dynamic scaling in miscible viscous fingering we consider dynamic scaling in gravity driven miscible viscous fingering we prove rigorous one sided bounds on bulk transport and coarsening in regimes of physical interest the analysis relies on comparison with solutions to one dimensional conservation laws and new scale invariant estimates our bounds on the size of the mixing layer are of two kinds a naive bound that is sharp in the absence of diffusion and a more careful bound that accounts for diffusion as a selection criterion in the limit of vanishingly small diffusion the naive bound is simple and robust but does not yield the experimental speed of transport in a reduced model derived by wooding 20 we prove a sharp upper bound on the size of the mixing layer in accordance with his experiments wooding s model also provides an example of a scalar conservation law where the entropy condition is not the physically appropriate selection criterion

arbitrary adaptive pole placement for linear multivariable systems this paper presents a methodology for adaptively assigning the closed loop poles of either continuous or discrete time linear mnltivariable systems the scheme is direct in nature in that no parametrized model of the unknown plant needs to be explicitely identified rather the control parameters and an equivalent plant parameterization are simultaneously estimated from input output data using linear parameter estimation procedures implementation of the scheme requires only knowledge of the system controllability indexes and an upper bound on the observabilily index

numerical assessment of time domain methods for the estimation of local arterial pulse wave speed a local estimation of pulse wave speed c an important predictor of cardiovascular events can be obtained at arterial locations where simultaneous measurements of blood pressure p and velocity u arterial diameter d and u flow rate q and cross sectional area a or p and d are available using the pu loop sum of squares 2 lndu loop qa loop or new d2p loop methods here these methods were applied to estimate c from numerically generated p u d q and a waveforms using a visco elastic one dimensional model of the 55 larger human systemic arteries in normal conditions theoretical c were calculated from the parameters of the model estimates of c given by the loop methods were closer to theoretical values and more uniform within each arterial segment than those obtained using the 2 the smaller differences between estimates and theoretical values were obtained using the d2p loop method with root mean square errors rmse smaller than 0 18ms 1 followed by averaging the two c given by the pu and lndu loops rmse 2 99ms 1 in general the errors of the pu lndu and qa loops decreased at locations where visco elastic effects were small and nearby junctions were well matched for forward travelling waves the 2 performed better at proximal locations

homogenization of the time discretized compressible navier stokes system abstract this paper is concerned with the homogenization of the time discretized compressible navier stokes system in a periodic porous medium of period e with dirichlet boundary conditions in two or three dimensions to this end we generalized the p o i n c a r e inequality in the porous medium we apply our results to this model and rigorously derive the so called porous medium equation as e the pore size tends to zero

new extremal characterizations of generalized inverses of linear operators abstract in 1956 r penrose studied best approximate solutions of the matrix equation ax b he proved that a b where a is the moore penrose inverse is the unique matrix of minimal frobenius norm among all matrices which minimize the frobenius norm of ax b in particular a is the unique best approximate solution of ax i the vector version of penrose s result that is the fact that the vector a b is the best approximate solution in the euclidean norm of the vector equation ax b has long been generalized to infinite dimensional hilbert spaces in this paper an infinite dimensional version of penrose s full result is given we show that a straightforward generalization is not possible and provide new extremal characterizations in terms of the hermitian order of a and of the classes of generalized inverses associated with minimal norm solutions of consistent operator equations or with least squares solutions for a certain class of operators we can phrase our characterizations in terms of a whole class of norms including the hilbert schmidt and the trace norms thus providing new extremal characterizations even in the matrix case we treat both operators with closed range and with not necessarily closed range finally we characterize a as the unique inner inverse of minimal hilbert schmidt norm if a 2

unbounded symmetrizable idempotents abstract the relationship between closed unbounded idempotents and dense decompositions of a hilbert space is explored by extending the notion of compatibility between closed subspaces and positive bounded operators

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

monotone difference approximations of bv solutions to degenerate convection diffusion equations we consider consistent conservative form monotone difference schemes for nonlinear convection diffusion equations in one space dimension since we allow the diffusion term to be strongly degenerate solutions can be discontinuous and in general are not uniquely determined by their data here we choose to work with weak solutions that belong to the bv in space and time class and in addition satisfy an entropy condition a recent result of wu and yin northeastern math j 5 1989 pp 395 422 states that these so called bv entropy weak solutions are unique the class of equations under consideration is very large and contains to mention only a few the heat equation the porous medium equation the two phase flow equation and hyperbolic conservation laws the difference schemes are shown to converge to the unique bv entropy weak solution of the problem in view of the classical theory for monotone difference approximations of conservation laws the main difficulty in obtaining a similar convergence theory in the present context is to show that the strongly degenerate discrete diffusion term is sufficiently smooth we provide the necessary regularity estimates by deriving and carefully analyzing a linear difference equation satisfied by the numerical flux of the difference schemes finally we make some concluding remarks about monotone difference schemes for multidimensional equations

