dynamic analysis of structures with unilateral constraints numerical integration and reduction of structural equations structural dynamic equations with unilateral constraints upon the displacements velocities and accelerations are employed in order to represent vibrating elastic structures with normal oblique impact and friction interaction points for obtaining a numerical integration scheme the lagrange multipliers and a minimum work approach are employed at each time step the algorithm is presented as an extension of the generalized newmark scheme it seems to retain the asymptotic features of the original one the reduction of the number of dynamic degrees of freedom of the unilaterally constrained structures is carried out by representing the equations of motion in modal co ordinates of the unconstrained structure and truncating the dynamic contributions of higher modes the presented techniques have been verified by investigating free longitudinal vibroimpact motion laws of an elastic vibroconverter and free longitudinal and bending vibration of a vibroconverter interacting with a moving rigid body by oblique impact and friction forces

determinants of laplacians the determinant of the laplacian on spinor fields on a riemann surface is evaluated in terms of the value of the selberg zeta function at the middle of the critical strip a key role in deriving this relation is played by the barnes double gamma function

bifurcation control via state feedback for systems with a single uncontrollable mode the state feedback control of bifurcations with quadratic or cubic degeneracy is addressed for systems with a single uncontrollable mode based on normal forms and invariants the classification of bifurcations for systems with a single uncontrollable mode is obtained table 1 using invariants stability characterizations are derived for a family of bifurcations including saddle node bifurcations transcritical bifurcations pitchfork bifurcations and bifurcations with a cusp or hysteresis phenomenon bifurcations in systems under perturbed feedbacks are also addressed in the case of a saddle node bifurcation continuous but not differentiable feedbacks are introduced to locally remove the bifurcation and to achieve the stability

a new explicit predictor multicorrector high order accurate method for linear elastodynamics abstract a new explicit predictor multicorrector high order accurate method is suggested for linear elastodynamics the method is derived from the implicit high order accurate method based on the time continuous galerkin method proposed earlier in our papers the basic unknowns for the method are displacements and velocities accelerations are not calculated the explicit method uses a predictor multicorrector technique with one or two passes in order to reach the fourth order of accuracy and has controllable numerical dissipation for the suppression of spurious high frequency oscillations in contrast to recently suggested explicit high order accurate methods based on the time discontinuous galerkin method the new method is more accurate has a higher order of accuracy and has better algorithmic properties e g a higher stability limit at the same computational efforts presented numerical examples show the performance of the new method the method appears to be competitive for medium and long term analysis when accuracy of numerical solutions arises an issue due to error accumulation

design of controllers for mg3 compressor models with general characteristics using graph backstepping we discuss the design of controllers for compressors with general characteristics including the right skewed ones the controllers can be represented graphically by plotting their throttle surfaces the graphical representation of controllers enhances understanding of controller action and allows to compare various controllers we discuss the issue of the right skewness of a compressor characteristic we show how to design controllers using a graph backstepping procedure involving the construction of the throttle surface we show that for a quite general compressor characteristic every potential axisymmetric equilibrium on the decreasing part of the compressor characteristic the peak of the characterisitic and every rotating stall equilibrium close to the peak can be globally or semi globally stabilized by an appropriate choice of the throttle surface and the controller gains we obtain lower bounds on the gains of the controller in terms of the divided differences related to compressor characteristic these bounds can be expressed using some bounds on the first and second derivatives of the characteristic in the region of operation in this way we establish a direct relationship between the shape of the compressor characteristic and the required controller gains we discuss controllers that stabilize a range of the desired equilibria and guarantee a soft bifurcation of the equilibria as a set point parameter varies we give an example of controller design for a right skew compressor we provide simple general guidelines for choosing the throttle surface

a unified set of single step algorithms part 2 theory part 1 of this paper1 presents a very general single step algorithm sspj for the numerical integration of first and second order time dependent differential equations in part 2 we present and discuss results of the accuracy and stability analysis for ss11 ss21 ss31 ss22 and ss32 there is also a detailed comparison of ss22 and the newmark algorithm

