two reliable methods for solving nonlinear evolution equations this paper aims to introduce a comparison of adomian decomposition and wavelet basis method for the numerical solution of nonlinear evolution equations test problems concerning the motion and interaction of solutions are used to compare between the two methods the comparisons shows that the adomian decomposition method in terms of accuracy is efficient and easy to use

reconstructing an unknown time dependent function in the boundary conditions of a parabolic pde this work investigates the parabolic inverse problem of reconstructing an unknown time dependent function in the boundary conditions from additional terminal integral or point observations a numerical scheme is developed for obtaining an approximate solution for this problem the method consists of reducing the solution of the inverse problem to a system of integral equations the properties of sinc function are then utilized for replacing the resulting integral equations by a system of linear algebraic equations several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method

open 3 manifolds whose fundamental groups have infinite center and a torus theorem for 3 orbifolds our main result is a characterization of open seifert fibered 3 manifolds in terms of the fundamental group and large scale geometric properties of a triangulation as an application we extend the seifert fiber space theorem and the torus theorem to a class of 3 orbifolds

extended immersed boundary method using fem and rkpm abstract the proposed extended immersed boundary method eibm has several distinct features in comparison with the immersed boundary ib method in the ib method the interaction between the immersed elastic boundary and the surrounding viscous fluid is replaced with an equivalent body force distribution within the fluid domain the key ingredient of the ib method is the enforcement of the energy input from the equivalent body force into the fluid domain to be the same at all time as that of the elastic forces within the ib in eibm instead of the volumeless immersed elastic boundary we consider the submerged elastic solid which occupies a finite volume within the fluid domain in particular we replace the kinematic and dynamic matching of the fluid solid interface and the effect of the submerged solid with a judiciously chosen collection of equivalent nodal forces calculated in the context of finite element formulations the employment of the finite element representation enables a realistic stress analysis for the submerged solid subject to large deformations finally in eibm we also replace the discretized delta function commonly used in the ib method with the kernel functions in meshless reproducing kernel particle method rkpm with this improvement using the same finite support domain we could improve the discretized delta function from c 1 to c n continuity where n is chosen according to the required smoothness and resolution of such functions and more importantly enables the use of non uniform meshing in the fluid domain these extensions may eventually open doors to the modelling of complex biological fluid involving molecular cellular and flexible vessel flow interactions

hybrid numerical methods for exponential models of growth abstract a series of novel numerical methods for the exponential models of growth are proposed based on these methods hybrid predictor corrector methods are constructed the hybrid numerical methods can increase the accuracy and the computing speed obviously as well as enlarge the stability domain greatly

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

a discontinuous hp finite element method for diffusion problems 1 d analysis abstract this paper presents the mathematical analysis of a new variant of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems not requiring auxiliary variables such as those used in mixed methods the focus of this study is on a class of linear second order boundary value problems for which we prove stability and a priori error estimates in both the finite and infinite dimensional spaces

the decorated teichmuller space of punctured surfaces a principal 5 bundle over the usual teichmuller space of ans times punctured surface is introduced the bundle is mapping class group equivariant and admits an invariant foliation several coordinatizations of the total space of the bundle are developed there is furthermore a natural cell decomposition of the bundle finally we compute the coordinate action of the mapping class group on the total space the total space is found to have a rich equivariant geometric structure we sketch some connections with arithmetic groups diophantine approximations and certain problems in plane euclidean geometry furthermore these investigations lead to an explicit scheme of integration over the moduli spaces and to the construction of a universal teichmuller space which we hope will provide a formalism for understanding some connections between the teichmuller theory the kp hierarchy and the virasoro algebra these latter applications are pursued elsewhere

a criterion for the conjugacy separability of amalgamated free products of conjugacy separable groups abstract we first prove a criterion for the conjugacy separability of generalized free products of two conjugacy separable groups amalgamating a cyclic subgroup applying this result we show that tree products of a finite number of conjugacy separable residually finitely generated torsion free nilpotent groups amalgamating cyclic subgroups are conjugacy separable from this we derive that tree products of finitely generated torsion free nilpotent groups free groups or surface groups amalgamating cyclic subgroups are conjugacy separable

