schur recursions error formulas and convergence of rational estimators for stationary stochastic sequences an exact and approximate realization theory for estimation and model filters of second order stationary stochastic sequences is presented the properties of j lossless matrices as a unifying framework are used necessary and sufficient conditions for the exact realization of an estimation filter and a model filter as a submatrix of a j lossless system are deduced an extension of the so called schur algorithm yields an approximate j lossless realization based on partial past information about the process the geometric properties of such partial realizations and their convergence are studied finally connections with the nevanlinna pick problem are made and how the techniques presented constitute a generalization of many aspects of the levinson szego theory of partial realizations is shown as a consequence generalized recursive formulas for reproducing kernels and christoffel darboux formulas are obtained in this paper the scalar case is considered the matrix case will be considered in a separate publication

on a rational approximation problem in the real hardy space h 2 1 introduction the problem of finding a rational approximation to a holomorphic function in a domain 52 often arises in practice let us give an example from system theory which has first motivated our work l system theory is concerned with the study of physical systems that can be described by a relation between inputs and outputs when considering discrete time systems it is a convention to denote by u z cksko ukzmk uker

orthogonal rational functions with real coefficients and semiseparable matrices when one wants to use orthogonal rational functions orfs in system identification or control theory it is important to be able to avoid complex calculations in this paper we study orfs whose numerator and denominator polynomial have real coefficients these orfs with real coefficients rorfs appear when the poles and the interpolation points appear in complex conjugate pairs which is a natural condition further we deduce that there is a strong connection between rorfs and semiseparable matrices

hyperbolic conservation laws with relaxation the effect of relaxation is important in many physical situations it is present in the kinetic theory of gases elasticity with memory gas flow with thermo non equilibrium water waves etc the governing equations often take the form of hyperbolic conservation laws with lower order terms in this article we present and analyze a simple model of hyperbolic conservation laws with relaxation effects dynamic subcharacteristics governing the propagation of disturbances over strong wave forms are identified stability criteria for diffusion waves expansion waves and traveling waves are found and justified nonlinearly time asymptotic expansion and the energy method are used in the analysis for dissipative waves the expansion is similar in spirit to the chapman enskog expansion in the kinetic theory for shock waves however a different approach is needed

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

mathematical and numerical modeling of solute dynamics in blood flow and arterial walls the numerical modeling of solutes absorption processes by the arterial wall is of paramount interest for the understanding of the relationships between the local features of blood flow the nourishing of the inner arterial wall by the blood solutes and the pathologies that can appear when this process is for some reason perturbed in the present work two models for the solutes dynamics are investigated in the first model which is essentially based on the one introduced by rappitsch and perktold j biomech engrg 118 1996 pp 511 519 and rappitsch perktold and pernkopf internat j numer methods fluids 25 1997 pp 847 857 the navier stokes equations for an incompressible fluid describing the blood velocity and pressure fields are coupled with an advection diffusion equation for the solute concentration the wellposedness of this model is discussed the second model considers also the solutes dynamics inside the arterial wall described by a pure diffusion equation actually this is a heterogeneous model coupling different equations in different parts of the domain at hand its wellposedness is proven moreover in view of the numerical study an iterative finite element method by subdomains is proposed and its convergence properties are analyzed finally several numerical results comparing the different models in situations of physiologic interest are illustrated

on approximation of stable linear dynamical systems using laguerre and kautz functions approximation of stable linear dynamical systems by means of so called laguerre and kautz functions which are the laplace transforms of a class of orthonormal exponentials is studied since the impulse response of a stable finite dimensional linear dynamical system can be represented by a sum of exponentials times polynomials it seems reasonable to use basis functions of the same type assuming that the transfer function of a system is bounded and analytic outside a given disc it is shown that laguerre basis functions are optimal in a mini max sense this result is extended to the two parameter kautz functions which can have complex poles while the poles of laguerre functions are restricted to the real axis by conformai mapping techniques the two parameter kautz approximation problem is recast as two laguerre approximation problems thus the well developed theory of laguerre functions can be applied to analyze kautz approximations unilateral shifts are used to further develop the connection between laguerre functions and kautz functions results on 2 and approximation using kautz models are given furthermore the weighted l2 kautz approximation problem is shown to be equivalent to solving a block toeplitz matrix equation

materials with internal variables and relaxation to conservation laws the theory of materials with internal state variables of coleman gurtin cg provides a natural framework to investigate the structure of relaxation approximations of conservation laws from the viewpoint of continuum thermomechanics after reviewing the requirements imposed on constitutive theories by the principle of consistency with the clausius duhem inequality we pursue two specific theories pertaining to stress relaxation and relaxation of internal energy they each lead to a relaxation framework for the theory of thermoelastic non conductors of heat equipped with globally defined entropy functions for the associated relaxation process next we consider a semilinear model problem of stress relaxation we discuss uniform stability and compactness for solutions of the relaxation system in the zero relaxation limit and establish convergence to the system of isothermal elastodynamics by using compensated compactness finally we prove a strong dissipation estimate for the relaxation approximations proposed in jin xin jx when the limit system is equipped with a strictly convex entropy

