brief paper identification and data driven model reduction of state space representations of lossless and dissipative systems from noise free data we illustrate procedures to identify a state space representation of a lossless or dissipative system from a given noise free trajectory important special cases are passive systems and bounded real systems computing a rank revealing factorization of a gramian like matrix constructed from the data a state sequence can be obtained the state space equations are then computed by solving a system of linear equations this idea is also applied to perform model reduction by obtaining a balanced realization directly from data and truncating it to obtain a reduced order model

weak solutions of a class of quasilinear hyperbolic integro differential equations describing viscoelastic materials global weak solutions of scalar second order quasilinear hyperbolic integro differential equations with singular kernels are constructed perturbations of rest states are shown to propagate with finite speed smoothing effects of the solution operator are exhibited and conditions for the asymptotic stability of rest states are given the equations arise in viscoelasticity

existence results for the flow of viscoelastic fluids with a differential constitutive law where 2 is the symmetric extra stress tensor the total stress is given by g pl i where p is the hydrodynamic pressure 4 is the rate of deformation tensor g u vu vu u being the velocity field a is the relaxation time a2 the retardation time 0 i a a1 and q is the fluid viscosity the symbol a d t denotes an objective frame indifferent derivative i 181 more precisely

passivity preserving model reduction by analytic interpolation abstract antoulas and sorensen have recently proposed a passivity preserving model reduction method of linear systems based on krylov projections the idea is to approximate a positive real rational transfer function with one of lower degree the method is based on an observation by antoulas in the single input single output case that if the approximant is preserving a subset of the spectral zeros and takes the same values as the original transfer function in the mirror points of the preserved spectral zeros then the approximant is also positive real however this turns out to be a special solution in the theory of analytic interpolation with degree constraint developed by byrnes georgiou and lindquist namely the maximum entropy central solution by tuning the interpolation points and the spectral zeros as prescribed by this theory one is able to obtain considerably better reduced order models we also show that in the multi input multi output case sorensen s algorithm actually amounts to tangential nevanlinna pick interpolation

passivity preserving model reduction via interpolation of spectral zeros abstract an algorithm is developed for passivity preserving model reduction of linear time invariant systems implementation schemes are described for both medium scale dense and large scale sparse applications the algorithm is based upon interpolation at selected spectral zeros of the original transfer function to produce a reduced transfer function that has the specified roots as its spectral zeros these interpolation conditions are satisfied through the computation of a basis for a selected invariant subspace of a certain block matrix which has the spectral zeros as its spectrum explicit interpolation is avoided and passivity of the reduced model is established instead through satisfaction of the necessary conditions of the positive real lemma it is also shown that this procedure indirectly solves the associated controllability and observability riccati equations and how to select the interpolation points to give maximal or minimal solutions of these equations from these a balancing transformation may be constructed to give a reduced model that is balanced as well as passive and stable

on degree constrained analytic interpolation with interpolation points close to the boundary in the recent article a theory for complexity constrained interpolation of contractive functions is developed in particular it is shown that any such interpolant may be obtained as the unique minimizer of a convex weighted entropy gain in this technical note we study this optimization problem in detail and describe how the minimizer depends on weight selection and on interpolation conditions we first show that if for a sequence of interpolants the values of the entropy gain of the interpolants converge to the optimum then the interpolants converge in h 2 but not in h infin this result is then used to describe the asymptotic behavior of the interpolant as an interpolation point approaches the boundary of the domain of analyticity for loop shaping to specifications in control design it might at first seem natural to place strategically additional interpolation points close to the boundary however our results indicate that such a strategy will have little effect on the shape another consequence of our results relates to model reduction based on minimum entropy principles where one should avoid placing interpolation points too close to the boundary

a local existence and uniqueness theorem for a k bkz fluid we consider the three dimensional motion of a viscoelastic liquid occupying all of space the constitutive law is assumed to be of the form suggested by kaye 13 and bernstein kearsley zapas 2 an existence and uniqueness result for solutions of the initial value problem on sufficiently short time intervals is proved using kato s theory of quasilinear hyperbolic equations

viscoelastic taylor couette flow bifurcation analysis in the presence of symmetries the morphogenesis of secondary vortices is investigated for the axisymmetric flow of a viscoelastic fluid confined between two independently rotating infinitely long cylinders in the region near the onset of instability of the purely azimuthal couette flow the oldroyd b constitutive equation is used to model viscoelasticity three characteristic regions in the parameter space corresponding to three distinct solution families have been investigated where the onset of instability is due primarily to inertia both inertia and elasticity and exclusively elasticity respectively the secondary flow corresponds to a steady taylor vortex in the first case but to a time periodic one when elasticity becomes important hopf bifurcation degenerate hopf bifurcation theory in the presence of symmetries o 2 s 1 has been used to show the existence of two different time periodic solution families each following either one of two possible patterns the rotating wave or the standing wave through a computer aided nonlinear analysis all of the steady and time periodic bifurcating solutions are shown to be supercritical implying that one and only one is stable these results are consistent with the conclusions of time dependent numerical simulations which have demonstrated an exchange of stabilities from the rotating to the standing wave pattern emerging after the bifurcation as the elasticity of the fluid increases