an embedded mesh method using piecewise constant multipliers with stabilization mathematical and numerical aspects summary an embedded mesh method using piecewise constant multipliers originally proposed by puso et al cmame 2012 is analyzed here to determine effects of the pressure stabilization term and small cut cells the approach is implemented for transient dynamics using the central difference scheme for the time discretization it is shown that the resulting equations of motion are a stable linear system with a condition number independent of mesh size next it is shown that the constraints and the stabilization terms can be recast as non proportional damping such that the time integration of the scheme is provably stable with a critical time step computed from the undamped equations of motion effects of small cuts are discussed throughout the presentation a mesh study is conducted to evaluate the effects of the stabilization on the discretization error and conditioning and is used to recommend an optimal value for stabilization scaling parameter several nonlinear problems are also analyzed and compared with comparable conforming mesh results finally several demanding problems highlighting the robustness of the proposed approach are shown copyright 2014 john wiley sons ltd

euclidean decompositions of noncompact hyperbolic manifolds on introduit une methode pour diviser une variete hyperbolique non compacte de volume fini en morceaux euclidiens canoniques

foliations with good geometry the goal of this article is to show that there is a large class of closed hyperbolic 3 manifolds admitting codimension one foliations with good large scale geometric properties we obtain results in two directions first there is an internal result a possibly singular foliation in a manifold is quasi isometric if when lifted to the universal cover distance along leaves is efficienit up to a bounded multiplicative distortion in measuring distance in the universal cover this means that leaves reflect very well the geometry in the large of the universal cover and are geometrically tight this is the best geometric behavior we previously proved that nonsingular codimension one foliations in closed hyperbolic 3 manifolds can never be quasi isometric in this article we produce a large class of singular quasi isometric codimension one foliations in closed hyperbolic 3 manifolds the foliations are stable and unstable foliations of pseudo anosov flows our second result is an external result relating nonsingular foliations in hyperbolic 3 manifolds with their limit sets in the universal cover that is showing that leaves in the universal cover have good asymptotic behavior let g be a reebless finite depth foliation in a closed hyperbolic 3 manifold then g is not quasi isometric but suppose that g is transverse to a quasigeodesic pseudo anosov flow with quasi isometric stable and unstable foliations which are given by the internal result we then show that the lifts of leaves of g to the universal cover extend continuously to the sphere at infinity and we also produce infinitely many examples satisfying the hypothesis the main tools used to prove these results are first a link between geometric properties of stable unstable foliations of pseudo anosov flows and the topology of these foliations in the tuniversal cover and second a topological theory of the joint structure of the pseudo anosov foliations in the universal cover reebless codimension one foliations are extremely useful for understanding the topology of 3 manifolds for instance they imply that the manifold is irreducible ro its universal cover is homeomorphic to r3 pa leaves are 7rl injective no and transversals are never null homotopic no hence they reflect topological properties of the manifold as for which manifolds have reebless foliations gabai gal ga2 ga3 proved that any compact oriented irreducible 3 manifold with nonzero first betti number has many reebless finite depth foliations roughly a

nitsche s method combined with space time finite elements for ale fluid structure interaction problems we propose a weak method for handling the fluid structure interface in finite element fluid structure interaction based on nitsche s method abh math univ hamburg 36 1971 9 we assume transient incompressible newtonian flow and for the structure undamped linear elasticity for the time discretization we use the time continuous energy conserving galerkin method for the structure and for the fluid we employ the time discontinuous galerkin method this means that the velocity becomes piecewise constant on each timestep for the fluid matching the time derivative of the displacements in the solid which is also piecewise constant over a time step we formulate the method and report some numerical examples using space time oriented elements for the fluid in order to mimic lagrangian or ale type simulations

generalized markoff maps and mcshane s identity abstract we study the relative sl 2 c character varieties of the one holed torus and the action of the mapping class group on the relative character variety we show that the subset of characters satisfying two simple conditions called the bowditch q conditions is open in the relative character variety and that the mapping class group acts properly discontinuously on this subset furthermore this is the largest open subset for which this holds we also show that a generalization of mcshane s identity holds for all characters satisfying the bowditch q conditions finally we show that further variations of the mcshane bowditch identity hold for characters which are fixed by an anosov element of the mapping class group and which satisfy a relative version of the bowditch q conditions with applications to identities for incomplete hyperbolic structures on punctured torus bundles over the circle and also for closed hyperbolic 3 manifolds which are obtained by hyperbolic dehn surgery on such manifolds

