evaluation of the external force term in the discrete boltzmann equation a representation of the forcing term in the boltzmann equation based on a hermite expansion of the boltzmann distribution function in velocity phase space is derived based on this description of the forcing term a systematic comparison of previous lattice boltzmann models describing a nonideal gas behavior is given

structured squaring down and zero assignment the problem of zero assignment by squaring down is considered for a system of p inputs n outputs and n states m p where not all outputs are free variables for design we consider the case where a k subset of outputs is preserved in the new output set and the rest are recombined to produce a total new set of p outputs new invariants for the problem are introduced which include a new class of fixed zeros and the methodology of the global linearization developed originally for the output feedback pole assignment problem is applied to this restricted form of the squaring down problem it is shown that the problem can be solved generically if p k m p where k k p is the number of fixed outputs and is a system and compensation scheme invariant which is defined as the restricted forney degree

assigning frequencies via determinantal equations new counterexamples and invariants the problem of arbitrary pole zero assignment by fixed structure compensators has been addressed so far in terms of either necessary or sufficient conditions the strongest existing condition is based on the rank of the differential of a related map on a degenerate controller and holds true generically when the degrees of freedom of the compensator exceed the number of frequencies to be assigned mp n for the output feedback problem the complete nongeneric solvability of the problem is still open even when complex controllers are considered a simple necessary solvability condition is that the linear map appearing as a factor of the main determinantal map defining the assignment problem is onto here we examine the special problem of assignment of matrix pencil zeros via diagonal perturbations and we present a new necessary and sufficient condition for complex solvability in terms of a new invariant involving the minors of this linear map based on this result we demonstrate that for the important case where the degrees of freedom of the controller are equal to the number of frequencies to be assigned the surjectivity of this linear map although it is necessary it is not sufficient for the solvability of the problem

on two generalized inverse eigenvalue problems for hessenberg upper triangular pencils and their application to the study of gmres convergence abstract we discuss two generalized inverse eigenvalue problems the first one for a given unreduced upper hessenberg matrix h find a nonsingular upper triangular matrix t such that all the pencils h k t k have prescribed eigenvalues where h k and t k are the leading k k principal submatrices of h and t respectively the second one for a given unitary unreduced upper hessenberg matrix q find a nonsingular upper triangular matrix t such that all the pencils t k q k have prescribed eigenvalues where t k is the leading k k principal submatrix of t and q k is the conjugate transpose of the leading k k principal submatrix of q we present the necessary and sufficient conditions for the solvability of the two problems our results lead to an alternative proof for the statement that any admissible ritz value set or admissible harmonic ritz value set is possible for the prescribed gmres residual norms here the term admissible means there are some restrictions on the sets if gmres stagnates at some iterations

use of particle filters in an active control algorithm for noisy nonlinear structural dynamical systems the problem of active control of nonlinear structural dynamical systems in the presence of both process and measurement noises is considered the focus of the study is on the use of particle filters for state estimation in feedback control algorithms for nonlinear structures when a limited number of noisy output measurements are available the control design is done using the state dependent riccati equation sdre method the stochastic differential equations sdes governing the dynamical systems are discretized using explicit forms of ito taylor expansions the bayesian bootstrap filter and that based on sequential important sampling sis are employed for state estimation the simulation results show the feasibility of using particle filters and sdre techniques in control of nonlinear structural dynamical systems

implementation of diffuse reflection boundary conditions in a thermal lattice boltzmann model with flux limiters we discuss three new implementation versions of diffuse reflection boundary conditions in a thermal lattice boltzmann model their accuracy is investigated in the case of couette flow by considering the slip regime the best results are recovered with versions 2 and 3 which rely on outgoing fluxes to express the particle distribution functions in the ghost nodes outside the flow domain version 2 is found to be more economical since it involves no interpolation procedure this version was thereafter used to investigate the temperature profile in couette flow for various values of prandtl number as well as the capability of the thermal lb model to capture the knudsen minimum in poiseuille flow