thermal non equilibrium flows in three space dimensions we study the equations describing the motion of a thermal non equilibrium gas in three space dimensions it is a hyperbolic system of six equations with a relaxation term the dissipation mechanism induced by the relaxation is weak in the sense that the shizuta kawashima criterion is violated this implies that a perturbation of a constant equilibrium state consists of two parts one decays in time while the other stays in fact the entropy wave grows weakly along the particle path as the process is irreversible we study thermal properties related to the well posedness of the nonlinear system we also obtain a detailed pointwise estimate on the green s function for the cauchy problem when the system is linearized around an equilibrium constant state the green s function provides a complete picture of the wave pattern with an exact and explicit leading term comparing with existing results for one dimensional flows our results reveal a new feature of three dimensional flows not only does the entropy wave not decay but the velocity also contains a non decaying part strongly coupled with its decaying one the new feature is supported by the second order approximation via the chapman enskog expansions which are the navier stokes equations with vanished shear viscosity and heat conductivity

analysis of differential equations modelling the reactive flow through a deformable system of cells a system of model equations coupling fluid flow deformation of solid structure and chemical reactions is formulated starting from processes in biological tissue the main aim of this paper is to analyse this non standard system where the elasticity modules are functionals of a concentration and the diffusion coefficients of the chemical substances are functions of their concentrations a new approach and new methods are required and adapted to these nonlinearities and the transmission conditions on the interface solid fluid strong solutions for the initial and boundary value problem are constructed under suitable regularity assumptions on the data and stability estimates of the solutions with respect to the initial and boundary values are proved these estimates imply uniqueness directly the approach of the paper can be used in more general problems modeling reactive flow and transport and its interaction with elastic cell structures in a forthcoming paper the approach of this paper is used for getting the upscaled system modeling reactive flow through biological tissue on the macroscopic scale starting from a system on the cell level

frequency localization duhamel principle and its application to the optimal decay of dissipative systems in low dimensions abstract recently a time decay framework l 2 r n b 2 s r n s 0 has been given by 49 for linearized dissipative hyperbolic systems which allows to pay less attention to the traditional spectral analysis however owing to interpolation techniques those decay results for nonlinear hyperbolic systems hold true only in higher dimensions n 3 and the analysis in low dimensions say n 1 2 was left open we try to give a satisfactory answer in the current work first of all we develop new time decay properties on the frequency localization duhamel principle and then it is shown that the classical solution and its derivatives of fractional order decay at the optimal algebraic rate in dimensions n 1 2 by using a new technique which is the so called piecewise duhamel principle in localized time weighted energy approaches compared to 49 finally as direct applications explicit decay statements are worked out for some relevant examples subjected to the same dissipative structure for instance damped compressible euler equations the thermoelasticity with second sound and timoshenko systems with equal wave speeds

orthogonal rational functions for system identification numerical aspects recently there has been a growing interest in the use of orthogonal rational functions orfs in system identification there are many advantages over more classical techniques probably due to a known explicit expression for the basis functions when the orthogonality weight is uniformly equal to 1 the so called malmquist basis the attention has been on the development of methods using this basis however for some discrete identification problems this choice of the orthogonality weight may still lead to serious numerical problems due to the ill conditioning of the linear system of equations to be solved in this note we give an algorithm based on a more general system of orf to overcome the numerical problem and which allows for a fast order update of the estimate

a coupled system of odes and quasilinear hyperbolic pdes arising in a multiscale blood flow model we study a coupled system of ordinary differential equations and quasilinear hyperbolic partial differential equations that models a blood circulatory system in the human body the mathematical system is a multiscale model in which a part of the system where the flow can be regarded as newtonian and homogeneous and the vessels are long and large is modeled by a set of hyperbolic pdes in a one spatial dimensional network and in the other part where either vessels are too thin or the flow pattern is too complicated such as in the heart the flow is modeled as a lumped element by a set of ordinary differential equations as an analog of an electric circuit the mathematical system consists of pairs of pdes one pair for each vessel coupled at each junction through a system of odes this model is a generalization of the widely studied models of arterial networks we give a proof of the well posedness of the initial boundary value problem by showing that the classical solution exists is unique and depends continuously on initial boundary and forcing functions and their derivatives

zero relaxation limit to centered rarefaction waves for a rate type viscoelastic system abstract we study a rate type viscoelastic system proposed by i suliciu 1990 internat j engrg sci 28 827 841 which is a 3 3 hyperbolic system with relaxation as the relaxation time tends to zero this system convergences to the well known p system formally in the case where the initial data are the riemann data such that the corresponding solutions of the p system are centered rarefaction waves we show that if the wave strength is suitably small then the solution for the relaxation system exists globally in time and converges to the solution of the corresponding rarefaction waves uniformly as the relaxation time goes to zero except for an initial layer the jump discontinuities in the solutions are decaying exponentially fast as time tends to infinity

gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation we study gas flow in vibrational nonequilibrium the model is a 4 4 nonlinear hyperbolic system with relaxation under physical assumptions properties of thermodynamic variables relevant to stability are obtained global existence for cauchy problems with smooth and small data is established and large time behavior is studied in the pointwise sense we formulate the fundamental solution in a systematic way for a general linear system with relaxation the fundamental solution provides insights to the behavior of the nonlinear system and is crucial to obtain our pointwise asymptotic picture for the nonequilibrium flow we also clarify in a general setting the relation between subcharacteristic conditions and a dissipative criterion that was originally proposed for hyperbolic parabolic systems and has now proved to be important also for hyperbolic systems with relaxation

