions for generalized periodic problems and applications abstract in this paper developing the method of guiding functions for differential inclusions with a generalized periodic condition we obtain the existence theorem for such problems it is shown how the abstract result can be applied to the study of differential games and anti periodic problems

on a class of second order anti periodic boundary value problems of concern is the existence and uniqueness of anti periodic solutions to a class of abstract nonlinear second order differential equations the investigation relies on the theory of m accretive operators in banach or hilbert spaces examples of boundary value problems for ordinary and partial differential equations are also discussed

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

weighted pseudo almost periodic mild solutions of semilinear evolution equations with nonlocal conditions in this paper applying the theory of semigroups of operators to evolution families and banach fixed point theorem we prove the existence and uniqueness of the weighted pseudo almost periodic mild solution of the semilinear evolution equation x t a t x t f t x t with nonlocal conditions x 0 x 0 g x in banach space x under some suitable hypotheses

analysis and control of differential inclusions with anti periodic conditions we deal with the optimal control of systems driven by differential inclusions with anti periodic conditions in banach spaces the operators in the differential inclusions describing the control system all depend on control variables by a solution of the control system we mean a trajectory control pair we first prove that for fixed control variables the set of solutions is non empty for the corresponding differential inclusion with anti periodic conditions we then show the functional topological properties of the set of solutions finally we investigate the existence of solutions to the optimal control problem these abstract results can be used to study optimal control systems of evolutionary hemi variational inequalities

analysis of commutation errors for functions with low regularity commutation errors arise in the derivation of the space averaged navier stokes equations the basic equations for the large eddy simulation of turbulent flows if the filter is non uniform or asymmetric skewed with non constant skewness these errors need to be analyzed for turbulent flow fields where one expects a limited regularity of the solution this paper studies the order of convergence of commutation errors as the filter width tends to zero for functions with low regularity several convergence results are proved and it is also shown that convergence may fail or its order decreases if the functions become less smooth the main results are those dealing with holder continuous functions and with functions having singularities the sharpness of the analytic results is confirmed with numerical illustrations

weighted pseudo almost periodic solutions of a class of abstract differential equations abstract for abstract linear functional differential equations with a weighted pseudo almost periodic forcing term we prove that the existence of a bounded solution on r implies the existence of a weighted pseudo almost periodic solution our results extend the classical theorem due to massera on the existence of periodic solutions for linear periodic ordinary differential equations to illustrate the results we consider the lotka volterra model with diffusion

weighted pseudo antiperiodic solutions for fractional integro differential equations in banach spaces in this paper we prove the existence of weighted pseudo antiperiodic mild solutions for fractional integro differential equations in the form d u t au t t a t s au s ds f t u t t r where f u is stepanov like weighted pseudo antiperiodic and a generates a resolvent family of bounded and linear operators on a banach space x a l loc 1 r and 0 here the fractional derivative is considered in the sense of weyl also we give a short proof to show that the vector valued space of stepanov like weighted pseudo antiperiodic functions is a banach space

synchronization in a system of globally coupled oscillators with time delay we study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling the self consistency equations for the order parameter are derived which depend explicitly on the amount of delay analysis of these equations reveals that the system in general exhibits discontinuous transitions in addition to the usual continuous transition between the incoherent state and a multitude of coherent states with different synchronization frequencies in particular the phase diagram is obtained on the plane of the coupling strength and the delay time and ubiquity of multistability as well as suppression of the synchronization frequency is manifested numerical simulations are also performed to give consistent results

stability and bifurcations in neural fields with finite propagation speed and general connectivity a stability analysis is presented for neural field equations in the presence of finite propagation speed along axons and for a general class of connectivity kernels and synaptic proper ties sufficient conditions are given for the stability of equilibrium solutions it is shown that the propagation delays play a significant role in nonstationary bifurcations of equilibria whereas the stationary bifurcations depend only on the connectivity kernel in the case of nonstationary bifurca tions bounds are determined on the frequencies of the resulting oscillatory solutions a perturbative scheme is used to calculate the types of bifurcations leading to spatial patterns oscillations and traveling waves for high propagation speeds a simple method is derived that allows the determi nation of the bifurcation type by visual inspection of the fourier transforms of the kernel and its first moment results are numerically illustrated on a class of neurologically plausible systems with combinations of gaussian excitatory and inhibitory connections