invariant helical subspaces for the navier stokes equations three dimensional solutions with helical symmetry are shown to form an invariant subspace for the navier stokes equations uniqueness of weak helical solutions in the sense of leray is proved and these weak solutions are shown to be regular strong solutions existing for arbitrary time t the global universal attractor for the infinite dimensional dynamical system generated by the corresponding semi group of helical flows is shown to be compact and finite dimensional the hausdorff and fractal dimensions of the global attractors are estimated in terms of the governing physical parameters and in terms of the helical parameters for several problems in the class with the most detailed results obtained for rotating hagen poiseuille pipe flow in this case the dimension either hausdorff or fractal up to an absolute constant is bounded from above by frac operatorname re sqrt alpha 2 n 2 where is the axial wavenumber n is the azimuthal wavenumber and re is the reynolds number based on the radius of the pipe these upper bounds are independent of the rotation rate

a comprehensive unified set of single step algorithms with controllable dissipation for dynamics part ii algorithms and analysis in part i a comprehensive unified set of single step algorithms with controllable dissipation based on the generalized galerkin formulation was presented in this paper the details of four lower order algorithms using parametrized temporal finite element are presented the analyses of the numerical stability dissipation and dispersion are also provided in comparison with the established algorithms the present algorithms facilitate controllable dissipation and yield results of higher order accuracy examples are also included to illustrate the validity of the algorithms

higher derivative explicit one step methods for non linear dynamic problems part i design and theory a new higher order explicit one step scheme is presented for use in the solution of a certain class of non linear problems in structural dynamics the generalized scheme covers some recently developed multistep algorithms as well as some new one step methods with improved numerical properties a weighted residual approach is used which contains new aspects for design of single step algorithms accuracy and stability are investigated for linear and non linear systems algorithms with higher accurary than the central difference method are developed and optimized to minimize the reduction in the stability limit

on the z2 index of the global attractor for a class of p laplacian equations by means of the z 2 index we study the geometrical property of the global attractor for a class of symmetric p laplacian equations u t div vertical bar del u vertical bar p 2 del u vertical bar u vertical bar r 2 u lambda vertical bar u vertical bar s 2 u f x u 0 where lambda 0 2 s p r we first provide under suitable assumptions the existence result for the symmetric global attractor a then when 2 s p r we prove that the z 2 index of the global attractor is infinite as a corollary we obtain that the fractal dimension of the global attractor is infinite for when 2 s p r we provide the lower bound of the z 2 index of the global attractor c 2010 elsevier ltd all rights reserved

evaluation of high order single step integrators for structural response calculation implicit single step integration methods which are absolutely stable and have fourth and sixth order accuracy are applied to linear structural dynamics equations test cases for which the discretized problems are solvable exactly are employed to determine the number of floating point operations needed to achieve specified accuracy levels examples involving longitudinal vibration of a bar and flexural vibration of a simply supported beam subjected to harmonic and impact loading are analyzed the central concern in this paper is efficiently to integrate a discretized system which may have been derived by using finite element or finite difference methods it is found that high order methods may permit sufficiently increased integration step size to reduce by a factor as high as six the total computation effort needed to achieve similar accuracy from traditional lower order methods

a rigorous treatment of experimental observations for the two dimensional navier stokes equations within a fully rigorous framework this paper shows that a finite number of point observations distributed in both space and time serve to determine the fully developed flow of a two dimensional fluid throughout the whole flow domain with the measurements taken at one fixed time the results imply that if the flow is resolved on a sufficiently small scale then its dynamics are entirely determined applied to experimental observations taken randomly from a small neighbourhood of one point in space but at staggered times they imply a version of taken s time delay embedding theorem

on a leray α model of turbulence in this paper we introduce and study a new model for three dimensional turbulence the leray model this model is inspired by the lagrangian averaged navier stokes model of turbulence also known navier stokes model or the viscous camassa holm equations as in the case of the lagrangian averaged navier stokes model the leray model compares successfully with empirical data from turbulent channel and pipe flows for a wide range of reynolds numbers we establish here an upper bound for the dimension of the global attractor the number of degrees of freedom of the leray model of the order of l l d 12 7 where l is the size of the domain and l d is the dissipation length scale this upper bound is much smaller than what one would expect for three dimensional models i e l l d 3 this remarkable result suggests that the leray model has a great potential to become a good sub grid scale large eddy simulation model of turbulence we support this observation by studying analytically and computationally the energy spectrum and show that in addition to the usual k 5 3 kolmogorov power law the inertial range has a steeper power law spectrum for wavenumbers larger than 1 finally we propose a prandtl like boundary layer model induced by the leray model and show a very good agreement of this model with empirical data for turbulent boundary layers