algorithms for model reduction of large dynamical systems three algorithms for the model reduction of large scale continuous time time invariant linear dynamical systems with a sparse or structured transition matrix and a small number of inputs and outputs are described they rely on low rank approximations to the controllability and observability gramians which can efficiently be computed by adi based iterative low rank methods the first two model reduction methods are closely related to the well known square root method and schur method which are balanced truncation techniques the third method is a heuristic balancing free technique the performance of the model reduction algorithms is studied in numerical experiments

an interpolation algorithm for orthogonal rational functions let a 1 2 be a sequence of numbers on the extended real line r r and a positive bounded borel measure with support in a subset of r we introduce rational functions n with poles 1 n that are orthogonal with respect to if all poles are at infinity we recover the polynomial situation it is well known that under certain conditions on the location of the poles the system n is regular such that the orthogonal functions satisfy a three term recurrence relation similar to the one for orthogonal polynomials to compute the recurrence coefficients one can use explicit formulas involving inner products we present a theoretical alternative to these explicit formulas that uses certain interpolation properties of the riesz herglotz nevanlinna transform of the measure error bounds are derived and some examples serve as illustration

analysis of the m1 model well posedness and diffusion asymptotics abstract this paper is devoted to the analysis of the m 1 model which arises in radiative transfer theory the derivation of the model is based on the entropy minimization principle which leads to a hyperbolic system of balance laws with relaxation in the multi dimensional case we establish the existence uniqueness of a globally defined smooth solution under a suitable smallness condition on the initial data in the one dimensional case we show that the smallness condition does not depend on the particles mean free path so that we can also rigorously justify the consistency of the model with the diffusion asymptotics the result extends the analysis of coulombel et al j f coulombel f golse t goudon diffusion approximation and entropy based moment closure for kinetic equations asymptotic analysis 45 2005 1 39 to the case where the entropy functional accounts for relaxation towards the planckian state which is physically more relevant

h sub spl infin model reduction with application to flexible systems in this note h sub spl infin model reduction of continuous time linear systems is revisited the main objective is to define a convex programming problem expressed in terms of linear matrix inequalities which provides a good suboptimal solution to the model reduction problem the quality of the proposed suboptimal solution is assessed through comparisons performed via simulation with the already classical balanced truncation method leading to the conclusion that the proposed method performs significantly better finally the proposed method is applied to the determination of a reduced order model of a flexible bar

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

on the numerical solution of the far field refractor problem abstract the far field refractor problem with a discrete target is solved with a numerical scheme that uses and simplify ideas from caffarelli et al 1999 a numerical implementation is carried out and examples are shown

hyperbolic compressible navier stokes equations abstract we consider the non isentropic compressible navier stokes equations with hyperbolic heat conduction and a law for the stress tensor which is modified correspondingly by maxwell s law these two relaxations turning the whole system into a hyperbolic one are not only treated simultaneously but are also considered in a version having galilean invariance for this more complicated relaxed system the global well posedness is proved for small data moreover for vanishing relaxation parameters the solutions are shown to converge to solutions of the classical system

model reduction of discrete time systems through linear matrix inequalities in this paper model reduction of discrete time linear systems is revisited the main objective is to define a convex programming problem expressed in terms of linear matrix inequalities which provides a good suboptimal solution to the model reduction problem the quality of the proposed suboptimal solution is assessed through comparisons performed via simulation with the already classical balanced truncation method the results lead to the conclusion that the proposed method performs equivalently when the h 2 norm of the reduction error is considered and significantly better when the h norm is considered instead

model order reduction of mimo bilinear systems by multi order arnoldi method abstract in this paper we present a time domain model order reduction method for multi input multi output mimo bilinear systems by general orthogonal polynomials the proposed method is based on a multi order arnoldi algorithm applied to construct the projection matrix the resulting reduced model can match a desired number of expansion coefficient terms of the original system the approximate error estimate of the reduced model is given and we also briefly discuss the stability preservation of the reduced model in some cases additionally in combination with krylov subspace methods we propose a two sided projection method to generate reduced models which capture properties of the original system in the time and frequency domain simultaneously the effectiveness of the proposed methods is demonstrated by two numerical examples

zero relaxation limit for piecewise smooth solutions to a rate type viscoelastic system in the presence of shocks abstract we study a rate type viscoelastic system proposed in i suliciu int j engng sci 28 1990 827 841 which is a 3 3 hyperbolic system with relaxation as the relaxation time tends to zero this system converges to the well known p system formally in the case that the solutions of the p system are piecewise smooth including finitely many noninteracting shock waves we show that there exist smooth solutions for suliciu s model which converge to those of the p system strongly as the relaxation time goes to zero the method used here is the so called matched asymptotic analysis suggested in j goodman and z p xin arch ration mech anal 121 1992 235 265 which includes two parts the matched asymptotic expansion and stability analysis