torsional effects in high order viscoelastic thin filament models the authors present an approximation theory for thin filaments fibers or jets which yields families of transient 1 d models time dependent one dimensional closed systems of pdes the spatial reduction from three dimensions to one is achieved by axisymmetry together with a local expansion in the radial jet coordinate this reduction is in contrast to the predominant viscoelastic models in the literature which average out the radial dimension and thereby require moment equations for the computation of higher order corrections the authors also allow torsional flow effects which are usually ignored in a general johnson segalman constitutive law a formal perturbation theory based on a slenderness parameter and a compatible velocity pressure stress ansatz is then constructed for the full 3 d free surface boundary problem this formalism contains all 1 d transient models that govern slender axisymmetric flows of inviscid viscous or viscoelastic fluids specific models follow by positing the dominant

higher order godunov methods for general systems of hyperbolic conservation laws abstract we describe an extension of higher order godunov methods to general systems of hyperbolic conservation laws this extension allow the method to be applied to problems that are not strictly hyperbolic and exhibit local linear degeneracies in the wave fields the method constructs an approximation of the riemann problem from local wave information a generalization of the engquist osher flux for systems is then used to compute a numerical flux based on this approximation this numerical flux replaces the godunov numerical flux in the algorithm thereby eliminating the need for a global riemann problem solution the additional modifications to the godunov methodology that are needed to treat loss of strict hyperbolicity are described in detail the method is applied to some simple model problems for which the global analytic structure is known the method is also applied to the black oil model for multiphase flow in petroleum reservoirs

on the solution of the minimal rational interpolation problem it is shown that the reachability and the observability indices of appropriately defined pairs of matrices provide the key for solving the minimal rational bitangen tial interpolation problem

balancing of lossless and passive systems different balancing techniques are applied to lossless nonlinear systems with open loop balancing applied to their scattering representation it is shown that they all lead to the same result the pair of to be balanced functions is given by two copies of the physical energy function yielding thus no information about the relative importance of the state components in a balanced realization in particular in the linear lossless case all balancing singular values and similarity invariants are equal to one this result is extended to general passive systems in which case the to be balanced functions are ordered into a single sequence of inequalities and the similarity invariants are all less than or equal to one

passivity preserving model reduction with finite frequency h approximation performance this paper is concerned with model reduction for passive systems for a given linear time invariant system that is stable and positive real pr our goal is to find a pr reduced order model to approximate it and our attention is focused on reducing the error with respect to a finite frequency h performance which is the most remarkable difference between the proposed approach and the existing ones first by applying multiplier expansion new conditions in terms of linear matrix inequalities are derived for characterizing the positive realness of the reduced order model and the finite frequency h performance of the error system a necessary and sufficient condition is then established for parameterizing a pr reduced order model with finite frequency h approximation performance based on which an iterative algorithm is constructed for numerically exploring such a reduced order model particularly a partial multiplier expansion treatment is introduced which greatly reduces the decision variables but does not cause conservatism to the derived conditions the proposed method is also extended to robust passivity reserving model reduction with polytopic uncertainty finally we provide two numerical examples about rlc circuits to show the effectiveness and advantages of the proposed model reduction method

existence and stability results for 3 d regular flows of viscoelastic fluids of white metzner type abstract this paper is concerned with regular flows of incompressible viscoelastic fluids which obey a differential constitutive law of white metzner type we study the existence and uniqueness of local solutions in 3 d domain as well as the global existence for small data by a classical stability argument we deduce the existence and stability of small periodic and stationary solutions we also generalize the 2 d results more precisely we prove that the results obtained by hakim j math anal appl 185 1994 675 remain true without any restriction on the smallness of the retardation parameter which is the linking coefficient between the equation of velocity navier stokes equation and the transport equation verified by the extra stress tensor the hypothesis of boundedness on the relaxation function is also dropped

new formulations positivity preserving discretizations and stability analysis for non newtonian flow models we propose a class of new discretization schemes for solving the rate type non newtonian constitutive equations the so called conformation tensor has been known to be symmetric and positive definite in a large class of constitutive equations preserving such a positivity property on the discrete level is believed to be crucially important but difficult high weissenberg number problems on numerical instabilities have been often associated with this issue in this paper we present various discretization schemes that preserve the positive definiteness of the conformation tensor regardless of the time and spatial resolutions moreover the robustness of the algorithm has been also demonstrated by the stability analysis using the discrete analogue of energy estimates new schemes presented in this paper are constructed based upon the newly discovered relationship between the rate type constitutive equations and the symmetric matrix riccati differential equations