low dimensional attractors arise from forcing at small scales abstract standard estimates of the dimension of the attractor of the 2d navier stokes equations are given in terms of a dimensionless grashof number that measures the total amount of energy injected into the flow however this result takes no account of whether the forcing is concentrated at large or small scales by a simple modification of the usual argument this paper provides a bound that is linear in a modified grashof number that reflects the spatial structure of the forcing in particular as a fixed amount of energy is injected at progressively smaller scales then the dimension of the attractor decreases

bifurcation analysis of axial flow compressor stability with a one mode truncation it is possible to reduce the moore greitzer model for compressor instability to a set of three ordinary differential equations these are approached from the point of view of bifurcation theory most of the bifurcations emerge from a degenerate takens bogdanov bifurcation point the bifurcation sets are completed using the numerical branch tracking scheme auto despite the severity of the truncation the agreement with experimental results is excellent

explicit predictor multicorrector time discontinuous galerkin methods for non linear dynamics abstract explicit predictor multicorrector time discontinuous galerkin tdg methods developed for linear structural dynamics are formulated and implemented in a form suitable for arbitrary non linear analysis of structural dynamics problems the formulation is intended to inherit the accuracy properties of the exact parent implicit tdg methods to this end suitable predictors and correctors are designed to achieve third order accuracy large stability limits and controllable numerical dissipation by means of an algorithmic parameter as the study of a general non linear case is rather complex the analysis of the convergence properties of the resulting algorithms are restricted to conservative duffing oscillators for which closed form solutions are available it is shown that the main properties of the underlying parent scheme can be retained finally results of representative numerical simulations relevant to duffing oscillators and to a stiff spring pendulum discretized with finite elements illustrate the performance of the numerical schemes and confirm the analytical estimates

a unified set of single step algorithms part 3 the beta m method a generalization of the newmark scheme introduced herein is a generalization of newmark s time marching integration scheme called the m method like the sspj method introduced in parts 1 and 2 of this series the m method provides a gcneral single step scheme applicable to any set of initial value problems the method is specialized by specifying the method order m along with rn integration parameters 0 1 m 1 for a particular choice of m the integration parameters provide a subfamily of methods which control accuracy and stability as well as offering options for explicit or implicit algorithms for the most part attention is focused on the application to structural dynamic equations most well known methods e g newmark wilson houbolt etc are shown to be special cases within the m family hence one computationally efficient and surprisingly simple algorithm unifies old and new methods stability and accuracy analyses are presented for method orders m 2 3 and 4 to determine optimal parameters for implicit and explicit schemes along with numerical verification

exact lyapunov dimension of the universal attractor for the complex ginzburg landau equation we present an exact analytic computation of the lyapunov dimension of the universal attractor of the complex ginzburg landau partial differential equation for a finite range of its parameter values we obtain upper bounds on the attractor s dimension when the parameters do not permit an exact evaluation by our methods the exact lyapunov dimension agrees with an estimate of the number of degrees of freedom based on a simple linear stability analysis and mode counting argument

basic control for the viscous moore greitzer partial differential equation the notions of basic controllability and basic control are defined a quadratic optimal control of the linearized viscous moore greitzer equation is presented and it is confirmed that stall is uncontrollable in this model a basic control is constructed for the nonlinear viscous moore greitzer equation which can control both surge and stall some extensions of this construction are discussed numerical simulations of the basic control are presented and its performance is compared to the performance of a backstepping control constructed by banaszuk hauksson and mezic siam j control optim 37 1999 pp 1503 1537 it is shown that the viscous moore greizer equation with throttle control is not basically controllable but under certain conditions adding air injection control will make the equation basically controllable

large time behavior via the method of l trajectories abstract the method of l trajectories is presented in a general setting as an alternative approach to the study of the large time behavior of nonlinear evolutionary systems it can be successfully applied to the problems where solutions suffer from lack of regularity or when the leading elliptic operator is nonlinear here we concentrate on systems of a parabolic type and apply the method to an abstract nonlinear dissipative equation of the first order and to a class of equations pertinent to nonlinear fluid mechanics in both cases we prove the existence of a finite dimensional global attractor and the existence of an exponential attractor

