moduli of fibered surface pairs from twisted stable maps in this paper we use the theory of twisted stable maps to construct compactifications of the moduli space of pairs x rightarrow c s f where x rightarrow c is a fibered surface s is a sum of sections f is a sum of marked fibers and x s f is a stable pair in the sense of the minimal model program this generalizes the work of abramovich vistoli who compactified the moduli space of fibered surfaces with no marked fibers furthermore we compare our compactification to alexeev s space of stable maps and the ksba compactification as an application we describe the boundary of a compactification of the moduli space of elliptic surfaces

a high order discontinuous galerkin method for wave propagation through coupled elastic acoustic media we introduce a high order discontinuous galerkin dg scheme for the numerical solution of three dimensional 3d wave propagation problems in coupled elastic acoustic media a velocity strain formulation is used which allows for the solution of the acoustic and elastic wave equations within the same unified framework careful attention is directed at the derivation of a numerical flux that preserves high order accuracy in the presence of material discontinuities including elastic acoustic interfaces explicit expressions for the 3d upwind numerical flux derived as an exact solution for the relevant riemann problem are provided the method supports h non conforming meshes which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength as well as dynamic adaptivity to track solution features the use of high order elements controls numerical dispersion enabling propagation over many wave periods we prove consistency and stability of the proposed dg scheme to study the numerical accuracy and convergence of the proposed method we compare against analytical solutions for wave propagation problems with interfaces including rayleigh lamb scholte and stoneley waves as well as plane waves impinging on an elastic acoustic interface spectral rates of convergence are demonstrated for these problems which include a non conforming mesh case finally we present scalability results for a parallel implementation of the proposed high order dg scheme for large scale seismic wave propagation in a simplified earth model demonstrating high parallel efficiency for strong scaling to the full size of the jaguar cray xt5 supercomputer

the grothendieck duality theorem via bousfield s techniques and brown representability grothendieck proved that if f x y is a proper morphism of nice schemes then rf has a right adjoint which is given as tensor product with the relative canonical bundle the original proof was by patching local data deligne proved the existence of the adjoint by a global argument and verdier showed that this global adjoint may be computed locally in this article we show that the existence of the adjoint is an immediate consequence of brown s representability theorem lit follows almost as imme diately by smashing arguments that the adjoint is given by tensor product with a dualising complex verdier s base change theorem is an easy conse quence department of mathematics university of virginia charlottesville virginia 22903 e mail address an3rqvirginia edu this content downloaded from 157 55 39 27 on wed 07 sep 2016 06 26 19 utc all use subject to http about jstor org terms

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

stable maps in higher dimensions we formulate a notion of stability for maps between polarised varieties which generalises kontsevich s definition when the domain is a curve and tian donaldson s definition of k stability when the target is a point we give some examples such as kodaira embeddings and fibrations we prove the existence of a projective moduli space of canonically polarised stable maps generalising the kontsevich alexeev moduli space of stable maps in dimensions one and two we also state an analogue of the yau tian donaldson conjecture in this setting relating stability of maps to the existence of certain canonical kahler metrics

p sv wave propagation in heterogeneous media velocity stress finite difference method i present a finite difference method for modeling p sv wave propagation in heterogeneous media this is an extension of the method i previously proposed for modeling sh wave propagation by using velocity and stress in a discrete grid the two components of the velocity cannot be defined at the same node for a complete staggered grid the stability condition and the p wave phase velocity dispersion curve do not depend on the poisson s ratio while the s wave phase velocity dispersion curve behavior is rather insensitive to the poisson s ratio therefore the same code used for elastic media can be used for liquid media where s wave velocity goes to zero and no special treatment is needed for a liquid solid interface typical physical phenomena arising with p sv modeling such as surface waves are in agreement with analytical results the weathered layer and corner edge models show in seismograms the same converted phases obtained by previous authors this method gives stable results for step discontinuities as shown for a liquid layer above an elastic half space the head wave preserves the correct amplitude finally the corner edge model illustrates a more complex geometry for the liquid solid interface as the poisson s ratio v increases from 0 25 to 0 5 the shear converted phases are removed from seismograms and from the time section of the wave field