an algorithmic method for the simplification of linear dynamic scalar systems a comprehensive method is proposed for obtaining reduced order models of a scalar linear time invariant system described by the transfer function g s the method is a viable alternative to the pade approximation technique for model order reduction it approximates the differential operations d i g s dsi proportional to the time moments by the divided difference equivalents and finally leads to linear equations in the unknown coefficients of the reduced model r s it is shown that a parameter governs the stability and the low frequency matching quality of the model heuristic criteria are given for selecting a proper the method is illustrated by some examples from the literature

construction of bgk models with a family of kinetic entropies for a given system of conservation laws we introduce a general framework for kinetic bgk models we assume to be given a system of hyperbolic conservation laws with a family of lax entropies and we characterize the bgk models that lead to this system in the hydrodynamic limit and that are compatible with the whole family of entropies this is obtained by a new characterization of maxwellians as entropy minimizers that can take into account the simultaneous minimization problems corresponding to the family of entropies we deduce a general procedure to construct such bgk models and we show how classical examples enter the framework we apply our theory to isentropic gas dynamics and full gas dynamics and in both cases we obtain new bgk models satisfying all entropy inequalities

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

asymptotic numerical solution of nonlinear systems of one dimensional balance laws abstract an asymptotic numerical method is proposed to solve nonlinear scalar dissipative balance laws as well as systems of them in one space dimension namely hyperbolic conservation laws affected by a certain kind of source term time asymptotics allows to obtain a hierarchy of coupled ordinary differential equations which can be solved by accurate methods these provide first the long time stationary solution and then corrections to it to obtain an approximation valid at lower times no accumulation of errors as time grows affects this method on the contrary results are more accurate at larger times in the scalar case an important role is played by the auxiliary function k u s u f u where f is the flux function and s is the source a similar role is played by a certain matrix in case of systems comparison is made with the godunov method and with the ahop asymptotic high order numerical methods recently developed by natalini et al

finite element approximation of the nonstationary navier stokes problem i regularity of solutions and second order error estimates for spatial discretization this is the first part of a work dealing with the rigorous error analysis of finite element solutions of the nonstationary navier stokes equations second order error estimates are proven for spatial discretization using conforming or nonconforming elements the results indicate a fluid like behavior of the approximations even in the case of large data so long as the solution remains regular the analysis is based on sharp a priori estimates for the solution particularly reflecting its behavior as t to 0 and as t to infty it is shown that the regularity customarily assumed in the error analysis for corresponding parabolic problems cannot be realistically assumed in the case of the navier stokes equations as it depends on nonlocal compatibility conditions for the data the results which are presented here are independent of such compatibility conditions which cannot be verified in practice

dynamic siso and miso system approximations based on optimal laguerre models a general procedure based on the knowledge of the input and the output signals is proposed to approximate the prescribed linear time invariant lti systems by means of optimal laguerre models the main contribution of this paper is to apply the newton raphson s iterative technique to compute the so called optimal laguerre pole in a continuous time case or optimal time scale factor in a discrete time case and especially to show that the gradient and the hessian can be expressed analytically moreover the excitations used are not limited to the ones that ensure the orthogonality of the outputs of laguerre filters i e dirac delta or white noise as is usually done in existing methods however persistently exciting input signal s are used the proposed procedure will be directly formulated for siso systems siso systems being a special case with the number of inputs equal to one the proposed algorithm has direct applications in system identification model reduction and noisy modeling

a hybrid genetic algorithm for estimating the optimal time scale of linear systems approximations using laguerre models we deal with the problem of finding the optimal time scale of the truncated laguerre series using numerical search techniques we develop a hybrid genetic algorithm ga to search the nonlinear multimodal squared error function that results from least squares approximations of the impulse response of causal linear time invariant stable systems the hybrid ga incorporates a newton raphson nr local optimizer for fast convergence to the global minimum point the proposed method competes favorably with the pure ga in solution accuracy the number of function evaluations being the same and with an established gradient directed optimization algorithm in number of function evaluations the solution accuracy being the same

a discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws abstract we present a new relaxation approximation to scalar conservation laws in several space variables by means of semilinear hyperbolic systems of equations with a finite number of velocities under a suitable multidimensional generalization of the whitham relaxation subcharacteristic condition we show the convergence of the approximated solutions to the unique entropy solution of the equilibrium cauchy problem

on the regularity of reflector antennas where is the outer normal to a at the point where the light ray hits a suppose that we have a light source located at o and are two domains in the sphere sn 1 f x is a positive function for x input illumination intensity and g x is a positive function for x output illumination intensity if light emanates from o with intensity f x for x the far field reflector antenna problem is to find a perfectly reflecting surface a parametrized by z x x for x such that all reflected rays by a fall in the directions in and the output illumination received in the direction x is g x that is t where t is given by 1 1 assuming there is no loss of energy in the reflection then by the law of conservation of energy

factorization methods for the numerical approximation of navier stokes equations we investigate a general approach for the numerical approximation of incompressible navier stokes equations based on splitting the original problem into successive subproblems which are cheaper to solve the splitting is obtained through an algebraic approximate factorization of the matrix arising from space and time discretization of the original equations several schemes based on approximate factorization are investigated for some of these methods a formal analogy with well known time advancing schemes such as the projection chorin temam s can be pointed out features and limits of this analogy that was earlier introduced in b perot j comp phys 108 1993 51 8 are addressed other new methods can also be formulated starting from this approach in particular we introduce the so called yosida method which can be investigated in the framework of quasi compressibility schemes numerical results illustrating the different performances of the different methods addressed are presented for a couple of test cases

