liouville action and weil petersson metric on deformation spaces global kleinian reciprocity and holography we rigorously define the liouville action functional for the finitely generated purely loxodromic quasi fuchsian group using homology and cohomology double complexes naturally associated with the group action we prove that classical action the critical value of the liouville action functional considered as a function on the quasi fuchsian deformation space is an antiderivative of a 1 form given by the difference of fuchsian and quasi fuchsian projective connections this result can be considered as global quasi fuchsian reciprocity which implies mcmullen s quasi fuchsian reciprocity we prove that the classical action is a kahler potential of the weil petersson metric we also prove that the liouville action functional satisfies holography principle i e it is a regularized limit of the hyperbolic volume of a 3 manifold associated with a quasi fuchsian group we generalize these results to a large class of kleinian groups including finitely generated purely loxodromic schottky and quasi fuchsian groups and their free combinations

on the renormalized volume of hyperbolic 3 manifolds the renormalized volume of hyperbolic manifolds is a quantity motivated by the ads cft correspondence of string theory and computed via a certain regularization procedure the main aim of the present paper is to elucidate its geometrical meaning we use another regularization procedure based on surfaces equidistant to a given convex surface n the renormalized volume computed via this procedure is equal to what we call the w volume of the convex region n given by the usual volume of n minus the quarter of the integral of the mean curvature over n the w volume satisfies some remarkable properties first this quantity is self dual in the sense explained in the paper second it verifies some simple variational formulas analogous to the classical geometrical schlafli identities these variational formulas are invariant under a certain transformation that replaces the data at n by those at infinity of m we use the variational formulas in terms of the data at infinity to give a simple geometrical proof of results of takhtajan et al on the kahler potential on various moduli spaces

eigenvalue approximation by mixed and hybrid methods note univ maryland dept math college pk md 20742 ecole polytech ctr math appl f 91128 palaiseau france univ paris 6 f 75230 paris 05 france mercier b cea limeil f 94190 villeneuve france isi document delivery no lq584times cited 29cited reference count 44 reference asn article 1981 005doi 10 2307 2007651 record created on 2006 08 24 modified on 2017 05 12

plissage des varietes hyperboliques de dimension 3 we give a characterization of the measured geodesic laminations which can occur as the bending measured lamination of some geometrically finite metric on a 3 manifold when the 3 manifold has incompressible boundary such a characterization has already been given by f bonahon and j p otal here we deal with the general case

finite element vibration analysis of fluid solid systems without spurious modes this paper deals with the finite element approximation of the vibration modes of a problem with fluid structure interaction displacement variables are used for both the fluid and the solid to avoid the typical spurious modes of this formulation we introduce a nonconforming discretization error estimates for the approximation of eigenvalues and eigenvectors are given

laminations mesurees de plissage des varietes hyperboliques de dimension 3 for a hyperbolic metric on a 3 dimensional manifold the boundary of its convex core is a surface which is almost everywhere totally geodesic but which is bent along a family of disjoint geodesics the locus and intensity of this bending is described by a measured geodesic lamination which is a topological object we consider two problems the topological characterization of those measured geodesic laminations which can occur as bending measured laminations of hyperbolic metrics and the uniqueness problem which asks whether a hyperbolic metric is uniquely determined by its bending measured lamination

conditional fault tolerant edge bipancyclicity of hypercubes with faulty vertices and edges let f be a faulty set in an n dimensional hypercube q n such that in q n f each vertex is incident to at least two edges and let f v f e be the numbers of faulty vertices and faulty edges in f respectively in this paper we consider the fault tolerant edge bipancyclicity of hypercubes it is shown that each edge in q n f for n 3 lies on a fault free cycle of any even length from 6 to 2 n 2 f v if f v f e 2 n 5 this gives an answer for a problem proposed by yang et al 2016 33 consider hypercubes with mixed faulty edges and faulty vertices under conditional fault model improve the previous results about the fault tolerant edge bipancyclicity of hypercubes give an affirmative answer for a problem proposed by yang et al 2016

a posteriori error estimates in finite element acoustic analysis we present an a posteriori error estimator for the approximations of the acoustic vibration modes obtained by a finite element method which does not present spurious or circulation modes for non zero frequencies we prove that the proposed estimator is equivalent to the error in the approximation of the eigenvectors up to higher order terms with constants independent of the eigenvalues numerical results for some test examples are presented which show the good behavior of the estimator when it is used as local error indicator for adaptive refinement

