statistical hydrodynamics of lattice gas automata we investigate the space and time behavior of spontaneous thermohydrodynamic fluctuations in a simple fluid modeled by a lattice gas automaton and develop the statistical mechanical theory of thermal lattice gases to compute the dynamical structure factor i e the power spectrum of the density correlation function a comparative analysis of the theoretical predictions with our lattice gas simulations is presented the main results are i the spectral function of the lattice gas fluctuations is fully compatible with the spectrum obtained from experimental measurements performed in real fluids ii in the long wavelength limit the correlations of lattice gas fluctuations are well described by the landau placzek theory iii at short wavelengths and or at low densities good agreement is obtained between the lattice gas simulation results and the boltzmann theory these results provide solid support to the validity of the thermal lattice gas automaton as a consistent model system for real fluids

differential algebraic systems as differential equations on manifolds based on the theory of differential equations on manifolds existence and uniqueness results are proved for a class of mixed systems of differential and algebraic equations as they occur in various applications both the autonomous and nonautonomous case are considered moreover a class of algebraically incomplete systems is introduced for which existence and uniqueness results only hold on certain lower dimensional manifolds this class includes systems for which the application of ode solvers is known to lead to difficulties finally some solution approach based on continuation techniques is outlined

a geometric treatment of implicit differential algebraic equations abstract a differential geometric approach for proving the existence and uniqueness of implicit differential algebraic equations is presented it provides for a significant improvement of an earlier theory developed by the authors as well as for a completely intrinsic definition of the index of such problems the differential algebraic equation is transformed into an explicit ordinary differential equation by a reduction process that can be abstractly defined for specific submanifolds of tangent bundles here called reducible submanifolds local existence and uniqueness results for differential algebraic equations then follow directly from the final stage of this reduction by means of an application of the standard theory of ordinary differential equations

weak detectability and the linear quadratic control problem of discrete time markov jump linear systems the paper deals with the stochastic concepts of weak detectability and weak observability for markov jump linear systems which is an special class of composite linear systems the concepts are explored here to strengthen the similarities with the corresponding concepts of deterministic detectability and observability we introduce a collection of matrices referred to as the observability matrices we show that weak observability is equivalent to full rank of each matrix in the set of observability matrices in addition we present a stochastic counterpart of the well known result on the invariance of trajectories within non observable subspaces these characterizations allow us to clarify the relationship between weak detectability and mean square detectability and to provide a testable condition for weak detectability relying on the assumption of weak detectability we develop a method for solving the linear quadratic problem that is based on iterations of uncoupled algebraic riccati equations which

on the numerical solution of the euler lagrange equations the paper presents a new approach to the numerical solution of the euler lagrange equations based upon the reduction of the problem to a second order ordinary differential equation ode on the constraint manifold the algorithm guarantees that the constraints are automatically satisfied and requires a minimal number of evaluations of second order derivative terms in fact second order derivatives are involved only through the second fundamental tensor of the constraint manifold this tensor may be computed either explicitly when second derivatives are available or via an approximation procedure with excellent accuracy examples are given along with comparisons with state of the art software

a lattice boltzmann equation for diffusion the formulation of lattice gas automata lga for given partial differential equations is not straightforward and still requires some sort of magic lattice boltzmann equation lbe models are much more flexible than lga because of the freedom in choosing equilibrium distributions with free parameters which can be set after a multiscale expansion according to certain requirements here a lbe is presented for diffusion in an arbitrary number of dimensions the model is probably the simplest lbe which can be formulated it is shown that the resulting algorithm with relaxation parameter 1 is identical to an explicit finite difference efd formulation at its stability limit underrelaxation 0 1 allows stable integration beyond the stability limit of efd the time step of the explicit lbe integration is limited by accuracy and not by stability requirements

