on the structural stability of the euler voigt and navier stokes voigt models abstract we consider the euler voigt equations and the navier stokes voigt equations which are obtained by an inviscid regularization from the corresponding equations the main result we show is the structural stability of the system in terms of the variations of both viscosity and regularization parameters

fake projective planes a fake projective plane is a complex surface different from but has the same betti numbers as the complex projective plane it is a complex hyperbolic space form and has the smallest euler poincare characteristic among smooth surfaces of general type the first example was constructed by mumford later on two more examples were found by ishida and kato a fourth possible one was recently proposed by keum in a recent joint work with gopal prasad we showed that there are seventeen non empty classes of fake projective planes and there can at most be four more specific classes higher dimensional analogues and examples were also obtained the main purpose of the talk is to explain the joint work with prasad and other related results such as arithmeticity of the lattices involved obtained earlier by klingler and yeung independently

conformally flat metrics on 4 manifolds we prove that for each closed smooth spin 4 manifold m there exists a closed smooth 4 manifold n such that m n admits a conformally flat riemannian metric

bisimulation relations for dynamical control and hybrid systems the fundamental notion of bisimulation equivalence for concurrent processes has escaped the world of continuous and subsequently hybrid systems inspired by the categorical framework of joyal nielsen and winskel we develop novel notions of bisimulation equivalence for dynamical systems as well as control systems we prove that these notions can be captured by the abstract notion of bisimulation as developed by joyal nielsen and winskel this is the first unified notion of system equivalence that transcends discrete and continuous systems furthermore this enables the development of a novel and natural notion of bisimulation for hybrid systems which is the final goal of this paper

variational bounds on energy dissipation in incompressible flows ii channel flow a variational principle for lower bounds on the time averaged mass flux for newtonian fluids driven by a pressure gradient in a channel is derived from the incompressible navier stokes equations when supplied with appropriate test background flow fields the variational formulation produces explicit estimates for the friction coefficient these rigorous bounds are compared with the predictions of conventional turbulence theory

on crank nicolson adams bashforth timestepping for approximate deconvolution models in two dimensions we consider a crank nicolson adams bashforth temporal discretization together with a finite element spatial discretization for efficiently computing solutions to approximate deconvolution models of incompressible flow in two dimensions we prove a restriction on the timestep that will guarantee stability and provide several numerical experiments that show the proposed method is very effective at finding accurate coarse mesh approximations for benchmark flow problems

the dual complex of calabi yau pairs a log calabi yau pair consists of a proper variety x and a divisor d on it such that k x d is numerically trivial a folklore conjecture predicts that the dual complex of d is homeomorphic to the quotient of a sphere by a finite group the main result of the paper shows that the fundamental group of the dual complex of d is a quotient of the fundamental group of the smooth locus of x hence its pro finite completion is finite this leads to a positive answer in dimension le 4 we also study the dual complex of degenerations of calabi yau varieties the key technical result we prove is that after a volume preserving birational equivalence the transform of d supports an ample divisor

on the existence of global attractors of the approximate deconvolution models of turbulence abstract in this report we consider the problem of the existence of global attractors of the weak solution of the approximate deconvolution models of turbulence the l 2 global attractors are known to exist for large eddy simulation models such as leray alpha leray deconvolution or ns omega models in the case of the approximate deconvolution model as the l 2 norm of the weak solution of the adm is not controlled by the l 2 norm of the initial data and the approximate deconvolution model is an approximation of the filtered nse we are led to the question of existence of h 1 global attractors we also prove better regularity of the weak solution of adm

on the application of congruent upwind discretizations for large eddy simulations upwind schemes were judged inappropriate for performing accurate large eddy simulations of turbulent flow owing to the artificial dissipation that is present at high wavenumbers of the energy content such a conclusion has been drawn also from some results obtained by adopting finite difference schemes the present paper illustrates the performances of some new finite volume upwind discretization of the convective terms in the case of the 1 d burgers model equation while studying the effects of numerical discretization on several sub grid scales turbulence models starting from the classical static and dynamic eddy viscosity models through the recent deconvolution based ones basing on previously published papers large eddy simulations along with a deconvolution based procedure for de filtering the evolving variable have been originally developed and applied it will be shown how the coherent application of the procedure allows us to develop high order accurate finite volume upwind schemes which maintain a good spectral resolution in the entire range of resolved scale such schemes can be candidate for performing accurate simulations of real turbulence