turbulence control simulation using the variational multiscale method the capabilities of the variational multiscale vms method are explored in the context of turbulence control by applying vms to the simulation of a simple opposition control strategy for turbulent channel flow with the results compared to prior direct numerical simulations and large eddy simulations based on the dynamic subgrid scale model in all cases the vms method is found to be more efficient and more accurate than the dynamic model and the simplicity accuracy and generality of vms makes it particularly attractive for turbulence control investigations

weighted pseudo almost automorphic functions and applications to abstract differential equations abstract this paper is concerned with weighted pseudo almost automorphic functions which are more general and complicated than weighted pseudo almost periodic functions using these properties we establish an existence and uniqueness theorem for pseudo almost automorphic mild solutions to semilinear differential equations in a banach space which extends known results

phase locked patterns and amplitude death in a ring of delay coupled limit cycle oscillators we study the existence and stability of phase locked patterns and amplitude death states in a closed chain of delay coupled identical limit cycle oscillators that are near a supercritical hopf bifurcation the coupling is limited to nearest neighbors and is linear we analyze a model set of discrete dynamical equations using the method of plane waves the resultant dispersion relation which is valid for any arbitrary number of oscillators displays important differences from similar relations obtained from continuum models we discuss the general characteristics of the equilibrium states including their dependencies on various system parameters we next carry out a detailed linear stability investigation of these states in order to delineate their actual existence regions and to determine their parametric dependence on time delay time delay is found to expand the range of possible phase locked patterns and to contribute favorably toward their stability the amplitude death state is studied in the parameter space of time delay and coupling strength it is shown that death island regions can exist for any number of oscillators n in the presence of finite time delay a particularly interesting result is that the size of an island is independent of n when n is even but is a decreasing function of n when n is odd

almost periodic solutions to some semilinear non autonomous thermoelastic plate equations abstract the paper is concerned with the existence of almost periodic solutions to the so called semilinear thermoelastic plate systems for that the strategy consists of seeing these systems as a particular case of the semilinear parabolic evolution equations x t a t x t f t x t t r where a t for t r is a family of sectorial linear operators on a banach space x satisfying the so called acquistapace terreni conditions and f is a function defined on a real interpolation space x for 0 1 under some reasonable assumptions it will be shown that has a unique almost periodic solution we then make use of the previous result to obtain the existence and uniqueness of an almost periodic solution to the thermoelastic plate systems

consensus reaching in multi agent packet switched networks with non linear coupling an important task for multi agent systems mas is to reach a consensus e g to align their velocity vectors recent results propose appropriate consensus protocols to achieve such tasks but most of them do not consider the effect of communication constraints such as the presence of time delays in the exchange of information between the agents in this article we provide conditions for a non linear locally passive mas of arbitrary size to reach a consensus when the agents communicate over a packet switched network that is characterised by a given topology both the cases of constant and switching topologies are considered the nature of the communication channel imposes constraints that are modelled using stochastic delays of arbitrary distribution we first embed this model in another distributed but deterministic delay model and provide conditions for the error introduced by this simplification in our main result we provide conditions for the locally passive mas with distributed delays to reach

existence results for quasilinear parabolic hemivariational inequalities abstract this paper is devoted to the periodic problem for quasilinear parabolic hemivariational inequalities at resonance as well as at nonresonance by use of the theory of multi valued pseudomonotone operators the notion of generalized gradient of clarke and the property of the first eigenfunction we build a landesman lazer theory in the nonsmooth framework of quasilinear parabolic hemivariational inequalities

existence and controllability for fractional evolution inclusions of clarke s subdifferential type in this paper by using the method of the measure of noncompactness the fixed points theorem of multivalued maps and the properties of clarke s subdifferential we give the existence result and controllability for the fractional evolution inclusions of clarke s subdifferential type in a separable reflexive banach space

transition from anticipatory to lag synchronization via complete synchronization in time delay systems the existence of anticipatory complete and lag synchronization in a single system having two different time delays that is feedback delay tau1 and coupling delay tau2 is identified the transition from anticipatory to complete synchronization and from complete to lag synchronization as a function of coupling delay tau2 with a suitable stability condition is discussed in particular it is shown that the stability condition is independent of the delay times tau1 and tau2 consequently for a fixed set of parameters all the three types of synchronizations can be realized further the emergence of exact anticipatory complete or lag synchronization from the desynchronized state via approximate synchronization when one of the system parameters b2 is varied is characterized by a minimum of the similarity function and the transition from on off intermittency via periodic structure in the laminar phase distribution