triangulated riemann surfaces with boundary and the weil petersson poisson structure given a hyperbolic surface with geodesic boundary s the lengths of a maximal system of disjoint simple geodesic arcs on s that start and end at s perpendicularly are coordinates on the teichmuller space t s we express the weil petersson poisson structure of t s in this system of coordinates and we prove that it limits pointwise to the piecewise linear poisson structure defined by kontsevich on the arc complex of s at the same time we obtain a formula for the first order variation of the distance between two closed geodesics under fenchel nielsen deformation

application of the sinc method to a dynamic elasto plastic problem this paper presents the application of sinc bases to simulate numerically the dynamic behavior of a one dimensional elastoplastic problem the numerical methods that are traditionally employed to solve elastoplastic problems include finite difference finite element and spectral methods however more recently biorthogonal wavelet bases have been used to study the dynamic response of a uniaxial elasto plastic rod giovanni f naldi karsten urban paolo venini a wavelet galerkin method for elastoplasticity problems report 181 rwth aachen igpm and math modelling and scient computing vol 10 2000 in this paper the sinc galerkin method is used to solve the straight elasto plastic rod problem due to their exponential convergence rates and their need for a relatively fewer nodal points sinc based methods can significantly outperform traditional numerical methods j lund k l bowers sinc methods for quadrature and differential equations siam philadelphia 1992 however the potential of sinc based methods for solving elastoplasticity problems has not yet been explored the aim of this paper is to demonstrate the possible application of sinc methods through the numerical investigation of the unsteady one dimensional elastic plastic rod problem

immersed finite element method abstract in this paper the immersed finite element method ifem is proposed for the solution of complex fluid and deformable structure interaction problems encountered in many physical models in ifem a lagrangian solid mesh moves on top of a background eulerian fluid mesh which spans over the entire computational domain hence the mesh generation is greatly simplified moreover both fluid and solid domains are modeled with the finite element methods and the continuity between the fluid and solid sub domains are enforced via the interpolation of the velocities and the distribution of the forces with the reproducing kernel particle method rkpm delta function in comparison with the immersed boundary ib method the higher ordered rkpm delta function enables the fluid domain to have nonuniform spatial meshes with arbitrary geometries and boundary conditions the use of such kernel functions may eventually open doors to multi scale and multi resolution modelings of complex fluid structure interaction problems rigid and deformable spheres dropping in channels are simulated to demonstrate the unique capabilities of the proposed method the results compare well with the experimental data to the authors knowledge these are the first solutions that deal with particulate flows with very flexible solids

an enriched finite element method and level sets for axisymmetric two phase flow with surface tension a finite element method for axisymmetric two phase flow problems is presented the method uses an enriched finite element formulation in which the interface can move arbitrarily through the mesh without remeshing the enrichment is implemented by the extended finite element method x fem which models the discontinuity in the velocity gradient at the interface by a local partition of unity it provides an accurate representation of the velocity field at interfaces on an eulerian grid that is not conformal to the weak discontinuity the interface is represented by a level set which is also used in the construction of the element enrichment surface tension effects are considered and the interface curvature is computed from the level set field the method is demonstrated by several examples copyright 2003 john wiley sons ltd

a fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies application to particulate flow abstract in this article we discuss a methodology that allows the direct numerical simulation of incompressible viscous fluid flow past moving rigid bodies the simulation methods rest essentially on the combination of a lagrange multiplier based fictitious domain methods which allow the fluid flow computations to be done in a fixed flow region b finite element approximations of the navier stokes equations occurring in the global model c time discretizations by operator splitting schemes in order to treat optimally the various operators present in the model the above methodology is particularly well suited to the direct numerical simulation of particulate flow such as the flow of mixtures of rigid solid particles and incompressible viscous fluids possibly non newtonian we conclude this article with the presentation of the results of various numerical experiments including the simulation of store separation for rigid airfoils and of sedimentation and fluidization phenomena in two and three dimensions