a parametric study on fluid structure interaction problems abstract this paper deals with finite element analysis of the fluid structure systems considering the coupled effect of elastic structure and fluid the equations of motion of the fluid considered inviscid and compressible are expressed in terms of the pressure variable alone the elastic structure and the fluid domain are treated as two separate systems and discretized with finite elements the solution of the coupled system is accomplished by solving the two systems separately with the interaction effects at the fluid solid interface enforced by a developed iterative scheme non divergent pressure and displacement are obtained simultaneously through a few numbers of iterations studies show the accuracy of the proposed algorithm while comparing with the existing ones available in the literature the parametric study of the coupled system shows the importance of fluid height and material property of the structure

finite element analysis of the vibration problem of a plate coupled with a fluid we consider the approximation of the vibration modes of an elastic plate in contact with a compressible fluid the plate is modelled by reissner mindlin equations while the fluid is described in terms of displacement variables this formulation leads to a symmetric eigenvalue problem reissner mindlin equations are discretized by a mixed method the equations for the fluid with raviart thomas elements and a non conforming coupling is used on the interface in order to prove that the method is locking free we consider a family of problems one for each thickness t 0 and introduce appropriate scalings for the physical parameters so that these problems attain a limit when t to 0 we prove that spurious eigenvalues do not arise with this discretization and we obtain optimal order error estimates for the eigenvalues and eigenvectors valid uniformly on the thickness parameter t finally we present numerical results confirming the good performance of the method

a new strategy for solving fluid structure problems a scheme for treating unsymmetrical coupled systems is outlined such systems occur naturally in connection with fluid structure interaction where an acoustic fluid is contained in an elastic structure the discretization is performed by means of the finite element method using displacement formulation in the structure and either pressure or displacement potential in the fluid based on the eigenvalues of each subdomain some simple steps give a standard eigenvalue problem it might also be concluded that the unsymmetrical matrices have real eigenvalues

hamiltonian connectivity and strongly hamiltonian laceability of folded hypercubes in this paper we analyze a hypercube like structure called the folded hypercube which is basically a standard hypercube with some extra links established between its nodes we first show that the n dimensional folded hypercube is bipartite when n is odd we also show that the n dimensional folded hypercube is strongly hamiltonian laceable when n is odd and is hamiltonian connected when n 1 or n 2 is even

a characterization of compact convex polyhedra in hyperbolic 3 space in this paper we study the extrinsic geometry of convex polyhedral surfaces in three dimensional hyperbolic spaceh 3 we obtain a number of new uniqueness results and also obtain a characterization of the shapes of convex polyhedra inh 3 in terms of a generalized gauss map this characterization greatly generalizes andre ev s theorem

schwarzian derivatives projective structures and the weil petersson gradient flow for renormalized volume to a complex projective structure on a surface thurston associates a locally convex pleated surface we derive bounds on the geometry of both in terms of the norms and 2 of the quadratic differential of given by the schwarzian derivative of the associated locally univalent map we show that these give a unifying approach that generalizes a number of important well known results for convex cocompact hyperbolic structures on 3 manifolds including bounds on the lipschitz constant for the nearest point retraction and the length of the bending lamination we then use these bounds to begin a study of the weil petersson gradient flow of renormalized volume on the space cc n of convex cocompact hyperbolic structures on a compact manifold n with incompressible boundary leading to a proof of the conjecture that the renormalized volume has infimum given by one half the simplicial volume of dn the double of n

hyper hamilton laceable and caterpillar spannable product graphs abstract we define a hamilton laceable graph g to be hyper hamilton laceable hyper hl if either 1 a g is equitable and if v is any node of g then g v is hl or 2 b g is nearly equitable and if v is any node in its larger color set then g v is hl in particular the hypercube q n is hyper hl a graph g is caterpillar spannable cs if it has a spanning tree which is a caterpillar we present several theorems concerning products of cs graphs it is shown that the product of two cs graphs such that at least one of them has maximum degree 3 is cs

pancyclicity and bipancyclicity of conditional faulty folded hypercubes a graph is said to be pancyclic if it contains cycles of every length from its girth to its order inclusive and a bipartite graph is said to be bipancyclic if it contains cycles of every even length from its girth to its order the pancyclicity or the bipancyclicity of a given network is an important factor in determining whether the network s topology can simulate rings of various lengths an n dimensional folded hypercube fq n is an attractive variant of an n dimensional hypercube q n that is obtained by establishing some extra edges between the vertices of q n fq n for any odd n is known to be bipartite in this paper we explore the pancyclicity and bipancyclicity of fq n for any fq n n 2 with at most 2n 3 faulty edges where each vertex is incident to at least two fault free edges we prove that there exists a fault free cycle of every even length from 4 to 2 n and when n 2 is even we prove there also exists a fault free cycle of every odd length from n 1 to 2 n 1 the result is optimal with respect to the number of faulty edges tolerated