bounds on dissipation for navier strokes flow with kologorov forcing abstract in this paper bounds on average viscous dissipation are derived for kolmogorov flow in a spatially periodic domain with steady and unsteady forcing at arbitrarily large grashof number g for a force of the form f 0 sin mz i or f 0 sin mz cos t i we derive various bounds on the total dissipation in the flow d u as well as on the dissipation d m obtained from the x velocity averaged over the x y plane the mean velocity of the flow we derive upper bounds on d u and d v d u d m as well as lower bounds on d m and d m d u adopting constraints of the kind introduced by howard and busse and assuming a steady force the background flow method introduced by doering and constantin is used to obtain an improved lower bound on d m d u of o g 1 and a lower bound on d u of o g 1 2 where g f0l3 2 is the grashof number some of these results are then generalized to time periodic forcing direct numerical simulation of the flow indicates that these bounds leave substantial gaps at large grashof number g the calculated d m g and d u g being o g 1 2 and o 1 respectively as g our theoretical bounds on d m d u are shown to be attained by steady laminar type flows for neighboring forcing functions which seems to indicate that these bounds cannot be improved by adding further dynamical constraints however our elementary upper bound on d v can probably be improved by placing more constraints on the flows these results serve to emphasize the difference between boundary driven turbulence and body force driven turbulence where the appropriate dissipation bound is believed saturated at least up to logarithms

bisimulation indexes and their applications bisimulation expresses the equivalence of processes whose external actions are identical sometimes we may meet two processes which are not exactly bisimilar but more or less bisimilar in the sense that whenever a process makes an action the other can make an action different from but very similar to the action performed by the first one to describe this kind of looser bisimulations we propose the concept of bisimulation index in a labelled transition system and give its various properties especially those properties related to the operations of transition systems furthermore we establish a modal logical characterization of bisimulation indexes this characterization is a generalization of hennessy milner logic we study strong and weak bisimulation indexes in the basic asynchronous process calculus and some of their fundamental properties are derived bisimulation indexes are not substitutive under composition to overcome this defect we introduce an approximate communication rule to replace the original rule in process calculus this enables us to recover some useful properties of composition with respect to bisimulation indexes finally we present three examples in timed ccs and real time acp to demonstrate the usage of bisimulation indexes in the analysis of real time systems these examples show that bisimulation indexes are suitable formal tools for describing approximate implementations of real time systems

reply to comments on bisimilarity control of partially observed nondeterministic discrete event systems and a test algorithm automatica 43 2007 1363 1368

on the accuracy of the finite element method plus time relaxation if u denotes a local spatial average of u then u u u is the associated fluctuation consider a time relaxation term added to the usual finite element method the simplest case for the model advection equation u t a u x t is u h t a u h v h u h v h f x t v h we analyze the error in this and more importantly higher order extensions and show that the added time relaxation term not only suppresses excess energy in marginally resolved scales but also increases the accuracy of the resulting finite element approximation

the regularized chapman enskog expansion for scalar conservation laws rosenao r has recently proposed a regularized version of the chapmanenskog expansion of hydrodynamics this regularized expansion resembles the usual navier stokes viscosity terms at low wave numbers but unlike the latter it has the advantage of being a bounded macroscopic approximation to the linearized collision operator in this paper we study the behavior of the rosenau regularization of the chapman enskog expansion r c e in the context of scalar conservation laws we show that this r c e model retains the essential properties of the usual viscosity approximation e g existence of travelling waves monotonicity upper lipschitz continuity etc and at the same time it sharpens the standard viscous shock layers we prove that the regularized r c e approximation converges to the underlying inviscid entropy solution as its mean free path e 0 and we estimate the convergence rate

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

chebychev optimized approximate deconvolution models of turbulence abstract if the navier stokes equations are averaged with a local spacial convolution type filter g the resulting system is not closed due to the filtered nonlinear term uu an approximate deconvolution operator d is a bounded linear operator which satisfies u d u o where is the filter width and 2 using a deconvolution operator as an approximate filter inverse yields the closure uu d u d u o the residual stress of this model and related models depends directly on the deconvolution error u d u this report derives deconvolution operators yielding an effective turbulence model which minimize the deconvolution error for velocity fields with finite kinetic energy we also give a convergence theory of deconvolution as 0 an ergodic theorem as the deconvolution order n and estimate the increase in accuracy obtained by parameter optimization the report concludes with numerical illustrations

grothendieck s problems concerning profinite completions and representations of groups in 1970 alexander grothendieck 6 posed the following problem let 1 and 2 be finitely presented residually finite groups and let u 1 2 be a homomorphism such that the induced map of profinite completions u 1 2 is an isomorphism does it follow that u is an isomorphism in this paper we settle this problem by exhibiting pairs of groups u p such that is a direct product of two residually finite hyperbolic groups p is a finitely presented subgroup of infinite index p is not