assessment of rod behaviour theories used in spectral finite element modelling abstract in this work different theories of rods have been discussed and compared the investigated theories are widely used in spectral finite element modelling of rod behaviour associated with propagation of symmetric longitudinal waves these are various single two mode and three mode theories including the elementary classical love and mindlin herrmann approaches as well as new two three and four mode theories proposed by the authors dispersion curves associated with each theory obtained by the use of hamilton s principle have been presented and discussed in the paper the investigation programme carried out by the authors aimed to show major differences and similarities between the rod theories and to discuss certain numerical aspects of their application great attention has been paid on properties limitations as well as difficulties associated with the use of the theories the results obtained from a wide program on numerical tests allowed the authors to draw certain general conclusions that are valid not only in the field of the spectral finite element method but also in the field of dynamics of engineering rod structures

order preservation in limit algebras abstract the matrix units of a digraph algebra a induce a relation known as the diagonal order on the projections in a masa in the algebra normalizing partial isometries in a act on these projections by conjugation they are said to be order preserving when they respect the diagonal order order preserving embeddings in turn are those embeddings which carry order preserving normalizers to order preserving normalizers this papers studies operator algebras which are direct limits of finite dimensional algebras with order preserving embeddings we give a complete classification of direct limits of full triangular matrix algebras with order preserving embeddings we also investigate the problem of characterizing algebras with order preserving embeddings

log canonical singularities are du bois a recurring difficulty in the minimal model program mmp is that while log terminal singularities are quite well behaved for instance they are rational log canonical singularities are much more complicated they need not even be cohenmacaulay the aim of this paper is to prove that as conjectured in kol92 1 13 log canonical singularities are du bois the concept of du bois singularities abbreviated as db was introduced by steenbrink in ste83 as a weakening of rationality it is not clear how to define du bois singularities in positive characteristic so we work over a field of characteristic 0 throughout the paper the precise definition is rather involved see 1 10 but our main applications rely only on the following consequence

non conforming curved finite element schemes for time dependent elastic acoustic coupled problems high order numerical methods for solving time dependent acoustic elastic coupled problems are introduced these methods based on finite element techniques allow for a flexible coupling between the fluid and the solid domain by using non conforming meshes and curved elements since characteristic waves travel at different speeds through different media specific levels of granularity for the mesh discretization are required on each domain making impractical a possible conforming coupling in between advantageously physical domains may be independently discretized in our framework due to the non conforming feature consequently an important increase in computational efficiency may be achieved compared to other implementations based on conforming techniques namely by reducing the total number of degrees of freedom differently from other non conforming approaches proposed so far our technique is relatively simpler and requires only a geometrical adjustment at the coupling interface at a preprocessing stage so that no extra computations are necessary during the time evolution of the simulation on the other hand as an advantage of using curvilinear elements the geometry of the coupling interface between the two media of interest is faithfully represented up to the order of the scheme used in other words higher order schemes are in consonance with higher order approximations of the geometry concerning the time discretization we analyze both explicit and implicit schemes these schemes are energy conserving and for the explicit case the stability is guaranteed by a cfl condition in order to illustrate the accuracy and convergence of these methods a set of representative numerical tests are presented

the pseudospectral method accurate representation of interfaces in elastic wave calculations when finite difference methods are used to solve the elastic wave equation in a discontinuous medium the error has two dominant components dispersive errors lead to artificial wave trains errors from interfaces lead to circular wavefronts emanating from each location where the interface appears jagged to the rectangular grid the pseudospectral method can be viewed as the limit of finite differences with infinite order of accuracy with this method dispersive errors are essentially eliminated the mappings introduced in this paper also eliminate the other dominant error source test calculations confirm that these mappings significantly enhance the already highly competitive pseudospectral method with only a very small additional cost although the mapping method is described here in connection with the pseudospectral method it can also be used with high order finite difference approximations

modelling thermal convection with large viscosity gradients in one block of the cubed sphere a numerical method solving thermal convection problems with variable viscosity in a spherical shell is presented several features of earlier programs solving the same problem in cartesian geometry are adopted because of their efficiency and robustness finite volume formulation multigrid flow solver parallel implementation a recent composite mesh gridding technique for a spherical surface termed the cubed sphere has proven to be successful in solving other partial differential equations in geophysical problems it is used here because of its various advantages absence of geometrical singularities same metric on each block simple coupling of adjacent blocks in addition it is a good tool to implement grid based methods proven efficient in the cartesian context since it provides a mesh reasonably close to uniform although as in the cartesian case convergence rates decrease with increasing viscosity gradients global contrasts up to 10 6 are obtained at a reasonable cost