on methods for stabilizing constraints over enriched interfaces in elasticity summary enriched finite element approaches such as the extended finite element method provide a framework for constructing approximations to solutions of non smooth problems internal features such as boundaries are represented in such methods by using discontinuous enrichment of the standard finite element basis within such frameworks however imposition of interface constraints and or constitutive relations can cause unexpected difficulties depending upon how relevant fields are interpolated on un gridded interfaces this work address the stabilized treatment of constraints in an enriched finite element context both the lagrange multiplier and penalty enforcement of tied constraints for an arbitrary boundary represented in an enriched finite element context can lead to instabilities and artificial oscillations in the traction fields we demonstrate two alternative variational methods that can be used to enforce the constraints in a stable manner in a bubble stabilized approach fine scale degrees of freedom are added over elements supporting the interface the variational form can be shown to have a similar form to a second approach we consider nitsche s method with the exception that the stabilization terms follow directly from the bubble functions in this work we examine alternative variational methods for enforcing a tied constraint on an enriched interface in the context of two dimensional elasticity we examine several benchmark problems in elasticity and show that only nitsche s method and the bubble stabilization approach produce stable traction fields over internal boundaries we also demonstrate a novel difference between the penalty method and nitsche s method in that the latter passes the patch test exactly regardless of the stabilization parameter s magnitude results for more complicated geometries and triple interface junctions are also presented copyright 2008 john wiley sons ltd

numerical approximations for population growth models this paper aims to introduce a comparison of adomian decomposition method and sinc galerkin method for the solution of some mathematical population growth models from the computational viewpoint the comparison shows that the adomian decomposition method is efficient and easy to use

subdivision stabilised immersed b spline finite elements for moving boundary flows an immersed finite element method is presented to compute flows with complex moving boundaries on a fixed cartesian grid the viscous incompressible fluid flow equations are discretized with b spline basis functions the two scale relation for b splines is used to implement an elegant and efficient technique to satisfy the lbb condition on non grid aligned fluid domains and at moving boundaries the boundary conditions are enforced with a consistent penalty method as originally proposed by nitsche in addition a special extrapolation technique is employed to prevent the loss of numerical stability in presence of arbitrarily small cut cells the versatility and accuracy of the proposed approach is demonstrated by means of convergence studies and comparisons with previous experimental and computational investigations

distance geometry for kissing spheres abstract a kissing sphere is a sphere that is tangent to a fixed reference ball we develop in this paper a distance geometry for kissing spheres which turns out to be a generalization of the classical euclidean distance geometry

a canonical cellular decomposition of the teichmuller space of compact surfaces with boundary using the euclidean decomposition of the hyperbolic surface r c penner gave a canonical cellular decomposition of the decorated teichmuller space of punctured surfaces which is invariant by the action of the mapping class group adapting his method we give a canonical cellular decomposition of the teichmuller space of compact orientable surfaces with non empty boundary

recognizing a relatively hyperbolic group by its dehn fillings dehn fillings for relatively hyperbolic groups generalize the topological dehn surgery on a non compact hyperbolic 3 manifold such as a hyperbolic knot complement we prove a rigidity result saying that if two non elementary relatively hyperbolic groups without suitable splittings have sufficiently many isomorphic dehn fillings then these groups are in fact isomorphic our main application is a solution to the isomorphism problem in the class of non elementary relatively hyperbolic groups with residually finite parabolic groups and with no suitable splittings

the immersed interface method for elliptic equations with discontinuous coefficients and singular sources the authors develop finite difference methods for elliptic equations of the form nabla cdot beta x nabla u x kappa x u x f x in a region omega in one or two space dimension

heegaard splittings the virtually haken conjecture and property τ the behaviour of finite covers of 3 manifolds is a very important but poorly understood topic there are three increasingly strong conjectures in the field that have remained open for over twenty years the virtually haken conjecture the positive virtual b1 conjecture and the virtually fibred conjecture any of these would have profound ramifications for 3 manifold theory in this paper we explore the interaction of these conjectures with the following seemingly unrelated areas eigenvalues of the laplacian and heegaard splittings