on the computation of multi dimensional solution manifolds of parametrized equations a new algorithm is presented for computing vertices of a simplicial triangulation of thep dimensional solution manifold of a parametrized equationf x 0 wheref is a nonlinear mapping fromr n tor m p n m 1 an essential part of the method is a constructive algorithm for computing moving frames on the manifold that is of orthonormal bases of the tangent spaces that vary smoothly with their points of contact the triangulation algorithm uses these bases together with a chord form of the gauss newton process as corrector to compute the desired vertices the jacobian matrix of the mapping is not required at all the vertices but only at the centers of certain local triangulation patches several numerical examples show that the method is very efficient in computing triangulations even around singularities such as limit points and bifurcation points this opens up new possibilities for determining the form and special features of such solution manifolds

on the computation of impasse points of quasi linear differential algebraic equations abstract we present computational algorithms for the calculation of impasse points and higher order singularities in quasilinear differential algebraic equations our method combines a reduction step transforming the dae into a singular ode with an augmentation procedure inspired by numerical bifurcation theory singularities are characterized by the vanishing of a scalar quantity that may be monitored along any trajectory two numerical examples with physical relevance are given

on a computational method for the second fundamental tensor and its application to bifurcation problems an algorithm is presented for the computation of the second fundamental tensorv of a riemannian submanifoldm ofr n fromv the riemann curvature tensor ofm is easily obtained moreover v has a close relation to the second derivative of certain functionals onm which in turn provides a powerful new tool for the computational determination of multiple bifurcation directions frequently in applications thed dimensional manifoldm is defined implicitly as the zero set of a submersionf onr n in this case the principal cost of the algorithm for computingv p at a given pointp m involves only the decomposition of the jacobiandf p off atp and the projection ofd d 1 neighboring points ontom by means of a local iterative process usingdf p several numerical examples are given which show the efficiency and dependability of the method

solving algebraically explicit daes with the manpak manifold algorithms abstract recently the author introduced a package of algorithms called manpak for effective computations on implicitly defined submanifolds of r n here algebraically explicit differential algebraic equations daes are considered that is daes in which either the algebraic equations and or the algebraic variables are explicitly specified existence proofs for several types of such daes of index one two and three are given which directly suggest computational approaches this is used in the development of solution algorithms for these daes all of them intrinsically based on the manpak routines some numerical examples for the methods are included

computing smooth solutions of daes for elastic multibody systems abstract multibody systems are considered which involve combinations of rigid and elastic bodies discretizations of the pdes describing the elastic members lead to a semidiscrete system of odes or daes asymptotic methods are introduced which provide a theoretical basis of various known engineering results for the ode case these results are then extended to the dae case by means of suitable local ode representations the recently developed manpak algorithms for computations on implicitly defined manifolds form the basic tools for a computational method which provides consistent approximate solutions of the semidiscrete dae that satisfy all constraints and are close to the smooth motion and an average solution several numerical examples indicate the effectiveness of this asymptotic method for elastic multibody systems

newton s method for concave operators with resolvent positive derivatives in ordered banach spaces abstract we prove a non local convergence result for newton s method applied to a class of nonlinear equations in ordered real banach spaces the key tools in our approach are special notions of concavity and the spectral theory of resolvent positive operators

lattice gas automata with self organization abstract self organization or dynamic phase transitions occur in computer simulations of a lattice gas model with strictly local collision dynamics conserving number of particles momentum and lattice symmetries the microscopic collision processes are biased i e they have asymmetric transition rates in this model a spatially uniform initial state is unstable at the onset of instability long wavelength sound modes drive the system into a state with very long range order with dynamics similar to spinodal decomposition the structure factor s k t and the selected wavelength for maximal growth max t are measured as a function of time the state with long range order is highly organized into moving stable spatial patterns of triangles or parallel strips of macroscopic size with two or one broken symmetry respectively the entropy suddenly drops at self organization both the onset of metastability and the detailed structure of the final patterns are explained by mean field theory

exact detectability and exact observability of discrete time linear stochastic systems with periodic coefficients abstract this paper is devoted to the problem of detectability and observability of a class of time varying stochastic systems the main contribution of this note is to propose a pbh type test which is equivalent to the detectability of the considered stochastic systems in the sense that all unstable modes produce some non zero output then we apply the obtained results in order to derive a criterion of exponential stability in mean square sense as well as existence conditions for the stabilizing solution of a class of discrete time time varying riccati equations

