continuous time additive hopfield type neural networks with impulses we investigate the global stability characteristics of a system of equations modelling the dynamics of additive hopfield type neural networks with impulses in the continuous time case

the method of lyapunov functionals and exponential stability of impulsive systems with time delay abstract this paper studies exponential stability of impulsive systems with time delay by employing the method of lyapunov functionals several exponential stability criteria are established our results have improved and generalized some of the known results found in the literature several examples are also discussed to illustrate our results

a semi implicit numerical scheme for reacting flow an additive semi implicit projection scheme for the simulation of unsteady combustion in two dimensions is constructed the scheme relies on a zero mach number formulation of the compressible conservation equations with detailed chemistry the governing equations are discretized in space using second order differences and integrated in time using a semi implicit approach time integration of the evolution equations for species mass fraction thermodynamic pressure and density is performed using a semi implicit nonsplit scheme that combines a second order predictor corrector treatment of convection and diffusion terms and a stiff integrator for the reaction source terms meanwhile the momentum equations are integrated using a second order projection scheme the projection scheme is based on a predictor corrector approach that couples the evolution of the velocity and density fields in order to stabilize computations of reacting flows with large density variations a pressure poisson equation is inverted following both the predictor and corrector steps using a fast solver the advantages of the stiff integration of reaction source terms are analyzed by comparing the performance of the scheme to that of a predictor corrector scheme in which reaction and diffusion are integrated in a similar nonstiff fashion the comparison in based on both one dimensional 1d unsteady tests of a premixed methane air flame and unsteady two dimensional tests of the same flame interacting with a counterrotating vortex pair in both cases the grimech1 2 reaction mechanism with 32 species and 177 elementary reactions is used computed results show that the stiff reaction scheme enables selection of larger time steps and thus leads to substantial improvement in the performance of the computations for the present reaction mechanism and flame conditions speedup factors of about 10 are achieved in the 1d tests and about five in two dimensions possible extensions of the present scheme to further improve efficiency are also discussed

impulsive delay differential inequality and stability of neural networks in this article a generalized model of neural networks involving time varying delays and impulses is considered by establishing the delay differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive delay model are obtained the results extend and improve the earlier publications an example is given to illustrate the theory

a splitting method for incompressible flows with variable density based on a pressure poisson equation a new fractional time stepping technique for solving incompressible flows with variable density is proposed the main feature of this method is that as opposed to other known algorithms the pressure is determined by just solving one poisson equation per time step which greatly reduces the computational cost the stability of the method is proved and the performance of the method is numerically illustrated

a high order numerical algorithm for dns of low mach number reactive flows with detailed chemistry and quasi spectral accuracy a novel and efficient algorithm is presented in this paper to deal with dns of turbulent reacting flows under the low mach number assumption with detailed chemistry and a quasi spectral accuracy the temporal integration of the equations relies on an operating split strategy where chemical reactions are solved implicitly with a stiff solver and the convection diffusion operators are solved with a runge kutta chebyshev method the spatial discretisation is performed with high order compact schemes and a fft based constant coefficient spectral solver is employed to solve a variable coefficient poisson equation the numerical implementation takes advantage of the 2decomp fft libraries developed by 1 which are based on a pencil decomposition method of the domain and are proven to be computationally very efficient an enhanced pressure correction method is proposed to speed up the achievement of machine precision accuracy it is demonstrated that a second order accuracy is reached in time while the spatial accuracy ranges from fourth order to sixth order depending on the set of imposed boundary conditions the software developed to implement the present algorithm is called holomac and its numerical efficiency opens the way to deal with dns of reacting flows to understand complex turbulent and chemical phenomena in flames

an hybrid finite volume finite element method for variable density incompressible flows this paper is devoted to the numerical simulation of variable density incompressible flows modeled by the navier stokes system we introduce an hybrid scheme which combines a finite volume approach for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint the breakthrough relies on the definition of a suitable footbridge between the two methods through the design of compatibility condition in turn the method is very flexible and allows to deal with unstructured meshes several numerical tests are performed to show the scheme capabilities in particular the viscous rayleigh taylor instability evolution is carefully investigated