a census of cusped hyperbolic 3 manifolds the census provides a basic collection of noncompact hyperbolic 3 manifolds of finite volume it contains descriptions of all hyperbolic 3 manifolds obtained by gluing the faces of at most seven ideal tetrahedra additionally various geometric and topological invariants are calculated for these manifolds the findings are summarized and a listing of all manifolds appears in the microfiche supplement

a new convergence proof of the adomian decomposition method for a mixed hyperbolic elliptic system of conservation laws in this paper we propose a new convergence proof of the adomian s decomposition method adm applied to the generalized nonlinear system of partial differential equations pde s based on new formula for adomian polynomials the decomposition scheme obtained from the adm yields an analytical solution in the form of a rapidly convergent series for a system of conservation laws systems of conservation laws is presented we obtain the stability of the approximate solution when the system changes type we show with an explicit example that the latter property is true for general cauchy problem satisfying convergence hypothesis the results indicate that the adm is effective and promising

construction and recognition of hyperbolic 3 manifolds with geodesic boundary we extend to the context of hyperbolic 3 manifolds with geodesic boundary thurston s approach to hyperbolization by means of geometric triangulations in particular we introduce moduli for partially truncated hyperbolic tetrahedra and we discuss consistency and completeness equations moreover building on previous work of ushijima we extend weeks tilt formula algorithm which computes the epstein penner canonical decomposition to an algorithm that computes the kojima decomposition our theory has been exploited to classify all the orientable finite volume hyperbolic 3 manifolds with non empty compact geodesic boundary admitting an ideal triangulation with at most four tetrahedra the theory is particularly interesting in the case of complete finite volume manifolds with geodesic boundary in which the boundary is non compact we include this case using a suitable adjustment of the notion of ideal triangulation and we show how this case arises within the theory of knots and links

computing trisections of 4 manifolds we describe an algorithm to compute trisections of orientable four manifolds using arbitrary triangulations as input this results in explicit complexity bounds for the trisection genus of a 4 manifold in terms of the number of pentachora 4 simplices in a triangulation

convergence of freely decomposable kleinian groups we consider a compact orientable hyperbolic 3 manifold with a compressible boundary suppose that we are given a sequence of geometrically finite hyperbolic metrics whose conformal boundary structures at infinity diverge to a projective lamination we prove that if this limit projective lamination is doubly incompressible then the sequence has compact closure in the deformation space as a consequence we generalise thurston s double limit theorem and solve his conjecture on convergence of function groups affirmatively

the discontinuous enrichment method for elastic wave propagation in the medium frequency regime the discontinuous enrichment method dem is specified and developed for the solution of two dimensional elastic wave propagation problems in the frequency domain the classical finite element polynomial approximation of the displacement field is enriched by the superposition of discontinuous pressure and shear wave functions the continuity of the solution across the element interfaces is weakly enforced by suitable lagrange multipliers higher order rectangular dem elements are constructed and benchmarked against the standard higher order polynomial galerkin elements for two dimensional problems in the medium frequency regime in general it is found that for such applications dem can achieve the same accuracy as the p finite element method using a similar computational complexity but with about 10 times fewer degrees of freedom this highlights the potential of this hybrid method for problems where the scale of vibrations is very small compared to the characteristic dimension of the physical medium copyright 2006 john wiley sons ltd

an embedded mesh method in a multiple material ale abstract a new approach for treating the mechanical interactions of overlapping finite element meshes is presented referred to as embedded mesh methods here these overlapping mesh methods typically include a foreground solid mesh and a background euler fluid grid or solid mesh a number of different approaches have been used in previous work to characterize the interactions of the background and foreground meshes at the interface lagrange multipliers are well suited to enforce the continuity constraints but care must be taken such that the resulting formulation is stable several lagrange multiplier techniques are examined in this work and applied to coupling solid meshes and fluid structure interaction type problems in addition details regarding implementation in a two step multi material arbitrary lagrangian eulerian ale code are presented example problems demonstrate convergence and applicability to a range of problems in particular the fluid structure interaction examples focus on blast applications