projected implicit runge kutta methods for differential algebraic equations in this paper a new class of numerical methods projected implicit runge kutta methods is introduced for the solution of index 2 hessenberg systems of initial and boundary value differential algebraic equations daes these types of systems arise in a variety of applications including the modeling of singular optimal control problems and parameter estimation for differential algebraic equations such as multibody systems the new methods appear to be particularly promising for the solution of dae boundary value problems where the need to maintain stability in the differential part of the system often necessitates the use of methods based on symmetric discretizations previously defined symmetric methods have severe limitations when applied to these problems including instability oscillation and loss of accuracy the new methods overcome these difficulties for linear problems we define an essential underlying boundary value ode and prove well conditioning of the differential or state space solutio

stress stress correlation functions in lattice gases beyond boltzmann s approximation the complete time dependence of the stress stress correlation functions in lattice gas cellular automata is calculated from the ring kinetic theory using numerical and analytical methods this provides corrections typically of 10 20 to the usual molecular chaos calculations where correlation functions decay exponentially the resulting correlation function crosses over from an initial exponential decay to the long time behavior calculated from mode coupling theory the present theory applied to the viscosity accounts for a substantial part of the observed difference between the boltzmann theory and simulations

phase transitions in a probabilistic cellular automaton growth kinetics and critical properties we investigate a discrete time kinetic model without detailed balance which simulates the phase segregation of a quenched binary alloy the model is a variation on the rothman keller cellular automaton in which particles of type a b move toward domains of greater concentration of a b modifications include a fully occupied lattice and the introduction of a temperature like parameter which endows the system with a stochastic evolution using computer simulations we examine domain growth kinetics in the two dimensional model for long times after a quench from disorder we find that the average domain sizer t t1 3 in agreement with the prediction of lifshitz slyozov wagner theory using a variety of methods we analyze the critical properties of the associated second order transition our analysis indicates that this model does not fall within either the ising or mean field classes

path planning for active tensegrity structures abstract this paper presents a path planning method for actuated tensegrity structures with quasi static motion the valid configurations for such structures lay on an equilibrium manifold which is implicitly defined by a set of kinematic and static constraints the exploration of this manifold is difficult with standard methods due to the lack of a global parameterization thus this paper proposes the use of techniques with roots in differential geometry to define an atlas i e a set of coordinated local parameterizations of the equilibrium manifold this atlas is exploited to define a rapidly exploring random tree which efficiently finds valid paths between configurations however these paths are typically long and jerky and therefore this paper also introduces a procedure to reduce their control effort a variety of test cases are presented to empirically evaluate the proposed method

manpak a set of algorithms for computations on implicitly defined manifolds abstract mathematical models often involve differentiable manifolds that are implicitly defined as the solution sets of systems of nonlinear equations the resulting computational tasks differ considerably from those arising for manifolds defined in parametric form here a collection of algorithms is presented for performing a range of essential tasks on general implicitly specified submanifolds of a finite dimensional space this includes algorithms for determining local parametrizations and their derivatives and for evaluating quantities related to the curvature with sensitivity measures the methods have been implemented as a fortran 77 package called manpak

implementation of the fchc lattice gas model on the connection machine the 4 dimensional fchc lattice gas model has been implemented on a connection machine cm 2 with 16k processors symmetries are used to reduce the collision table to a size that fits into local memory this method avoids the degradation of the reynolds coefficientr but at the price of increased computing time bit shuffling between parallel lattices is introduced to reduce the discrepancy between measured viscosities and those predicted from the boltzmann approximation thereby a model with a negative shear viscosity is obtained a fluid having a uniform initial velocity is unstable and organized nonuniform motions develop because of the buildup of very strong correlations between the parallel lattices the discrepancy with the boltzmann values decreases only very slowly with the number of parallel lattices