decomposition of weighted pseudo almost periodic functions abstract first we show by constructing two counterexamples that the decomposition of weighted pseudo almost periodic functions is not unique in general then we prove that the decomposition of such functions is unique if p a p 0 x is translation invariant but not necessarily unique without the assumption moreover we give an example to show that the mean value under a certain weight may not exist for all almost periodic functions with these results we answer some fundamental questions on weighted pseudo almost periodic functions

a two level variational multiscale method for convection dominated convection diffusion equations this paper studies the error in the efficient implementation of and time stepping methods for a variational multiscale method vms for solving convection dominated problems the vms studied uses a fine mesh c0 finite element space xh to approximate the concentration and a coarse mesh discontinuous vector finite element space lh for the large scales of the flux in the two scale discretization our tests show that these choices lead to an efficient vms whose complexity is further reduced if a locally l2 orthogonal basis for lh is used a fully implicit and a semi implicit treatment of the terms which link effects across scales are tested and compared the semi implicit vms was much more efficient the observed global accuracy of the most straightforward vms implementation was much better than the artificial diffusion stabilization and comparable to a streamline diffusion finite element method in our tests

phase models with explicit time delays studying weakly connected oscillators leads to phase models it has been proven recently that weakly connected oscillators with delayed interactions do not lead to phase models with time delays even when the delay is of the same order of magnitude as the period of oscillation this has resulted in a fading interest in such models we prove here that if the interaction delay between weakly connected oscillators is much longer than the period of oscillation then the corresponding phase model does have an explicit time delay

existence of anti periodic solutions for quasilinear parabolic hemivariational inequalities abstract in this paper we consider the problem of the existence of anti periodic solutions for quasilinear parabolic hemivariational inequalities with a pseudomonotone operator using regularized approximating and first eigenfunction methods and the surjectivity result we prove the existence of solutions for quasilinear parabolic hemivariational inequalities

scale separating operators for variational multiscale large eddy simulation of turbulent flows a general class of scale separating operators based on combined multigrid operators is proposed and analyzed in this work the operators of this class are designed for variational multiscale large eddy simulation using a finite volume or finite element method two representatives are compared to discrete smooth filters which are widely used in the traditional large eddy simulation literature the comparison shows that they are not only theoretically different but also yield considerable differences in the respective numerical results dynamic as well as constant coefficient based subgrid scale modeling is used within the multiscale environment all of the scale separating operators are implemented in a second order accurate energy conserving finite volume method and tested for the case of a turbulent channel flow one operator shows particularly remarkable results in the framework of the variational multiscale large eddy simulation that is profiles are obtained for velocity and kinetic energy which are considerably closer to the respective profiles from a direct numerical simulation than are the profiles resulting from the application of the other operators considered in the present study furthermore this particular operator proves to be very efficient with regard to the important aspect of computational cost that is a reduction in computing time ranging from about 25 up to about 150 compared to the other operators the introduction of a substantial amount of subgrid viscosity to the small scales particularly in the buffer layer of the channel appears to be crucial for the good results achieved with this method

existence of weighted pseudo anti periodic solutions to some non autonomous differential equations abstract in this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti periodicity which generalize respectively the well known notions of periodicity and that of anti periodicity basic properties of these new functions are discussed furthermore the existence of weighted pseudo anti periodic solutions to some damped non autonomous second order differential equations will be investigated to illustrate our abstract results the existence of weighted pseudo anti periodic solutions to a plate like equation is discussed

cluster synchronization stability for stochastic complex dynamical networks with probabilistic interval time varying delays the paper investigates the cluster synchronization stability problem for a class of complex dynamical networks with stochastic nonlinearities and probabilistic interval time varying delays the stochastic nonlinearities are considered here to reflect more realistic dynamical behaviors of complex networks the delay in this paper is assumed to be random and its probability distribution is known a priori based on the stochastic analysis techniques and the properties of the kronecker product delay dependent cluster synchronization stability criteria are derived in the form of linear matrix inequalities which can be readily solved by using the lmi toolbox in matlab the solvability of derived conditions depends on not only the size of the delay but also the probability of the delay taking values in some intervals finally a numerical example is given to illustrate the feasibility and effectiveness of the proposed method