regular article a semi implicit numerical scheme for reacting flow a stiff 1 operator split projection scheme is constructed for the simulation of unsteady two dimensional reacting flow with detailed kinetics the scheme is based on the compressible conservation equations for an ideal gas mixture in the zero mach number limit the equations of motion are spatially discretized using second order centered differences and are advanced in time using a new stiff predictor corrector approach the new scheme is a modified version of the additive stiff scheme introduced in a previous effort by h n najm p s wyckoff and o m knio 1998 j comput phys 143 381 the predictor updates the scalar fields using a strang type operator split integration step which combines several explicit diffusion sub steps with a single stiff step for the reaction terms such that the global time step may significantly exceed the critical diffusion stability limit convection terms are explicitly handled using a second order multi step scheme the velocity field is advanced using a projection scheme which consists of a partial convection diffusion update followed by a pressure correction step a split approach is also adopted for the convection diffusion step in the momentum update this splitting combines an explicit treatment of the convective terms at the global time step with several explicit fractional steps for diffusion finally a corrector step is implemented in order to couple the evolution of the density and velocity fields and to stabilize the computations the corrector acts only on the convective terms and the pressure field while the predicted updates due to diffusion and reaction are left unchanged the correction of the scalar fields is implemented using a single step non split non stiff second order time integration a similar procedure is used for the velocity field which is followed by a pressure projection step the performance and behavior of the operator split scheme are first analyzed based on tests for a nonlinear reaction diffusion equation in one space dimension followed by computations with a detailed c 1c 2 methane air mechanism in one and two dimensions the tests are used to verify that the scheme is effectively second order in time and to suggest guidelines for selecting integration parameters including the number of fractional diffusion steps and tolerance levels in the stiff integration for two dimensional simulations with the present reaction mechanism flame conditions and resolution parameters speedup factors of about 5 are achieved over the previous additive scheme and about 25 over the original explicit scheme

suitable initial conditions the aim of this note is to draw attention on a computational problem related to the initial simulation of very large time dependant systems the underlying theoretical problem has been the object of many relevant works in theoretical mathematical and in the applied literature as well but it seems that its computational implications are not familiar to many we hope that this note will help

time accurate calculation of variable density flows with strong temperature gradients and combustion a time accurate algorithm is proposed for low mach number variable density flows with or without chemical reactions the algorithm is based on a predictor corrector time integration scheme that employs a projection method for the momentum equation a constant coefficient poisson equation is solved for the pressure following both the predictor and corrector steps to fully satisfy the continuity equation at each time step spatial discretization is performed on a collocated grid system that offers computational simplicity and straightforward extension to curvilinear coordinate systems to avoid the pressure odd even decoupling that is typically encountered in such grids a flux interpolation technique is introduced for the equations governing variable density flows an important characteristic of the proposed algorithm is that it can be applied to flows in both open and closed domains its robustness and accuracy are illustrated with a series of numerical experiments in particular we present simulations of non isothermal turbulent channel flow as well as simulations of a premixed flame vortex interaction

a projection fem for variable density incompressible flows abstract this work describes a new finite element projection method for the computation of incompressible viscous flows of nonuniform density one original idea of the proposed method consists in factorizing the density variable partly outside and partly inside the time evolution operator in the momentum equation to prevent spatial discretization errors in the mass conservation to affect the kinetic energy balance of the fluid it is shown that unconditional stability in the incremental version of the projection method is possible provided two projections are performed per time step in particular a second order accurate bdf projection method is presented and its numerical performance is illustrated by test computations and comparisons

boundary conditions for a divergence free velocity pressure formulation of the navier stokes equations new sets of boundary conditions for the velocity pressure formulation of the incompressible navier stokes equations are derived the boundary conditions have the same form on both inflow and outflow boundaries and lead to a divergence free solution moreover the specific form of the boundary condition makes it possible derive a symmetric positive definite equation system for the internal pressure numerical experiments support the theoretical conclusions