global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy we consider the cauchy problem for a general one dimensional n n hyperbolic symmetrizable system of balance laws it is well known that in many physical examples for instance for the isentropic euler system with damping the dissipation due to the source term may prevent the shock formation at least for smooth and small initial data our main goal is to find a set of general and realistic sufficient conditions to guarantee the global existence of smooth solutions and possibly to investigate their asymptotic behavior for systems which are entropy dissipative a quite natural generalization of the kawashima condition for hyperbolic parabolic systems can be given in this paper we first propose a general framework for this kind of problem by using the so called entropy variables then we go on to prove some general statements about the global existence of smooth solutions under different sets of conditions in particular the present approach is suitable for dealing with most of the physical examples of systems with a relaxation extension our main tools will be some refined energy estimates and the use of a suitable version of the kawashima condition

dissipative structure and entropy for hyperbolic systems of balance laws in this paper we introduce an entropy condition for hyperbolic systems of balance laws under this condition we use the chapman enskog expansion to derive the corresponding viscous conservation laws further structural conditions are discussed in order to develop local and global existence theories for the balance laws and viscous conservation laws

2d partial unwinding a novel non linear phase decomposition of images this paper aims at proposing a novel 2d non linear phase decomposition of images which performs the image processing tasks better than the traditional fourier transformation linear phase decomposition but further it has additional mathematical properties allowing more effective image analysis including adaptive decomposition components and positive instantaneous phase derivatives 1d unwinding blaschke decomposition has recently been proposed and studied through factorization it expresses arbitrary 1d signal into an infinite linear combination of blaschke products it offers fast converging positive frequency decomposition in the form of rational approximation however in the multi dimensional cases the usual factorization mechanism does not work as a consequence there is no genuine unwinding decomposition for multi dimensions in this paper a 2d partial unwinding decomposition based on algebraic transforms reducing multi dimensions to the 1d case is proposed and analyzed the result shows that the fast convergence offers efficient image reconstruction the tensor type decomposing terms are mutually orthogonal giving rise to 2d positive frequency decomposition the comparison results show that the proposed method outperforms the standard greedy algorithm and the most commonly used methods in the fourier category an application in watermarking is presented to demonstrate its potential in applications

discrete kinetic schemes for multidimensional systems of conservation laws we present here some numerical schemes for general multidimensional systems of conservation laws based on a class of discrete kinetic approximations which includes the relaxation schemes by s jin and z xin these schemes have a simple formulation even in the multidimensional case and do not need the solution of the local riemann problems for these approximations we give a suitable multidimensional generalization of the whitham s stability subcharacteristic condition in the scalar multidimensional case we establish the rigorous convergence of the approximated solutions to the unique entropy solution of the equilibrium cauchy problem

asymptotic stability in a second order symmetric hyperbolic system modeling the relativistic dynamics of viscous heat conductive fluids with diffusion abstract this paper establishes nonlinear asymptotic stability of homogeneous reference states in dissipative relativistic fluid dynamics the result is a counterpart for general non barotropic fluids of one obtained by the author in a previous paper on barotropic fluids differently from that of this earlier finding the proof here crucially relies on analyzing the corresponding linearized problem in fourier space with different scalings for small and large wave numbers

semilinear behavior for totally linearly degenerate hyperbolic systems with relaxation we investigate totally linearly degenerate hyperbolic systems with relaxation we aim to study their semilinear behavior which means that the local smooth solutions cannot develop shocks and the global existence is controlled by the supremum bound of the solution in this paper we study two specific examples the it suliciu type and the it kerr debye type models for the suliciu model which arises from the numerical approximation of isentropic flows the semilinear behavior is obtained using pointwise estimates of the gradient for the kerr debye systems which arise in nonlinear optics we show the semilinear behavior via energy methods for the original kerr debye model thanks to the special form of the interaction terms we can show the global existence of smooth solutions

on backward shift algorithm for estimating poles of systems abstract in this paper we present an algorithm for estimating poles of linear time invariant systems by using the backward shift operator we prove that poles of rational functions including zeros and multiplicities are solutions to an algebraic equation which can be obtained by taking backward shift operator to the shifted cauchy kernels in the unit disc case the algorithm is accordingly developed for frequency domain identification we also prove the robustness of this algorithm some illustrative examples are presented to show the efficiency in systems with distinguished and multiple poles

hyperbolic principal subsystems entropy convexity and subcharacteristic conditions we consider a system of n balance laws compatible with an entropy principle and convex entropy density using the special symmetric form induced by the main field we define the concept of principal subsystem associated with the system we prove that the 2 n 2 principal subsystems are also symmetric hyperbolic and satisfy a subentropy law moreover we can verify that for each principal subsystem the maximum minimum characteristic velocity is not larger smaller than the maximum minimum characteristic velocity of the full system these are the subcharacteristic conditions we present some simple examples in the case of the euler fluid then in the case of dissipative hyperbolic systems we consider an equilibrium principal subsystem and we discuss the consequences in the setting of extended thermodynamics finally in the moments approach to the boltzmann equation we prove as a consequence of the previous result that the maximum characteristic velocity evaluated at the equilibrium state does not decrease when the number of moments increases