a one dimensional model of viscous blood flow in an elastic vessel in this paper we present a one dimensional model of blood flow in a vessel segment with an elastic wall consisting of several anisotropic layers the model involves two variables the radial displacement of the vessel s wall and the pressure and consists of two coupled equations of parabolic and hyperbolic type numerical simulations on a straight segment of a blood vessel demonstrate that the model can produce realistic flow fields that may appear under normal conditions in healthy blood vessels as well as flow that could appear during abnormal conditions in particular we show that weakening of the elastic properties of the wall may provoke a reverse blood flow in the vessel

adaptive regulation of mimo linear discrete time systems without requiring a persistent excitation an adaptive regulator which does not require a persistent excitation is developed for multiinput multioutput mimo linear discrete time systems the assumptions on the plant are 1 an upper bound on the system dimension is known 2 the unknown system parameters belong to known bounded intervals 3 the plant is stabilizable for all possible values of the unknown system parameters the stabilizability condition can be tested before the system is put into operation a recursive parameter estimation scheme is given which forces the parameter estimates to converge to the known intervals using this estimator an adaptive regulator is derived which results in a globally stable closed loop system

homogenization of the navier stokes equations in open sets perforated with tiny holes ii non critical sizes of the holes for a volume distribution and a surface distribution of holes this paper is devoted to the homogenization of the stokes or navier stokes equations with a dirichlet boundary condition in a domain containing many tiny solid obstacles periodically distributed in each direction of the axes for obstacles of critical size it was established in part i that the limit problem is described by a law of brinkman type here we prove that for smaller obstacles the limit problem reduces to the stokes or navier stokes equations and for larger obstacles to darcy s law we also apply the abstract framework of part i to the case of a domain containing tiny obstacles periodically distributed on a surface for example in three dimensions consider obstacles of size e2 located at the nodes of a regular plane mesh of period e this provides a mathematical model for fluid flows through mixing grids based on a special form of the brinkman law in which the additional term is concentrated on the plane of the grid

asymptotic analysis of linearly elastic shells iii justification of koiter s shell equations we consider as in part i a family of linearly elastic shells of thickness 2 all having the same middle surfaces r3 where r2 is a bounded and connected open set with a lipschitz continuous boundary and l3 r3 the shells are clamped on a portion of their lateral face whose middle line is 0 where 0 is any portion of withlength 0 0 we make an essential geometrical assumption on the middle surfaces and on the set 0 which states that the space of inextensional displacements begin gathered v f omega eta eta i in h 1 omega times h 1 omega times h 2 omega hfill eta i partial v eta 3 0 on gamma 0 gamma alpha beta eta 0 in omega hfill end gathered where gamma alpha beta are the components of the linearized change is metric tensor ofs contains non zero functions this assumption is satisfied in particular ifs is a portion of cylinder and 0 is contained in a generatrix ofs

earliest effects of sudden occlusions on pressure profiles in selected locations of the human systemic arterial system we have developed a numerical simulation method for predicting the time dependence wave form of pressure at any location in the systemic arterial system in humans the method uses the matlab simulink environment the input data include explicitly the geometry of the arterial tree treated up to an arbitrary bifurcation level and the elastic properties of arteries as well as rheological parameters of blood thus the impact of anatomic details of an individual subject can be studied the method is applied here to reveal the earliest stages of mechanical reaction of the pressure profiles to sudden local blockages thromboses or embolisms of selected arteries the results obtained with a purely passive model provide reference data indispensable for studies of longer term effects due to neural and humoral mechanisms the reliability of the results has been checked by comparison of two available sets of anatomic elastic and rheological data involving i 55 and ii 138 arterial segments the remaining arteries have been replaced with the appropriate resistive elements both models are efficient in predicting an overall shift of pressure whereas the accuracy of the 55 segment model in reproducing the detailed wave forms and stabilization times turns out dependent on the location of the blockage and the observation point

weighted least squares solutions of the equation axb c 0 abstract let h be a hilbert space l h the algebra of bounded linear operators on h and w l h a positive operator such that w 1 2 is in the p schatten class for some 1 p given a b l h with closed range and c l h we study the following weighted approximation problem analyze the existence of 0 1 m i n x l h a x b c p w where x p w w 1 2 x p we also study the related operator approximation problem analyze the existence of 0 2 m i n x l h a x b c w a x b c where the order is the one induced in l h by the cone of positive operators in this paper we prove that the existence of the minimum of 0 2 is equivalent to the existence of a solution of the normal equation a w a x b c 0 we also give sufficient conditions for the existence of the minimum of 0 1 and we characterize the operators where the minimum is attained