the uniform attractor for the 2d non autonomous navier stokes flow in some unbounded domain abstract by using the energy equation method the existence of the uniform attractor for the 2d non autonomous navier stokes equations in some unbounded domains with usual settings is obtained without the restriction of the forcing term belonging to some weighted sobolev space and for the quasi periodic forcing term the estimation of the hausdorff dimension of such attractors is also obtained

a family of single step houbolt time integration algorithms for structural dynamics a new family of implicit single step time integration methods is presented for solving structural dynamics problems the proposed method is unconditionally stable second order accurate and asymptotically annihilating it is spectrally equivalent to houbolt s method but is cast in single step form rather than multi step form thus the new algorithm computationally is more convenient an explicit predictor correcter algorithm is presented based upon the new implicit scheme the explicit algorithm is spectraily equivalent to the central difference method the two new algorithms are merged into an implicit explicit method resulting in an improved algorithm for solving structural dynamics problems composed of soft and stiff domains numerical results are presented demonstrating the improved performance of the new implicit explicit method compared to previously developed implicit explicit schemes for structural dynamics

a new stabilized enhanced strain element with equal order of interpolation for soil consolidation problems abstract in order to accurately model the behaviour of geostructures it is usually not possible to neglect the interaction between the soil skeleton and the pore fluid classical finite element models taking into account this interaction are formulated in terms of the displacement and pore pressure fields and are based on the assumption that the fluid acceleration relative to the soil skeleton is negligible this type of mixed problems is similar to others found in solid and fluid mechanics and might give rise to numerical instabilities unless certain requirements are met there are two classical approaches to this problem the first is usually known as the zienkiewicz taylor patch test for mixed formulations as a consequence of this test the interpolation degree of the displacement field is required to be higher than the corresponding one of the pressure field mathematically speaking this is a necessary condition for stability the second approach mathematically more involved is usually known as the bab ska brezzi inf sup condition and constitutes a sufficient condition for stability however it is possible to obtain stable formulations circumventing the interpolation degree requirement through the so called stabilization techniques these techniques were initially applied in the context of fluid mechanics and later extended to solid mechanics this article presents a new formulation in which stabilization is achieved through an approach based on the simo rifai enhanced strain element

a finite dimensional attractor of the moore greitzer pde model the moore greitzer pde model with viscosity is presented and the equations are rewritten as an evolution equation on a hilbert space it is proven that the model has a unique global solution which is smooth in space and time furthermore it is proven that there exists a global attractor i e a compact set which attracts all bounded sets finally it is shown that the attractor has a finite fractal dimension

finite dimensional global attractors in banach spaces we provide bounds on the upper box counting dimension of negatively invariant subsets of banach spaces a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius as an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations semilinear equations in banach spaces are finite dimensional c 2010 elsevier inc all rights reserved

a unified set of single step algorithms part 1 general formulation and applications a general algorithm for a single step time marching scheme for use in dynamic or diffusion equations is presented this algorithm is easily programmed in its universal form for all orders of approximation and covers most of the currently used schemes as well as presenting many new possibilities in many cases it presents a computationally advantageous form over conventional procedures this is particularly so when compared with the newmark algorighm and its variants

l2 index and the selberg trace formula abstract a method is developed for computing the l 2 index of a locally symmetric elliptic differential operator d acting on a locally symmetric manifold m g k with g semisimple of real rank one and of finite co volume based on applying the selberg trace formula to the difference of the two heat kernels associated to d the applications include an extension of the osborne warner multiplicity formula to certain non integrable discrete series derived from the l 2 spinor formula and showing the existence in some cases of non invariant l 2 cohomology classes in the middle dimension via the l 2 signature formula

a further look at newmark houbolt etc time stepping formulae this paper looks at some well known methods for the numerical integration of the vibration equation from the point of view of various groupings of the independent equations involved new forms are given of the general three parameter method introduced by zienkiewicz 1 some new one step methods are introduced these are of great practical importance because of the ease with which the size of time step can be changed