liouville action and holography on quasi fuchsian deformation spaces we study the liouville action for quasi fuchsian groups with parabolic and elliptic elements in particular when the group is fuchsian the contribution of elliptic elements to the classical liouville action is derived in terms of the bloch wigner functions we prove the first and second variation formulas for the classical liouville action on the quasi fuchsian deformation space we prove an equality expressing the holography principle which relates the liouville action and the renormalized volume for quasi fuchsian groups with parabolic and elliptic elements we also construct the potential functions of the kahler forms corresponding to the takhtajan zograf metrics associated to the elliptic elements in the quasi fuchsian groups

on almost fuchsian manifolds almost fuchsian manifold is a class of complete hyperbolic threemanifolds a such three manifold is a quasi fuchsian manifold that contains a closed incompressible minimal surface with principal curvatures everywhere in the range of 1 1 in such a manifold the minimal surface is unique and embedded hence one can parametrize these hyperbolic three manifolds by their minimal surfaces in this paper we obtain estimates on several geometric and analytical quantities of an almost fuchsian manifold m in terms of the data on the minimal surface in particular we obtain an upper bound for the hyperbolic volume of the convex core of m and an upper bound on the hausdorff dimension of the limit set associated to m we also constructed a quasi fuchsian manifold which admits more than one minimal surface and it does not admit a foliation of closed surfaces of constant mean curvature

a virtual element method for the acoustic vibration problem we analyze in this paper a virtual element approximation for the acoustic vibration problem we consider a variational formulation relying only on the fluid displacement and propose a discretization by means of mathrm h mathrm div h div virtual elements with vanishing rotor under standard assumptions on the meshes we show that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates with this end we prove approximation properties of the proposed virtual elements we also report some numerical tests supporting our theoretical results

edge pancyclicity and edge bipancyclicity of faulty folded hypercubes let f v and f e be sets of faulty vertices and faulty edges respectively in the folded hypercube fq n so that f v f e n 2 for n 2 choose any fault free edge e if n 3 then there is a fault free cycle of length l in fq n containing e for every even l ranging from 4 to 2 n 2 f v if n 2 is even then there is a fault free cycle of length l in fq n containing e for every odd l ranging from n 1 to 2 n 2 f v 1

vibration analysis of fluid solid systems using a finite element displacement formulation this report presents a finite element solution for the vibration interaction between an inviscid fluid and a solid the equation of motion governing the inviscid fluid is expressed in terms of the displacements reduced integration is used when computing the element stiffness matrix contributed by the fluid in addition a projection is used on the element mass matrix in order to remove the spurious modes which result from the use of reduced integration

finite element analysis of pressure formulation of the elastoacoustic problem in this paper we analyze the non symmetric pressure displacement formulation of the elastoacoustic vibration problem and show its equivalence with the symmetric stiffness coupling formulation we introduce discretizations for these problems based on lagrangian finite elements we show that both formulations are also equivalent at discrete level and prove optimal error estimates for eigenfunctions and eigenvalues both formulations are rewritten such as to be solved with a standard matlab eigensolver we report numerical results comparing the efficiency of the methods over some test examples

the twisted n cube with application to multiprocessing it is shown that by exchanging any two independent edges in any shortest cycle of the n cube n or 3 its diameter decreases by one unit this leads to the definition of a new class of n regular graphs denoted tq sub n with 2 sup n vertices and diameter n 1 which has the n 1 cube as subgraph other properties of tq sub n such as connectivity and the lengths of the disjoints paths are also investigated moreover it is shown that the complete binary tree on 2 sup n 1 vertices which is not a subgraph of the n cube is a subgraph of tq sub n how these results can be used to enhance hypercube multiprocessors is discussed

time harmonic solution for acousto elastic interaction with controllability and spectral elements the classical way of solving the time harmonic linear acousto elastic wave problem is to discretize the equations with finite elements or finite differences this approach leads to large scale indefinite complex valued linear systems for these kinds of systems it is difficult to construct efficient iterative solution methods that is why we use an alternative approach and solve the time harmonic problem by controlling the solution of the corresponding time dependent wave equation in this paper we use an unsymmetric formulation where fluid structure interaction is modeled as a coupling between pressure and displacement the coupled problem is discretized in space domain with spectral elements and in time domain with central finite differences after discretization exact controllability problem is reformulated as a least squares problem which is solved by the conjugate gradient method

