estimation of acoustic source strength by inverse methods part i conditioning of the inverse problem this paper deals with the discrete inverse problem in acoustics it is assumed that a number of acoustic sources are located at known spatial positions and that the acoustic pressure is measured at a number of spatial positions in the radiated field the transfer functions relating the strengths of the acoustic sources to the radiated pressures are also assumed known in principle the strengths of the acoustic sources can be deduced from the measured acoustic pressures by inversion of this matrix of transfer functions the accuracy of source strength reconstruction in the presence of noise which contaminates the measured pressures is crucially dependent on the conditioning of the matrix to be inverted this paper examines the conditioning of this inverse problem particularly with regard to the geometry and number of sources and measurement positions and the non dimensional frequency a preliminary investigation is also presented of methods such as tikhonov regularization and singular value discarding which can improve the accuracy of source strength reconstruction in poorly conditioned cases results are also presented which enable the solution of the inverse problem when the time histories of the acoustic sources are time stationary random processes and the spectra and cross spectra are measured at a number of positions in the radiated field the paper illustrates the possibilities and limitations of the use of inverse methods in the deduction of acoustic source strength from radiated field measurements

symbolic extensions and smooth dynamical systems let f x x be a homeomorphism of the compact metric space x a symbolic extension of f x is a subshift on a finite alphabet g y which has f as a topological factor we show that a generic c1 non hyperbolic i e non anosov area preserving diffeomorphism of a compact surface has no symbolic extensions for r 1 we exhibit a residual subset mathcal r of an open set mathcal u of cr diffeomorphisms of a compact surface such that if f in mathcal r then any possible symbolic extension has topological entropy strictly larger than that of f these results complement the known fact that any c diffeomorphism has symbolic extensions with the same entropy we also show that cr generically on surfaces homoclinic closures which contain tangencies of stable and unstable manifolds have hausdorff dimension two

dynamical coherence of partially hyperbolic diffeomorphisms of tori isotopic to anosov we show that partially hyperbolic diffeomorphisms of d dimensional tori isotopic to an anosov diffeomorphism where the isotopy is contained in the set of partially hyperbolic diffeomorphisms are dynamically coherent moreover we show a global stability result i e every partially hyperbolic diffeomorphism as above is leaf conjugate to the linear one as a consequence we obtain intrinsic ergodicity and measure equivalence for partially hyperbolic diffeomorphisms with one dimensional center direction that are isotopic to anosov diffeomorphisms through such a path

the metric entropy of diffeomorphisms part ii relations between entropy exponents and dimension on considere f m m m m un c 2 diffeomorphisme f d une variete de riemann compacte m preservant une mesure de probabilite de borel m soit hm f l entropie metrique de f et 1 x r x x les exposants de lyapunov distincts en x on etablit une formule qui relie h m f et les r x x

experimental force estimation in a constrained vibrating structure using modal based methods abstract in this paper three recently developed traction vector techniques will be experimentally validated common ground for the techniques are based on a modal expansion of the displacement field and utilization of sets of normal eigenmodes and displacement measurements in order to yield detailed descriptions of the traction vector field acting at the boundary comparison between the methods is made regarding the experimental estimation of traction vectors both point wise and in an l2 norm over the boundary in question the results are good especially regarding the normed results

horseshoes for diffeomorphisms preserving hyperbolic measures we give extensions of katok s horseshoe constructions comment on related results and provide a self contained proof we consider either a c 1 alpha diffeomorphism preserving a hyperbolic measure or a c 1 diffeomorphism preserving a hyperbolic measure whose support admits a dominated splitting

the metric entropy of diffeomorphisms part i characterization of measures satisfying pesin s entropy formula soit m une variete de riemann compacte soit f m m un diffeomorphisme et soit m une mesure de probabilite de borel f invariante sur m on identifie les mesures pour lesquelles l inegalite de margulis et ruelle qui relie l entropie aux exposants de lyapunov atteint l egalite on demontre une formule valable pour toutes les mesures invariantes