lur e equations and even matrix pencils abstract in this work we consider the so called lur e matrix equations that arise e g in model reduction and linear quadratic infinite time horizon optimal control we characterize the set of solutions in terms of deflating subspaces of even matrix pencils in particular it is shown that there exist solutions which are extremal in terms of definiteness it is shown how these special solutions can be constructed via deflating subspaces of even matrix pencils

lax wendroff methods for hyperbolic history value problems this paper is concerned with lax wendroff methods for a class of hyperbolic history value problems these problems have the feature that globally in time smooth solutions exist if the data are sufficiently small and that solutions develop singularities for large data we prove second order convergence of the lax wendroff method for smooth solutions and investigate numerically the dependence on the initial data we demonstrate the occurrence of shock type singularities and compare the results to the quasilinear wave equation without volterra term

bounded real and positive real balanced truncation using σ normalised coprime factors in this article we will extend the method of balanced truncation using normalised right coprime factors of the system transfer matrix by meyer 1990 3 to balanced truncation with preservation of half line dissipativity special cases are preservation of positive realness and bounded realness we consider a half line dissipative input output system with quadratic supply rate given by a nonsingular symmetric matrix sigma with the property that its positive signature is equal to the number of input components of the system the transfer matrix of such system allows a sigma normalised right coprime factorisation we associate with such factorisation two lyapunov equations one of which is nonstandard involving the indefinite matrix sigma balancing will be based on making the unique solutions of these two lyapunov equations equal and diagonal the diagonal elements will be called the hankel sigma singular values because their squares are the nonzero eigenvalues of the composition of the graph hankel operator multiplication by sigma and the adjoint graph hankel operator this method of balanced truncation will be shown to preserve stability minimality and half line dissipativeness we will characterize the classical positive real and bounded real characteristic values in terms of the new hankel sigma singular values finally we will derive one step error bounds for the special case of balanced truncation of bounded real systems c 2009 elsevier b v all rights reserved

model reduction by moment matching for linear and nonlinear systems the model reduction problem for single input single output linear and nonlinear systems is addressed using the notion of moment a re visitation of the linear theory allows to obtain novel results for linear systems and to develop a nonlinear enhancement of the notion of moment this in turn is used to pose and solve the model reduction problem by moment matching for nonlinear systems to develop a notion of frequency response for nonlinear systems and to solve model reduction problems in the presence of constraints on the reduced model connections between the proposed results projection methods the covariance extension problem and interpolation theory are presented finally the theory is illustrated by means of simple worked out examples and case studies

finite element approximation of viscoelastic fluid flow existence of approximate solutions and error bounds we study a finite element approximation of viscoelastic fluid flow obeying an oldroyd b type constitutive law the approximate stress velocity and pressure are respectivelyp 1 discontinuous p 2 continuous p 1 continuous we use the method of lesaint raviart for the convection of the extra stress tensor we suppose that the continuous problem admits a sufficiently smooth and sufficiently small solution we show by a fixed point method that the approximate problem has a solution and we give an error bound

iterative convergence to cesaro means for continuous pseudocontractive mappings abstract let f be a fixed strongly pseudocontractive mapping and t be a continuous pseudocontractive mapping with f t 0 the sequence z m is iteratively defined as follows z m t m f z m 1 t m 1 m 1 j 0 m t j z m m 0 where t m 0 1 satisfies the condition lim m t m 0 we prove that z m converges strongly to the unique solution p to some variational inequality in f t our results develop and complement the corresponding ones by matsushita daishi kuroiwa j math anal appl 294 2004 206 214 and shioji takahashi arch math 72 1999 354 359 and moore nnoli j math anal appl 260 2001 269 278 and su li appl math comput 181 2006 332 341 and song chen appl math comput 186 2007 1120 1128 and wangkeeree appl math comput 201 2008 239 249

rational interpolation and state variable realizations abstract the problem is considered of passing from interpolation data for a real rational transfer function matrix to a minimal state variable realization of the transfer function matrix the tool is a loewner matrix which is a generalization of the standard hankel matrix of linear system realization theory and which possesses a decomposition into a product of generalized observability and controllability matrices

spectral collocation domain decomposition method for viscoelastic flow simulations in model porous geometries abstract a domain decomposition spectral collocation ddsc method is developed for the solution of steady state non linear viscoelastic flow problems it is applied in simulations of viscoelastic flows through model porous media represented by arrays of cylinders the technique uses a splitting of the computational domain in sub elements in a fashion similar to finite elements at each element the solution is represented by using high order orthogonal polynomials static condensation is used for the solution of the linearized system of equations resulting from the application of newton s method this approach is suggested by the limited connectivity between neighboring elements mesh converged solutions have been obtained for the flow of an oldroyd b fluid through a square array of cylinders up to we 5 0 and for the flow past a single row of cylinders up to to we 4 0