on conjugacy of masas and the outer automorphism group of the cuntz algebra we investigate the structure of the outer automorphism group of the cuntz algebra and closely related with this problem of conjugacy of masaa in on in particular we exhibit an uncountable family of masas conjugate to the standard masa dn via bogolubov automorphisms that are not inner conjugate to dn

cohomology and base change for algebraic stacks we prove that cohomology and base change holds for algebraic stacks generalizing work of brochard in the tame case we also show that hom spaces on algebraic stacks are represented by abelian cones generalizing results of grothendieck brochard olsson lieblich and roth starr to accomplish all of this we prove that a wide class of relative ext functors in algebraic geometry are coherent in the sense of m auslander

the cubed sphere a new gridding technique for the solution of partial differential equations in spherical geometry is presented the method is based on a decomposition of the sphere into six identical regions obtained by projecting the sides of a circumscribed cube onto a spherical surface by choosing the coordinate lines on each region to be arcs of great circles one obtains six coordinate systems which are free of any singularity and define the same metric taking full advantage of the symmetry properties of the decomposition a variation of the composite mesh finite difference method can be applied to couple the six grids and obtain with a high degree of efficiency very accurate numerical solutions of partial differential equations on the sphere the advantages of this new technique over both spectral and uniform longitude latitude grid point methods are discussed in the context of applications on serial and parallel architectures we present results of two test cases for numerical approximations to the shallow water equations in spherical geometry the linear advection of a cosine bell and the nonlinear evolution of a rossby haurwitz wave performance analysis for this latter case indicates that the new method can provide with substantial savings in execution times numerical solutions which are as accurate as those obtainable with the spectral transform method

a fourier spectral element algorithm for thermal convection in rotating axisymmetric containers we present a fourier spectral element approach for modeling thermal convection in a rotating axisymmetric container following the theory detailed in bernardi et al c bernardi m dauge y maday spectral methods for axisymmetric domains gauthier villars paris 1999 a fourier expansion of the field variables is performed in the periodic direction and the resulting collection of meridional problems is discretized by means of a parallel spectral element method a gauss lobatto jacobi 0 1 quadrature which incorporates the cylindrical radius in its weight is introduced to avoid a potential degeneracy of the discrete set of equations due to those nodes located on the axis of symmetry a second order timestepping scheme is presented which treats the coriolis and viscous forces implicitly numerical comparisons with analytical and published numerical solutions in spherical and cylindrical geometries are presented which highlight the accuracy of the model and demonstrate its spectral convergence properties

fibred surfaces varieties isogenous to a product and related moduli spaces a fibration of an algebraic surface s over a curve b with fibres of genus at least 2 has constant moduli iff it is birational to the quotient of a product of curves by the action of a finite group g a variety isogenous to a higher product is the quotient of a product of curves of genus at least 2 by the free action of a finite group theorem b gives a characterization of surfaces isogenous to a higher product in terms of the fundamental group and of the euler number theorem c classifies the groups thus occurring and shows that after fixing the group and the euler number one obtains an irreducible moduli space the result of theorem b is extended to higher dimension in theorem g thus generalizing cf also theorem h results of jost yau and mok concerning varieties whose universal cover is a polydisk theorem a shows that fibrations where the fibre genus and the genus of the base b are at least 2 are invariants of the oriented differentiable structure the main theorems d and e characterize surfaces carrying constant moduli fibrations as surfaces having a zariski open set satisfying certain topological conditions e g having the right euler number the right fundamental group and the right fundamental group at infinity 0 introduction the study of fibrations of a smooth algebraic surface s over a smooth algebraic curve b lies at the heart of the classification theory and of the geometry of algebraic surfaces our main results in this paper theo rems d e concern a topological characterization of surfaces admitting a constant moduli fibration these results are intimately related to a series of variations on the same theme also in higher dimension and to a circle of allied techniques which we present in the course of the paper the first new result we have in this direction and which is presented in section 2 after we recall several known results some classical some quite recent is the following theorem on the dif ferentiable invariance of the genus of fibres cf theorem 2 9 for a more precise statement theorem a let f s b be a fibration of the surface s over a curve b of genus b 2 and with fibre f of genus g 1 assume that s is another smooth compact kahler surface which is orientedly diffeomorphic to s then the subspace of h 1 s corresponding to f h 1 b determines a fibration f s b with