analysis of nonlinear poro elastic and poro visco elastic models we consider the initial and boundary value problem for a system of partial differential equations describing the motion of a fluid solid mixture under the assumption of full saturation the ability of the fluid phase to flow within the solid skeleton is described by the permeability tensor which is assumed here to be a multiple of the identity and to depend nonlinearly on the volumetric solid strain in particular we study the problem of the existence of weak solutions in bounded domains accounting for non zero volumetric and boundary forcing terms we investigate the influence of viscoelasticity on the solution functional setting and on the regularity requirements for the forcing terms the theoretical analysis shows that different time regularity requirements are needed for the volumetric source of linear momentum and the boundary source of traction depending on whether or not viscoelasticity is present the theoretical results are further investigated via numerical simulations based on a novel dual mixed hybridized finite element discretization when the data are sufficiently regular the simulations show that the solutions satisfy the energy estimates predicted by the theoretical analysis interestingly the simulations also show that in the purely elastic case the darcy velocity and the related fluid energy might become unbounded if indeed the data do not enjoy the time regularity required by the theory

discrete time model following adaptive control for multivariable non minimum phase systems in this paper a control system design that is applicable to both minimum and non minimum phase plants is discussed the output of this system can follow an arbitrary reference output with a bounded input in the first part of this paper we propose a new concept which is a bounded input calculation method of following a reference output it is then used to design a model following control system mfcs for multivariable non minimum phase plants corresponding to the right and left coprime factorizations of the plant two mfcs designs are given an extension of the mfcs to adaptive control is discussed and numerical examples are given to illustrate the effectiveness of the proposed adaptive system design

global adaptive pole positioning adaptive pole positioning for linear time invariant discrete time systems is considered under the constraint that the controller consists of an identifier the gains in which do not go to zero an observer and a state feedback law the latter two elements being viewed in transfer function form a globally convergent algorithm is presented for achieving a prescribed set of closed loop poles persistency of excitation of an external input is required together with an underbound on the magnitude of the sylvester resultant of the plant numerator and denominator polynomials this in effect being an underbound on the product of a measure of pole zero separation and a generalized gain

explicit robin neumann schemes for the coupling of incompressible fluids with thin walled structures abstract we introduce a class of explicit coupling schemes for the numerical solution of fluid structure interaction problems involving a viscous incompressible fluid and a general thin walled structure e g including damping and non linear behavior the fundamental ingredient in these methods is a parameter free explicit robin interface condition for the fluid which enables the fluid solid splitting through appropriate extrapolations of the solid velocity and fluid stress on the interface the resulting solution procedures are genuinely partitioned stability and error estimates are provided for all the variants depending on the extrapolations using energy arguments within a representative linear setting in particular we show that one of them simultaneously yields added mass free unconditional stability and optimal first order time accuracy a comprehensive numerical study involving different examples from the literature supports the theory

homogenization of richards equation in permeability fields with different connectivities 1 large scale modeling of transient flow in the unsaturated zone is important for the estimation of the water budget and solute transport in the vadose zone upscaled flow models need to capture the impact of small scale heterogeneities which are not resolved by the model on large scale flow we perform upscaling of the richards equation in heterogeneous porous media with continuous distributions of the soil hydraulic parameters using homogenization theory and stochastic averaging techniques we restrict the analysis to flow regimes in which the capillary equilibrium assumption holds on the small scale in order to account for effects of capillary entry pressure we apply the brooks corey model for the soil retention and relative permeability curves and consider leverett scaling for the coupling of intrinsic permeability and entry pressure for this model we derive and analyze the ensemble averaged parameter functions for the macroscopic flow equations the effects of a definite entry pressure vanish with increasing variance of the log intrinsic permeability we compare the statistically averaged parameter functions to numerically calculated effective functions for parameter fields with different connectivity properties these results illustrate that soils with well connected coarse materials differ in the relative permeability from those with well connected fine materials or those without particular connectedness

homogenization of the navier stokes equations in open sets perforated with tiny holes i abstract framework a volume distribution of holes this paper treats the homogenization of the stokes or navier stokes equations with a dirichlet boundary condition in a domain containing many tiny solid obstacles periodically distributed in each direction of the axes for example in the three dimensional case the obstacles have a size of e3 and are located at the nodes of a regular mesh of size e a suitable extension of the pressure is used to prove the convergence of the homogenization process to a brinkman type law in which a linear zero order term for the velocity is added to a stokes or navier stokes equation

a centre manifold description of containment dispersion in channels with varying flow properties high order asymptotic approximations to the equation governing the longitudinal dispersion of a passive contaminant in poiseuille channel flow are derived and their validity discussed the derivation uses centre manifold theory which provides a systematic and near rigorous approach to calculating each successive approximation it also enables the derivation of the correct initial conditions for the taylor model of shear dispersion approximations that are valid when the channel is of a varying cross section are systematically derived via this approach and the effects of time dependent flow and variable diffusivity are also investigated the resultant modifications to the effective advection velocity and the effective dispersion coefficient are calculated and some general trends indicated