viscosity approximation methods for nonexpansive mappings abstract viscosity approximation methods for nonexpansive mappings are studied consider a nonexpansive self mapping t of a closed convex subset c of a banach space x suppose that the set fix t of fixed points of t is nonempty for a contraction f on c and t 0 1 let x t c be the unique fixed point of the contraction x tf x 1 t tx consider also the iteration process x n where x 0 c is arbitrary and x n 1 n f x n 1 n tx n for n 1 where n 0 1 if x is either hilbert or uniformly smooth then it is shown that x t and under certain appropriate conditions on n x n converge strongly to a fixed point of t which solves some variational inequality

mann iteration of cesaro means for asymptotically non expansive mappings abstract let k be a nonempty closed convex subset of a uniformly convex banach space e with a uniformly g teaux differentiable norm suppose that t k k is an asymptotically non expansive mapping and for arbitrary initial value x 0 k we will introduce the mann iteration of its cesaro means x n 1 n x n 1 n 1 n 1 j 0 n t j x n n 0 and prove its strong and weak convergence whenever n 0 b n and n is a real sequence in 0 1 satisfying one of the conditions either i lim n n 0 or ii n 0 n 1 n or iii 0 lim inf n n lim sup n n 1

stability preserving rational approximation subject to interpolation constraints a quite comprehensive theory of analytic interpolation with degree constraint dealing with rational analytic interpolants with an a priori bound has been developed in recent years in this paper we consider the limit case when this bound is removed and only stable interpolants with a prescribed maximum degree are sought this leads to weighted h 2 minimization where the interpolants are parameterized by the weights the inverse problem of determining the weight given a desired interpolant profile is considered and a rational approximation procedure based on the theory is proposed this provides a tool for tuning the solution to specifications the basic idea could also be applied to the case with bounded analytic interpolants

model reduction for systems with inhomogeneous initial conditions abstract we consider the model reduction problem for linear time invariant dynamical systems having nonzero but otherwise indeterminate initial conditions building upon the observation that the full system response is decomposable as a superposition of the response map for an unforced system having nontrivial initial conditions and the response map for a forced system having null initial conditions we develop a new approach that involves reducing these component responses independently and then combining the reduced responses into an aggregate reduced system response this approach allows greater flexibility and offers better approximation properties than other comparable methods

a stable and convergent scheme for viscoelastic flow in contraction channels we present a new algorithm to simulate unsteady viscoelastic flows in abrupt contraction channels in our approach we split the viscoelastic terms of the oldroyd b constitutive equation using duhamel s formula and discretize the resulting pdes using a semi implicit finite difference method based on a lax wendroff method for hyperbolic terms in particular we leave a small residual elastic term in the viscous limit by design to make the hyperbolic piece well posed a projection method is used to impose the incompressibility constraint we are able to compute the full range of unsteady elastic flows in an abrupt contraction channel from the viscous limit to the elastic limit in a stable and convergent manner we demonstrate the range of our method for unsteady flow of a maxwell fluid with and without viscosity in planar contraction channels we also demonstrate stable and convergent results for benchmark high weissenberg number problems at we 1 and we 10

strong convergence of averaged iteration for asymptotically non expansive mappings abstract let e be a uniformly convex banach space e with a weakly continuous duality mapping j and k be a non empty bounded closed convex subset of e for an asymptotically non expansive mapping t k k an arbitrary initial values z 1 x 1 k and an anchor point u k we define iteratively the sequences z m and x n as follows z m t m u 1 t m 1 m 1 j 0 m t j z m m 0 x n 1 n u 1 n 1 n 1 j 0 n t j x n n 0 where t m 0 1 and n 0 1 satisfy proper conditions we prove that z m and x n converge strongly to some p f t respectively

a partial pade via lanczos method for reduced order modeling abstract the classical lanczos process can be used to efficiently generate pade approximants of the transfer function of a given single input single output time invariant linear dynamical system unfortunately in general the resulting reduced order models based on pade approximation do not preserve the stability and possibly passivity of the original linear dynamical system in this paper we describe the use of partial pade approximation for reduced order modeling partial pade approximants have a number of prescribed poles and zeros while the remaining degrees of freedom are used to match the taylor expansion of the original transfer function in as many leading coefficients as possible we present an algorithm for computing partial pade approximants via suitable rank 1 updates of the tridiagonal matrices generated by the lanczos process numerical results for two circuit examples are reported