efficient unconditionally stable and optimally accurate fe algorithms for approximate deconvolution models this paper addresses an open question of how to devise numerical schemes for approximate deconvolution fluid flow models that are efficient unconditionally stable and optimally accurate we propose analyze and test a scheme for these models that has each of these properties for the case of homogeneous dirichlet velocity boundary conditions there are several important components of the derivation both at the continuous and discrete levels which allow for these properties to hold the proofs of stability and convergence are carried out through the use of a special choice of test function and some technical estimates numerical tests are provided that confirm the effectiveness of the scheme

stabilized approximation to degenerate transport equations via filtering abstract we analyze a stabilization technique for degenerate transport equations of particular interest are coupled parabolic hyperbolic problems when the diffusion coefficient is zero in part of the domain the unstabilized computed approximations of these problems are highly oscillatory and several techniques have been proposed and analyzed to mitigate the effects of the sub grid errors that contribute to the oscillatory behavior in this paper we modify a time relaxation algorithm proposed in 1 and further studied in 10 our modification introduces the relaxation operator as a post processing step the operator is not time dependent so the discrete relaxation system need only be factored once we provide convergence analysis for our algorithm along with numerical results for several model problems

l infinity pairs and applications to singularities abstract over a field of characteristic zero every deformation problem with cohomology constraints is controlled by a pair consisting of a differential graded lie algebra together with a module unfortunately these pairs are usually infinite dimensional we show that every deformation problem with cohomology constraints is controlled by a typically finite dimensional l pair as a first application we show that for complex algebraic varieties with no weight zero 1 cohomology classes the components of the cohomology jump loci of rank one local systems containing the constant sheaf are tori this imposes restrictions on the fundamental groups the same holds for links and milnor fibers

truncation of scales by time relaxation abstract we study a time relaxation regularization of flow problems proposed and tested extensively by stolz and adams the aim of the relaxation term is to drive the unresolved fluctuations in a computational simulation to zero exponentially fast by an appropriate and often problem dependent choice of its coefficient this relaxation term is thus intermediate between a tunable numerical stabilization and a continuum modeling term our aim herein is to understand how this term by itself acts to truncate solution scales and to use this understanding to give insight into parameter selection

computations of slowly moving shocks computations of slowly moving shocks by shock capturing schemes may generate oscillations that appear as a wavy tail attached to the shock front these oscillations are generated already by first order schemes but become more pronounced in higher order schemes due to their lower dissipation we focus on two first order schemes which seem to exhibit different behaviors i the first order upwind uw scheme which generates strong oscillations and ii the lax friedrichs scheme which appears not to generate any disturbances at all a key observation is that in the uw case the numerical viscosity in the shock family vanishes inside the slow shock layer simple scaling arguments show that third order effects on the solution may no longer be neglected we derive the third order modified equation for the uw scheme and regard the oscillatory solution as a traveling wave solution of the parabolic modified equation plus a small perturbation we then look at the governing equation for the perturbation which points to a plausible mechanism by which postshock oscillations are generated it contains a third order source term that becomes significant inside the shock layer and a nonlinear coupling term which projects the perturbation on all characteristic fields including those not associated with the shock family

a regularization of the burgers equation using a filtered convective velocity this paper examines the properties of a regularization of the burgers equation in one and multiple dimensions using a filtered convective velocity which we have dubbed as the convectively filtered burgers cfb equation a physical motivation behind the filtering technique is presented an existence and uniqueness theorem for multiple dimensions and a general class of filters is proven multiple invariants of motion are found for the cfb equation which are shown to be shared with the viscous and inviscid burgers equations traveling wave solutions are found for a general class of filters and are shown to converge to weak solutions of the inviscid burgers equation with the correct wave speed numerical simulations are conducted in 1d and 2d cases where the shock behavior shock thickness and kinetic energy decay are examined energy spectra are also examined and are shown to be related to the smoothness of the solutions this approach is presented with the hope of being extended to shock regularization of compressible euler equations

legendre pseudospectral viscosity method for nonlinear conservation laws in this paper the legendre spectral viscosity sv method for the approximate solution of initial boundary value problems associated with nonlinear conservation laws is studied the authors prove that by adding a small amount of sv bounded solutions of the legendre sv method converge to the exact scalar entropy solution the convergence proof is based on compensated compactness arguments and therefore applies to certain 2 times 2 systems finally numerical experiments for scalar as well as the one dimensional system of gas dynamics equations are presented which confirm the convergence of the legendre sv method moreover these numerical experiments indicate that by post processing the sv approximation one can recover the entropy solution within spectral accuracy

a stabilized semi implicit galerkin scheme for navier stokes equations by introducing a time relaxation term for the time derivative of higher frequency components we proposed a stabilized semi implicit galerkin scheme for evolutionary navier stokes equations in this paper analysis shows that such a scheme has weaker stability conditions than that of a classical semi implicit galerkin scheme and when a suitable relaxation parameter s is chosen it generates an approximate solution with the same accuracy as the classical one that means the proposed scheme might use a larger time step to generate a bounded approximate solution thus it is more suitable for long time simulations