non conforming high order approximations of the elastodynamics equation in this paper we formulate and analyze two non conforming high order strategies for the approximation of elastic wave problems in heterogeneous media namely the mortar spectral element method and the discontinuous galerkin spectral element method starting from a common variational formulation we make a full comparison of the two techniques from the points of view of accuracy convergence grid dispersion and stability

a space time finite element method for structural acoustics in infinite domains part 1 formulation stability and convergence abstract a space time finite element method for solution of the exterior structural acoustics problem involving the interaction of vibrating elastic structures submerged in an infinite acoustic fluid is formulated in particular time discontinuous galerkin and galerkin least squares gls variational formulations for coupled structural acoustics in unbounded domains are developed and analyzed for stability and convergence the formulation employs a finite computational fluid domain surrounding the structure and incorporates time dependent non reflecting boundary conditions on the fluid truncation boundary energy estimates are obtained which allow us to prove the unconditional stability of the method for the coupled fluid structure problem with absorbing boundaries the methods developed are especially useful for the application of adaptive solution strategies for transient acoustics in which unstructured space time meshes are used to track waves propagating along space time characteristics an important feature of the space time formulation is the incorporation of temporal jump operators which allow for finite element interpolations that are discontinaous in time for additional stability least squares operators based on local residuals of the structural acoustics equations including the non reflecting boundary conditions are incorporated the energy decay estimates and high order accuracy predicted by our a priori error estimates are demonstrated numerically in a simple canonical example

solving elastodynamics in a fluid solid heterogeneous sphere a parallel spectral element approximation on non conforming grids we present a spectral element approach for modeling elastic wave propagation in a solid fluid sphere where the local effects of gravity are taken into account the equations are discretized in terms of the displacement in the solid and the velocity potential in a neutrally stratified fluid the spatial approximation is based upon a spherical mesh of hexahedra in which local refinement allows for adapting the discretization to the variation of elastic parameters in both the solid and the fluid regions continuity constraints across the non conforming interfaces are introduced through lagrange multipliers which are further discretized by the mortar element method due to the spherical nature of the non conforming interfaces the mortar method turns out to be functionally conforming and allows for an equal order interpolation of the primal variables and the lagrange multipliers the method is shown to provide an accurate solution when compared to analytical calculations obtained for radial models of elastic parameters its parallel implementation is based upon a simple domain decomposition strategy which makes it efficient to solve large problems as those imposed by planetary scales

free boundary conditions of arbitrary polygonal topography in a two dimensional explicit elastic finite difference scheme we present a simple method for simulating 2 d elastic waves in a model with free surface topography of polygonal shape i e a continuous but irregular surface composed of line segments our method requires special treatment for each of the six specific cases involving line segments of various slopes as well as transition points between the sloping segments for brevity only nonnegatively sloping segments are specifically included on an inclined free surface vanishing stress conditions are implemented using a rotated coordinate system parallel to the inclined boundary at transition points on the topography between line segments we use a first order approximate boundary condition in a locally rotated coordinate system aligned with the bisector of the corner as in the classical one sided explicit approximation scheme widely used for the flat free surface case these extrapolation formulas are accurate to first order in spatial increment numerical tests indicate that the present scheme is stable over

fourth order finite difference p sv seismograms i describe the properties of a fourth order accurate space second order accurate time two dimensional p sk finite difference scheme based on the madariagavirieux staggered grid formulation the numerical scheme is developed from the first order system of hyperbolic elastic equations of motion and constitutive laws expressed in particle velocities and stresses the madariaga virieux staggered grid scheme has the desirable quality that it can correctly model any variation in material properties including both large and small poisson s ratio materials with minimal numerical dispersion and numerical anisotropy dispersion analysis indicates that the shortest wavelengths in the model need to be sampled at 5 gridpoints wavelength the scheme can be used to accurately simulate wave propagation in mixed acoustic elastic media making it ideal for modeling marine problems explicitly calculating both velocities and stresses makes it relatively simple to initiate a source at the free surface or within a layer and to satisfy free surface boundary conditions benchmark comparisons of finite difference and analytical solutions to lamb s problem are almost identical as are comparisons of finite difference and reflectivity solutions for elastic elastic and acoustic elastic layered models