dynamics of shear flow of a non newtonian fluid abstract viscoelastic materials with fading memory e g polymers suspensions and emulsions exhibit behavior that is intermediate between the nonlinear hyperbolic response of purely elastic materials and the strongly diffusive parabolic response of viscous fluids many popular numerical methods used in the computation of steady viscoelastic flows fail in important flow regimes and thus do not capture significant non newtonian phenomena a key to satisfactory explanation of these phenomena is the study of the full dynamics of the flow this paper studies the dynamics of shear flow presenting a description of non newtonian phenomena caused by a non monotone relation between the steady shear stress and shear strain rate analytical results for such phenomena are surveyed and three distinct numerical methods are developed to accurately compute the dynamics the computations reproduce experimental measurements of non newtonian spurt in shearing flow through a slit die they also predict related phenomena such as hysteresis and shape memory experiments are suggested to verify these predictions

on mann implicit iterations for strongly accretive and strongly pseudo contractive mappings abstract for a lipschitz strongly accretive map considered by chidume in c e chidume picard iteration for strongly accretive and strongly pseudo contractive lipschitz maps ictp preprint no ic2000098 c e chidume iterative algorithms for nonexpansive mappings and some of their generalizations nonlinear analysis and applications to v lakshmikantam on his 80th birthday vols 1 and 2 kluwer acad publ dordrecht 2003 pp 383 429 it is known that a classical picard type iteration process converges strongly to a zero of the operator he also proved that the rate of convergence in this case is at least as fast as a geometric progression in this paper we study the mann implicit iteration sequence for strongly accretive and strongly pseudo contractive mappings we showed that this implicit scheme gives better convergence rate estimate presented results improve the corresponding results of c e chidume picard iteration for strongly accretive and strongly pseudo contractive lipschitz maps ictp preprint no ic2000098 c e chidume iterative algorithms for nonexpansive mappings and some of their generalizations nonlinear analysis and applications to v lakshmikantam on his 80th birthday vols 1 and 2 kluwer acad publ dordrecht 2003 pp 383 429 l liu approximation of fixed points of a strictly pseudo contractive mapping proc am math soc 125 2 1997 1363 1366 w r sastry g v r babu approximation of fixed points of strictly pseudo contractive mappings on arbitrary closed convex sets in a banach space proc amer math soc 128 2000 2907 2909 y song r chen viscosity approximative methods to cesaro means for non expansive mappings appl math comput 186 2 2007 1120 1128

numerical modelling of viscoelastic cavity driven flow using finite difference simulations abstract a study of the unsteady flow of viscoelastic liquids contained in an cavity driven by a moving wall has been undertaken as a first step toward understanding heat and mass transport in polymer processing equipment the material was represented by the constitutive equation for a upper convected criminale ericson filbey cef model solution to the vorticity equation for various moving walls and different aspect ratios were obtained numerically the solutions were found to be stable and convergent for limited value of weissenberg numbers despite this fact some new results which are governed by inertia elasticity and aspect ratio were obtained and this has been documented first time

model order reduction with preservation of passivity non expansivity and markov moments a new model order reduction technique is presented which preserves passivity and non expansivity it is a projection based method which exploits the solution of linear matrix inequalities to generate a descriptor state space format which preserves positive realness and bounded realness in the case of both non singular and singular systems solving the linear matrix inequality can be replaced by equivalently solving an algebraic riccati equation which is known to be a more efficient approach a new algebraic riccati equation and a frequency inversion technique are also presented to specifically deal with the important singular case the preservation of markov moments is also guaranteed by the judicious choice of a projection matrix three pertinent examples comparing the present approach with positive real balanced truncation show the strength and accuracy of the present approach

slender jets and thin sheets with surface tension simplified equations governing the potential flow and the shape of slender jets and thin sheets of liquid are derived taking into account surface tension families of similarity solutions of these equations are introduced for jets and for symmetrical sheets they satisfy ordinary differential equations the properties of these similarity solutions are examined analytically and numerically they can be used to describe the motion of a liquid sheet on a solid the thickening and flow following the breaking of jets the merging of two jets the formation or closing of holes or slits in sheets etc some applications to such problems are given

structure preserving model reduction of port hamiltonian systems by moment matching at infinity model reduction of port hamiltonian systems by means of the krylov methods is considered aiming at port hamiltonian structure preservation it is shown how to employ the arnoldi method for model reduction in a particular coordinate system in order to preserve not only a specific number of the markov parameters but also the port hamiltonian structure for the reduced order model furthermore it is shown how the lanczos method can be applied in a structure preserving manner to a subclass of port hamiltonian systems which is characterized by an algebraic condition in fact for the same subclass of port hamiltonian systems the arnoldi method and the lanczos method turn out to be equivalent in the sense of producing reduced order port hamiltonian models with the same transfer function