numerical integration of structural dynamics equations including natural damping and periodic forcing terms this paper shows that it is comparatively simple to analyse algorithms for the numerical integration of the space discretized equations from structural dynamics when applied to instead of the usual and suggests that this should be done in order to gain some insight into the effect with natural damping and or a periodic forcing term the method is illustrated on some three and four time level schemes

a step size selection strategy for explicit runge kutta methods based on lyapunov exponent theory using a stability result for variable time step runge kutta methods applied to nonautonomous real linear scalar test problem that decays exponentially fast a step size selection algorithm is devised the step size selection algorithm is based partly on stability information obtained by estimating the discrete lyapunov exponent of a runge kutta method applied to a nonautonomous linear scalar problem the utility of the approach is illustrated in numerical experiments that demonstrate how the new algorithm performs against a standard accuracy based step size selection strategy

a unified set of single step algorithms part 4 backward error analysis applied to the solution of the dynamic vibration equation this paper applies the method of backward error analysis to the numerical solution of the dynamic vibration equation by the single step algorithms proposed in references 1 3 and obtains some general rules to help with the choice of parameters

dynamic transient analysis by a mixed iterative method summary mixed methods solved by an iterative process have been shown to provide an inexpensive procedure for improving the results of standard displacement analysis this paper shows the possibilities present in their application to dynamic problems where again accuracy improvement is achieved at small additional expense the advantages of the formulation presented are particularly noteworthy in explicit forms where the difficulties of hour glass modes associated with minimal integration rules ae avoided without cost increase

a new family of explicit time integration methods for linear and non linear structural dynamics a new family of explicit single step time integration methods with controllable high frequency dissipation is presented for linear and non linear structural dynamic analyses the proposed methods are second order accurate and completely explicit with a diagonal mass matrix even when the damping matrix is not diagonal in the linear structural dynamics or the internal force vector is a function of velocities in the non linear structural dynamics stability and accuracy of the new explicit methods are analysed for the linear undamped damped cases furthermore the new methods are compared with other explicit methods

energy conserving and decaying algorithms in non linear structural dynamics a generalized formulation of the energy momentum methodwill be developed within the framework of the generalizedmethodwhich allows at the same time guaranteed conservation or decay of total energy and controllable numerical dissipation of unwanted high frequency response furthermore the latter algorithm will be extended by the consistently integrated constraints of energy and momentum conservation originally derived for the constraint energy momentum algorithm the goal of this general approach of implicit energyconserving and decaying time integration schemes is to compare these algorithms on the basis of an equivalent notation by the means of an overall algorithmic design and hence to investigate their numerical properties numerical stability and controllable numerical dissipation of high frequencies will be studied in application to non linear structural dynamics among the methods considered will be the newmark method the classical methods the energy momentum methodwith and without numerical dissipation the constraint energymomentum algorithm and the constraint energy method copyright 1999 john wiley sons ltd

determinant expression of selberg zeta functions ii we will prove that for psl 2 r and its cofinite subgroup the selberg zeta function is expressed by the determinant of the laplacian we will also give an explicit calculation in case of congruence subgroups and deduce that the part of the determinant of the laplacian composed of the continuous spectrum is expressed by dirichlet functions the first discovery of the relation between the selberg zeta function and the determinant of the laplacian was by physicists 3 4 7 sarnak 14 and voros 15 obtained the determinant expression of selberg zeta functions for compact riemann surfaces with torsionfree fundamental groups in those cases all the spectrum of the laplacians are discrete the determinant was defined via the holomorphy at the origin of the spectral zeta function of minakshisundaram and pleijel 13 for noncompact but finite riemann surfaces with torsion free fundamental groups these results are generalized by efrat 5 in this case there exist both discrete and continuous spectrum he constructs the spectral zeta function composed not only of eigenvalues but some values concerning continuous spectrum which are decided by all the poles of the scattering de terminant in the selberg trace formula the determinant of the laplacian is defined by the standard method with the holomorphy of the spectral zeta func tion at the origin the aim of the present paper is to generalize his results to the case with any fundamental group y 3 and to give some arithmetic examples of the determinant of the laplacians 4 in 4 we restrict ourselves to the case when y is a congruence subgroup of psl 2 z in this case the partial spectral zeta function composed of only eigenvalues is also holomorphic at the origin 11 theorem 3 3 hence we have a decomposition of the determinant into parts corresponding to the discrete and continuous spectrum the scatter ing determinant is expressed very explicitly by huxley 8 in terms of dirichlet 7 functions i x almost all the poles of the scattering determinant are de scribed by nontrivial zeros of l s x the continuous part of the determinant