renormalized area and properly embedded minimal surfaces in hyperbolic 3 manifolds we study the renormalized area functional mathcal a in the ads cft correspondence specifically for properly embedded minimal surfaces in convex cocompact hyperbolic 3 manifolds and somewhat more broadly poincare einstein spaces our main results include an explicit formula for the renormalized area of such a minimal surface y as an integral of local geometric quantities as well as formulae for the first and second variations of mathcal a which are given by integrals of global quantities over the asymptotic boundary loop of y all of these formulae are also obtained for a broader class of nonminimal surfaces the proper setting for the study of this functional when the ambient space is hyperbolic requires an understanding of the moduli space of all properly embedded minimal surfaces with smoothly embedded asymptotic boundary we show that this moduli space is a smooth banach manifold and develop a mathbb z valued degree theory for the natural map taking a minimal surface to its boundary curve we characterize the nondegenerate critical points of mathcal a for minimal surfaces in mathbb h 3 and finally discuss the relationship of mathcal a to the willmore functional

a symplectic map between hyperbolic and complex teichmuller theory let s be a closed orientable surface of genus at least 2 the space th ml where th is the hyperbolic teichmuller space of s and ml is the space of measured geodesic laminations on s is naturally a real symplectic manifold the space cp of complex projective structures on s is a complex symplectic manifold a relation between these spaces is provided by thurston s grafting map gr we prove that this map although not smooth is symplectic the proof uses a variant of the renormalized volume defined for hyperbolic ends

every edge lies on cycles embedding in folded hypercubes with vertex fault tolerant the folded hypercube is a well known variation of hypercube structure and can be constructed from a hypercube by adding a link to every pair of vertices with complementary addresses an n dimensional folded hypercube fq n for short for any odd n is known to be bipartite in this paper let f be a faulty vertex in fq n it has been shown that 1 every edge of fq n f lies on a fault free cycle of every even length l with 4 l 2 n 2 where n 3 2 every edge of fq n f lies on a fault free cycle of every odd length l with n 1 l 2 n 1 where n 2 is even in terms of every edge lies on a fault free cycle of every odd length in fq n f our result improves the result of cheng et al 2013 where odd cycle length up to 2 n 3

numerical study and comparison of alternative time discretization schemes for an ultrasonic guided wave propagation problem coupled with fluid structure interaction abstract discretization is a crucial step in the numerical treatment of coupled multiphysics problems in the present paper we focus on the numerical solution of ultrasonic guided waves ugws propagation problem coupled with fluid structure interaction we track ugws propagation through fluid solid and their interface where the structure is in motion discretization is done via a finite element method for this we follow the rothe method in which discretization in time is followed by space discretization solving the resulting problem according to the monolithic approach further we provide a systematic analysis of alternative discretization schemes time steps and mesh refinements specifically we contrast one first order time discretization scheme cf backward euler and three second order schemes cf crank nicolson shifted crank nicolson and fractional step first we establish the robustness of the convergence result second we estimate the experimental order of convergence for alternative schemes and space time discretization combinations

analysis of a finite element method for pressure potential formulation of elastoacoustic spectral problems a finite element method to approximate the vibration modes of a structure enclosing an acoustic fluid is analyzed the fluid is described by using simultaneously pressure and displacement potential variables whereas displacement variables are used for the solid a mathematical analysis of the continuous spectral problem is given the problem is discretized on a simplicial mesh by using piecewise constant elements for the pressure and continuous piecewise linear finite elements for the other fields error estimates are settled for approximate eigenvalues and eigenfrequencies finally implementation issues are discussed

quasi fuchsian manifolds with particles we consider 3 dimensional hyperbolic cone manifolds which are convex cocompact in a natural sense with cone singularities along infinite lines such singularities are sometimes used by physicists as models for massive spinless point particles we prove an infinitesimal rigidity statement when the angles around the singular lines are less than any infinitesimal deformation changes either these angles or the conformal structure at infinity with marked points corresponding to the endpoints of the singular lines moreover any small variation of the conformal structure at infinity and of the singular angles can be achieved by a unique small deformation of the cone manifold structure these results hold also when the singularities are along a graph i e for interacting particles

linear array and ring embeddings in conditional faulty hypercubes the n dimensional hypercube qn is a graph having 2n vertices labeled from 0 to 2n 1 two vertices are connected by an edge if their binary labels differ in exactly one bit position in this paper we consider the faulty hypercube qn with n 3 that each vertex of qn is incident to at least two nonfaulty edges based on this requirement we prove that qn contains a hamiltonian path joining any two different colored vertices even if it has up to 2n 5 edge faults moreover we show that there exists a path of length 2n 2 between any two the same colored vertices in this faulty qn furthermore we also prove that the faulty qn still contains a cycle of every even length from 4 to 2n inclusive