conservative high order finite difference schemes for low mach number flows three finite difference algorithms are proposed to solve a low mach number approximation for the navier stokes equations these algorithms exhibit fourth order spatial and second order temporal accuracy they are dissipation free and thus well suited for dns and les of turbulent flows the key ingredient common to each of the methods presented is a poisson equation with variable coefficient that is solved for the hydrodynamic pressure this feature ensures that the velocity field is constrained correctly it is shown that this approach is needed to avoid violation of the conservation of kinetic energy in the inviscid limit which would otherwise arise through the pressure term in the momentum equation an existing set of finite difference formulae for incompressible flow is generalized to handle arbitrary large density fluctuations with no violation of conservation through the non linear convective terms an algorithm which conserves mass momentum and kinetic energy fully is obtained when an approximate equation of state is used instead of the exact one results from a model problem are used to show both spatial and temporal convergence rates and several test cases are presented to illustrate the performance of the algorithms

gauge uzawa methods for incompressible flows with variable density two new gauge uzawa schemes are constructed for incompressible flows with variable density one is in the conserved form while the other is in the convective form it is shown that the first order versions of both schemes in their semi discretized form are unconditionally stable numerical experiments indicate that the first order resp second order versions of the two schemes lead to first order resp second order convergence rate for all variables and that these schemes are suitable for handling problems with large density ratios such as in the situation of air bubble rising in water

a robust colocated implicit algorithm for direct numerical simulation of compressible turbulent flows a non dissipative robust implicit algorithm is proposed for direct numerical and large eddy simulation of compressible turbulent flows the algorithm addresses the problems caused by low mach numbers and under resolved high reynolds numbers it colocates variables in space to allow easy extension to unstructured grids and discretely conserves mass momentum and total energy the navier stokes equations are non dimensionalized using an incompressible scaling for pressure and the energy equation is used to obtain an expression for the velocity divergence a pressure correction approach is used to solve the resulting equations such that the discrete divergence is constrained by the energy equation as a result the discrete equations analytically reduce to the incompressible equations at very low mach number i e the algorithm overcomes the acoustic time scale limit without preconditioning or solution of an implicit system of equations the algorithm discretely conserves kinetic energy in the incompressible inviscid limit and is robust for inviscid compressible turbulence on the convective time scale these properties make it well suited for dns les of compressible turbulent flows results are shown for acoustic propagation the incompressible taylor problem periodic shock tube problem and isotropic turbulence

high order splitting methods for the incompressible navier stokes equations abstract a new pressure formulation for splitting methods is developed that results in high order time accurate schemes for the solution of the incompressible navier stokes equations in particular improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods a new family of stiffly stable schemes is employed in mixed explicit implicit time intgration rules these schemes exhibit much broader stability regions as compared to adams family schemes typically used in splitting methods their stability properties remain almost constant as the accuracy of the integration increases so that robust third or higher order time accurate schemes can readily be constructed that remain stable at relatively large cfl number the new schemes are implemented within the framework of spectral element discretizations in space so that flexibility and accuracy is guaranteed in the numerical experimentation a model stokes problem is studied in detail and several examples of navier stokes solutions of flows in complex geometries are reported comparison is made with the previously used first order in time spectral element splitting and non splitting e g uzawa schemes high order splitting spectral element methods combine accuracy in space and time and flexibility in geometry and thus can be very efficient in direct simulations of turbulent flows in complex geometries

generalized conservative approximations of split convective derivative operators we propose a strategy to design locally conservative finite difference approximations of convective derivatives for shock free compressible flows with arbitrary order of accuracy that generalizes the approach of ducros et al 2000 1 and that can be applied as a building block of low dissipative hybrid shock capturing methods the approximations stem from application of standard central difference formulas to split forms of the convective terms in the compressible euler equations which guarantee strong numerical stability and near energy preservation in the inviscid limit a convenient implementation of the high order fluxes is suggested which guarantees improved computational efficiency over existing methods numerical tests performed for isotropic turbulence at zero viscosity show stability of schemes with order of accuracy up to ten and effectiveness of convective splitting of kennedy and gruber 2008 2 in providing extra stability in the presence of strong density variations numerical simulations of compressible turbulent boundary layer flow indicate suitability of the method for non uniform grids and overall support superior computational efficiency of high order schemes