determination of the solutions of the navier stokes equations by a set of nodal values we consider the navier stokes equations of a viscous incompresible fluid and we want to see to what extent these solutions can be determined by a discrete set of nodal values of these solutions the results presented here are exact results and not approximate ones we show in several cases that the solutions are entirely determined by their values on a discrete set provided this set contains enough points and these points are sufficiently densely distributed in a sense described in the article two typical results are the following ones two stationary solutions coincide if they coincide on a set sufficiently dense but finite similarly if the large time behavior of the solutions to the navier stokes equations is known on an appropriate discrete set then the large time behavior of the solution itself is totally determined

brief paper local l2 gain of bifurcation stabilization local l 2 gain analysis of a class of stabilizing controllers for nonlinear systems with both stationary and hopf bifurcations is studied in particular a family of lyapunov functions is first constructed for the corresponding critical system and simplified sufficient conditions to compute the l 2 gain are derived by solving the hamilton jacobi bellman hjb inequalities local robust analysis for a class of bifurcation stabilizing controllers can then be conducted through computing the local l 2 gain achieved by these controllers at the critical situation the results obtained in this paper provide useful guidance for selecting a robust controller from a given class of stabilizing controllers in terms of l 2 gain as an example application to an axial flow compressor control is discussed in detail

accuracy of a composite implicit time integration scheme for structural dynamics summary a comprehensive study of the two sub steps composite implicit time integration scheme for the structural dynamics is presented in this paper a framework is proposed for the convergence accuracy analysis of the generalized composite scheme the local truncation errors of the acceleration velocity and displacement are evaluated in a rigorous procedure the presented and proved accuracy condition enables the displacement velocity and acceleration achieving second order accuracy simultaneously which avoids the drawback that the acceleration accuracy may not reach second order the different influences of numerical frequencies and time step on the accuracy of displacement velocity and acceleration are clarified the numerical dissipation and dispersion and the initial magnitude errors are investigated physically which measure the errors from the algorithmic amplification matrix s eigenvalues and eigenvectors respectively the load and physically undamped damped cases are naturally accounted an optimal algorithm bathe composite method bathe and baig 2005 bathe 2007 bathe and noh 2012 is revealed with unconditional stability no overshooting in displacement velocity and acceleration and excellent performance compared with many other algorithms the proposed framework also can be used for accuracy analysis and design of other multi sub steps composite schemes and single step methods under physical damping and or loading copyright 2016 john wiley sons ltd

global well posedness and finite dimensional global attractor for a 3 d planetary geostrophic viscous model in this paper we consider a three dimensional planetary geostrophic viscous model of the gyre scale mid latitude ocean we show the global existence and uniqueness of the weak and strong solutions to this model moreover we establish the existence of a nite dimensional global attractor to this dissipative evolution system c 2003 wiley periodicals inc

spectral functions special functions and the selberg zeta function the functional determinant of an eigenvalue sequence as defined by zeta regularization can be simply evaluated by quadratures we apply this procedure to the selberg trace formula for a compact riemann surface to find a factorization of the selberg zeta function into two functional determinants respectively related to the laplacian on the compact surface itself and on the sphere we also apply our formalism to various explicit eigenvalue sequences reproducing in a simpler way classical results about the gamma function and the barnesg function concerning the latter our method explains its connection to the selberg zeta function and evaluates the related glaisher kinkelin constanta

stabilization of minimum phase nonlinear systems by dynamic output feedback in this paper the stabilization problem of minimum phase nonlinear systems by dynamic output feedback is investigated it is shown that if the zero dynamics of an affine nonlinear system is asymptotically stable according to the kth approximation then the system is stabilizable by dynamic output feedback the proof is constructive which provides a method to design the stabilizer the result is applied to investigating the stabilization problem of the rotating stall in axial flow compressors