existence of anti periodic mild solutions for semilinear evolution equations in this paper we study the existence of anti periodic mild solutions for a class of semilinear evolution equations in banach spaces and extend some related results in this direction an example is given to illustrate our results

synchronization of networks of chaotic units with time delayed couplings a network of chaotic units is investigated where the units are coupled by signals with a transmission delay any arbitrary finite network is considered where the chaotic trajectories of the uncoupled units are a solution of the dynamic equations of the network it is shown that chaotic trajectories cannot be synchronized if the transmission delay is larger than the time scales of the individual units for several models the master stability function is calculated which determines the maximal delay time for which synchronization is possible

frequency synchronization and phase agreement in kuramoto oscillator networks with delays we investigate frequency synchronization and phase agreement in networks of non identical kuramoto oscillators with delayed coupling we provide delay dependent lower bounds for the coupling gain so that a network with all to all coupling and constant heterogeneous delays achieves synchronization the given bounds are determined explicitly by the system parameters furthermore we show that frequency synchronization and phase agreement are possible in general directed networks of non identical oscillators which contain a spanning tree if the delays satisfy a self consistency condition networks with delays differ at this point notably from networks without delays because phase agreement is not possible in undelayed non identical kuramoto oscillator networks in addition to the sufficient conditions for synchronization we investigate the connection between phase agreement and the existence of solutions of a necessary self consistency condition

existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations this paper is concerned with the study of weighted pseudo almost periodic solutions to some classes of hyperbolic differential equations upon making some suitable assumptions the existence and uniqueness of a weighted pseudo almost periodic solution is obtained to illustrate our main result we study the existence of a weighted pseudo almost periodic solution to a system of partial differential equations arising in control systems described by abstract retarded functional differential equations with feedback control

isochronal synchronization of time delay and delay coupled chaotic systems this paper studies the problem of isochronal synchronization of time delay chaotic systems featuring also coupling delay based on the lyapunov krasovskii stability theory sufficient conditions are derived for the stability of isochronal synchronization between a pair of identical chaotic systems such criteria permit the proper design of stable proportional linear feedback controller more specifically the design of adequate proportional feedback gain matrices the proposed criteria are suited to systems with i intrinsic delay ii coupling delay or iii both numerical simulations of the synchronization of delay coupled systems are presented as examples of the application of the criteria

anti periodic solutions to nonlinear evolution equations abstract we deal with anti periodic problems for nonlinear evolution equations with nonmonotone perturbations the main tools in our study are the maximal monotone property of the derivative operator with anti periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings

wave formation by time delays in randomly coupled oscillators we study the dynamics of randomly coupled oscillators when interactions between oscillators are time delayed due to the finite and constant speed of coupling signals numerical simulations show that the time delays proportional to the euclidean distances between interacting oscillators can induce near regular waves in addition to near in phase synchronous oscillations even though oscillators are randomly coupled we discuss the stability conditions for the wave states and the in phase synchronous states

existence of weighted pseudo almost periodic solutions to some classes of differential equations with sp weighted pseudo almost periodic coefficients abstract in this paper we introduce the concept of weighted pseudo almost periodicity in the sense of stepanov also called s p weighted pseudo almost periodicity and study its properties next we present a result on the existence of weighted pseudo almost periodic solutions to the n dimensional heat equation with s p weighted pseudo almost periodic coefficients

anti periodic solutions to a class of nonlinear differential equations in hilbert space abstract a broad class of nonlinear non monotone anti periodic boundary value problems in a hilbert space is considered as a preliminary step the existence uniqueness and continuous dependence upon data of anti periodic solutions to some first and second order evolution equations associated to odd noncoercive monotone operators is established applications of the theory to nonlinear partial differential equations are also discussed

initial boundary value problems and optimal control for nonautonomous parabolic systems a large class of linear nonautonomous parabolic systems in bounded domains is considered with control acting on the boundary through dirichlet or neumann conditions from the point of view of semigroup theory the results from rend sem mat univ padova 78 1987 pp 47 107 on fundamental solutions for abstract parabolic equations lecture notes in math vol 1223 springer verlag berlin heidelberg 1986 pp 1 11 on abstract homogeneous parabolic cauchy problems allow operators with varying domains and holder continuous coefficients to be handled a representation formula for solutions corresponding to square integrable control functions is derived and used to solve a linear quadratic regulator problem over finite time horizon by a direct study of the associated integral riccati equation