variational bounds on shear driven turbulence and turbulent boussinesq convection abstract based on earlier studies by hopf 1941 doering and constantin 1992 1994 1995 have recently formulated a new background technique for obtaining upper bounds on turbulent fluid flow quantities this method produces upper bounds on the limit supremum of long time averages making no statistical assumptions about the flow in contrast to the well known howard busse approach the full optimisation problems posed by this method for the momentum transport in turbulent couette flow and the heat transport with zero background flow in turbulent boussinesq convection are solved here for the first time at asymptotically large reynolds number and rayleigh number within busse s multiple boundary layer approximation to extract the best lowest possible upper bounds available intriguingly the original bounds isolated by busse 1969 1970 within the confines of statistical stationarity are recovered exactly using this new formalism the optimal background velocity profile for turbulent couette flow is found to be shearless in the interior thus differing from busse s 1 4 mean shear result in the convective case an interesting degeneracy in the formulation of the background variational problem leads to an indeterminacy in the optimal background temperature profile only for one special choice is the isothermal core feature of busse s mean profile recovered

a spectral vanishing viscosity method for large eddy simulations a new simulation approach for high reynolds number turbulent flows is developed combining concepts of monotonicity in nonlinear conservation laws with concepts of large eddy simulation the spectral vanishing viscosity svv first introduced by e tadmor siam j numer anal 26 30 1989 is incorporated into the navier stokes equations for controlling high wavenumber oscillations unlike hyperviscosity kernels the svv approach involves a second order operator which can be readily implemented in standard finite element codes in the work presented here discretization is performed using hierarchical spectral hp methods accommodating effectively an ab initio intrinsic scale separation the key result is that monotonicity is enforced via svv leading to stable discretizations without sacrificing the formal accuracy i e exponential convergence in the proposed discretization several examples are presented to demonstrate the effectiveness of the new approach including a comparison with eddy viscosity spectral les of turbulent channel flow in its current implementation the svv approach for controlling the small scales is decoupled from the large scales but a procedure is proposed that will provide coupling similar to the classical les formulation

numerical analysis of filter based stabilization for evolution equations we consider filter based stabilization for evolution equations in general and for the navier stokes equations in particular the first method we consider is to advance in time one time step by a given method and then to apply an uncoupled and modular filter to get the approximation at the new time level this filter based stabilization although algorithmically appealing is viewed in the literature as introducing far too much numerical dissipation to achieve a quality approximate solution we show that this is indeed the case we then consider a modification evolve one time step filter deconvolve then relax to get the approximation at the new time step we give a precise analysis of the numerical diffusion and error in this process and show it has great promise confirmed in several numerical experiments

fundamental groups of links of isolated singularities 2014 american mathematical society all rights reserved we study fundamental groups of projective varieties with normal crossing singularities and of germs of complex singularities we prove that for every finitely presented group g there is a complex projective surface s with simple normal crossing singularities only so that the fundamental group of s is isomorphic to g we use this to construct 3 dimensional isolated complex singularities so that the fundamental group of the link is isomorphic to g lastly we prove that a finitely presented group g is q superperfect has vanishing rational homology in dimensions 1 and 2 if and only g if is isomorphic to the fundamental group of the link of a rational 6 dimensional complex singularity

bisimulation and cocongruence for probabilistic systems we introduce a new notion of bisimulation called event bisimulation on labelled markov processes and compare it with the now standard notion of probabilistic bisimulation originally due to larsen and skou event bisimulation uses a sub algebra as the basic carrier of information rather than an equivalence relation the resulting notion is thus based on measurable subsets rather than on points hence the name event bisimulation applies smoothly for general measure spaces bisimulation on the other hand is known only to work satisfactorily for analytic spaces we prove the logical characterization theorem for event bisimulation without having to invoke any of the subtle aspects of analytic spaces that feature prominently in the corresponding proof for ordinary bisimulation these complexities only arise when we show that on analytic spaces the two concepts coincide we show that the concept of event bisimulation arises naturally from taking the cocongruence point of view for probabilistic systems we show that the theory can be given a pleasing categorical treatment in line with general coalgebraic principles as an easy application of these ideas we develop a notion of almost sure bisimulation the theory comes almost for free once we modify giry s monad appropriately