on stabilizability and exact observability of stochastic systems with their applications this paper mainly studies the stabilizability and exact observability of stochastic linear controlled systems and their applications with the aid of the operator spectrum a necessary and sufficient condition is given for the stabilizability of stochastic systems some new concepts such as unremovable spectrum and strong solution are introduced an unremovable spectral theorem and a stochastic popov belevith hautus criterion for exact observability are presented as applications a comparison theorem for stochastic algebraic riccati equations and a result on lyapunov type equations are obtained

staggered diffusivities in lattice gas cellular automata the majority of lgcas has spurious conservation laws the so called staggered invariants first discovered by kadanoff mcnamara and zanetti consequently there are additional hydrodynamic modes of diffusive type which modify mode coupling theories and the nonlinear fluid dynamic equations the diffusivities of these staggered modes are evaluated in the mean field approximation for lgcas on triangular lattices starting from the green kubo formulas for the staggered diffusivities

generalized lyapunov equation approach to state dependent stochastic stabilization detectability criterion in this paper the generalized lyapunov equation approach is used to study stochastic stabilization detectability with state multiplicative noise some practical test criteria for stochastic stabilization and detectability such as stochastic popov belevitch hautus criterion for exact detectability are obtained moreover useful properties of the generalized lyapunov equation are derived based on critical stability and exact detectability introduced in this paper as applications first the stochastic linear quadratic regulator as well as the related generalized algebraic riccati equation are discussed extensively second the infinite horizon stochastic h 2 h infin control with state and control dependent noise is also investigated which extends and improves the recently published results

on impasse points of quasilinear differential algebraic equations abstract this paper presents a mathematical characterization of the impasse points of quasilinear dae s a x g x where then a x is a nxn matrix having constant but not full r n in the domain of interest we show that a reduction procedure permits to reduce the dae to a quasilinear ode al xi xi g1 xi rr and that impasse points correspond to special singularities of the reduced ode impasse points of higher index dae s can also be defined the only difference is that the above reduction procedure takes more than one step

hydrodynamics and time correlation functions for cellular automata hydrodynamic excitations in lattice gas cellular automata are described in terms of equilibrium time correlation functions for the local conserved variables for large space and time scales the linearized hydrodynamic equations are obtained to navier stokes order exact expressions for the associated susceptibilities and transport coefficients are identified in terms of correlation functions the general form of the time correlation functions for conserved densities in the hydrodynamic limit is given and illustrated by some examples suitable for comparison with computer simulation the transport coefficients are related to time correlation functions for the conserved fluxes in a way analogous to the green kubo expressions for continuous fluids the general results are applied for a one component fluid and several types of binary diffusion also discussed are the effects of unphysical slow modes such as staggered particle or momentum densities

propagating staggered waves in cellular automata fluids the majority of lattice gases have apart from the physical conserved quantities of particle number momentum and energy spurious ones usually staggered in space and time at the level of linear excitations these staggered modes may be purely diffusive or damped propagating waves in the eight and nine bit model on the square lattice one finds a large number of new spurious modes and the authors derive green kubo relations for the diffusivities and damping constants and calculate them in the boltzmann approximation

on the sensitivity of solutions of parameterized equations the sensitivity of a solution of a parameterized equation f z lambda 0 with respect to the parameter vector lambda is usually defined as the change of the state z in dependence of lambda in other words for any solution expressible in the form z lambda lambda with some smooth function z z lambda the sensitivity is the derivative dz lambda typically the solutions form a manifold m in the product of 1the state space and the parameter space and this sensitivity is available only at those points of m where the parameters can be used to define a local coordinate system this paper introduces a general sensitivity concept which applies at all solutions on m and which includes the earlier definition some general geometric interpretations of the new measure are presented and it is shown that the sensitivity analysis can be easily integrated into the solution process the theory also suggests the introduction of a readily computable second order sensitivity measure reflectin