brief adaptive control of compressor surge instability in this paper we propose a simple high gain type adaptive control scheme for surge stabilization in a compression system we consider a typical configuration in which the plenum throttle position is the control input while the measured output is given by the total pressure at the compressor inlet we prove convergence of the control scheme using a simplified but widely accepted second order model the system does not satisfy strict minimum phase assumptions usually introduced in the high gain type adaptive control context and therefore the proof has been tailored to the specific problem we finally validate the proposed controller by means of both numerical simulation and experiments on a real plant

computer aided analysis of imperfect bifurcation diagrams i simple bifurcation point and isola formation centre quantitative information from the theory for imperfect bifurcation by golubit sky and schaeffer singularities and groups in bifurcation theory vol i springer verlag new york 1985 can be obtained at the cost of some numerical effort the information is used to get a local approximation of the imperfect bifurcation diagrams for simple bifurcation points or isola formation centres

positivity and the attractor dimension in a fourth order reaction diffusion equation in this paper we investigate the semilinear partial differential equation ut fuxxxx uxx u 1 u2 with a view particularly to obtaining some insight into how one might establish positivity preservation results for equations containing fourth order spatial derivatives the maximum principle cannot be applied to such equations however progress can be made by employing some very recent best possible interpolation inequalities due to the third named author in which the interpolation constants are both explicitly known and sharp these are used to estimate the lx distance between u and 1 during the evolution a positivity preservation result can be obtained under certain restrictions on the initial datum we also establish an explicit two sided estimate for the fractal dimension of the attractor which is sharp in terms of the physical parameters

application of level set approach to moving interfaces and free surface problems in flow through porous media abstract the level set technique introduced by osher and sethian has been widely used in computational fluid dynamics problems involving two or more immiscible fluids with sharp interfaces this paper presents an application of the level set to unconfined seepage problems where a free surface or a sharp interface exists it is based on considering the movement of both fluids introducing a smooth indicator function with a level set describing the interface position the proposed method can be applied to other flow in porous media problems involving immiscible fluids such as oil recovery applications

on the error in computing lyapunov exponents by qr methods we consider the error introduced using qr methods to approximate lyapunov exponents we give a backward error statement for linear non autonomous systems and further discuss nonlinear autonomous problems in particular for linear systems we show that one approximates a nearby discontinuous problem where how nearby is measured in terms of local errors and a measure of non normality for nonlinear problems we use a type of shadowing result

characteristic exponents for a viscous fluid subjected to time dependent forces we consider a viscous incompressible fluid enclosed in a bounded region of 2 or 3 and subjected to time dependent forces using bound state estimates for the schrodinger operator we obtain rigorous bounds for the characteristic exponents entropy kolmogorov sinai invariant and hausdorff dimension of attracting sets our methods are of potential use for more general time evolutions described by nonlinear partial differential equations

on characteristic exponents in turbulence ruelle has found upper bounds to the magnitude and to the number of non negative characteristic exponents for the navier stokes flow of an incompressible fluid in a domain the latter is particularly important because it yields an upper bound to the hausdorff dimension of attracting sets however ruelle s bound on the number has three deficiences i it relies on some unproved conjectures about certain constants ii it is valid only in dimensions 3 and not 2 iii it is valid only in the limit in this paper these deficiences are remedied and in addition the final constants in the inequality are improved

a backstepping controller for a nonlinear partial differential equation model of compression system instabilities we prove the existence and uniqueness of solutions in sobolev spaces for the moore greitzer nonlinear partial differential equation pde model for compression system instabilities with mild conditions on the shape of the compressor characteristic and on the throttle control to achieve this the model is reformulated as an evolution equation on a banach space using this new representation we design a backstepping control of the model global stabilization of any axisymmetric equilibrium to the right of the peak of the compressor characteristic is achieved we also prove that the dynamics can be restricted to the small neighborhood of the point on the left of the peak of the compressor characteristic thus it is possible to restrict the magnitude of stall to arbitrary small values in addition finite dimensional galerkin projections of the partial differential equation model are studied it is shown that truncated control laws stabilize truncated models numerical simulations of the model with and without control are presented