accuracy of higher order lattice boltzmann methods for microscale flows with finite knudsen numbers accuracy of the lattice boltzmann lb method for microscale flows with finite knudsen numbers is investigated we employ up to the eleventh order gauss hermite quadrature for the lattice velocities and diffuse scattering boundary condition for fluid wall interactions detailed comparisons with the direct simulation monte carlo dsmc method and the linearized boltzmann equation are made for planar couette and poiseuille flows all higher order lb methods considered here give improved results as compared with the standard lb method the accuracy of the lb hierarchy however does not monotonically increase with the order of the gauss hermite quadrature at moderate and large knudsen numbers the results also show the sensitivity to a quadrature chosen even when the gauss hermite quadratures have the same order of formal accuracy among the schemes investigated here d2q16 is the most efficient method and offers a quantitative prediction in the slip and transition regimes the higher order lb methods predict the knudsen layer up to kn o 0 1 the knudsen layer however rapidly disappears when the knudsen number approaches unity due to a finite number of the lattice velocities while it is still present for kn o 1 in the boltzmann equation it is also found that the higher order lb methods adopted here do not capture the asymptotic behavior of the boltzmann equation at large knudsen numbers

a knudsen layer theory for lattice gases abstract a knudsen layer theory is presented for lattice gases with arbitrary boundary conditions analytical results are obtained for two special orientations these exhibit anisotropic knudsen layers provided suitable conditions are satisfied however the standard boundary conditions used in previous simulations are shown to be isotropic the bulk steady state extending everywhere in the gas this theory allows a more accurate localization of the obstacle with respect to the lattice nodes these results are in good agreement with the numerical simulations

high order upwind compact finite difference lattice boltzmann method for viscous incompressible flows abstract in this work a high order upwind compact finite difference lattice boltzmann method ucdlbm is developed to efficiently solve viscous incompressible flow problems a fifth order upwind compact difference scheme is adopted to discretize the spatial derivatives of the lattice boltzmann equation and the third order total variation diminishing runge kutta scheme is utilized for the discretization of the temporal term compared to the existing central compact finite difference lattice boltzmann method cfdlbm the present ucdlbm can prevent non physical oscillations without filtering due to the natural dissipative property of upwind schemes three benchmark problems involving the taylor green vortex problem the doubly periodic shear layer flow problem and the lid driven square cavity flow problem are numerically solved to demonstrate the accuracy and efficiency of the present method numerical results computed are in good agreement with the analytical solution or other available numerical results and the present ucdlbm is less time consuming than the cfdlbm without degenerating the order of accuracy of the numerical solutions

high order lattice boltzmann models for wall bounded flows at finite knudsen numbers we analyze a large number of high order discrete velocity models for solving the boltzmann bhatnagar gross krook equation for finite knudsen number flows using the chapman enskog formalism we prove for isothermal flows a relation identifying the resolved flow regimes for low mach numbers although high order lattice boltzmann models recover flow regimes beyond the navier stokes level we observe for several models significant deviations from reference results we found this to be caused by their inability to recover the maxwell boundary condition exactly by using supplementary conditions for the gas surface interaction it is shown how to systematically generate discrete velocity models of any order with the inherent ability to fulfill the diffuse maxwell boundary condition accurately both high order quadratures and an exact representation of the boundary condition turn out to be crucial for achieving reliable results for poiseuille flow we can reproduce the mass flow and slip velocity up to the knudsen number of 1 moreover for small knudsen numbers the knudsen layer behavior is recovered

matrices with prescribed eigenvalues and principal submatrices abstract we give a necessary and sufficient condition for the existence of a square matrix with prescribed eigenvalues and prescribed complementary principal blocks

boundary conditions for the upwind finite difference lattice boltzmann model evidence of slip velocity in micro channel flow we conduct a systematic study of the effect of various boundary conditions bounce back and three versions of diffuse reflection for the two dimensional first order upwind finite difference lattice boltzmann model simulation of couette flow in a micro channel using the diffuse reflection boundary condition reveals the existence of a slip velocity that depends on the knudsen number e l l where l is the mean free path and l is the channel width for walls moving in opposite directions with speeds u w the slip velocity satisfies u s l i p 2 eu w a l l 1 2 e in the case of poiseuille flow in a micro channel the slip velocity is found to depend on the lattice spacing ds and knudsen number e to both first and second order the best results are obtained for diffuse reflection boundary conditions that allow thermal mixing at a wall located at half lattice spacing outside the boundary nodes