strong convergence of averaging iterations of nonexpansive nonself mappings abstract let c be a closed convex subset of hilbert space h t a nonexpansive nonself mapping from c into h and x0 x y0 y elements of c in this paper we study the convergence of the two sequences generated by x n 1 1 n 1 j 0 n n x 1 n pt j x n for n 0 1 2 y n 1 1 n 1 j 0 n p n y 1 n tp j y n for n 0 1 2 where n is a real sequence such that 0 n 1 and p is the metric projection from h onto c

equivalent theorems of the convergence between proximal type algorithms abstract the main aim of this work is to give the equivalence of the convergence between proximal type algorithms our convergence analysis covers rockafellar type proximal point algorithm with a weak contraction for finding zeros of accretive operators as well as browder and halpern type iterations and viscosity approximation methods for finding fixed points of nonexpansive type mappings in banach spaces we also provide simple proofs of some results of wong sahu and yao n c wong d r sahu j c yao solving variational inequalities involving nonexpansive type mappings nonlinear anal 69 12 2008 4732 4753

strong convergence theorems on two iterative method for non expansive mappings abstract in this paper we study the convergence of two type iteration processes as follows i x n 1 n x 1 n t n x 1 n tx n ii x n 1 n n x 1 n tx n 1 n a n x n where a n 1 n 1 j 0 n t j c c in uniformly convex banach space x which possesses a weakly sequentially continuous duality mapping j and in uniformly convex banach space x with a uniformly gateaux differentiable norm respectively and prove that above sequences converge strongly to px when the real sequence n n satisfies appropriate conditions where p is sunny non expansive from c onto f t

a parametrisation for dissipative behaviours the matrix case we study linear time invariant dynamical systems that are dissipative with respect to a generalised power defined by a quadratic differential form we address several cases in an increasing order of complexity and show how dissipative systems can be parametrised in this process we also establish a number of results for polynomial matrices that are of independent interest the present article is a generalisation of our earlier work that dealt with single input single output dissipative systems pendharkar i and pillai h k 2004 a parametrization for dissipative behaviours systems and control letters 51 123 132

a real time procedure for affinely dependent parametric model order reduction using interpolation on grassmann manifolds summary model order reduction helps to reduce the computational time in dealing with large dynamical systems for example during simulation control optimization in many cases the considered model depends on parameters model order reduction techniques are therefore preferred to symbolically preserve this dependence or to be adaptive to the change of the model caused by the variation in the values of the parameters in this paper we first present the application of the interpolation technique on grassmann manifolds to this problem we then improve the method for the models whose system matrices depend affinely on parameters by considerably reducing the computational complexity on the basis of analyzing the structure of sums of singular value decompositions and decomposing the whole procedure into offline and online stages a numerical example is shown to illustrate the method as well as to prove its effectiveness copyright 2012 john wiley sons ltd

viscosity approximation methods with weak contraction for l lipschitzian pseudocontractive self mapping abstract in this paper under the framework of real reflexive banach space which admits a weakly sequentially continuous duality mapping from e to e we study the strong convergence of an implicit and an explicit composite viscosity approximation algorithm i and ii respectively for a pseudocontractive mapping t by using the weakly contractive mapping f as follows i x t s t f x t s 1 t y t s y t s s x t s 1 s t x t s and ii x n 1 n f x n 1 n y n y n n x n 1 n t x n n 0 our results unify improve and complement several recent ones existing in the current literature

least squares p r finite element methods for incompressible non newtonian flows a least squares mixed p type finite element method is developed for numerical solution of incompressible non newtonian flows hierarchical piecewise polynomials are introduced as element basis functions while singularities and boundary layers are treated by a combination of mesh redistribution and polynomial refinement scaling of the original differential equations is found to be important for the least squares minimization process we discuss both nonlinear algebraic and differential constitutive models and present numerical examples to illustrate benefits and shortcomings of the present approach

viscosity approximative methods to cesaro mean iterations for nonexpansive nonself mappings in banach spaces let e be a real uniformly convex banach space which admits a weakly sequentially continuous duality mapping from e to e e c a closed convex subset of e which is also a sunny nonexpansive retract of e let t c et c e be a nonexpansive nonself mapping with f t f t and f c cf c c be a fixed contractive mapping the implicit viscosity iterative sequence zm zm is defined by tm 0 1 tm 0 1 zm 1m 1 j 0mp tmf zm 1 tm tp jzm for m 0m 0 and two explicit viscosity iterative sequences xn xn and yn yn are given by x0 c xn 1 nf xn 1 n 1n 1 j 0n pt jxn and y0 c yn 1 1n 1 j 0np nf yn 1 n tp jyn for n 0n 0 where n n is a sequence in 0 1 0 1 and p is a sunny nonexpansive retraction of e onto c we prove that under appropriate conditions imposed on tm tm and n n the sequences zm zm xn xn and yn yn converge strongly to some fixed point of t which solves some variational inequalities the results presented extend and improve the corresponding results of matsushita and kuroiwa s matsushita d kuroiwa strong convergence of averaging iterations of nonexpansive nonself mappings j math anal appl 294 2004 206 214 song and chen y song r chen viscosity approximation methods to cesaro means for nonexpansive mappings appl math comput 186 2007 1120 1128 and many authors