convexity of the renormalized volume of hyperbolic 3 manifolds the hessian of the renormalized volume of geometrically finite hyperbolic 3 manifolds without rank 1 cusps computed at the hyperbolic metric g rm geod with totally geodesic boundary of the convex core is shown to be a strictly positive bilinear form on the tangent space to teichm uller space the metric g rm geod is known from results of bonahon and storm to be an absolute minimum for the volume of the convex core we deduce the strict convexity of the functional volume of the convex core at its minimum point

finite element computation of the vibration modes of a fluid solid system abstract in this paper we solve the interior elastoacoustic problem by a finite element method which does not present spurious or circulation modes for nonzero frequencies it consists of classical triangular lagrangian elements for the solid and lowest order triangular raviart thomas elements for the fluid transmission conditions at the fluid solid interface are taken into account in a weak sense numerical results for some test examples are presented which show the good performance of the proposed methodology

finite element analysis for a pressure stress formulation of a fluid structure interaction spectral problem the aim of this paper is to analyze an elastoacoustic vibration problem employing a dual mixed formulation in the solid domain the cauchy stress tensor and the rotation are the primary variables in the elastic structure while the standard pressure formulation is considered in the acoustic fluid the resulting mixed eigenvalue problem is approximated by a conforming galerkin scheme based on the lowest order lagrange and arnold falk winther finite element subspaces in the fluid and solid domains respectively we show that the scheme provides a correct approximation of the spectrum and prove quasi optimal error estimates finally we report some numerical experiments

an optimization based approach for solving a time harmonic multiphysical wave problem with higher order schemes this study considers developing numerical solution techniques for the computer simulations of time harmonic fluid structure interaction between acoustic and elastic waves the focus is on the efficiency of an iterative solution method based on a controllability approach and spectral elements we concentrate on the model in which the acoustic waves in the fluid domain are modeled by using the velocity potential and the elastic waves in the structure domain are modeled by using displacement traditionally the complex valued time harmonic equations are used for solving the time harmonic problems instead of that we focus on finding periodic solutions without solving the time harmonic problems directly the time dependent equations can be simulated with respect to time until a time harmonic solution is reached but the approach suffers from poor convergence to overcome this challenge we follow the approach first suggested and developed for the acoustic wave equations by bristeau glowinski and periaux thus we accelerate the convergence rate by employing a controllability method the problem is formulated as a least squares optimization problem which is solved with the conjugate gradient cg algorithm computation of the gradient of the functional is done directly for the discretized problem a graph based multigrid method is used for preconditioning the cg algorithm

prescribing curvature on compact surfaces with conical singularities we study the berger nirenberg problem on surfaces with conical singularities i e we discuss conditions under which a function on a riemann surface is the gaussian curvature of some conformal metric with a prescribed set of singularities of conical types

tau function and chern simons invariant abstract we define a chern simons invariant for schottky hyperbolic 3 manifolds of infinite volume we then prove an expression relating the bergman tau function on a fiber space over the teichmuller space to the lifting of the function f defined by zograf on teichmuller space and a holomorphic function on this space which we introduce if the point in this space corresponds to a marked riemann surface x then this function is constructed from the renormalized volume and our chern simons invariant for the bounding 3 manifold of x given by schottky uniformization together with a regularized polyakov integral we also obtain a relation between the chern simons invariant and the eta invariant of the bounding 3 manifold with defect given by the phase of the bergman tau function of x

fault tolerant path embedding in folded hypercubes with both node and edge faults the folded hypercube fq n is a well known variation of the hypercube structure fq n is superior to q n in many measurements such as diameter fault diameter connectivity and so on let email protected fq n resp email protected fq n denote the set of faulty nodes resp faulty edges in fq n in the case that all nodes in fq n are fault free it has been shown that fq n contains a fault free path of length 2 n 1 resp 2 n 2 between any two nodes of odd resp even distance if email protected fq n n 1 where n 1 is odd and fq n contains a fault free path of length 2 n 1 between any two nodes if email protected fq n n 2 where n 2 is even in this paper we extend the above result to obtain two further properties which consider both node and edge faults as follows 1 fq n contains a fault free path of length at least 2 n 2 email protected fq n 1 resp 2 n 2 email protected fq n 2 between any two fault free nodes of odd resp even distance if email protected fq n email protected fq n n 1 where n 1 is odd 2 fq n contains a fault free path of length at least 2 n 2 email protected fq n 1 between any two fault free nodes if email protected fq n email protected fq n n 2 where n 2 is even