the existence of maps of nonzero degree between aspherical 3 manifolds for any two closed orientable surfaces there is a map of nonzero degree from one to another this result is based on the fact that the orientable closed surface are classified completely there is no such a classification in dimension 3 in this paper all closed aspherical 3 manifolds are divided into eight classes a complete answer of the existences of nonzero degree maps between 3 manifolds in the different classes is obtained in a reasonable sense the existence of nonzero degree maps between 3 manifolds in the same class are also discussed there are several results of independent interest it is noted that the existence of a map of nonzero degree between two 3 manifolds is a very restrictive condition posed on those two 3 manifolds which is much different from the case of dimension 2 the shape of our work is certainly influenced by thurston however both the statements and the proofs of our theorems do not involve the thurston s geometries we understand that if we state the results in the category of haken manifolds and thurston s geometrical manifolds and invoke the g r o m o v norm of hyperbol ic 3 manifold see chap 6 of r t l and chap 4 of gro the proof of some result in the paper can be simplified we present our work in the way below for two reasons a we prefer to prove all results in a uniform elementary way in the sense of using only the fundamental groups and the incompressible surfaces of 3 manifolds b since the thurston s most famous conjecture that every atoroidal closed irreducible 3 manifold has a hyperbolic structure is still open we get the results in a theoretically wider category there are 5 sections after the introduction all manifolds and maps under consideration are piece wise linear there is nothing lost under this assumption see chap 1 of hi in the first four sections of these five all 3 manifolds are orientable and irreducible section 1 states the theorems proved in the paper section 2 provides results which are used to prove the theorems section 3 and sect 4 are the proofs of the theorems various examples are given in sect 4

an extended finite element method lagrange multiplier based approach for fluid structure interaction abstract this paper presents a new fixed grid fluid structure interaction scheme that can be applied to the interaction of most general structures with incompressible flow it is based on an extended finite element method xfem based strategy the extended eulerian fluid field and the lagrangian structural field are partitioned and iteratively coupled using lagrange multiplier techniques for non matching grids the approach allows the simulation of the interaction of thin and bulky structures exhibiting large deformations finally qualitative examples and a benchmark computation demonstrate key features and accuracy of the method

dedekind zeta motives for totally real number fields let k be a totally real number field for every odd n 3 we construct an element in the category mt k of mixed tate motives over k out of the quotient of a product of hyperbolic spaces by an arithmetic group by a volume calculation we prove that its period is a rational multiple of pi n k mathbb q zeta k 1 n where zeta k 1 n denotes the special value of the dedekind zeta function of k we deduce that the group mathrm ext 1 mathrm mt k mathbb q 0 mathbb q n is generated by the cohomology of a quadric relative to hyperplanes and that zeta k 1 n is a determinant of volumes of geodesic hyperbolic simplices defined over k

analytical approximations and pade approximants for volterra s population model in this paper an analytic approximation for volterra s model for population growth of a species in a closed system is presented the nonlinear integro differential model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation the series solution method and the decomposition method are implemented independently to the model and to a related ode the pade approximants that often show superior performance over series approximations are effectively used in the analysis to capture the essential behavior of the population u t of identical individuals

the immersed fictitious element method for fluid structure interaction volumetric consistency compressibility and thin members a weak form and an implementation are given for fluid structure interaction by the immersed fictitious element method for compressible fluids the weak form is applicable to models where the fluid is described by eulerian coordinates while the solid is described by lagrangian coordinates which suits their intrinsic characteristics a unique feature of the method is the treatment of the fictitious fluid by a lagrangian description which simplifies the interface conditions methods for enforcing volumetric consistency between the fluid and solid and treating thin members are given although a compressible viscous fluid is considered here the new developments can be applied to incompressible fluids

dislocations by partition of unity a new finite element method for accurately modelling the displacement and stress fields produced by a dislocation is proposed the methodology is based on a local enrichment of the finite element space by closed form solutions for dislocations in infinite media via local partitions of unity this allows the treatment of both arbitrary boundary conditions and interfaces between materials the method can readily be extended to arrays of dislocations 3d problems large strains and non linear constitutive models results are given for an edge dislocation in a hollow cylinder and in an infinite medium for the cases of a glide plane intersecting a rigid obstacle and an interface between two materials copyright 2005 john wiley sons ltd