some norm inequalities concerning generalized inverses 2 abstract we extend to the von neumann schatten classes c p and norms psome inequalities concerning generalized inverses we extend penrose s result on minimizing ax b 2 to the p norm we also minimize x p where x varies such that 1 b a ax a ab and 2 a ax a in both cases a b fixed local considerations are adduced in each result here global minima and critical points coincide

numerical analysis of the navier stokes darcy coupling we consider a differential system based on the coupling of the navier stokes and darcy equations for modeling the interaction between surface and porous media flows we formulate the problem as an interface equation we analyze the associated nonlinear steklov poincare operators and we prove its well posedness we propose and analyze iterative methods to solve a conforming finite element approximation of the coupled problem

analytical approximations for effective relative permeability in the capillary limit we present an analytical method for calculating two phase effective relative permeability krjeff where j designates phase here co2 and water under steady state and capillary limit assumptions these effective relative permeabilities may be applied in experimental settings and for upscaling in the context of numerical flow simulations e g for co2 storage an exact solution for effective absolute permeability keff in two dimensional log normally distributed isotropic permeability k fields is the geometric mean we show that this does not hold for since log normality is not maintained in the capillary limit phase permeability field kkrj when capillary pressure and thus the saturation field is varied nevertheless the geometric mean is still shown to be suitable for approximating krjeff when the variance of ln k is low for high variance cases we apply a correction to the geometric average gas effective relative permeability using a winsorized mean which neglects large and small kj values symmetrically the analytical method is extended to anisotropically correlated log normal permeability fields using power law averaging in these cases the winsorized mean treatment is applied to the gas curves for cases described by negative power law exponents flow across incomplete layers the accuracy of our analytical expressions for is demonstrated through extensive numerical tests using low and high variance permeability realizations with a range of correlation structures we also present integral expressions for geometric mean and power law average krjeff for the systems considered which enable derivation of closed form series solutions for without generating permeability realizations this article is protected by copyright all rights reserved

a posteriori error estimates for a discontinuous galerkin method applied to elliptic problems log number r74 abstract a posteriori error estimates for locally mass conservative methods for subsurface flow are presented these methods are based on discontinuous approximation spaces and referred to as discontinuous galerkin methods in the case where penalty terms are added to the bilinear form one obtains the nonsymmetric interior penalty galerkin methods in a previous work we proved optimal rates of convergence of the methods applied to elliptic problems here h adaptivity is investigated for flow problems in 2d we derive global explicit estimators of the error in the l 2 norm and we numerically investigate an implicit indicator of the error in the energy norm model problems with discontinuous coefficients are considered

fluid structure interaction in blood flow capturing non zero longitudinal structure displacement we present a new model and a novel loosely coupled partitioned numerical scheme modeling fluid structure interaction fsi in blood flow allowing non zero longitudinal displacement arterial walls are modeled by a linearly viscoelastic cylindrical koiter shell model capturing both radial and longitudinal displacement fluid flow is modeled by the navier stokes equations for an incompressible viscous fluid the two are fully coupled via kinematic and dynamic coupling conditions our numerical scheme is based on a new modified lie operator splitting that decouples the fluid and structure sub problems in a way that leads to a loosely coupled scheme which is unconditionally stable this was achieved by a clever use of the kinematic coupling condition at the fluid and structure sub problems leading to an implicit coupling between the fluid and structure velocities the proposed scheme is a modification of the recently introduced kinematically coupled scheme for which the newly proposed modified lie splitting significantly increases the accuracy the performance and accuracy of the scheme were studied on a couple of instructive examples including a comparison with a monolithic scheme it was shown that the accuracy of our scheme was comparable to that of the monolithic scheme while our scheme retains all the main advantages of partitioned schemes such as modularity simple implementation and low computational costs

pulse wave propagation in a model human arterial network assessment of 1 d visco elastic simulations against in vitro measurements a numerical model based on the nonlinear one dimensional 1 d equations of pressure and flow wave propagation in conduit arteries is tested against a well defined experimental 1 1 replica of the human arterial tree the tree consists of 37 silicone branches representing the largest central systemic arteries in the human including the aorta carotid arteries and arteries that perfuse the upper and lower limbs and the main abdominal organs the set up is mounted horizontally and connected to a pulsatile pump delivering a periodic output similar to the aortic flow terminal branches end in simple resistance models consisting of stiff capillary tubes leading to an overflow reservoir that reflects a constant venous pressure the parameters required by the numerical algorithm are directly measured in the in vitro set up and no data fitting is involved comparison of experimental and numerical pressure and flow waveforms shows the ability of the 1 d time domain formulation to capture the main features of pulse wave propagation measured throughout the system test as a consequence of the simple resistive boundary conditions used to reduce the uncertainty of the parameters involved in the simulation the experimental set up generates waveforms at terminal branches with additional non physiological oscillations the frequencies of these oscillations are well captured by the 1 d model even though amplitudes are overestimated adding energy losses in bifurcations and including fluid inertia and compliance to the purely resistive terminal models does not reduce the underdamped effect suggesting that wall visco elasticity might play an important role in the experimental results nevertheless average relative root mean square errors between simulations and experimental waveforms are smaller than 4 for pressure and 19 for the flow at all 70 locations studied

a priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems we analyze three discontinuous galerkin approximations for solving elliptic problems in two or three dimensions in each one the basic bilinear form is nonsymmetric the first one has a penalty term on edges the second has one constraint per edge and the third is totally unconstrained for each of them we prove hp error estimates in the h1 norm optimal with respect to h the mesh size and nearly optimal with respect to p the degree of polynomial approximation we establish these results for general elements in two and three dimensions for the unconstrained method we establish a new approximation result valid on simplicial elements l2 estimates are also derived for the three methods

motion of an elastic solid inside an incompressible viscous fluid the motion of an elastic solid inside an incompressible viscous fluid is ubiquitous in nature mathematically such motion is described by a pde system that couples the parabolic and hyperbolic phases the latter inducing a loss of regularity which has left the basic question of existence open until now in this paper we prove the existence and uniqueness of such motions locally in time when the elastic solid is the linear kirchhoff elastic material the solution is found using a topological fixed point theorem that requires the analysis of a linear problem consisting of the coupling between the time dependent navier stokes equations set in lagrangian variables and the linear equations of elastodynamics for which we prove the existence of a unique weak solution we then establish the regularity of the weak solution this regularity is obtained in function spaces that scale in a hyperbolic fashion in both the fluid and solid phases our functional framework is optimal and provides the a priori estimates necessary for us to employ our fixed point procedure

formal upscaling and numerical validation of unsaturated flow models in fractured porous media abstract in this work we consider a mathematical model for describing flow in an unsaturated porous medium containing a fracture both the flow in the fracture as well as in the matrix blocks are governed by richards equation coupled by natural transmission conditions using formal asymptotics we derive upscaled models as the limit of vanishing e the ratio of the width and length of the fracture our results show that the ratio of porosities and permeabilities in the fracture to matrix determine to the leading order of approximation the appropriate effective model in these models the fracture is a lower dimensional object for which different transversally averaged models are derived depending on the ratio of the porosities and permeabilities of the fracture and respective matrix blocks we obtain a catalogue of effective models which are validated by numerical computations

modeling viscoelastic behavior of arterial walls and their interaction with pulsatile blood flow fluid structure interaction describing wave propagation in arteries driven by the pulsatile blood flow is a complex problem whenever possible simplified models are called for one dimensional models are typically used in arterial sections that can be approximated by the cylindrical geometry allowing axially symmetric flows although a good first approximation to the underlying problem the one dimensional model suffers from several drawbacks the model is not closed an ad hoc velocity profile needs to be prescribed to obtain a closed system and the model equations are quasi linear hyperbolic oversimplifying the viscous fluid dissipation typically producing shock wave solutions not observed in healthy humans in this manuscript we derived a simple closed reduced model that accounts for the viscous fluid dissipation to the leading order the resulting fluid structure interaction system is of hyperbolic parabolic type arterial walls were modeled by a novel linearly viscoelastic cylindrical koiter shell model and the flow of blood by the incompressible viscous navier stokes equations kelvin voigt type viscoelasticity was used to capture the hysteresis behavior observed in the measurements of the arterial stress strain response using the a priori estimates obtained from an energy inequality together with the asymptotic analysis and ideas from homogenization theory for porous media flows we derived an effective model which is an 2 approximation to the three dimensional axially symmetric problem whereis the aspect ratio of the cylindrical arterial section our model shows two interesting features of the underlying problem bending rigidity often times neglected in the arterial wall models plays a nonnegligible role in the 2 approximation of the original problem and the viscous fluid dissipation imparts long term viscoelastic memory effects on the motion of the arterial walls this does not to the leading order influence the hysteresis behavior of arterial walls the resulting model although two dimensional is in the form that allows the use of one dimensional finite element method techniques producing fast numerical solutions we devised a version of the douglas rachford time splitting algorithm to solve the underlying hyperbolic parabolic problem the results of the numerical simulations were compared with the experimental flow measurements performed at the texas heart institute and with the data corresponding to the hysteresis of the human femoral artery and the canine abdominal aorta excellent agreement was observed