detectability observability and lyapunov type theorems of linear discrete time varying stochastic systems with multiplicative noise abstractthe objective of this paper is to study detectability observability and related lyapunov type theorems of linear discrete time time varying stochastic systems with multiplicative noise some new concepts such as uniform detectability k exact detectability resp kwft exact detectability kft exact detectability kn exact detectability and k exact observability resp kwft exact detectability kft exact detectability kn exact detectability are introduced respectively and nice properties associated with uniform detectability exact detectability and exact observability are also obtained moreover some lyapunov type theorems associated with generalised lyapunov equations and exponential stability in mean square sense are presented under uniform detectability kn exact observability and kn exact detectability respectively

an algorithm to compute a sparse basis of the null space leta be a realm n matrix with full row rankm in many algorithms in engineering and science such as the force method in structural analysis the dual variable method for the navier stokes equations or more generally null space methods in quadratic programming it is necessary to compute a basis matrixb for the null space ofa hereb isn r r n m of rankr withab 0 in many instancesa is large and sparse and often banded the purpose of this paper is to describe and test a variation of a method originally suggested by topcu and called the turnback algorithm for computing a banded basis matrixb two implementations of the algorithm are given one using gaussian elimination and the other using orthogonal factorization by givens rotations the fortran software was executed on an ibm 3081 computer with an fps 164 attached array processor at the triangle universities computing center and on a cyber 205 vector computer test results on a variety of structural analysis problems including two and three dimensional frames plane stress plate bending and mixed finite element problems are discussed these results indicate that both implementations of the algorithm yielded a well conditioned banded basis matrixb whena is well conditioned however the orthogonal implementation yielded a better conditionedb for large illconditioned problems

a decreasing sequence of upper bounds for the perron root abstract we obtain a decreasing sequence of upper bounds for the perron root of a nonnegative matrix these upper bounds are new and readily computable for any nonnegative matrix with zero trace the mentioned sequence converges to the perron root we apply these results to the adjacency matrix of a graph

relaxation and transport in fchc lattice gases fchc lattice gases are the basic models for studying flow problems in three dimensional systems this paper presents a self contained theoretical analysis and some computer simulations of such lattice gases extended to include an arbitrary number of rest particles with special emphasis on non semi detailed balance nsdb models the special fchc lattice symmetry guarantees isotropy of the navier stokes equations and enumerates the 12 spurious conservation laws staggered momenta the kinetic theory is based on the mean field approximation or the nonlinear boltzmann equation it is shown how calculation of the eigenvalues of the linearized boltzmann equation offers a simple alternative to the chapman enskog method or the multi time scale methods for calculating transport coefficients and relaxation rates the simulated values for the speed of sound in nsdb models slightly disagree with the boltzmann prediction

on unified concepts of detectability and observability for continuous time stochastic systems this paper is concerned with detectability and observability of continuous time stochastic linear systems by adopting the idea used in defining these two concepts for time varying systems and markovian jump linear systems that have been studied in the literature corresponding definitions for continuous time stochastic linear systems are proposed these two definitions are not only able to unify some recent definitions on these two concept reported in the literature but also allow us to propose an efficient rank criterion to test observability of continuous time stochastic linear systems it seems that this rank criterion is quite analogous to the rank criterion for deterministic linear systems with the help of these two concepts and the new criteria the stochastic lyapunov equation is revisited and some recent published work on this equation are generalized numerical examples are given to illustrate the effectiveness of the proposed approach

brief paper on detectability of stochastic systems we discuss notions of detectability for stochastic linear control systems of ito type a natural concept of detectability requires a non zero output if the state process is unstable we show that this property can equivalently be characterized by a generalized version of the hautus test the proof is based on spectral theory for positive operators

solving more general index 2 differential algebraic equations abstract the paper deals with a class of quasilinear index 2 differential algebraic equations which covers both linear variable coefficient systems as well as hessenberg form equations supposing low smoothness only the solvability of initial value problems is stated via classical analytical techniques for that class of differential algebraic equations backward differentiation formulas and runge kutta methods as well as projected versions are discussed with respect to feasibility in stability convergence and asymptotical behaviour