impulsive control for existence uniqueness and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays in this paper a class of recurrent neural networks with discrete and continuously distributed delays is considered sufficient conditions for the existence uniqueness and global exponential stability of a periodic solution are obtained by using contraction mapping theorem and stability theory on impulsive functional differential equations the proposed method which differs from the existing results in the literature shows that network models may admit a periodic solution which is globally exponentially stable via proper impulsive control strategies even if it is originally unstable or divergent two numerical examples and their computer simulations are offered to show the effectiveness of our new results

exponential stability of high order bidirectional associative memory neural networks with time delays in this paper exponential stability is studied for a class of high order bidirectional associative memory bam neural networks with time delays by employing the linear matrix inequality lmi and the lyapunov functional methods several sufficient conditions are obtained for ensuring the system to be globally exponentially stable two illustrative examples are also given in the end of this paper to show the effectiveness of our results

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

a numerical method for dns les of turbulent reacting flows a spatially non dissipative implicit numerical method to simulate turbulent reacting flows over a range of mach numbers is described the compressible navier stokes equations are rescaled so that the zero mach number equations are discretely recovered in the limit of zero mach number the dependent variables are co located in space and thermodynamic variables are staggered from velocity in time the algorithm discretely conserves kinetic energy in the incompressible inviscid non reacting limit the chemical source terms are implicit in time to allow for stiff chemical mechanisms the algorithm is readily extended to complex chemical mechanisms numerical examples using both simple and complex chemical mechanisms are presented

on mass conservation and solvability of the discretized variable density zero mach navier stokes equations abstract this paper presents a study of a variable density zero mach navier stokes discretization and subtle difficulties associated with the pressure a consistent compatibility condition between the temperature and velocity is first derived it is shown that one can accurately and efficiently solve all primitive variables with the uniform order of accuracy of the specified discretization and time marching schemes it is shown that higher density ratios than those commonly reported are achievable and it is in part traced to the solvability of the pressure poisson equation numerical properties are assessed with the method of manufactured solutions and several classical testing cases are carried out to validate the code ranging from variable density mixing problems to premixed flames with forcing

direct numerical simulation of a turbulent reactive plume on a parallel computer a computational algorithm is described for direct numerical simulation dns of a reactive plume in spatially evolving grid turbulence the algorithm uses sixth order compact differencing in conjunction with a fifth order compact boundary scheme which has been developed and found to be stable a compact filtering method is discussed as a means of stabilizing calculations where the viscous diffusive terms are differenced in their conservative form this approach serves as an alternative to nonconservative differencing previously advocated as a means of damping the 2 waves in numerically solving the low mach number equations the time derivative of the density field in the pressure poisson equation was found to be the most destabilizing part of the calculation even ordered finite difference approximations to this derivative were found to be more stable allow for larger density gradients than odd ordered approximations turbulence at the inlet boundary is generated by scanning through an existing three dimensional field of fully developed turbulence in scanning through the inlet field it was found that a high order interpolation e g cubic spline interpolation is necessary in order to provide continuous velocity derivatives regarding pressure a neumann inlet condition combined with a dirichlet outlet condition was found to work well the chemistry follows the single step irreversible global reaction fuel r oxidizer 1 r product heat with parameters chosen to match experimental data as far as allowed by resolution constraints simulation results are presented for four different cases in order to examine the effects of heat release damkohler number and arrhenius kinetics on the flow physics statistical data from the dns are compared to theory and wind tunnel data and found in reasonable agreement with regard to growth of turbulent length scales decay of turbulent kinetic energy decay of centerline scalar concentration decrease in scalar rms and spread of plume profile reactive scalar statistics are consistent with expected behavior