approximately finitely acting operator algebras let e be an operator algebra on a hilbert space with finite dimensional c algebra c e a classification is given of the locally finite algebras a0 formula ak k and the operator algebras a formula ak k obtained as limits of direct sums of matrix algebras over e with respect to star extendible homomorphisms the invariants in the algebraic case consist of an additive semigroup with scale which is a right module for the semiring ve homu e e of unitary equivalence classes of star extendible homomorphisms this semigroup is referred to as the dimension module invariant in the operator algebra case the invariants consist of a metrized additive semigroup with scale and a contractive right module ve action subcategories of algebras determined by restricted classes of embeddings such as 1 decomposable embeddings between digraph algebras are also classified in terms of simplified dimension modules

solution of the equations of dynamic elasticity by a chebychev spectral method we present a spectral method for solving the two dimensional equations of dynamic elasticity based on a chebychev expansion in the vertical direction and a fourier expansion for the horizontal direction the technique can handle the free surface boundary condition more rigorously than the ordinary fourier method the algorithm is tested against problems with known analytic solutions including lamb s problem of wave propagation in a uniform elastic half space reflection from a solid solid interface and surface wave propagation in a haft space containing a low velocity layer agreement between the solutions is very good a fourth example of wave propagation in a laterally heterogeneous structure is also presented results indicate that the method is very accurate and only about a factor of two slower than the fourier method

accuracy of finite difference and finite element modeling of the scalar and elastic wave equations numerical solutions of the scalar and elastic wave equations have greatly aided geophysicists in both forward modeling and migration of seismic wave fields in complicated geologic media and they promise to be invaluable in solving the full inverse problem this paper quantitatively compares finite difference and finite element solutions of the scalar and elastic hyperbolic wave equations for the most popular implicit and explicit time domain and frequency domain techniques in addition to versatility and ease of implementation it is imperative that one choose the most cost effective solution technique for a fixed degree of accuracy to be of value a solution technique must be able to minimize 1 numerical attenuation or amplification 2 polarization errors 3 numerical anisotropy 4 errors in phase and group velocities 5 extraneous numerical parasitic modes 6 numerical diffraction and scattering and 7 errors and transmission coefficients this paper shows that in homogeneous media the

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

forward modeling by a fourier method a fourier or pseudospectral forward modeling algorithm for solving the two dimensional acoustic wave equation is presented the method utilizes a spatial numerical grid to calculate spatial derivatives by the fast fourier transform time derivatives which appear in the wave equation are calculated by second order differcncing the scheme requires fewer grid points than finite diffcrcnce methods to achieve the same accuracy it is therefore believed that the fourier method will prove more efficient than finitedifference methods especially when dealing with threedimensional models the fourier forward modeling method was tested against two problems a single layer problem with a known analytic solution and a wedge problem which was also tested by physical modeling the numerical results agreed with both the analytic and physical model results furthermore the numerical model facilitates the explanation of certain events on the time section of the physical model which otherwise could not easily be taken into account

projectivity of the moduli space of stable log varieties and subadditivity of log kodaira dimension reference epfl article 231100doi 10 1090 jams 871 url http dx doi org 10 1090 jams 871 record created on 2017 09 19 modified on 2017 10 02

how to render second order accurate time stepping algorithms fourth order accurate while retaining the stability and conservation properties abstract for a fairly general class of second order accurate algorithms a sub stepping procedure is described which achieves fourth order accuracy while retaining the stability conservation properties and implementation of the underlying second order method two features render the proposed approach especially attractive from a computational perspective over conventional fourth order methods first the improved fourth order accuracy is attained merely by two additional residual evaluations with no changes in the implementation of the underlying second order method in particular no additional storage or extra computations of high order gradients are required second for hamiltonian systems the stability properties and possible conservation properties of the underlying second order method such as energy momentum and symplectic character are preserved the new technique is applied to a number of standard algorithms for elastodynamics structural and rigid body dynamics in particular when applied to the recently proposed second order accurate energy momentum method this approach results in a fourth order accurate energy linear and angular momentum conserving algorithm for general hamiltonian systems