large eddy simulation of shock turbulence interaction the approximate deconvolution model adm for large eddy simulation les is adapted for use with a central fourth order finite volume jameson type scheme widely applied for aerodynamics calculations of industrial interest with adm an approximation of the unfiltered solution is obtained by repeated filtering and given a good approximation of the unfiltered solution the nonlinear terms of the filtered navier stokes equation are computed directly the effect of scales not represented on the numerical grid is modeled by a relaxation regularization involving a secondary filter operation and a relaxation parameter the supersonic turbulent boundary layer along a compression ramp at a freestream mach number of m 3 and a reynolds number based on free stream quantities and the mean momentum thickness at inflow of re 1685 is computed to evaluate the ability of adm to represent discontinuities and turbulent flow regions it was observed that a unified modeling of discontinuities and turbulence required a local adaptation of the secondary filter used for the relaxation regularization the les results are compared with corresponding filtered direct numerical simulation dns data very good agreement between the filtered dns and the les is observed for the mean fluctuating and averaged wall quantities

complexes of groups complexes of groups are higher dimensional analogues of graphs of groups triangles of groups are a special class of 2 complexes of groups results of bass serre and gersten stallings are generalized to complexes of groups

decentralized diagnosis of stochastic discrete event systems we investigate the decentralized diagnosis of stochastic discrete event systems sdess by using multiple local stochastic diagnosers each possessing its own sensors to deal with different information we formalize the notions of decentralized diagnosis for sdess by defining the concept of codiagnosability for stochastic automata in which any communication among the local stochastic diagnosers or to any coordinators is not involved these notions are weaker than the corresponding notions of decentralized diagnosis of classical dess a stochastic system being codiagnosable means that a fault can be detected by at least one local stochastic diagnoser within a finite delay we construct a codiagnoser from a given stochastic system with a finite number of projections whose each diagnosis component uses the complete model of the system we also deal with a number of basic properties of the codiagnoser in particular a necessary and sufficient condition of the codiagnosability for sdess is presented which generalizes the corresponding results of centralized diagnosis for sdess also we give a computing method in detail to check the codiagnosability of sdess as an application of our results some examples are described

topology and geometry of cohomology jump loci we elucidate the key role played by formality in the theory of characteristic and resonance varieties we define relative characteristic and resonance varieties v k and r k related to twisted group cohomology with coefficients of arbitrary rank we show that the germs at the origin of v k and r k are analytically isomorphic if the group is 1 formal in particular the tangent cone to v k at 1 equals r k these new obstructions to 1 formality lead to a striking rationality property of the usual resonance varieties a detailed analysis of the irreducible components of the tangent cone at 1 to the first characteristic variety yields powerful obstructions to realizing a finitely presented group as the fundamental group of a smooth complex quasi projective algebraic variety this sheds new light on a classical problem of j p serre applications to arrangements configuration spaces coproducts of groups and artin groups are given

dirichlet fundamental domains and topology of projective varieties we prove that for every finitely presented group g there exists a 2 dimensional irreducible complex projective variety w with the fundamental group g so that all singularities of w are normal crossings and whitney umbrellas

comment on bisimilarity control of partially observed nondeterministic discrete event systems and a test algorithm automatica 47 2011 782 788 an article on bisimilarity enforcing supervisory control of discrete event systems was published recently in 2011 issue 4 volume 47 pages 782 788 of automatica the article introduced a certain definition of composition of plant and supervisor to define a controlled system so as to come up with an existence condition of bisimilarity enforcing control such definition changes the semantics of event based control to transition based control selectively disabling nondeterministic transitions any results reported in the paper thus raise question about value and applicability

kolmogorov theory via finite time averages abstract several relations from the kolmogorov theory of fully developed three dimensional turbulence are rigorously established for finite time averages over leray hopf weak solutions of the navier stokes equations the navier stokes equations are considered with periodic boundary conditions and an external forcing term the main parameter is the grashof number associated with the forcing term the relations rigorously proved in this article include estimates for the energy dissipation rate the kolmogorov wavenumber the taylor wavenumber the reynolds number and the energy cascade process for some estimates the averaging time depends on the macroscale wavenumber and the kinematic viscosity alone while for others such as the kolmogorov energy dissipation law and the energy cascade the estimates depend also on the grashof number as compared with earlier works by some of the authors the more physical concept of finite time average is replacing the concept of infinite time average used before

temporally regularized direct numerical simulation abstract experience with fluid flow simulation suggests that in some instances under resolved direct numerical simulation dns without a residual stress model per se but with artificial damping of small scales to account for energy lost in the cascade from resolved to unresolved scales may be as reliable as simulations based on more complex models of turbulence one efficient and versatile manner to selectively damp under resolved spatial scales is by a relaxation regularization e g stolz and adams s stolz n a adams an approximate deconvolution procedure for large eddy simulation phys fluids ii 1999 1699 1701 we consider the analogous approach based on time scales time filtering and damping of under resolved temporal features the paper explores theoretical and practical aspects of temporally damped fluid flow simulations we prove existence of solutions to the resulting continuum model we also establish the effect of the damping of under resolved temporal features as the energy balance and dissipation and prove that the time fluctuations 0 in a precise sense the method is then demonstrated to obtain both steady state and time dependent coarse grid solutions of the navier stokes equations