a variational multiscale method for turbulent flow simulation with adaptive large scale space in turbulent flows it is only feasible to simulate large flow structures variational multiscale vms methods define these flow structures by projections onto appropriate function spaces this paper presents a finite element vms method which chooses the large scale projection space adaptively the adaption controls the influence of an eddy viscosity model and it is based on the size of the so called resolved small scales the adaptive procedure is described in detail numerical studies at a turbulent channel flow and a turbulent flow around a cylinder are presented it is shown that the method selects the large scale space in a reasonable way and that appropriately chosen parameters improve the results compared to the basic method which uses the same local large scale space in the whole domain and for all times

existence of solutions for anti periodic boundary value problems abstract by using schauder s fixed point theorem and the lower and upper solutions method we discuss the anti periodic boundary value problem for a class of second order differential equations some sufficient conditions for the existence of solutions are obtained

pseudo almost automorphic mild solutions to nonautonomous differential equations and applications abstract in this paper we introduce a new concept of bi almost automorphic functions and obtain new existence and uniqueness theorems for pseudo almost automorphic mild solutions to several nonautonomous differential equations moreover two examples are given to illustrate the general theorems

analysis of some finite elements for the stokes problem we study some finite elements which are used in the approximation of the stokes problem so as to obtain error estimates of optimal order resume nous etudions deux elements finis utilises pour l approximation du probleme de stokes et obtenons des estimations d erreur d ordre optimal

synchronization of chaotic networks with time delayed couplings an analytic study networks of nonlinear units with time delayed couplings can synchronize to a common chaotic trajectory although the delay time may be very large the units can synchronize completely without time shift for networks of coupled bernoulli maps analytic results are derived for the stability of the chaotic synchronization manifold for a single delay time chaos synchronization is related to the spectral gap of the coupling matrix for networks with multiple delay times analytic results are obtained from the theory of polynomials finally the analytic results are compared with networks of iterated tent maps and lang kobayashi equations which imitate the behavior of networks of semiconductor lasers

strong effects of network architecture in the entrainment of coupled oscillator systems random networks of coupled phase oscillators representing an approximation for systems of coupled limit cycle oscillators are considered entrainment of such networks by periodic external forcing applied to a subset of their elements is numerically and analytically investigated for a large class of interaction functions we find that the entrainment window with a tongue shape becomes exponentially narrow for networks with higher hierarchical organization however the entrainment is significantly facilitated if the networks are directionally biased i e closer to the feedforward networks furthermore we show that the networks with high entrainment ability can be constructed by evolutionary optimization processes the neural network structure of the master clock of the circadian rhythm in mammals is discussed from the viewpoint of our results

the total s energy of a multiagent system we introduce the total s energy of a multiagent system with time dependent links this provides a new analytical perspective on bidirectional agreement dynamics which we use to bound the convergence rates of dynamical systems for synchronization flocking opinion dynamics and social epistemology

an assessment of two models for the subgrid scale tensor in the rational les model les models seek to approximate the large scales of a flow which are defined by a space average u p of the velocity u and the pressure p of the flow a natural question which arises is given reliable data for u p how accurate is the approximation of u p by the solution computed with a les model this paper presents numerical studies of this question at a 2d and 3d mixing layer problem for the rational les model with two types of models for the subgrid scale tensor the smagorinsky model and a model proposed by iliescu and layton whereas in the 2d mixing layer problem the model by iliescu and layton showed better results the behaviour of both models was similar in the 3d mixing layer problem

existence of anti periodic mild solutions to semilinear nonautonomous evolution equations abstract in this paper applying the theory of evolution family and schauder s fixed point theorem we prove the anti periodic mild solutions for semilinear nonautonomous evolution equations in banach space under conditions furthermore an example is given to illustrate our results

evolutionary variational hemivariational inequalities existence and comparison results we consider an evolutionary quasilinear hemivariational inequality under constraints represented by some closed and convex subset our main goal is to systematically develop the method of sub supersolution on the basis of which we then prove existence comparison compactness and extremality results the obtained results are applied to a general obstacle problem we improve the corresponding results in the recent monograph s carl v k le d motreanu nonsmooth variational problems and their inequalities comparison principles and applications springer monogr math springer new york 2007

weighted pseudo almost periodic solutions for some partial functional differential equations abstract in this work we give sufficient conditions for the existence and uniqueness of a weighted pseudo almost periodic solution for some partial functional differential equations to illustrate our main result we study the existence of a weighted pseudo almost periodic solution for some diffusion equation with delay