paper parameterization issues in multivariable adaptive control this paper gives both an overview of multivariable adaptive control algorithms which have evolved to date and presents some new approaches to the design of indirect multivariable adaptive control systems all algorithms are presented using a unified pole placement approach furthermore the emphasis is on parameterization issues such as types of control structures necessary for implementation required prior information necessary for implementation and techniques for reducing the size of the resulting parameter estimation problem

numerical study of shear dependent non newtonian fluids in compliant vessels the aim of this contribution is to present recent results on numerical modelling of non newtonian flow in compliant stenosed vessels with application in hemodynamics we consider two models of shear thinning non newtonian fluids and compare them with the newtonian model for the structure problem the generalized string equation for radial symmetric tubes is used and extended to a stenosed vessel the global iterative approach to approximate the fluid structure interaction is used finally we present numerical experiments for some non newtonian models comparisons with the newtonian model and the results for hemodynamic wall parameters such as the wall shear stress and the oscillatory shear index

darcy s law for slow viscous flow past a stationary array of bubbles we examine slow viscous flow past a concentrated bed of small stationary viscous bubbles of a second fluid and derive darcy s law relating the average fluid velocity to the overall pressure gradient and body force

design of g interactor and its application to direct multivariable adaptive control in the design of multi input multi output mimo adaptive control systems an interactor plays an important role the derivation of the interactor requires system parameter values unless the interactor is in diagonal form this is a considerable restriction when the interactor is applied to the adaptive control system design in mimo adaptive control many parameters must be estimated to achieve good tracking over parametrization causes many problems e g bad tracking performance and long calculation time of control input a design of interactor called a g interactor for unknown mimo plants is given it is applied to mimo adaptive control systems the g interactor requires minimum information on the plant such as the relative degree of each element of the plant transfer matrix for this design a canonical form called the g canonical form of a matrix a is investigated the canonical form is also used to eliminate redundant parameters of mimo adaptive control systems numerical examples show the effect

weighted procrustes problems abstract let h be a hilbert space l h the algebra of bounded linear operators on h and w l h a positive operator such that w 1 2 is in the p schatten class for some 1 p given a l h with closed range and b l h we study the following weighted approximation problem analyze the existence of m i n x l h a x b p w where x p w w 1 2 x p in this paper we prove that the existence of this minimum is equivalent to a compatibility condition between r b and r a involving the weight w and we characterize the operators which minimize this problem as w inverses of a in r b

a stabilized mixed discontinuous galerkin method for darcy flow abstract a new mixed stabilized discontinuous galerkin formulation for darcy flow is presented the formulation combines several attributes not simultaneously satisfied by other methods it is convergent for any combination of velocity and pressure interpolation higher than first order it exactly satisfies a mass balance on each element and it passes two and three dimensional constant flow patch tests for distorted element geometries the key ingredient in the formulation is a volumetric residual based stabilization term that does not involve any mesh dependent parameters

global minimum and orthogonality in c1 classes abstract in this paper we characterize the global minimum of an arbitrary function defined on a banach space in terms of a new concept of derivatives adapted for our case from a recent work due to d j keckic j operator theory submitted for publication using these results we establish several new characterizations of the global minimum of the map f u r defined by f x x 1 where u c 1 is a map defined by x s x and b h b h is a linear map s c1 and u x b h x c 1 further we apply these results to characterize the operators which are orthogonal to the range of elementary operators

numerical schemes for a pseudo parabolic burgers equation discontinuous data and long time behaviour we consider a simplified model for vertical non stationary groundwater flow which includes dynamic capillary pressure effects specifically we consider a viscous burgers type equation that is extended with a third order term containing mixed derivatives in space and time we analyse the one dimensional boundary value problem and investigate numerically its long time behaviour the numerical schemes discussed here take into account possible discontinuities of the solution

the interaction between quasilinear elastodynamics and the navier stokes equations the interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations coupled to one another along the moving material interface through the continuity of the velocity and traction vectors we prove the existence and uniqueness locally in time of strong solutions in sobolev spaces for quasilinear elastodynamics coupled to the incompressible navier stokes equations unlike our approach in 5 for the case of linear elastodynamics we cannot employ a fixed point argument on the nonlinear system itself and are instead forced to regularize it by a particular parabolic artificial viscosity term we proceed to show that with this specific regularization we obtain a time interval of existence which is independent of the artificial viscosity together with a priori estimates we identify the global solution in both phases as well as the interface motion as a weak limit in strong norms of our sequence of regularized problems