the spectral element method for the shallow water equations on the sphere the spectral element method is implemented for the shallow water equations in spherical geometry and its performance is compared with other models this is the first step in evaluating the suitability of spectral elements for climate modeling the potential advantages and disadvantages of spectral elements over more conventional models used for climate studies are discussed the method requires that the sphere be tiled with rectangles for which we make use of the gnomonic projection to map the sphere onto the cube to measure the performance of the method relative to other models results are presented from a standard suite of shallow water test cases for the sphere these results confirm the spectral accuracy of the method

fibered stable varieties reference epfl article 231103doi 10 1090 tran 6386 url http dx doi org 10 1090 tran 6386 record created on 2017 09 19 modified on 2017 10 02

numerical simulation of interface waves by high order spectral modeling techniques few problems in elastodynamics have a closed form analytical solution the others can be investigated with semianalytical methods but in general one is not sure whether these methods give reliable solutions the same happens with numerical techniques for instance finite difference methods solve in principle any complex problem including those with arbitrary inhomogeneities and boundary conditions however there is no way to verify the quantitative correctness of the solutions the major problems are stability with respect to material properties numerical dispersion and the treatment of boundary conditions in practice these problems may produce inaccurate solutions in this paper the study of complex problems with two different numerical grid techniques in order to cross check the solutions is proposed interface waves in particular are emphasized since they pose the major difficulties due to the need to implement boundary conditions the first method is based on global differential operators where the solution is expanded in terms of the fourier basis and chebyshev polynomials while the second is the spectral element method an extension of the finite element method that uses chebyshev polynomials as interpolating functions both methods have spectral accuracy up to approximately the nyquist wave number of the grid moreover both methods implement the boundary conditions in a natural way particularly the spectral element algorithm we first solve lamb s problem and compare numerical and analytical solutions then the problem of dispersed rayleigh waves and finally the two quarter space problem we show that the modeling algorithms correctly reproduce the analytical solutions and yield a perfect matching when these solutions do not exist the combined modeling techniques provide a powerful tool for solving complex problems in elastodynamics

homology for operator algebras ii stable homology for non self adjoint algebras new homology groups are defined for a non self adjoint operator algebra with a distinguished masa which is based upon cycles and boundaries associated with complexes of partial isometries in the stable algebra under natural hypotheses the zeroth order group coincides with thek0group of the generatedc algebra several identifications and applications are given and in particular it is shown how stable homology is significant for the classification of regular subalgebras and regular limit algebras

geophysical astrophysical spectral element adaptive refinement gaspar object oriented h adaptive fluid dynamics simulation an object oriented geophysical and astrophysical spectral element adaptive refinement gaspar code is introduced like most spectral element codes gaspar combines finite element efficiency with spectral method accuracy it is also designed to be flexible enough for a range of geophysics and astrophysics applications where turbulence or other complex multiscale problems arise the formalism accommodates both conforming and non conforming elements several aspects of this code derive from existing methods but here are synthesized into a new formulation of dynamic adaptive refinement dare of non conforming h type as a demonstration of the code several new 2d test cases are introduced that have time dependent analytic solutions and exhibit localized flow features including the 2d burgers equation with straight curved radial and oblique colliding fronts these are proposed as standard test problems for comparable dare codes quantitative errors are reported for 2d spatial and temporal convergence of dare

explicit second order isogeometric discretizations for acoustic wave problems abstract this paper presents a stability analysis of isogeometric iga and explicit newmark discretizations for acoustic wave problems with absorbing boundary conditions in spite of the very ill conditioned iga mass and stiffness matrices especially with respect to the polynomial degree p of the b splines and non uniform rational b splines nurbs basis functions employed the stability bounds of the proposed newmark iga method depend linearly on the meshsize h of the iga mesh and inversely on the iga polynomial degree p several numerical tests in the plane confirm these stability bounds and additionally explore the newmark iga order of convergence with respect to h p t domain deformation and the absorbing boundary conditions performance in the presence of a ricker wavelet in a nurbs domain

arakelov parshin rigidity of towers of curve fibrations arakelov parshin rigidity is concerned with varieties mapping rigidly to the moduli stack mathfrak m h of canonically polarized manifolds affirmative answer for any class of maps implies finiteness of the given class this article studies arakelov parshin rigidity on an open subspace of mathfrak m h on the locus mathfrak k mathfrak f h of iterated kodaira fibrations first we prove rigidity for all complete curves mapping finitely onto mathfrak k mathfrak f h then for generic affine curves mapping into mathfrak k mathfrak f h rigidity is shown when deg h 2 the method used in the latter part is showing that the iterated kodaira spencer map is injective