extreme fluctuations in stochastic network coordination with time delays we study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks we obtain the average size of the fluctuations at the nodes from the behavior of the underlying modes of the network we then obtain the scaling behavior of the extreme fluctuations with system size as well as the distribution of the extremes on complex networks and compare them to those on regular one dimensional lattices for large complex networks when the delay is not too close to the critical one fluctuations at the nodes effectively decouple and the limit distributions converge to the fisher tippett gumbel density in contrast fluctuations in low dimensional spatial graphs are strongly correlated and the limit distribution of the extremes is the airy density finally we also explore the effects of nonlinear couplings on the stability and on the extremes of the synchronization landscapes

analysis of numerical errors in large eddy simulation we consider the question of numerical errors in large eddy simulation it is often claimed that straightforward discretization and solution using centered methods of models for large eddy motion can simulate the motion of turbulent flows with complexity independent of the reynolds number and dependence only on the resolution delta of the eddies sought this report considers this question analytically is it possible to prove error estimates for discretizations of actually used large eddy models whose error constants depend only on delta but not re we consider the most common simplest and most mathematically tractable model and the most mathematically clear discretization in two cases we prove such an error estimate and try to explain why our technique of proof fails in the most general case our analysis aims to assume as little time regularity on the true solution as possible

finite element les and vms methods on tetrahedral meshes finite element methods for problems given in complex domains are often based on tetrahedral meshes this paper demonstrates that the so called rational large eddy simulation model and a projection based variational multiscale method can be extended in a straightforward way to tetrahedral meshes numerical studies are performed with an inf sup stable second order pair of finite elements with discontinuous pressure approximation

pseudo almost periodic solutions of some differential equations ii we first present some results about pseudo almost periodic functions then we use these results to show some theorems about existence and uniqueness of the pseudo almost periodic solutions of the linear and the quasi linear nonautonomous equations finally we set up some theorems of the existence of pseudo almost periodic solutions implying the existence of almost periodic solutions of general ordinary differential equation systems

a finite element variational multiscale method for the navier stokes equations this paper presents a variational multiscale method vms for the incompressible navier stokes equations which is defined by a large scale space lh for the velocity deformation tensor and a turbulent viscosity nu t the connection of this method to the standard formulation of a vms is explained the conditions on lh under which the vms can be implemented easily and efficiently into an existing finite element code for solving the navier stokes equations are studied numerical tests with the smagorinsky large eddy simulation model for nu t are presented

stability of synchronized states in networks of phase oscillators the stability of synchronized states frequency locked states in networks of phase oscillators is investigated for several network topologies it is shown that for some topologies there is more than one stable synchronized state according to the sign of coupling strength between oscillators it is also shown that in some cases the synchronized state corresponds to zero order parameter

a comparison of time discretization linearization approaches for the incompressible navier stokes equations abstract this paper presents a numerical study of two ways for discretizing and linearizing the time dependent incompressible navier stokes equations one approach consists in first applying a semi discretization in time by a fully implicit scheme then in each discrete time the equations are linearized by a fixed point iteration the number of iterations to reach a given stopping criterion is a priori unknown in this approach in the second approach rosenbrock schemes with s stages are used as temporal discretization the non linearity of the navier stokes equations is treated internally in the rosenbrock methods in each discrete time exactly s linear systems of equations have to be solved the numerical study considers five two dimensional problems with distinct features four implicit time stepping schemes and five rosenbrock methods are involved

antiperiodic solutions of semilinear integrodifferential equations in banach spaces abstract we are concerned in this paper with the existence of antiperiodic mild solutions of some semilinear integrodifferential equations in a banach space we study further properties of antiperiodic functions including a new composition theorem and introduce the new concept of asymptotically antiperiodic functions

diffusive influence systems influence systems seek to model how influence broadly defined spreads across a dynamic network we build a general analytical framework which we then use to prove that while turing complete influence dynamics of the diffusive type is almost surely asymptotically periodic in addition to resolving the dynamics of a widely used family of multiagent systems we introduce a general renormalization method for the bifurcation analysis of multiagent systems