an iterative svd krylov based method for model reduction of large scale dynamical systems abstract in this paper we propose a model reduction algorithm for approximation of large scale linear time invariant dynamical systems the method is a two sided projection combining features of the singular value decomposition svd based and the krylov based model reduction techniques while the svd side of the projection depends on the observability gramian the krylov side is obtained via iterative rational krylov steps the reduced model is asymptotically stable matches certain moments and solves a restricted h 2 minimization problem we present modifications to the proposed approach for employing low rank gramians in the reduction step and also for reducing discrete time systems several numerical examples from various disciplines verify the effectiveness of the proposed approach it performs significantly better than the q cover a yousouff r e skelton covariance equivalent realizations with applications to model reduction of large scale systems in c t leondes ed control and dynamic systems vol 22 academic press 1985 pp 273 348 a yousouff d a wagie r e skelton linear system approximation via covariance equivalent realizations journal of math anal and appl 196 1985 91 115 and the least squares s gugercin a c antoulas model reduction of large scale systems by least squares linear algebra appl 415 2 3 2006 290 321 methods that have a similar projection structure to the proposed method also in terms of both the h 2 and h error measures its performance is comparable to or sometimes better than that of balanced truncation moreover the method proves to be robust with respect to the perturbations due to usage of approximate gramians

a hyperbolic system of equations of blood flow in an arterial network we study a coupled system of the navier stokes equation and the equation of conservation of mass in a network the system models the blood circulation in arterial networks a special feature of the system is that the equations are coupled through boundary conditions at joints of the network we use a fixed point method to prove the existence and uniqueness of the classic solution to the initial boundary value problem and discuss the continuity of dependence of the solution and its derivatives on initial boundary and forcing functions and their derivatives we develop a numerical scheme that generates discretized solutions and we also prove the convergence of the scheme

pointwise time asymptotic behavior of solutions to a general class of hyperbolic balance laws abstract in this paper we are interested in a general class of hyperbolic balance laws within the frame work of existence of a convex entropy function that symmetrizes the system in certain sense and the kawashima shizuta condition we study the large time behavior of the solution to the cauchy problem in one space dimension for a solution around a constant equilibrium state we predetermine the asymptotic solution as a superposition of the constant state and diffusion waves along the equilibrium characteristic directions we estimate the remainder in the pointwise sense both in space and in time the decay rates in various directions are optimal which further give the optimal l p rates with 1 p applications to several examples including the kerr debye model are given

optimality conditions for truncated kautz networks with two periodically repeating complex conjugate poles presents optimality conditions for the approximation of a siso system by a truncated kautz network with two repeating complex conjugate poles both the continuous and the discrete time cases are discussed the author approaches the problem in a system approximation framework and he does not assume that the input signal is white or an impulse the results obtained generalize the results already known for truncated laguerre networks

partitioned formulation of internal and gravity waves interacting with flexible structures abstract this paper presents a partitioned modeling of internal and gravity fluid waves that interact with flexible structures the governing interaction model consists of three completely partitioned entities fluid model structural model and interface model that acts as an internal constraint on the fluid structure interface boundary thus the proposed partitioned multi physics modeling can employ two completely modular fluid and structure software modules plus an interface solver hence amenable to partitioned solution algorithms the interface discretization can exploit the nonmatching interface algorithm previously developed via the method of localized lagrange multipliers also noted is that the present fluid model can make use of widely available finite element software for standard poisson type problems

system identification by discrete rational atoms a novel adaptive frequency domain system identification method for linear time invariant systems is proposed in this paper it finds poles for discrete rational atoms with discrete frequency responses the theoretical foundation including adaptive decomposition principle and decomposition convergence rate is established the algorithm of the adaptive pursuit is also provided in this paper

an anatomically based model of transient coronary blood flow in the heart an efficient finite difference model of blood flow through the coronary vessels is developed and applied to a geometric model of the largest six generations of the coronary arterial network by constraining the form of the velocity profile across the vessel radius the three dimensional navier stokes equations are reduced to one dimensional equations governing conservation of mass and momentum these equations are coupled to a pressure radius relationship characterizing the elasticity of the vessel wall to describe the transient blood flow through a vessel segment the two step lax wendroff finite difference method is used to numerically solve these equations the flow through bifurcations where three vessel segments join is governed by the equations of conservation of mass and momentum the solution to these simultaneous equations is calculated using the multidimensional newton raphson method simulations of blood flow through a geometric model of the coronary network are presented demonstrating phy