multicomponent fluid flow by discontinuous galerkin and mixed methods in unfractured and fractured media 1 a discrete fracture model for the flow of compressible multicomponent fluids in homogeneous heterogeneous and fractured media is presented in single phase in the numerical model we combine the mixed finite element mfe and the discontinuous galerkin dg methods we use the cross flow equilibrium concept to approximate the fractured matrix mass transfer the discrete fracture model is numerically superior to the single porosity model and overcomes limitations of the dual porosity models including the use of a shape factor the mfe method provides a direct and accurate approximation for the velocity field which is crucial for the convective terms in the flow equations the dg method associated with a slope limiter is used to approximate the species balance equations this method can capture the sharp moving fronts the calculation of the fracture fracture flux across three and higher intersecting fracture branches is a challenge in this work we provide an accurate approximation of these fluxes by using the mfe formulation numerical examples in unfractured and fractured media illustrate the efficiency and robustness of the proposed numerical model

effective equations for two phase flow with trapping on the micro scale in this paper we consider water drive for recovering oil from a strongly heterogeneous porous column the two phase model uses corey relative permeabilities and brooks corey capillary pressure the heterogeneities are perpendicular to the flow and have a periodic structure this results in one dimensional flow and a space periodic absolute permeability reflecting alternating coarse and fine layers assuming many or thin layers we use homogenization techniques to derive the effective transport equations the form of these equations depends critically on the capillary number the analysis is confirmed by numerical experiments

multivariable adaptive control without a prior knowledge of the delay matrix this paper is concerned with the structure and role of the time delay matrix in discrete time multivariable processes interpretations and properties of this matrix as a multivariable generalization of the siso delay term are discussed it is formally shown that a finite time horizon or multi step cost function for the multivariable case can be minimized subject to a suitable choice of output and control horizons and without prior knowledge of the system delay matrix

comparisons between reduced order models and full 3d models for fluid structure interaction problems in haemodynamics when modelling the cardiovascular system the effect of the vessel wall on the blood flow has great relevance arterial vessels are complex living tissues and three dimensional specific models have been proposed to represent their behaviour the numerical simulation of the 3d 3d fluid structure interaction fsi coupled problem has high computational costs in terms of required time and memory storage even if many possible solutions have been explored to speed up the resolution of such problem we are far from having a 3d 3d fsi model that can be solved quickly in 3d 3d fsi models two of the main sources of complexity are represented by the domain motion and the coupling between the fluid and the structural part nevertheless in many cases we are interested in the blood flow dynamics in compliant vessels whereas the displacement of the domain is small and the structure dynamics is less relevant in these situations techniques to reduce the complexity of the problem can be used one consists in using transpiration conditions for the fluid model as surrogate for the wall displacement thus allowing problem s solution on a fixed domain another strategy consists in modelling the arterial wall as a thin membrane under specific assumptions figueroa et al 2006 nobile and vergara 2008 instead of using a more realistic but more computationally intensive 3d elastodynamic model using this strategy the dynamics of the vessel motion is embedded in the equation for the blood flow combining the transpiration conditions with the membrane model assumption we obtain an attractive formulation in fact instead of solving two different models on two moving physical domains we solve only a navier stokes system in a fixed fluid domain where the structure model is integrated as a generalized robin condition in this paper we present a general formulation in the boundary conditions which is independent of the time discretization scheme choice and on the stress strain constitutive relation adopted for the vessel wall structure our aim is first to write a formulation of a reduced order model with zero order transpiration conditions for a generic time discretization scheme then to compare a 3d 3d fsi model and a reduced fsi one in two realistic patient specific cases a femoropopliteal bypass and an aorta in particular we are interested in comparing the wall shear stresses in fact this quantity can be used as a risk factor for some pathologies such as atherosclerosis or thrombogenesis more in general we want to assess the accuracy and the computational convenience to use simpler formulations based on reduced order models in particular we show that in the case of small displacements using a 3d 3d fsi linear elastic model or the correspondent reduced order one yields many similar results

kinematic splitting algorithm for fluid structure interaction in hemodynamics abstract in this paper we study a kinematic splitting algorithm for fluid structure interaction problems this algorithm belongs to the class of loosely coupled fluid structure interaction schemes we will present stability analysis for a coupled problem of non newtonian shear dependent fluids in moving domains with viscoelastic boundaries fluid flow is described by the conservation laws with nonlinearities in convective and diffusive terms for simplicity of presentation the structure is modelled by the generalized string equation but the results presented in the paper may be generalized to more complex structure models the arbitrary lagrangian eulerian approach is used in order to take into account moving computational domain numerical experiments including numerical error analysis and comparison of hemodynamic parameters for newtonian and non newtonian fluids demonstrate reliability of the proposed scheme

minimizing drag in a moving boundary fluid elasticity interaction abstract our goal is to minimize the fluid vorticity in the case of an elastic body moving and deforming inside the fluid using a distributed control this translates into analyzing an optimal control problem subject to a moving boundary fluid structure interaction fsi the fsi is described by the coupling of navier stokes and wave equations the control is inherently a nonlinear control acting as feedback on the moving frame its action depends on the flow map of the domain which is itself defined through the dynamics of the problem a key ingredient in the optimal control problem is represented by the long time behavior of the forced dynamics which was an open problem in the field our main results include existence of solutions for all times with small distributed sources and small initial data as well as existence of optimal control for the problem of minimization of drag in the fluid