the behavior of flux difference splitting schemes near slowly moving shock waves abstract an investigation of the behavior of shock capturing schemes which compute the numerical flux from a solution of riemann s problem is performed the schemes of godunov roe and osher are examined for a one dimensional model problem consisting of a nearly stationary shock both scalar and systems of equations are examined it is found that for slow shocks there is a significant error generated when solving systems of equations while the scalar results are well behaved this error consists of a long wavelength noise in the downstream running wave families that is not effectively damped by the dissipation of the scheme the source of this error is shown and the implications for the performance of these schemes are considered this error may contribute to the slow convergence to steady state reported by many researchers

improved variational principle for bounds on energy dissipation in turbulent shear flow we extend the doering constantin approach to upper bounds on energy dissipation in turbulent flows by introducing a balance parameter into the variational principle this parameter governs the relative weight of different contributions to the dissipation rate its optimization leads to improved bounds without entailing additional technical difficulties for plane couette flow the high re bounds obtainable with one dimensional background flows are methodically lowered by a factor of 2732

safe diagnosability of stochastic discrete event systems recently safe diagnosability of discrete event systems dess was investigated by paoli and lafortune which was viewed as the first necessary step of fault tolerant supervision in this paper we consider the problem of safe diagnosability in the framework of stochastic discrete event systems sdess we define the notion of safe diagnosability for stochastic automata in which fault detection occurs before any given forbidden string in the failed mode of system is executed the relationship between diagnosability and safe diagnosability for sdess is analyzed in particular a necessary and sufficient condition for safe diagnosability of sdess is presented by constructing the recognizer of illegal language and the safe diagnoser some examples are described to illustrate the results

numerical analysis and computational comparisons of the ns alpha and ns omega regularizations we study stability accuracy and efficiency of algorithms for a new regularization of the nse the ns model in which the vorticity term u is averaged given by u t u q q v u f u 0 this is similar to the ns model in which the nonlinear term is x v x u but the small difference opens attractive algorithmic possibilities we give tests both confirming the predicted rates of convergence and exhibiting some shared limitations of both models the experiments also show the discrete ns simulation has greater accuracy tables 3 and 4 at less cost table 2 and requires significantly fewer degrees of freedom section 1 1 than a comparable ns simulation the experiments suggest consideration of adding grad div stabilization and higher accuracy ns deconvolution models as a next logical step in fact this combination produced accurate results see figs 10 and 11 on the coarsest mesh mesh 1 upon which all other methods models and variants tested failed

numerical analysis of a nonlinear time relaxation model of fluids abstract this report investigates a time relaxation model for the regularization of the strong solution of the navier stokes equations following the earlier works of adams stolz and kleiser 37 38 ervin layton and neda 11 layton and neda 26 the nonlinear term investigated herein aims to better control the generalized turbulent fluctuations thus providing better stabilization effect on the underlying model we study the numerical properties of the resulting model and prove that the addition of the nonlinear term does not affect the overall order of convergence to the strong solution of the navier stokes equation our theoretical results based on the finite element method are confirmed by the numerical tests performed in the last section of the paper

topology of nonarchimedean analytic spaces and relations to complex algebraic geometry this note surveys basic topological properties of nonarchimedean analytic spaces in the sense of berkovich including the recent tameness results of hrushovski and loeser we also discuss interactions between the topology of nonarchimedean analytic spaces and classical algebraic geometry

algebraic laws for nondeterminism and concurrency since a nondeterministic and concurrent program may in general communicate repeatedly with its environment its meaning cannot be presented naturally as an input output function as is often done in the denotational approach to semantics in this paper an alternative is put forth first a definition is given of what it is for two programs or program parts to be equivalent for all observers then two program parts are said to be observation congruent if they are in all program contexts equivalent the behavior of a program part that is its meaning is defined to be its observation congruence class the paper demonstrates for a sequence of simple languages expressing finite terminating behaviors that in each case observation congruence can be axiomatized algebraically moreover with the addition of recursion and another simple extension the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties

unification of variational principles for turbulent shear flows the background method of doering constantin and the mean fluctuation formulation of howard busse abstract the recent discovery of a new variational formulation for bounding turbulent flow quantities has rekindled interest in the whole field of producing rigorous inequality results directly from the navier stokes equations initiated by howard and busse in the 1960s the new background method introduced by doering and constantin 1992 1994 1995 1996 for bounding turbulent viscous dissipation appears to differ so fundamentally from that of howard and busse that any connection between the two methods has been fascinatingly unclear recently highly suggestive results obtained asymptotically kerswell 1997 have indicated that the variational problems produced for both cases of shear flow and convection may be equivalent here we confirm this for the shear flow case by uncovering the common underlying functional which both approaches seek to make stationary busse s upper bound problem is found to be the optimal dual or complementary variational problem to that which emerges from the doering constantin approach this ensures that busse s best bound exactly coincides with that available within the doering constantin formalism for all reynolds numbers

convergence tests for the piecewise parabolic method and navier stokes solutions for homogeneous compressible turbulence the need to simulate fully developed turbulence with wide range of scales led us to use the piecewise parabolic method ppm to solve the euler equations of motions to obtain data for 3 d homogeneous compressible decaying turbulence numerical simulations were performed on computational meshes of up to 10243 zones these data were compared with data obtained by solving the navier stokes ns equations results of studying the kinetic energy enstrophy and the energy power spectra with different resolutions are presented for both the ppm and ns data the results of the comparison show convergence of the ppm and ns solutions to the same limit

well posedness of a reduced order approximate deconvolution turbulence model abstract we prove well posedness for a recently proposed turbulence model and derive an estimate for its modeling error the model is derived from the fourth order representation of the stolz adams approximate deconvolution model by making an additional deconvolution approximation to reduce the model to second order which also allows the model to be computed with efficient and unconditionally stable algorithms

bisimulation relations for weighted automata bisimulation is a well known equivalence relation for discrete event systems and has been extended to probabilistic and stochastic systems this paper introduces a general definition of bisimulation which can be applied to finite automata where weights and labels are assigned to transitions it is shown that this general view contains several known bisimulations as special cases and defines naturally equivalences for different classes of models apart from the well known forward bisimulation also backward bisimulation is introduced and it is shown that both types of bisimulation preserve different types of results furthermore it is shown that forward and backward bisimulation are congruences according to commonly known composition operations for automata

toroidal varieties and the weak factorization theorem we develop the theory of stratified toroidal varieties which gives together with the theory of birational cobordisms 73 a proof of the weak factorization conjecture for birational maps in characteristic zero a birational map between complete nonsingular varieties over an algebraically closed field k of characteristic zero is a composite of blow ups and blow downs with smooth centers

bisimilar linear systems the notion of bisimulation in theoretical computer science is one of the main complexity reduction methods for the analysis and synthesis of labeled transition systems bisimulations are special quotients of the state space that preserve many important properties expressible in temporal logics and in particular reachability in this paper the framework of bisimilar transition systems is applied to various transition systems that are generated by linear control systems given a discrete time or continuous time linear system and a finite observation map we characterize linear quotient maps that result in quotient transition systems that are bisimilar to the original system interestingly the characterizations for discrete time systems are more restrictive than for continuous time systems due to the existence of an atomic time step we show that computing the coarsest bisimulation which results in maximum complexity reduction corresponds to computing the maximal controlled or reachability invariant subspace inside the kernel of the observations map these results establish strong connections between complexity reduction concepts in control theory and computer science

brief paper bisimilarity control of partially observed nondeterministic discrete event systems and a test algorithm in this paper the bisimilarity control of discrete event systems dess under partial observations is investigated where the plant and the specification are allowed to be nondeterministic a notation of simulation based controllability and a synchronization scheme for the supervised system are formalized based on the simulation relation between the specification and the plant it is shown that the existence of bisimilarity supervisors is characterized by the notions of the simulation based controllability and the language observability which extends the traditional results of supervisory control from language equivalence to bisimulation equivalence in addition a polynomial algorithm to test the simulation based controllability is developed by constructing a computing tree this algorithm together with the test of language observability can be used to check the existence of bisimilarity supervisors

numerical analysis of leray tikhonov deconvolution models of fluid motion this report develops and studies a new family of navier stokes equation regularizations leray tikhonov regularizations with time relaxation models this new family of turbulence models is based on a modification consistent with the large scales of tikhonov lavrentiev regularization with this approach we obtain an approximation of the unfiltered solution by one filtering step we introduce the modified tikhonov deconvolution operator and study its mathematical properties we also perform rigorous numerical analysis of a computationally attractive algorithm for this family of models and present numerical experiments using it