two dimensional thermal model of the finite difference lattice boltzmann method with high spatial isotropy the existing lattice boltzmann method multispeed thermal models show a limited accuracy this paper proposes a two dimensional multispeed thermal model for the finite difference lattice boltzmann method fdlbm to recover correct fluid equations up to fourth orders of local flow velocity should be retained in the local equilibrium distribution function and tensors of particle velocities should have up to seventh rank isotropy in the fdlbm particle velocities can be selected independently from the lattice configuration therefore particle velocities of octagonal directions which have up to seventh rank isotropic tensors are adopted the proposed model was verified by two simulations the model showed excellent numerical stability in addition to strict accuracy

output feedback pole assignment for transfer functions with symmetries this paper studies the problem of pole assignment for symmetric and hamiltonian transfer functions a necessary and sufficient condition for pole assignment by complex symmetric output feedback transformations is given moreover in the case where the mcmillan degree coincides with the number of parameters appearing in the symmetric feedback transformations we derive an explicit combinatorial formula for the number of pole assigning symmetric feedback gains the proof uses intersection theory in projective space as well as a formula for the degree of the complex lagrangian grassmann manifold

lattice boltzmann modeling of microchannel flow in slip flow regime we present the lattice boltzmann equation lbe with multiple relaxation times mrt to simulate pressure driven gaseous flow in a long microchannel we obtain analytic solutions of the mrt lbe with various boundary conditions for the incompressible poiseuille flow with its walls aligned with a lattice axis the analytical solutions are used to realize the dirichlet boundary conditions in the lbe we use the first order slip boundary conditions at the walls and consistent pressure boundary conditions at both ends of the long microchannel we validate the lbe results using the compressible navier stokes ns equations with a first order slip velocity the information preservation direct simulation monte carlo ip dsmc and dsmc methods as expected the lbe results agree very well with ip dsmc and dsmc results in the slip velocity regime but deviate significantly from ip dsmc and dsmc results in the transition flow regime in part due to the inadequacy of the slip velocity model while still agreeing very well with the slip ns results possible extensions of the lbe for transition flows are discussed

matrices with prescribed rows and invariant factors abstract in this paper we solve the problem of the existence of an n n matrix over an arbitrary field when its invariant polynomials and either some rows or columns are prescribed the solution is given in terms of invariant factor inequalities and of majorization inequalities involving controllability indices and the degrees of the invariant polynomials

spectrally arbitrary patterns abstract an n n sign pattern matrix s is an inertially arbitrary pattern iap if each nonnegative triple n 1 n 2 n 3 with n 1 n 2 n 3 n is the inertia of a matrix with sign pattern s analogously s is a spectrally arbitrary pattern sap if for any given real monic polynomial r x of order n there is a matrix with sign pattern s and characteristic polynomial r x focusing on tree sign patterns consider the n n tridiagonal sign pattern t n with each superdiagonal entry positive each subdiagonal entry negative the 1 1 entry negative the n n entry positive and every other entry zero it is conjectured that t n is an iap by constructing matrices a n with pattern t n it is proved that t n allows any inertia with n 3 0 1 2 n 1 n for all n 2 this leads to a proof of the conjecture for n 5 the truth of the conjecture is extended to n 7 by showing the stronger result that t n is a sap the proof of this latter statement involves finding a matrix a n with pattern t n that is nilpotent further questions about patterns that are saps and iaps are considered

special loop connections of linear systems in this paper we completely determine the possible eigenvalues of a matrix of a system obtained as a result of special loop connections of arbitrary many linear systems

on the finite difference based lattice boltzmann method in curvilinear coordinates the lattice boltzmann method is a microscopic based approach for solving the fluid flow problems at the macroscopic scales the presently popular method uses regularly spaced lattices and cannot handle curved boundaries with desirable flexibility to circumvent such difficulties a finite difference based lattice boltzmann method fdlbm in curvilinear coordinates is explored using body fitted coordinates with non uniform grids several test cases including the impulsively started cylindrical couette flow steady state cylindrical couette flow steady flow over flat plates and steady flow over a circular cylinder are used to examine various issues related to the fdlbm the effect of boundary conditions for the distribution functions on the solution the merits between second order central difference and upwind schemes for advection terms and the effect of the reynolds number are investigated favorable results are obtained using fdlbm in curvilinear coordinates indicating that the method is potentially capable of solving finite reynolds number flow problems in complex geometries