on the existence of anti periodic solutions to a nonlinear evolution equation associated with odd subdifferential operators the existence of anti periodic solutions hence also that of periodic solutions to the nonlinear parabolic type evolution equation ddt u t u t f t u t 0 t r is shown under the assumptions that the subdifferential operator is odd and that f t t r is a family of monotone operators satisfying the anti periodicity condition f t t v f t v v d f t hence f t t v f t v v d d f t t r for a fixed t r here coerciveness of is not assumed an application to a heat equation is given without assuming boundedness of the domain of rxn

anti periodic solutions for semilinear evolution equations in this paper we use the homotopy method to establish the existence and uniqueness of anti periodic solutions for the nonlinear anti periodic problem a t x bx f t a e t r x t t x t where a t x is a nonlinear map and b is a bounded linear operator from r n to r n sufficient conditions for the existence of the solution set are presented also we consider the nonlinear evolution problems with a perturbation term which is multivalued we show that for this problem the solution set is nonempty and weakly compact in w 1 2 i r n for the case of convex valued perturbation and prove the existence theorems of anti periodic solutions for the nonconvex case all illustrative examples are provided

synchronization in oscillator networks with delayed coupling a stability criterion we derive a stability criterion for the synchronous state in networks of identical phase oscillators with delayed coupling the criterion applies to any network whether regular or random low dimensional or high dimensional directed or undirected in which each oscillator receives delayed signals from k others where k is uniform for all oscillators

a composition theorem for weighted pseudo almost automorphic functions and applications abstract in this paper we establish a composition theorem for weighted pseudo almost automorphic functions under a weaker lipschitz condition our composition theorem generalizes some known results moreover the existence and uniqueness of pseudo almost automorphic solutions for abstract semilinear evolution equations are studied

almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations abstract in this paper applying the theory of semigroups of operators to evolution family and banach fixed point theorem we prove the existence and uniqueness of an a almost automorphic weighted pseudo almost automorphic mild solution of the semilinear evolution equation x t a t x t f t x t in banach space under conditions

extremal solutions of quasilinear parabolic inclusions with generalized clarke s gradient abstract in this paper we consider an initial boundary value problem for a parabolic inclusion whose multivalued nonlinearity is characterized by clarke s generalized gradient of some locally lipschitz function and whose elliptic operator may be a general quasilinear operator of leray lions type recently extremality results have been obtained in case that the governing multivalued term is of special structure such as multifunctions given by the usual subdifferential of convex functions or subgradients of so called dc functions the main goal of this paper is to prove the existence of extremal solutions within a sector of appropriately defined upper and lower solutions for quasilinear parabolic inclusions with general clarke s gradient the main tools used in the proof are abstract results on nonlinear evolution equations regularization comparison truncation and special test function techniques as well as tools from nonsmooth analysis

second order differential variational inequalities involving anti periodic boundary value conditions abstract this paper deals with a new class of second order nonlinear differential variational inequalities firstly we study the properties of a solution set for a variational inequality by using the kkm technique and a monotonicity property then we prove the existence of solutions to a second order nonlinear differential variational inequality with anti periodic boundary value conditions not assuming the lipschitz continuity of the nonlinear term our approaches which are essentially different from previous research methods in differential variational inequalities are based on the topological degree theory and the filippov implicit function lemma

numerical studies of finite element variational multiscale methods for turbulent flow simulations different realizations of variational multiscale vms methods within the framework of finite element methods are studied in turbulent channel flow simulations one class of vms methods uses bubble functions to model resolved small scales whereas the other class contains the definition of the resolved small scales by an explicit projection in its set of equations all methods are employed with eddy viscosity models of smagorinsky type the simulations are performed on grids for which a direct numerical simulation blows up in finite time

karhunen loeve decomposition approach to analyzing complex network synchronization in this paper the approach of the karhunen lo ve decomposition known also as the proper orthogonal modes poms is taken to analyze phase synchronization of various complex networks with different topologies namely the classic kuramoto model coupled chaotic maps with gaussian delays and a chain of diffusively coupled bistable oscillators in the case of the kuramoto model the poms reveal the tendency and the level of synchronization with the increase of the coupling strength for globally coupled networks and scale free networks while periodic poms are found in nearest neighbor coupled networks furthermore for cluster networks on the kuramoto model the first leading poms based on different time intervals reveal that different sub groups of nodes synchronize gradually to different levels eventually leading to the complete phase synchronization in the case of coupled chaotic maps some properties of phase synchronization change with the coupling strength value in the case of the chain of diffusively coupled bistable oscillators several main poms not only determine the network phase synchronization but also provide good reconstruction of the network responses