angled decompositions of arborescent link complements this paper describes a way to subdivide a 3 manifold into angled blocks namely polyhedral pieces that need not be simply connected when the individual blocks carry dihedral angles that fit together in a consistent fashion we prove that a manifold constructed from these blocks must be hyperbolic the main application is a new proof of a classical unpublished theorem of bonahon and siebenmann that all arborescent links except for three simple families of exceptions have hyperbolic complements in the 1990s andrew casson introduced a powerful technique for constructing and studying cusped hyperbolic 3 manifolds his idea was to subdivide a manifold m into angled ideal tetrahedra that is tetrahedra whose vertices are removed and whose edges carry prescribed dihedral angles when the dihedral angles of the tetrahedra add up to 2 around each edge of m the triangulation is called an angled triangulation casson proved that every orientable cusped 3 manifold that admits an angled triangulation must also admit a hyperbolic metric and outlined a possible way to find the hyperbolic metric by studying the volumes of angled tetrahedra an idea also developed by rivin 17 the power of casson s approach lies in the fact that the defining equations of an angled triangulation are both linear and local making angled triangulations relatively easy to find and deform much easier than to study an actual hyperbolic triangulation as in 14 20 or in some aspects of thurston s seminal approach 22 the aim of this paper is to extend this approach to larger and more complicated building blocks these blocks can be ideal polyhedra instead of tetrahedra but they may also have nontrivial topology in general an angled block will be a 3 manifold whose boundary is subdivided into faces looking locally like the faces of an ideal polyhedron in a sense to be defined the edges between adjacent faces carry prescribed dihedral angles in section 2 we will describe the precise combinatorial conditions that the dihedral angles must satisfy these conditions will imply the following generalization of a result by lackenby 11 corollary 4 6

discontinuous galerkin methods for non linear elasticity this paper presents the formulation and a partial analysis of a class of discontinuous galerkin methods for quasistatic non linear elasticity problems these methods are endowed with several salient features the equations that define the numerical scheme are the euler lagrange equations of a one field variational principle a trait that provides an elegant and simple derivation of the method in consonance with general discontinuous galerkin formulations it is possible within this framework to choose different numerical fluxes numerical evidence suggests the absence of locking at near incompressible conditions in the finite deformations regime when piecewise linear elements are adopted finally a conceivable surprising characteristic is that as demonstrated with numerical examples these methods provide a given accuracy level for a comparable and often lower computational cost than conforming formulations stabilization is occasionally needed for discontinuous galerkin methods in linear elliptic problems in this paper we propose a sufficient condition for the stability of each linearized non linear elastic problem that naturally includes material and geometric parameters the latter needed to account for buckling we then prove that when a similar condition is satisfied by the discrete problem the method provides stable linearized deformed configurations upon the addition of a standard stabilization term we conclude by discussing the complexity of the implementation and propose a computationally efficient approach that avoids looping over both elements and element faces several numerical examples are then presented in two and three dimensions that illustrate the performance of a selected discontinuous galerkin method within the class copyright 2006 john wiley sons ltd

a local space time discontinuous finite element method we present a locally enriched space time finite element method for solving hyperbolic problems with discontinuities the space time formulation is coupled to a standard semidiscrete finite element method the discontinuities are captured by a space time version of the extended finite element method which treats arbitrary moving discontinuities since the discontinuities are local the enriched space time method is only needed around the discontinuities which provides significant computational savings the coupling is implemented through a weak enforcement of the continuity of the flux between the space time and semidiscrete domains in a manner similar to discontinuous galerkin methods the method is illustrated through one dimensional problems it displays remarkable accuracy in capturing moving discontinuities both in their amplitude and speed

recognizing constant curvature discrete groups in dimension 3 we characterize those discrete groups g which can act properly discontinuously isometrically and cocompactly on hyperbolic 3 space ihi3 in terms of the combinatorics of the action of g on its space at infinity the major ingredients in the proof are the properties of groups that are negatively curved in the large that is gromov hyperbolic the combinatorial riemann mapping theorem and the sullivan tukia theorem on groups which act uniformly quasiconformally on the 2 sphere

fluid structure interaction by the discontinuous galerkin method for large deformations a discontinuous galerkin method for large deformation fluid structure interaction problems is developed the fluid structure interface can be arbitrarily aligned relative to the fluid grid an eulerian description is used for the fluid with a lagrangian description of the solid results are presented for several examples that show excellent agreement with immersed fictitious element methods copyright 2008 john wiley sons ltd