global solution to a hyperbolic problem arising in the modeling of blood flow in circulatory systems abstract this paper considers a system of first order hyperbolic partial differential equations in the domain of a one dimensional network the system models the blood flow in human circulatory systems as an initial boundary value problem with boundary conditions of either algebraic or differential type the differential equations are nonhomogeneous with frictional damping terms and the state variables are coupled at internal junctions the existence and uniqueness of the local classical solution have been established in our earlier work w ruan m e clark m zhao a curcio a hyperbolic system of equations of blood flow in an arterial network j appl math 64 2 2003 637 667 w ruan m e clark m zhao a curcio blood flow in a network nonlinear anal real world appl 5 2004 463 485 w ruan m e clark m zhao a curcio a quasilinear hyperbolic system that models blood flow in a network in charles v benton ed focus on mathematical physics research nova science publishers inc new york 2004 pp 203 230 this paper continues the analysis and gives sufficient conditions for the global existence of the classical solution we prove that the solution exists globally if the boundary data satisfy the dissipative condition 2 3 or 3 2 and the norms of the initial and forcing functions in a certain sobolev space are sufficiently small this is only the first step toward establishing the global existence of the solution to physiologically realistic models because in general the chosen dissipative conditions 2 3 and 3 2 do not appear to hold for the originally proposed boundary conditions 1 3 1 12

improved routh pade spl acute approximants a computer aided approach a geometric programming based computer aided method to derive a reduced order rth order approximant for a given stable siso linear continuous time system is presented in this method stability and the first r time moments markov parameters are preserved as well as the errors between a set of subsequent time moments markov parameters of the system and those of the model are minimized

on worst case approximation of feasible system sets via orthonormal basis functions this note deals with the approximation of sets of linear time invariant systems via orthonormal basis functions this problem is relevant to conditional set membership identification where a set of feasible systems is available from observed data and a reduced complexity model must be estimated the basis of the model class is made of impulse responses of linear filters the objective of the note is to select the basis function poles according to a worst case optimality criterion suboptimal conditional identification algorithms are introduced and tight bounds are provided on the associated identification errors

a fast adaptive model reduction method based on takenaka malmquist systems abstract an adaptive model reduction method is proposed for linear time invariant systems based on the continuous time rational orthogonal basis takenaka malmquist basis the method is to find an adaptive approximation in the energy sense by selecting optimal points for the rational orthogonal basis the stability of the reduced models holds and the steady state values of step responses are kept to be equal furthermore the method automatically ensures the reduced system to be in the hardy space h 2 the existence of the best approximation in the hardy space h 2 by n blaschke forms is proved in the proposed approach the effectivity of this method is illustrated through three well known examples

a domain decomposition method for advection diffusion processes with application to blood solutes in the present paper we consider a heterogeneous model for the dynamics of a blood solute both in the vascular lumen and inside the arterial wall in the lumen we consider an advection diffusion equation where the convective field is provided by the velocity of blood which is in turn obtained by solving the navier stokes equations inside the arterial wall we consider a pure diffusive dynamics since the endothelial layer at the interface between the lumen and the wall acts as a permeable membrane whose permeability depends on the shear rate exerted by the blood the solute concentration is discontinuous across this membrane a possible approach for the numerical study of this kind of problem is inspired by domain decomposition techniques in particular we introduce a splitting in the computation and alternate the solution of the advection diffusion equation in the lumen with that of the diffusion equation in the wall we set up an efficient iterative method based on a suitable reformulation of the problem in terms of a steklov poincare interface equation this formulation is a nonstandard one because of the concentration discontinuity at the lumen wall interface and plays a key role in the proof of convergence of our method in particular we prove that the convergence rate performed by the proposed method is independent of the finite element space discretization and provides a criterion for the selection of an acceleration parameter several numerical results referred to as biomedical applications support our theoretical conclusions and illustrate the efficiency of this algorithm

mathematical and numerical models for transfer of low density lipoproteins through the arterial walls a new methodology for the model set up with applications to the study of disturbed lumenal flow in this work we introduce and discuss several mathematical models based on partial differential equations devised to study the coupled transport of macromolecules as low density lipoproteins in the blood stream and in the arterial walls these models are accurate provided that a suitable set of physical parameters characterizing the physical properties of the molecules and of the wall layers are available here we turn our attention on this aspect and propose a new methodology to compute the physical parameters needed for the model set up starting from available in vivo measurements then we focus on the study of the accumulation of low density lipoproteins in vascular districts featuring a highly disturbed flow our results demonstrate that mathematical models whose set up procedure benefits from an experimental feedback provide reliable information not only qualitatively but also quantitatively their application to geometrically perturbed vascular districts as for example a severe stenosis shows that geometrical parameters such as curvature and variations of the lumenal section strongly influence the accumulation of low density lipoproteins within the wall for instance in a stenotic segment with 75 area constriction the ldl concentration at the lumenal side of the wall is about 10 higher than for the undisturbed segment

far field reflector problem and intersection of paraboloids in this article we propose a numerical approach to the far field reflector problem which is an inverse problem arising in geometric optics caffarelli et al contemp math 226 13 32 1999 proposed an algorithm that involves the computation of the intersection of the convex hull of confocal paraboloids we show that computing this intersection amounts to computing the intersection of a power diagram a generalization of the voronoi diagram with the unit sphere this allows us to provide an algorithm that computes efficiently the intersection of confocal paraboloids using the exact geometric computation paradigm furthermore using an optimal transport formulation we cast the far field reflector problem into a concave maximization problem this allows us to numerically solve the far field reflector problem with up to 15k paraboloids we also investigate other geometric optic problems that involve union of confocal paraboloids and also intersection and union of confocal ellipsoids in all these cases we show that the computation of these surfaces is equivalent to the computation of the intersection of a power diagram with the unit sphere