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

implicit spectral element methods and neumann neumann preconditioners for acoustic waves abstract a numerical approximation of the acoustic wave equation with first order absorbing boundary conditions is considered the discretization is based on conforming spectral elements in space and implicit finite differences in time a stability analysis based on the energy method is developed for the fully discrete scheme the linear system arising at each step is solved by the conjugate gradient method with balancing neumann neumann preconditioning several numerical results illustrate the stability and convergence properties of the approximation schemes that result spectrally accurate in space and up to second order in time while the neumann neumann solver at each time step is scalable and quasi optimal

relative positions of matroid algebras abstract a classification is given for regular positions d d d of jones index 4 where equation omitted is an even matroid algebra and where the individual summands have index 2 a similar classification is obtained for positions of direct sums of 2 symmetric algebras and in the odd case for the positions of sums of 2 symmetric c algebras in matroid c algebras the approach relies on an analysis of intermediate non self adjoint operator algebras and the classifications are given in terms of k0 invariants partial isometry homology and scales in the composite invariant k0 h1

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

homology for operator algebras abstract a 4 cycle algebra is a finite dimensional digraph algebra csl algebra whose reduced digraph is a 4 cycle a rigid embedding between such algebras is a direct sum of certain nondegenerate multiplicity one star extendible embeddings a complete classification is obtained for the regular isomorphism classes of direct systems a of 4 cycle algebras with rigid embeddings the critical invariant is a binary relation in k 0 a h 1 a generalising the scale of the k 0 group called the joint scale the joint scale encapsulates other invariants and compatibility conditions of regular isomorphism these include the scale of h 1 a the scale of h 0 a h 1 a sign compatibility congruence compatibility and h 0 h 1 coupling classes these invariants are also important for lifting k 0 h 1 isomorphisms to algebra isomorphisms we resolve this lifting problem for various classes of 4 cycle algebra direct systems

a highly accurate discontinuous galerkin method for complex interfaces between solids and moving fluids we have extended a new highly accurate numerical scheme for unstructured 2d and 3d meshes based on the discontinuous galerkin approach to simulate seismic wave propagation in heterogeneous media containing fluid solid interfaces because of the formulation of the wave equations as a unified first order hyperbolic system in velocity stress the fluid can be in movement along the interface the governing equations within the moving fluid are derived from well known first principles in fluid mechanics the discontinuous galerkin approach allows for jumps of the material parameters and the solution across element interfaces which are handled by riemann solvers or numerical fluxes the use of riemann solvers at the element interfaces makesthe treatment of the fluid particularly simple bysetting the shearmodulus in the fluid region to zero no additional compatibility relations such as vanishing shear stress or continuity of normal stresses are necessary to couple the solid and fluid along an interface the

modeling of the acoustic wave equation with transform methods numerical methods are described for the simulation of wave phenomena with application to the modeling of seismic data two separate topics are studied the first deals with the solution of the acoustic wave equation the second topic treats wave phenomena whose direction of propagation is restricted within 90 degrees from a given axis in the numerical methods developed here the wave field is advanced in time by using standard time differencing schemes on the other hand expressions including space derivative terms are computed by fourier transform methods this approach to computing derivatives minimizes truncation errors another benefit of transform methods becomes evident when attempting to restrict propagation to upward moving waves e g to avoid multiple reflections constraints imposed on the direction of the wave propagation are accomplished most precisely in the wavenumber domain the error analysis of the algorithms shows that truncation errors are due mainly to time discretization such er

the application of high order differencing to the scalar wave equation the second order central difference is often used to approximate the derivatives of the wave equation it is demonstrated that gains in computational efficiency can be made by using high order approximations for these derivatives a one dimensional model is used to illustrate the relative accuracy of o t2 x2 o t2 x4 o t4 x4 ando t4 x10 central difference schemes for comparison o t2 ando t4 pseudospectral schemes are used as an additional measure of performance the results indicate that o t4 x10 differencing can achieve similar accuracy as the o t4 spectral scheme for practical illustration a two dimensional form of the o t4 x10 algorithm is used to compute the exploding reflector response of a salt dome model and compared with a fine grid o t2 x4 result transmissive sponge like boundary conditions are also examined and shown to be effective