non local yield limit degradation presented is a new type of a non local continuum model which avoids problems of convergence at mesh refinement and spurious mesh sensitivity in a softening continuum characterized by degradation of the yield limit the key idea which has recently been proposed in a general context and has already been applied to softening damage due to stiffness degradation is to apply the non local concept only to those parameters which cause the degradation while keeping the definition of the strains local compared to the previously advanced fully non local continuum formulation the new approach has the advantage that the stresses are subjected to the standard differential equations of equilibrium and standard boundary or interface conditions the new formulation exhibits no zero energy periodic modes imbrication of finite elements is unnecessary and finite elements with standard continuity requirements are sufficient two dimensional finite element solutions with up to 3248 degrees of freedom are presented to document convergence and efficacy the formulation is applied to tunnel excavation in a soil stabilized by cement grouting with the objective of preventing cave in burst of the tunnel sides due to compression softening

a mathematical biography of danny c sorensen abstract on the occasion of his 65th birthday we briefly recount dan sorensen s profound contributions to optimization numerical linear algebra and model order reduction for dynamical systems

matrix nearness based guaranteed passive system approximation abstract in this paper we present a new approach towards global passive approximation in order to find a passive real rational transfer function g s that is an arbitrarily close approximation of the passive transfer function nearest to a non passive square transfer function h s it is based on existing solutions to pertinent matrix nearness problems it is shown that the key point in constructing the passive real rational transfer function g s is to find a good rational approximation of the well known ramp function over an interval defined by the minimum and maximum dissipation of h s the proposed algorithms rely on the stable anti stable decomposition of a given transfer function pertinent examples are given to show the scope and accuracy of the proposed algorithms

viscosity approximative methods to cesaro means for non expansive mappings abstract in this paper we defined viscosity iterative sequence zm and xn of the cesaro means for non expansive mappings t and proved that zm and xn converge strongly to some p f t respectively where p is a unique solution in f t to the following variational inequality f i p j u p 0 for all u f t our results developed and complemented the corresponding ones by shin ya matsushita and daishi kuroiwa strong convergence of averaging iterations of nonexpansive nonself mappings j math anal appl 294 2004 206 214 and h k xu viscosity approximation methods for nonexpansive mappings j math anal appl 298 2004 279 291 and yongfu su and suhong li strong convergence theorems on two iterative method for non expansive mappings appl math comput available from accessed 28 02 06

hyperbolicity and change of type in the flow of viscoelastic fluids the equations governing the flow of viscoelastic liquids are classified according to the symbol of their differential operators propagation of singularities is discussed and conditions for a change of type are investigated the vorticity equation for steady flow can change type when a critical condition involving speed and stresses is satisfied this leads to a partitioning of the field of flow into subcritical and supercritical regions as in the problem of transonic flow

h2 model reduction for negative imaginary systems this paper studies the h2 model reduction problem for negative imaginary ni systems for a given high order system that is stable and ni our goal is to approximate it by a low order ni system so

the interpolation problem with a degree constraint the author previously 1983 1987 showed that there is a correspondence between nonnegative hermitian trigonometric polynomials of degree spl les n and solutions to the standard nevanlinna pick caratheodory interpolation problem with n 1 constraints which are rational and also of degree spl les n it was conjectured that the correspondence under suitable normalization is bijective and thereby that it results in a complete parametrization of rational solutions of degree spl les n the conjecture was proven by byrnes et al 1995 along with a detailed study of this parametrization however byrnes et al used a slightly restrictive assumption that the trigonometric polynomials are positive and accordingly the corresponding solutions have positive real part the purpose of the present note is to extend the result to the case of nonnegative trigonometric polynomials as well we present the arguments in the context of the general nevanlinna pick caratheodory fejer interpolation

positive real and bounded real balancing for model reduction of descriptor systems we present an extension of the positive real and bounded real balanced truncation model reduction methods to large scale descriptor systems these methods are based on balancing the solutions of the projected lur e matrix equations important properties of these methods are that respectively passivity and contractivity are preserved in the reduced order models and that there exist approximation error bounds we also discuss the numerical solution of the projected lur e equations numerical examples are given