multivariable nyquist criteria root loci and pole placement a geometric viewpoint classical control theory is concerned with the topics in our title in the context of single input single output systems there is now a large and growing literature on the extension of these ideas to the multiinput multioutput case this development has posed certain difficulties some due to the intrinsic nature of the problem and some we would argue due to an inadequate reflection on what the multivariable problem calls for in this paper we describe what seems to us to be the natural multivariable analogs of these concepts from classical control theory a rather satisfactory generalization of the nyquist criterion will be described and a clear analog of the asymptotic properties of the root locus will be obtained in the multiparameter case however an example is given which illustrates the quite surprising fact that the root locus map is not always continuous at infinite gains this calls for a new ingredient a compactification of the space of gains and perhaps the most interesting new feature in this circle of ideas comes in the area of pole placement this problem is difficult in the multivariable case but by establishing a correspondence with a classical set of problems in geometry we are able to understand its main aspects and to derive results on pole placement by output feedback over the real field

pole placement and matrix extension problems a common point of view this paper studies a general inverse eigenvalue problem which generalizes many well studied pole placement and matrix extension problems it is shown that the problem corresponds geometrically to a so called central projection from some projective variety the degree of this variety represents the number of solutions the inverse problem has in the critical dimension we are able to compute this degree in many instances and we provide upper bounds in the general situation

a characteristic galerkin method for discrete boltzmann equation abstract the characteristic galerkin finite element method for the discrete boltzmann equation is presented to simulate fluid flows in complex geometries the inherent geometric flexibility of the finite element method permits the easy use of simple cartesian variables on unstructured meshes and the mesh clustering near large gradients the characteristic galerkin procedure with appropriate boundary condition results in accurate solutions with little numerical diffusion several test cases are conducted including unsteady couette flows lid driven cavity flows and steady flow past a circular cylinder on unstructured meshes the numerical results are in good agreement with previous analytical if applicable numerical and experimental results

nonlinear feedback control of slewing beams abstract this paper is concerned with feedback control of slewing beams it allows for the hub to have finite rotation which leads to a fully nonlinear system it uses the method of state dependent riccati equation sdre to obtain feedback control laws the model assumes finite rigid body rotations and infinitesimal small elastic displacements it considers both the classical euler bermoulli model and the timoshenko model for the beam it uses finite element method to obtain approximate equations that can be used to construct feedback control laws

zero assignment of matrix pencils by additive structured transformations abstract matrix pencil models are natural descriptions of linear networks and systems changing the values of elements of networks that is redesigning them implies changes in the zero structure of the associated pencil and this is achieved by structured additive transformations the paper examines the problem of zero assignment of regular matrix pencils by a special type of structured additive transformations for a certain family of network redesign problems the additive perturbations may be described as diagonal perturbations and such modifications are considered here this problem has certain common features with the pole assignment of linear systems by structured static compensators and thus the new powerful methodology of global linearization j leventides n karcanias sufficient conditions for arbitrary pole assignment by constant decentralised output feedback mathematics of control for signals and systems 8 1995 222 240 j leventides n karcanias global asymptotic linearisation of the pole placement map a closed form solution for the constant output feedback problem automatica 31 1995 1303 1309 can be used for regular pencils with infinite zeros families of structured degenerate additive transformations are defined and parameterized and this lead to the derivation of conditions for zero structure assignment as well as methodology for computing such solutions the case of regular pencils with no infinite zeros is also considered and conditions of zero assignment are developed the results here provide the means for studying problems of linear network redesign by modification of the non dynamic elements

approximation theory for linear quadratic guassian optimal control of flexible structures this paper presents approximation theory for the linear quadratic gaussian optimal control problem for flexible structures whose distributed models have bounded input and output operators the main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator which is infinite dimensional design of the optimal compensator separates into an optimal linear quadratic control problem and a dual optimal state estimation problem the solution to each problem lies in the solution to an infinite dimensional riccati operator equation the approximation scheme in the paper approximates the infinite dimensional lqg problem with a sequence of finite dimensional lqg problems defined for a sequence of finite dimensional usually finite element or modal approximations of the distributed model of the structure two riccati matrix equations determine the solution to each approximating problem the finite dimensional equations for numerical approximation