stability of artificial neural networks with impulses sufficient conditions are obtained for the existence and asymptotic stability of a unique equilibrium of a hopfield type neural network with lipschitzian activation functions without assuming their boundedness monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time both the continuous time and their corresponding discrete time networks are considered the sufficient conditions of the discrete time network do not restrict the step size appearing in the discretization process and these conditions approach as the step size tends to zero those of the conditions of the continuous time networks the sufficient conditions are in terms of the parameters of the network only and are easy to verify also when the impulsive jumps are absent the results reduce to those of the non impulsive systems

an overview of projection methods for incompressible flows a series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper these methods are often referred to in the literature as projection methods and can be classified into three classes namely the pressure correction methods the velocity correction methods and the consistent splitting methods for each class of schemes theoretical and numerical convergence results available in the literature are reviewed and open questions are discussed the essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners published by elsevier b v msc 65n35 65n22 65f05 35j05

exponential stability of linear delay impulsive differential equations for an impulsive delay differential equation with bounded delay and bounded coefficients the following result is established if each solution is bounded on 0 together with its derivative for each bounded right hand side then the equation is exponentially stable an explicit stability theorem is presented

a solution for the odd even decoupling problem in pressure correction algorithms for variable density flows when the navier stokes equations are solved on a colocated mesh a spurious mode for the pressure can appear if no special attention is paid to the discretization of the pressure this pressure mode can be suppressed by a pressure weighted interpolation formula for the mass flux over a cell face in this paper a similar cure is presented in the framework of pressure correction methods in variable density flow special attention is given to the solvability condition for the resulting poisson like equation for the pressure it consists of two remedies a correction term for the cell face velocity is introduced and the stencil for the discrete laplacian is compacted we finally show the applicability of the method on general curvilinear coordinate systems in three dimensions

skew symmetric form of convective terms and fully conservative finite difference schemes for variable density low mach number flows the form of convective terms for compressible flow equations is discussed in the same way as for an incompressible one by morinishi et al y morinishi t s lund o v vasilyev p moin fully conservative higher order finite difference schemes for incompressible flow j comput phys 124 1998 90 and fully conservative finite difference schemes suitable for shock free unsteady compressible flow simulations are proposed commutable divergence advective and skew symmetric forms of convective terms are defined by including the temporal derivative term for compressible flow these forms are analytically equivalent if the continuity is satisfied and the skew symmetric form is secondary conservative without the aid of the continuity while the divergence form is primary conservative the relations between the present and existing quasi skew symmetric forms are also revealed commutable fully discrete finite difference schemes of convection are then derived in a staggered grid system and they are fully conservative provided that the corresponding discrete continuity is satisfied in addition a semi discrete convection scheme suitable for compact finite difference is presented based on the skew symmetric form the conservation properties of the present schemes are demonstrated numerically in a three dimensional periodic inviscid flow the proposed fully discrete fully conservative second order accurate scheme is also used to perform the dns of compressible isotropic turbulence and the simulation of open cavity flow

global exponential stability of impulsive high order hopfield type neural networks with delays in this paper we investigate the global exponential stability of impulsive high order hopfield type neural networks with delays by establishing the impulsive delay differential inequalities and using the lyapunov method two sufficient conditions that guarantee global exponential stability of these networks are given and the exponential convergence rate is also obtained a numerical example is given to demonstrate the validity of the results

numerically stable formulations of convective terms for turbulent compressible flows abstract a systematic analysis of the discrete conservation properties of non dissipative central difference approximations of the compressible navier stokes equations is reported a generalized splitting of the nonlinear convective terms is considered and energy preserving formulations are fully characterized by deriving a two parameter family of split forms previously developed formulations reported in literature are shown to be particular members of this family novel splittings are introduced and discussed as well furthermore the conservation properties yielded by different choices for the energy equation i e total and internal energy entropy are analyzed thoroughly it is shown that additional preserved quantities can be obtained through a suitable adaptive selection of the split form within the derived family local conservation of primary invariants which is a fundamental property to build high fidelity shock capturing methods is also discussed in the paper numerical tests performed for the taylor green vortex at zero viscosity fully confirm the theoretical findings and show that a careful choice of both the splitting and the energy formulation can provide remarkably robust and accurate results