a hamiltonian krylov schur type method based on the symplectic lanczos process we discuss a krylov schur like restarting technique applied within the symplectic lanczos algorithm for the hamiltonian eigenvalue problem this allows to easily implement a purging and locking strategy in order to improve the convergence properties of the symplectic lanczos algorithm the krylov schur like restarting is based on the sr algorithm some ingredients of the latter need to be adapted to the structure of the symplectic lanczos recursion we demonstrate the efficiency of the new method for several hamiltonian eigenproblems

dynamics of slender viscoelastic free jets previous studies of slender viscoelastic and newtonian free surface jets have focused mainly on steady state predictions guided primarily by industrial textile applications dynamical analyses and simulations of fiber flows even the linearized stability analysis of nontrivial steady states have lagged behind considerable experimental and textile processing observations and advances the foundational work of chang and lodge rheol acta 10 1971 pp 448 449 and petrie rheol acta 14 1975 pp 955 957 elongational flows pitman london 1979 has been extended by the axisymmetric modeling and simulation of beris and liu j non newtonian fluid mech 26 1988 pp 363 394 comput methods appl mech engrg 76 1989 pp 179 204 for maxwell fluids and markovich and renardy j non newtonian fluid mech 17 1985 pp 13 22 for johnson segalman fluids the model in markovich and renardy is a single nonlinear parabolic equation in which elastic retardation provides dominant smooth

families of moment matching based low order approximations for linear systems the problem of finding a framework for linear moment matching based approximation of linear systems is discussed it is shown that it is possible to define five equivalent notions of moments i e one from a complex s domain point of view two using krylov projections and two from a time domain perspective based on these notions classes of parameterized reduced order models that achieve moment matching are obtained we analyze the controllability and observability properties of the models belonging to each of the classes of reduced order models we find the subclasses of models of orders lower than the number of matched moments i e we find the sets of parameters that allow for pole zero cancellations to occur furthermore we compute the subclass of minimal order model s the minimal order is equal to half of the number of matched moments i e generically the largest number of possible pole zero cancellations is half of the number of matched moments finally we present classes of reduced order models that match larger numbers of moments based on interconnections between reduced order models

three dimensional numerical simulations of viscoelastic flows predictability and accuracy in this paper fully three dimensional 3 d numerical simulations of viscoelastic flows using an implicit finite volume method are discussed with the focus on the predictability and accuracy of the method the viscoelastic flow problems involving the stress singularity including plane stick slip flow the flow past a junction in a channel and the 3 d edge flow are used to test the ability of the method to predict the singularity features with accuracy the accuracy of the numerical predictions is judged by comparing with the known asymptotic behaviour for newtonian fluids and some viscoelastic fluids and the investigations are extended to the viscoelastic cases with unknown singular behaviour the phan thien tanner ptt model and in some cases the upper convected maxwell ucm model are used to describe viscoelastic fluids the numerical results with mesh refinement show that the accuracy is quite satisfactory especially for newtonian flows for viscoelastic flows the asymptotic results for the flow around a re entrant corner for the ucm as well as the ptt fluid are reproduced numerically in the stick slip flow a newtonian like asymptotic behaviour is predicted for the ucm fluid in edge flow it is verified numerically that the kinematics are newtonian for viscoelastic fluids described by models with a constant viscosity and a zero second normal stress difference for viscoelastic fluids described by the models with a shear thinning viscosity and zero second normal stress difference the fluid behaves like a power law fluid and the difference from its newtonian kinematics is localized in the region near the singularity and to capture the asymptotic behaviour a parameter dependent mesh has to be used with the 3 d simulations it is confirmed that in edge flow the flow around the edge could not be rectilinear and some secondary flows on the plane normal to the primary flow direction are expected for viscoelastic fluids described by the models with a shear dependent second normal stress difference such as the full ptt model the strength of the secondary flows will depend on the level of the departure of the second normal stress difference from a fixed constant multiple of viscosity of the fluid

a new result on passivity preserving model reduction abstract the problem of model reduction with preservation of passivity is investigated the approach is based on positive real interpolation and is inspired by the similarity between lowner and pick matrices the former are important in problems of general rational interpolation while the latter in problems of interpolation by positive real functions it follows that interpolation of the original set of data together with an appropriately defined mirror image set of data yields automatically positive real interpolants subsequently we show how this result can be implemented using a krylov projection procedure the ensuing model reduction method preserves stability and passivity and can be implemented efficiently for the large scale systems

on the problem of stable rational interpolation abstract aspects of the stability issue in connection with rational interpolation are investigated in particular it is shown that unconstrained interpolation of a given set of points together with an associated mirror image set of points yields a one parameter family of stable interpolating functions as an application it is also shown that if a certain number of markov parameters are given by appropriate choice of the moments stable realizations are obtained