matrices with prescribed characteristic polynomial and principal blocks ii abstract in this paper we present some new sufficient conditions for the existence of a square matrix with prescribed characteristic polynomial and two complementary principal submatrices

viscosity of finite difference lattice boltzmann models two dimensional finite difference lattice boltzmann models for single component fluids are discussed and the corresponding macroscopic equations for mass and momentum conservation are derived by performing a chapman enskog expansion in order to recover the correct mass equation characteristic based finite difference schemes should be associated with the forward euler scheme for the time derivative while the space centered and second order upwind schemes should be associated to second order schemes for the time derivative in the incompressible limit the characteristic based schemes lead to spurious numerical contributions to the apparent value of the kinematic viscosity in addition to the physical value that enters the navier stokes equation formulae for these spurious numerical viscosities are in agreement with results of simulations for the decay of shear waves

reduced basis approximation and a posteriori error estimation for a boltzmann model abstract we present a reduced basis approximation and associated rigorous a posteriori output flow rate error bound for a simple linearized bgk boltzmann model for flow in a channel we consider two parameters the knudsen number and the accommodation coefficient the reduced basis approximation is built upon and the reduced basis error is measured relative to a truth mapped weighted spectral discretization of a stabilized petrov galerkin weak formulation we exploit the affine nature of the parametric dependence to provide an offline online computational procedure that decouples the spectral and reduced basis quantities the computational complexity of the online stage in which given a new parameter value we evaluate the reduced basis flow rate prediction and associated error bound depends only on the typically very small dimension of the reduced basis space n and not on the typically very large dimension of the truth spectral approximation n we demonstrate that the reduced basis approximation converges very rapidly with n and that the error estimator effectivities remain bounded albeit somewhat large in the online stage the reduced basis approximation achieves a certifiable relative accuracy of 10 2 with respect to the truth spectral result at only 1 100th the computational effort the method is appropriate in the many query and real time e g parameter estimation contexts in which there is a premium on reduced marginal cost and a tolerance for significant offline pre processing effort

the role of non linear theories in transient dynamic analysis of flexible structures abstract transient dynamic analysis of flexible structures undergoing large motions is considered for rotating structures it is explicitly shown that appropriate account of the influence of centrifugal force on the bending stiffness requires the use of a geometrically non linear at least second order beam theory use of a first order linearized linear beam theory results in a spurious loss of bending stiffness for a rotating plane beam a set of linear partial differential equations of motion that includes all inertia effects coriolis centrifugal acceleration of revolution and coupling between extensional and flexural deformations is derived from the fully non linear beam theory by consistent linearization the analysis is subsequently extended to the more general case of a plate accomodating shear deformation and undergoing a general three dimensional rotating motion the discretization process of the resulting linear equations of motion for the beam and the plate is also discussed

slip velocity and knudsen layer in the lattice boltzmann method for microscale flows we present mesoscopic fluid wall interaction models for lattice boltzmann lb model simulations of microscale flows the exact solution of the slip velocity for the lb equation with the bhatnagar gross krook collision operator is obtained for poiseuille flow at finite knudsen numbers with a consistent definition of the knudsen number the slip coefficients of the lb equation with the standard d2q9 scheme are found to be slightly larger than those of the boltzmann equation with the same boundary condition which makes the standard lb method remain quantitatively accurate only for small knudsen numbers by modifying the nonequilibrium energy flux or introducing the effective relaxation time the lb method is analytically shown to reproduce the slip phenomena up to second order in the knudsen number for the standard lb method the knudsen layer is captured only with modification of the relaxation dynamics such as in the effective relaxation time model

computational algorithm for controlling a timoshenko beam abstract this paper is concerned with computational algorithms for lqr control of a timoshenko slewing beam problem the algorithm make use of a conforming finite element scheme that is shown to produce convergent control laws it is shown that the closed loop feedback can effectively control the vibrations due to an initial displacement it is also shown that when the system parameters are such that an euler bernoulli model is adequate to describe the dynamics of the beam the functional gains using the full timoshenko model are qualitatively similar to the ones using an euler bernoulli model