variational bounds on energy dissipation in incompressible flows iii convection building on a method of analysis for the navier stokes equations introduced by hopf math ann 117 764 1941 a variational principle for upper bounds on the largest possible time averaged convective heat flux is derived from the boussinesq equations of motion when supplied with appropriate test background fields satisfying a spectral constraint reminiscent of an energy stability condition the variational formulation produces rigorous upper bounds on the nusselt number nu as a function of the rayleigh number ra for the case of vertical heat convection between parallel plates in the absence of sidewalls a simplified but rigorous formulation of the optimization problem yields the large rayleigh number bound nu ensuremath le 0 167 mathrm ra 1 2 1 nonlinear euler lagrange equations for the optimal background fields are also derived which allow us to make contact with the upper bound theory of howard j fluid mech 17 405 1963 for statistically stationary flows the structure of solutions of the euler lagrange equations are elucidated from the geometry of the variational constraints which sheds light on busse s j fluid mech 37 457 1969 asymptotic analysis of general solutions to howard s euler lagrange equations the results of our analysis are discussed in the context of theory recent experiments and direct numerical simulations textcopyright 1996 the american physical society

turbulent channel without boundaries the periodic kolmogorov flow the kolmogorov flow provides an ideal instance of a virtual channel flow it has no boundaries but it possesses well defined mean flow in each half wavelength we exploit this remarkable feature for the purpose of investigating the interplay between the mean flow and the turbulent drag of the bulk flow by means of a set of direct numerical simulations at increasing reynolds number we show the dependence of the bulk turbulent drag on the amplitude of the mean flow further we present a detailed analysis of the scale by scale energy balance which describes how kinetic energy is redistributed among different regions of the flow while being transported toward small dissipative scales our results allow us to obtain an accurate prediction for the spatial energy transport at large scales

structure selection techniques applied to continous time nonlinear models this paper addresses the problem of choosing the multinomials that should compose a polynomial mathematical model starting from data the mathematical representation used is a nonlinear differential equation of the polynomial type some approaches that have been used in the context of discrete time models are adapted and applied to continuous time models two examples are included to illustrate the main ideas models obtained with and without structure selection are compared using topological analysis the main differences between structure selected models and complete structure models are i the former are more parsimonious than the latter ii a predefined fixed point configuration can be guaranteed for the former and iii the former set of models produce attractors that are topologically closer to the original attractor than those produced by the complete structure models 2001 elsevier science b v all rights reserved

explicit filtering and exact reconstruction of the sub filter stresses in large eddy simulation explicit filtering has the effect of reducing numerical or aliasing errors near the grid scale in large eddy simulation les we use a differential filter namely the inverse helmholtz operator which is readily applied to unstructured meshes the filter is invertible which allows the sub filter scale sfs stresses to be exactly reconstructed in terms of the filtered solution unlike eddy viscosity models the method of filtering and reconstruction avoids making any physical assumptions and is therefore valid in any flow regime the sub grid scale sgs stresses are not recoverable by reconstruction but the second order finite element method used here is an adequate source of numerical dissipation in lieu of an sgs model results for incompressible turbulent channel flow at re 180 are presented which show that explicit filtering and exact sfs reconstruction is a significant improvement over the standard les approach of implicit filtering and eddy viscosity sgs modelling

a subgrid scale deconvolution approach for shock capturing we develop a method for the modeling of flow discontinuities which can arise as weak solutions of inviscid conservation laws due to its similarity with recently proposed approximate deconvolution models for large eddy simulation the method potentially allows for a unified treatment of flow discontinuities and turbulent subgrid scales a filtering approach is employed since for the filtered evolution equations the solution is smooth and can be solved for by standard central finite difference schemes without special consideration of discontinuities a sufficiently accurate representation of the filtered nonlinear combination of discontinuous solution components which arise from the convection term can be obtained by a regularized deconvolution applied to the filtered solution for stable integration the evolution equations are supplemented by a relaxation regularization based on a secondary filter operation and a relaxation parameter an estimate for the relaxation parameter is provided the method is related to the spectral vanishing viscosity method and the regularized chapman enskog expansion method for conservation laws we detail the approach and demonstrate its efficiency with the inviscid and viscous burgers equations the isothermal shock problem and the one dimensional euler equations

convergence of spectral methods for nonlinear conservation laws we discuss the convergence of fourier methods for scalar nonlinear conservation laws that exhibit spontaneous shock discontinuities numerical tests indicate that the convergence may and in fact in some cases we prove it must fail with or without post processing of the numerical solution instead we introduce here a new kind of spectrally accurate vanishing viscosity to augment the fourier approximation of such nonlinear conservation laws using compensated compactness arguments augmented by the assumption of l infty stability we show for the inviscid burgers model equation that this spectral viscosity method prevents oscillations and convergence to the unique entropy solution follows

local systems on analytic germ complements abstract we prove that the cohomology jump loci of rank one local systems on the complement in a small ball of a germ of a complex analytic set are finite unions of torsion translates of subtori this is a generalization of the classical monodromy theorem stating that the eigenvalues of the monodromy on the cohomology of the milnor fiber of a germ of a holomorphic function are roots of unity