three dimensional manifolds kleinian groups and hyperbolic geometry 1 a conjectural picture of 3 manifolds a major thrust of mathematics in the late 19th century in which poincare had a large role was the uniformization theory for riemann surfaces that every conformai structure on a closed oriented surface is represented by a riemannian metric of constant curvature for the typical case of negative euler characteristic genus greater than 1 such a metric gives a hyperbolic structure any small neighborhood in the surface is isometric to a neighborhood in the hyperbolic plane and the surface itself is the quotient of the hyperbolic plane by a discrete group of motions the exceptional cases the sphere and the torus have spherical and euclidean structures three manifolds are greatly more complicated than surfaces and i think it is fair to say that until recently there was little reason to expect any analogous theory for manifolds of dimension 3 or more except perhaps for the fact that so many 3 manifolds are beautiful the situation has changed so that i feel fairly confident in proposing the

a general discontinuous galerkin method for finite hyperelasticity formulation and numerical applications a discontinuous galerkin formulation of the boundary value problem of finite deformation elasticity is presented the primary purpose is to establish a discontinuous galerkin framework for large deformations of solids in the context of statics and simple material behaviour with a view toward further developments involving behaviour or models where the dg concept can show its superiority compared to the continuous formulation the method is based on a general hu washizu de veubeke functional allowing for displacement and stress discontinuities in the domain interior it is shown that this approach naturally leads to the formulation of average stress fluxes at interelement boundaries in a finite element implementation the consistency and linearized stability of the method in the non linear range as well as its convergence rate are proven an implementation in three dimensions is developed showing that the proposed method can be integrated into conventional finite element codes in a straightforward manner in order to demonstrate the versatility accuracy and robustness of the method examples of application and convergence studies in three dimensions are provided copyright 2006 john wiley sons ltd

an eulerian lagrangian method for fluid structure interaction based on level sets abstract we describe a method for fluid structure interaction with the interface and free surfaces defined by level sets the fluid is treated by an eulerian mesh whereas the solid or structure by a lagrangian mesh the level set method provides a compact framework for writing the weak form and for developing and computing the discretized equations lagrange multiplier methods and penalty methods are used to couple the fluid and structure results are presented for a few compressible fluid problems representative of high pressure waves

the meshless finite element method a meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n and the condition that the shape functions depend only on the node positions furthermore the method proposed also shares several of the advantages of the finite element method such as a the simplicity of the shape functions in a large part of the domain b c0 continuity between elements which allows the treatment of material discontinuities and c ease of introduction of the boundary conditions copyright 2003 john wiley sons ltd

word hyperbolic dehn surgery in the late 1970 s thurston dramatically changed the nature of 3 manifold theory with the introduction of his geometrisation conjecture and by proving it in the case of haken 3 manifolds 23 the conjecture for general closed orientable 3 manifolds remains perhaps the most important unsolved problem in the subject a weaker form of the conjecture 19 deals with the fundamental group of a closed orientable 3 manifold it proposes that either it contains z z as a subgroup or it is word hyperbolic in the sense of gromov 11 word hyperbolic groups are precisely those groups which satisfy a linear isoperimetric inequality they are of fundamental importance in geometric group theory and have very many useful properties

a symmetric positive definite formulation for monolithic fluid structure interaction in this paper we consider a strongly coupled monolithic fluid structure interaction framework for incompressible flow as opposed to a loosely coupled partitioned method this requires solving a single linear system that combines the unknown velocities of the structure with the unknown pressures of the fluid in our previous work we were able to obtain a symmetric formulation of this coupled system however it was also indefinite making it more difficult to solve in fact in practice there have been cases where we have been unable to invert the system in this paper we take a novel approach that consists of factoring the damping matrix of deformable structures and show that this can be used to obtain a symmetric positive definite system at least to the extent that the uncoupled systems were symmetric positive definite we use a traditional mac grid discretization of the fluid and a fully lagrangian discretization of the structures for the sake of exposition noting that our procedure can be generalized to other scenarios for the special case of rigid bodies where there are no internal damping forces we exactly recover the system of batty et al 2007 4