exponential stability for impulsive delay differential equations by razumikhin method abstract in this paper we study exponential stability for impulsive delay differential equation of the form x t f t x t t t k x t i k t x t t t k k n by employing the razumikhin technique and lyapunov functions several exponential stability criteria are established some examples are also discussed to illustrate our results

exponential stability of impulsive cellular neural networks with time delay via lyapunov functionals this paper investigates the problem of exponential stability for a class of impulsive cellular neural networks with time delay by dividing the network state variables into subgroups according to the characters of the neural networks some sufficient conditions for exponential stability are derived by lyapunov functionals and the method of variation of parameters these conditions are given in terms of some blocks of the interconnection matrix which extend and improve some of the known results in the literature our results show that impulses may be used to stabilize the cellular neural networks with time delay if they are not stable or exponentially stable on the other hand if impulses are input disturbances criteria on the magnitude and frequency of the impulses are also established to maintain the stability property of the original system our results generalize and improve some known results two examples with numerical simulations are given to illustrate our results

global asymptotic stability of high order hopfield type neural networks with time delays abstract this paper studies the problem of global asymptotic stability of a class of high order hopfield type neural networks with time delays by utilizing lyapunov functionals we obtain some sufficient conditions for the global asymptotic stability of the equilibrium point of such neural networks in terms of linear matrix inequality lmi numerical examples are given to illustrate the advantages of our approach

globally exponential stabilization of neural networks with mixed time delays via impulsive control the impulsive stabilization problem of neural networks with discrete time varying delays and unbounded continuously distributed delays is considered by using impulse time dependent lyapunov function based techniques to capture the hybrid structure characteristics of the considered impulsive neural networks two novel global exponential stability criteria are obtained in terms of linear matrix inequalities which are capable of dealing with the case where both the continuous and discrete dynamics are unstable when the original continuous time delayed neural networks are not stable sufficient conditions are developed for the design of exponentially stable linear impulsive state feedback controllers four numerical examples are given to illustrate the less conservatism and effectiveness of the proposed results

formulae for mean integrated squared error of nonlinear wavelet based density estimators we provide an asymptotic formula for the mean integrated squared error mise of nonlinear wavelet based density estimators we show that unlike the analogous situation for kernel density estimators this mise formula is relatively unaffected by assumptions of continuity in particular it is available for densities which are smooth in only a piecewise sense another difference is that in the wavelet case the classical mise formula is valid only for sufficiently small values of the bandwidth for larger bandwidths mise assumes a very different form and hardly varies at all with changing bandwidth this remarkable property guarantees a high level of robustness against oversmoothing not encountered in the context of kernel methods we also use the mise formula to describe an asymptotically optimal empirical bandwidth selection rule

a conservative adaptive projection method for the variable density incompressible navier stokes equations in this paper we present a method for solving the equations governing time dependent variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids the method is based on a projection formulation in which we first solve advection diffusion equations to predict intermediate velocities and then project these velocities onto a space of approximately divergence free vector fields our treatment of the first step uses a specialized second order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high reynolds number flow density and other scalars are advected in such a way as to maintain conservation if appropriate and free stream preservation our approach to adaptive refinement uses a nested hierarchy of logically rectangular girds with simultaneous refinement of the girds in both space and time the integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized the single grid algorithm is described briefly but the emphasis here is on the time stepping procedure for the adaptive hierarchy numerical examples are presented to demonstrate the algorithms s accuracy and convergence properties and illustrate the behavior of the method an additional example demonstrates the performance of the method on a more realistic problem namely a three dimensional variable density shear layer