identification and rational l 2 approximation a gradient algorithm this paper deals with the identification of linear constant dynamical systems when formalized as a rational approximation problem the criterion is the l2 norm of the transfer function which is of interest in a stochastic context the problem can be expressed as nonlinear optimization in a hilbert space but standard algorithms are usually not well adapted we present a generic recursive procedure to find a local optimum of the criterion in the case of scalar systems our methods are borrowed from differential theory mixed with a bit of classical complex analysis to our knowledge the algorithm described in this paper is the first that ensures convergence to a local minimum

initial boundary value problems for conservation laws abstract we establish some general concepts concerning boundary conditions for systems of conservation laws defined on one dimensional space intervals and prove some general results among these is an extension of glimm s existence theorem to initial boundary value problems we also prove the convergence of the time averages of the solutions to certain initial boundary value problems for systems arising in fluid flows in porous media isentropic gas dynamics and elasticity theory

power diagrams properties algorithms and applications the power pow x s of a point x with respect to a sphere s in euclidean d space e d is given by d 2 x z r 2 where d denotes the euclidean distance function and z and r are the center and the radius of s the power diagram of a finite set s of spheres in e d is a cell complex that associates each s in s with the convex domain x in e d operatorname pow x s operatorname pow x t text for all t in s s the close relationship to convex hulls and arrangements of hyperplanes is investigated and exploited efficient algorithms that compute the power diagram and its order k modifications are obtained among the applications of these results are algorithms for detecting k sets for union and intersection problems for cones and paraboloids and for constructing weighted voronoi diagrams and voronoi diagrams for spheres upper space bounds for these geometric problems are derived

entropy and global existence for hyperbolic balance laws this paper presents a general result on the existence of global smooth solutions to hyperbolic systems of balance laws in several space variables we propose an entropy dissipation condition and prove the existence of global smooth solutions under initial data close to a constant equilibrium state in addition we show that a system of balance laws satisfies a kawashima condition if and only if its first order approximation namely the hyperbolic parabolic system derived through the chapman enskog expansion satisfies the corresponding kawashima condition the result is then applied to bouchut s discrete velocity bgk models approximating hyperbolic systems of conservation laws

large time behavior of solutions for hyperbolic balance laws we study the existence and the large time behavior of global solutions to the initial value problem for hyperbolic balance laws in n space dimensions with n 3 admitting an entropy and satisfying the stable condition we first construct global existence of the solutions to such a system around a steady state if the initial energy is small enough then we show that k order derivatives of these solutions approach a constant state in the lp norm at a rate o t 12 k n2 np with p 2 and 0 n2 provided that initially z0 b 2 where b 2 is a homogeneous besov space these decay results do not impose an additional smallness assumption on lp norm of the initial data and we thus improve the results in 3 19 we also show faster decay results in the sense that if pz0 b 2 i p z0 b 2 1 with n2 n 22 k order derivatives of the solutions approach a constant state in the lp norm at a rate o t 12 k 1 n2 np

the sinkhorn algorithm parabolic optimal transport and geometric monge ampere equations we show that the discrete sinkhorn algorithm as applied in the setting of optimal transport on a compact manifold converges to the solution of a fully non linear parabolic pde of monge ampere type in a large scale limit the latter evolution equation has previously appeared in different contexts e g on the torus it can be be identified with the ricci flow this leads to algorithmic approximations of the potential of the optimal transport map as well as the optimal transport distance with explicit bounds on the arithmetic complexity of the construction and the approximation errors as applications we obtain explicit schemes of nearly linear complexity at each iteration for optimal transport on the torus and the two sphere as well as the far field antenna problem connections to quasi monte carlo methods are exploited

convergence to equilibrium for the relaxation approximations of conservation laws we study the cauchy problem for 2 2 semilinear and quasilinear hyperbolic systems with a singular relaxation term special comparison and compactness properties are established by assuming the subcharacteristic condition therefore we can prove the convergence to equilibrium of the solutions of these problems as the singular perturbation parameter tends to 0 this research was strongly motivated by the recent numerical investigations of s jin and z xin on the relaxation schemes for conservation laws 1996 john wiley sons inc

discontinuous galerkin methods for mass transfer through semipermeable membranes a discontinuous galerkin dg method for the numerical solution of initial boundary value multicompartment partial differential equation models interconnected with interface conditions is presented and analyzed the study of interface problems is motivated by models of mass transfer of solutes through semipermeable membranes more specifically a model problem consisting of a system of semilinear parabolic advection diffusion reaction partial differential equations in each compartment equipped with respective initial and boundary conditions is considered nonlinear interface conditions modeling selective permeability congestion and partial reflection are applied to the compartment interfaces an interior penalty dg method is presented for this problem and it is analyzed in the space discrete setting the a priori analysis shows that the method yields optimal a priori bounds provided the exact solution is sufficiently smooth numerical experiments indicate agreement with the theoretical bounds and highlight the stability of the numerical method in the advection dominated regime