an optimization problem with volume constraint for a degenerate quasilinear operator abstract we consider the optimization problem of minimizing u p d x with a constraint on the volume of u 0 we consider a penalization problem and we prove that for small values of the penalization parameter the constrained volume is attained in this way we prove that every solution u is locally lipschitz continuous and that the free boundary u 0 is smooth

symbolic extensions and dominated splittings for generic c 1 diffeomorphisms let mathrm diff 1 m be the set of all c 1 diffeomorphisms f m rightarrow m where m is a compact boundaryless d dimensional manifold d ge 2 we prove that there is a residual subset mathfrak r of mathrm diff 1 m such that if f in mathfrak r and if h p is the homoclinic class associated with a hyperbolic periodic point p then either h p admits a dominated splitting of the form e oplus f 1 oplus dots oplus f k oplus g where f i is not hyperbolic and one dimensional or f h p has no symbolic extensions

regularity of the free boundary in an optimization problem related to the best sobolev trace constant in this paper we study the regularity properties of a free boundary problem arising in the optimization of the best sobolev trace constant in the immersion h 1 omega hookrightarrow l q partial omega for functions that vanish in a subset of omega this problem is also related to a minimization problem for steklov eigenvalues

a constrained shape optimization problem in orlicz sobolev spaces abstract in this manuscript we study the following optimization problem given a bounded and regular domain r n we look for an optimal shape for the w vanishing window on the boundary with prescribed measure over all admissible profiles in the framework of the orlicz sobolev spaces associated to constant for the sobolev trace embedding in this direction we establish existence of minimizer profiles and optimal sets as well as we obtain further properties for such extremals finally we also place special emphasis on analyzing the corresponding optimization problem involving an a vanishing hole inside the domain with volume constraint

a minimum problem with free boundary in orlicz spaces abstract we consider the optimization problem of minimizing g u u 0 d x in the class of functions w 1 g with u 0 w 0 1 g for a given 0 0 and bounded w 1 g is the class of weakly differentiable functions with g u d x the conditions on the function g allow for a different behavior at 0 and at we prove that every solution u is locally lipschitz continuous that it is a solution to a free boundary problem and that the free boundary u 0 is a regular surface also we introduce the notion of weak solution to the free boundary problem solved by the minimizers and prove the lipschitz regularity of the weak solutions and the c 1 regularity of their free boundaries near flat free boundary points

the entropy theory of symbolic extensions fix a topological system x t with its space k x t of t invariant borel probabilities if y s is a symbolic system subshift and y s x t is a topological extension factor map then the function h ext on k x t which assigns to each the maximal entropy of a measure on y mapping to is called the extension entropy function of the infimum of such functions over all symbolic extensions is called the symbolic extension entropy function and is denoted by h sex in this paper we completely characterize these functions in terms of functional analytic properties of an entropy structure on x t the entropy structure is a sequence of entropy functions h k defined with respect to a refining sequence of partitions of x or of x z for some auxiliary system z r with simple dynamics whose boundaries have measure zero for all the invariant borel probabilities we develop the functional analysis and computational techniques to produce many dynamical examples for instance we resolve in the negative the question of whether the infimum of the topological entropies of symbolic extensions of x t must always be attained and we show that the maximum value of h sex need not be achieved at an ergodic measure we exhibit several characterizations of the asymptotically h expansive systems of misiurewicz which emerge as a fundamental natural class in the context of the entropy structure the results of this paper are required for the downarowicz newhouse results dn on smooth dynamical systems

construction of three dimensional orthogonal surface basis functions and well conditioned boundary traction vector estimation a well conditioned technique for the solution of the inverse problem of boundary traction estimation in the frequency domain from measured vibration responses on a solid structure is proposed the technique is based on recent results regarding lack of mode orthogonality on sub domains of the structure this is one of the reasons that modal based solutions to the inverse problems may be numerically ill conditioned herein construction of orthogonal three dimensional basis functions over a sub domain of the structure and a well posed model for inverse boundary traction estimation are proposed the technique is validated on a three dimensional example using direct fe calculated responses as simulation of measured responses with very good results