asymptotic upper bounds for the errors of richardson extrapolation with practical application in approximate computations the results produced by richardson extrapolation though in general very accurate are inexact numerical evaluation of this inexactness and implementation of the evaluation in practice are the objectives of this paper first considering linear changes of errors in the convergence plots asymptotic upper bounds are proposed for the errors then the achievement is extended to the results produced by richardson extrapolation and finally an error controlling procedure is proposed and successfully implemented in approximate computations originated in science and engineering copyright 2009 john wiley sons ltd

asymptotic analysis of the navier stokes equations abstract new bounds are established on the number of modes which determine the solutions of the navier stokes equations in two dimensions the best bound available at present is nearly proportional to the generalized grashof number defined in the paper and less than logarithmically dependent on the spatial structure or the shape of the force driving the flow to the extent than for the case of 2 dimensional rayleigh benard convection the generalized grashof number may be identified with the usual grashof number the resulting bound on the number of modes is found to differ only slightly from a bound obtained earlier on heuristic grounds

on the dimension of the attractors in two dimensional turbulence abstract using a new version of the sobolev lieb thirring inequality we derive an upper bound for the dimension of the universal attractor for two dimensional space periodic navier stokes equations this estimate is optimal up to a logarithmic correction the relevance of this estimate to turbulence and related results are also briefly discussed

analysis and control of hopf bifurcations in this paper control systems with two uncontrollable modes on the imaginary axis are studied the main contributions include the local orientation control of periodic solutions and center manifolds the quadratic normal form of systems with two imaginary uncontrollable modes the stabilization of the hopf bifurcation by state feedback and the quadratic invariants that characterize the nonlinearity of a system and its hopf bifurcation

distributed control design for parabolic evolution equations application to compressor stall control we present a theoretical study of distributed control design for semilinear parabolic nonlocal evolution equations with an application to axial compressor stall control using air injection by taking advantage of the spatial invariance of the equations a linear controller is constructed following bamieh et al via linear quadratic control of each fourier mode we derive sufficient conditions for the linear controller to stabilize the full nonlinear system concepts such as controller decentralization finite dimensional implementation inverse optimality and beneficial nonlinearities are discussed in the second part of this paper these developments are applied to a model of axial compressor control with air injection the unactuated model is derived following the work of moore and greitzer and the model coupled with air injection actuation follows the works of behnken et al and weigl et al a numerical study of the control designs is pursued and the comparison of controller performance is discussed the techniques presented here are expected to be useful for distributed control design of a much broader class of nonlinear reaction diffusion systems

lagrange constraints for transient finite element surface contact a new approach to enforce surface contact conditions in transient non linear finite element problems is developed in this paper the method is based on the lagrange multiplier concept and is compatible with explicit time integration operators compatibility with explicit operators is established by referencing lagrange multipliers one time increment ahead of associated surface contact displacement constraints however the method is not purely explicit because a coupled system of equations must be solved to obtain the lagrange multipliers an important development herein is the formulation of a highly efficient method to solve the lagrange multiplier equations the equation solving strategy is a modified gauss seidel method in which non linear surface contact force conditions are enforced during iteration the new surface contact method presented has two significant advantages over the widely accepted penalty function method surface contact conditions are satisfied more precisely and the method does not adversely affect the numerical stability of explicit integration transient finite element analysis results are presented for problems involving impact and sliding with friction a brief review of the classical lagrange multiplier method with implicit integration is also included

convergence results for a class of spectrally hyperviscous models of 3 d turbulent flow abstract we consider the spectrally hyperviscous navier stokes equations shnse which add hyperviscosity to the nse but only to the higher frequencies past a cutoff wavenumber m 0 in guermond and prudhomme 2003 18 subsequence convergence of shnse galerkin solutions to dissipative solutions of the nse was achieved in a specific spectral vanishing viscosity setting our goal is to obtain similar results in a more general setting and to obtain convergence to the stronger class of leray solutions in particular we obtain subsequence convergence of shnse strong solutions to leray solutions of the nse by fixing the hyperviscosity coefficient while the spectral hyperviscosity cutoff m 0 goes to infinity this formulation presents new technical challenges and we discuss how its motivation can be derived from computational experiments e g those in borue and orszag 1996 1998 3 4 we also obtain weak subsequence convergence to leray weak solutions under the general assumption that the hyperviscous coefficient goes to zero with no constraints imposed on the spectral cutoff in both of our main results the aubin compactness theorem provides the underlying framework for the convergence to leray solutions