existence of a solution to a fluid multi layered structure interaction problem abstract we study a nonlinear unsteady moving boundary fluid structure interaction fsi problem in which the structure is composed of two layers a thick layer and a thin layer which serves as a fluid structure interface with mass the fluid flow which is driven by the time dependent dynamic pressure data is modeled by the navier stokes equations for an incompressible viscous fluid defined on a 2d cylinder the elastodynamics of the cylinder wall is governed by the 1d linear wave equation modeling the thin structural layer and by the 2d equations of linear elasticity modeling the thick structural layer we prove existence of a weak solution to this nonlinear fsi problem as long as the cylinder radius is greater than zero the spaces of weak solutions presented in this manuscript reveal a striking new feature the presence of a thin fluid structure interface with mass regularizes solutions of the coupled problem

an indirect adaptive controller with a self excitation capability an indirect adaptive pole placement controller is presented which stabilizes and asymptotically regulates any discrete time single input single output linear time invariant plant which is of known order n is controllable and observable and has unknown parameters to avoid singular points in the algorithm the adaptive controller solves the pole placement design equation asymptotically with time rather than trying to solve it exactly at each time instant the stability of the adaptive control system and the asymptotic regulation of the plant output to zero are ensured by an additional self excitation generated by the adaptive controller a novel kind of an error signal to control the magnitude of the self excitation is obtained by suitably filtering the self exciting signal and monitoring changes of the controller parameters as they are generated by the adaptive algorithm

analytical and variational numerical methods for unstable miscible displacement flows in porous media the miscible displacement of one fluid by another in a porous medium has received considerable attention in sub surface environmental and petroleum engineering applications when a fluid of higher mobility displaces another of lower mobility unstable patterns referred to as viscous fingering may arise their physical and mathematical study has been the object of numerous investigations over the past century the objective of this paper is to present a review of these contributions with particular emphasis on variational methods these algorithms are tailored to real field applications thanks to their advanced features handling of general complex geometries robustness in the presence of rough tensor coefficients low sensitivity to mesh orientation in advection dominated scenarios and provable convergence with fully unstructured grids this paper is dedicated to the memory of dr jim douglas jr for his seminal contributions to miscible displacement and variational numerical methods

stable loosely coupled type algorithm for fluid structure interaction in blood flow we introduce a novel loosely coupled type algorithm for fluid structure interaction between blood flow and thin vascular walls this algorithm successfully deals with the difficulties associated with the added mass effect which is known to be the cause of numerical instabilities in fluid structure interaction problems involving fluid and structure of comparable densities our algorithm is based on a time discretization via operator splitting which is applied in a novel way to separate the fluid sub problem from the structure elastodynamics sub problem in contrast with traditional loosely coupled schemes no iterations are necessary between the fluid and structure sub problems this is due to the fact that our novel splitting strategy uses the added mass effect to stabilize rather than to destabilize the numerical algorithm this stabilizing effect is obtained by employing the kinematic lateral boundary condition to establish a tight link between the velocities of the fluid and of the structure in each sub problem the stability of the scheme is discussed on a simplified benchmark problem and we use energy arguments to show that the proposed scheme is unconditionally stable due to the crucial role played by the kinematic lateral boundary condition the proposed algorithm is named the kinematically coupled scheme

existence of a weak solution to a nonlinear fluid structure interaction problem modeling the flow of an incompressible viscous fluid in a cylinder with deformable walls we study a nonlinear unsteady moving boundary fluid structure interaction fsi problem arising in modeling blood flow through elastic and viscoelastic arteries the fluid flow which is driven by the time dependent pressure data is governed by two dimensional incompressible navier stokes equations while the elastodynamics of the cylindrical wall is modeled by the one dimensional cylindrical koiter shell model two cases are considered the linearly viscoelastic and the linearly elastic koiter shell the fluid and structure are fully coupled two way coupling via the kinematic and dynamic lateral boundary conditions describing continuity of velocity the no slip condition and the balance of contact forces at the fluid structure interface we prove the existence of weak solutions to the two fsi problems the viscoelastic and the elastic case as long as the cylinder radius is greater than zero the proof is based on a novel semi discrete operator splitting numerical scheme known as the kinematically coupled scheme introduced in guidoboni et al j comput phys 228 18 6916 6937 2009 to numerically solve the underlying fsi problems the backbone of the kinematically coupled scheme is the well known marchuk yanenko scheme also known as the lie splitting scheme we effectively prove convergence of that numerical scheme to a solution of the corresponding fsi problem