topological entropy on points without physical like behaviour for c 1 transitive anosov diffeomorphisms we consider the sets of irregular points without physical like behaviour and regular points without physical like behaviour respectively and show that they all carry full topological entropy roughly speaking physical like measures do not affect the dynamical complexity of the regular set and the irregular set in the sense of topological entropy

continuity properties of entropy on donne une borne superieure sur le defaut en semicontinuite superieure des entropies topologiques et metriques d une auto application c r d une variete c r r 1

a free boundary problem for the p x laplacian abstract we consider the optimization problem of minimizing 1 p x u p x x u 0 d x in the class of functions w 1 p with u 0 w 0 1 p for a given 0 0 and bounded w 1 p is the class of weakly differentiable functions with u p x d x we prove that every solution u is locally lipschitz continuous that it is a solution to a free boundary problem and that the free boundary u 0 is a regular surface

an optimization problem with volume constraint in orlicz spaces we consider the optimization problem of minimizing g u dx in the class of functions w1 g with a constraint on the volume of u 0 the conditions on the function g allow for a different behavior at 0 and at we consider a penalization problem and we prove that for small values of the penalization parameter the constrained volume is attained in this way we prove that every solution u is locally lipschitz continuous and that the free boundary u 0 is smooth

simulation of damped vibrations based on augmented hooke s law and elastic modes of vibration abstract a linear unconditionally convergent modal vibration response modelling technique is presented material damping is simulated using the augmented hooke s law introduced by dovstam dovstam k 1995 augmented hooke s law in frequency domain a three dimensional material damping formulation international journal of solids and structures 32 2835 2852 the method is based on continuous elastic displacement modes and vibrational stress modes dual to the traditional displacement modes the stress modes are implicitly used to derive a generally convergent modal response model in generally damped cases with boundary traction excitation the real eigenvalue problem defining the stress modes is formulated and explicit frequency domain modal system equations of motion for computation of needed stress and displacement mode coefficient spectra are derived introduced parameters accounting for the interdependence of the different modal contributions modal coupling to the response are computable from known material properties elastic and damping and geometry by post processing results from three dimensional standard finite element fe eigenvalue calculations practical means for predicting whether modal coupling will occur or not are thus provided as well as means for predicting damped resonance frequencies when applied to an isotropic material the new response model for small damping approaches the modal receptance model recently introduced and discussed by dovstam dovstam k 1997 receptance model based on isotropic damping functions and elastic displacement modes international journal of solids and structures 34 2733 2754 a close agreement between direct fe calculations and response simulations using the proposed method is obtained for a highly damped three dimensional cantilever test plate

perturbation of the lyapunov spectra of periodic orbits we describe all lyapunov spectra that can be obtained by perturbing the derivatives along periodic orbits of a diffeomorphism the description is expressed in terms of the finest dominated splitting and lyapunov exponents that appear in the limit of a sequence of periodic orbits and involves the majorization partial order among the applications we give a simple criterion for the occurrence of universal dynamics

an optimization problem with volume constraint we consider the optimization problem of minimizing dirichlet integral int omega nabla u 2 with volume constraint on the set u 0 we use a penalization method which for small values of the penalization parameter leads to a solution of the original problem

entropy of c 1 diffeomorphisms without a dominated splitting a classical construction due to newhouse creates horseshoes from hyperbolic periodic orbits with large period and weak domination through local c 1 perturbations our main theorem shows that when one works in the c 1 topology the entropy of such horseshoes can be made arbitrarily close to an upper bound deriving from ruelle s inequality i e the sum of the positive lyapunov exponents or the same for the inverse diffeomorphism whichever is smaller adapting classical techniques we use perturbations that are local and can be chosen to preserve volume or symplectic form or a homoclinic connection this optimal entropy creation yields a number of consequences for c 1 generic diffeomorphisms especially in the absence of a dominated splitting for instance in the conservative settings we find formulas for the topological entropy deduce that the topological entropy is continuous but not locally constant at the generic diffeomorphism and we prove that these generic diffeomorphisms have no measure of maximum entropy in the dissipative setting we show the locally generic existence of infinitely many homoclinic classes with entropy bounded away from zero