biased lattice gases with correlated equilibrium states the approach to and structure of the equilibrium state is studied for a 7 bit lattice gas with biased forward and backward transition rates by means of mean field theory and computer simulations if the rate constants obey the factorizability and the detailed balance conditions the occupations of different velocity directions are uncorrelated anh theorem is valid and a nonuniversal equilibrium state exists that depends explicitly on the transition rates in case the above conditions are not satisfied theh theorem is no longer valid and mean field theory also predicts nontrivial velocity correlations in postcollision states the simulations are mainly concentrated on the time dependence of pre and postcollision velocity correlations on a single node and on slowly increasing fluctuations that might indicate metastable behavior

low viscosity lattice gases a class of lattice gas models are studied which are variants of the fchc model the aim is to achieve the highest possible reynolds coefficient inverse dimensionless viscosity for efficient simulations of the three dimensional incompressible navier stokes equations the models include an arbitrary number of rest particles and violation of semi detailed balance within the framework of the boltzmann approximation exact expressions are obtained for the reynolds coefficients the minimization of the viscosity is done by solving a hitchcock type optimization problem for the fine tuning of the collision rules when the number of rest particles exceeds one there is a range of densities at which the viscosity takes negative values various optimal models with up to 26 bits per node have been implemented on a cray 2 and their true transport coefficients have been measured with good accuracy fairly large discrepancies with boltzmann values are observed when semi detailed balance is violated in particular no negative viscosity is obtained still the best model has a reynolds coefficient of 13 5 twice that of the best previously implemented model and thus is about 16 times more efficient computationally suggestions are made for further improvements it is proposed to use models with very high reynolds coefficients for sub grid scale modeling of turbulent flows

on the detectability and observability of discrete time markov jump linear systems abstract this paper presents a new detectability concept for discrete time markov jump linear systems with finite markov state which generalizes the ms detectability concept found in the literature the new sense of detectability can similarly assure that the solution of the coupled algebraic riccati equation associated to the quadratic control problem is a stabilizing solution in addition the paper introduces a related observability concept that also generalizes previous concepts a test for detectability based on a coupled matrix equation is derived from the definition and a test for observability is presented which can be performed in a finite number of steps the results are illustrated by examples including one that shows that a system may be detectable in the new sense but not in the ms sense

the computation of simplicial approximations of implicitly defined p dimensional manifolds abstract a method is presented for the computation of a simplicial approximation covering a subset m 0 of a p dimensional manifold m in r n defined implicitly as the solution set of a nonlinear system f x 0 of n p equations in n unknowns n p 2 the subset m 0 is either the intersection of m with some polyhedral domain in r n and is assumed to be bounded and nonempty or it is an entire manifold component which has no boundary such as a sphere the method represents a generalization of a simplicial approximation process for the case p 2 developed earlier by the author and w rheinboldt

real time integration methods for mechanical system simulation this study focuses on the mechanical system dynamics applications of differential algebraic equations dae selected papers develop the foundations of dae as they appear in mechanical system dynamics applications and explore the foundations of contemporary methods for the numerical solution of dae in mechanical system dynamics many theoretical methods and methods of generalized co ordinate partitioning for the numerical integration of dae are examined the text has been designed to encompass a broad range of applications in engineering and applied physics

brief paper detectability and observability of discrete time stochastic systems and their applications this paper studies detectability and observability of discrete time stochastic linear systems based on the standard notions of detectability and observability for time varying linear systems corresponding definitions for discrete time stochastic systems are proposed which unify some recently reported detectability and exact observability concepts for stochastic linear systems the notion of observability leads to the stochastic version of the well known rank criterion for observability of deterministic linear systems by using these two concepts the discrete time stochastic lyapunov equation and riccati equations are studied the results not only extend some of the existing results on these two types of equation but also indicate that the notions of detectability and observability studied in this paper take analogous functions as the usual concepts of detectability and observability in deterministic linear systems it is expected that the results presented may play important roles in many design problems in stochastic linear systems