the restricted weyl group of the cuntz algebra and shift endomorphisms it is shown that modulo the automorphisms which fix the canonical diagonal masa point wise the group of those automorphisms of on which globally preserve both the diagonal and the core uhf subalgebra is isomorphic via restriction with the group of those homeomorphisms of the full one sided n shift space which eventually commute along with their inverses with the shift transformation the image of this group in the outer automorphism group of on can be embedded into the quotient of the automorphism group of the full two sided n shift by its center generated by the shift if n is prime then this embedding is an isomorphism msc 2010 46l40 37b10

the spectral element method for elastic wave equations application to 2 d and 3 d seismic problems a spectral element method for the approximate solution of linear elastodynamic equations set in a weak form is shown to provide an efficient tool for simulating elastic wave propagation in realistic geological structures in two and three dimensional geometries the computational domain is discretized into quadrangles or hexahedra defined with respect to a reference unit domain by an invertible local mapping inside each reference element the numerical integration is based on the tensor product of a gauss lobatto legendre 1 d quadrature and the solution is expanded onto a discrete polynomial basis using lagrange interpolants as a result the mass matrix is always diagonal which drastically reduces the computational cost and allows an efficient parallel implementation absorbing boundary conditions are introduced in variational form to simulate unbounded physical domains the time discretization is based on an energy momentum conserving scheme that can be put into a classical explicit implicit predictor multicorrector format long term energy conservation and stability properties are illustrated as well as the efficiency of the absorbing conditions the accuracy of the method is shown by comparing the spectral element results to numerical solutions of some classical two dimensional problems obtained by other methods the potentiality of the method is then illustrated by studying a simple three dimensional model very accurate modelling of rayleigh wave propagation and surface diffraction is obtained at a low computational cost the method is shown to provide an efficient tool to study the diffraction of elastic waves and the large amplification of ground motion caused by three dimensional surface topographies copyright 1999 john wiley sons ltd

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

time harmonic elasticity with controllability and higher order discretization methods the time harmonic solution of the linear elastic wave equation is needed for a variety of applications the typical procedure for solving the time harmonic elastic wave equation leads to difficulties solving large scale indefinite linear systems to avoid these difficulties we consider the original time dependent equation with a method based on an exact controllability formulation the main idea of this approach is to find initial conditions such that after one time period the solution and its time derivative coincide with the initial conditions the wave equation is discretized in the space domain with spectral elements the degrees of freedom associated with the basis functions are situated at the gauss lobatto quadrature points of the elements and the gauss lobatto quadrature rule is used so that the mass matrix becomes diagonal this method is combined with the second order central finite difference or the fourth order runge kutta time discretization as a consequence of these choices only matrix vector products are needed in time dependent simulation this makes the controllability method computationally efficient

spectral domain decomposition methods for the solution of acoustic and elastic wave equations a new spectral domain decomposition method is presented for acoustic and elastodynamic wave propagation in 2 d heterogeneous media starting from a variational formulation of the problem two different approaches are proposed for the spatial discretization a mixed fourier legendre and a full legendre collocation the matching conditions at subdomain interfaces are carefully analyzed and the stability and efficiency of time advancing schemes are investigated the numerical validation with some significant test cases illustrates the accuracy flexibility and robustness of our methods these allow the treatment of complex geometries and heterogeneous media while retaining spectral accuracy

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

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

the uniqueness of af diagonals in regular limit algebras necessary and sufficient conditions are obtained for the uniqueness of standard regular af maximal abelian self adjoint algebras in regular limit algebras up to approximate inner unitary equivalence

finiteness theorems for the picard objects of an algebraic stack abstract we prove some finiteness theorems for the picard functor of an algebraic stack in the spirit of sga 6 exp xii and xiii in particular we give a stacky version of raynaud s relative representability theorem we give sufficient conditions for the existence of the torsion component of the picard functor and for the finite generation of the neron severi groups or of the picard group itself we give some examples and applications in appendix a we prove the semicontinuity theorem for a non necessarily tame algebraic stack

hom stacks and restriction of scalars fix an algebraic space s and let x and y be separated artin stacks of finite presentation over s with finite diagonals over s we define a stack homs x y classifying morphisms between x and y assume that x is proper and flat over s and assume fppf locally on s that there exists a finite finitely presented flat cover z x with z an algebraic space then we show that homs x y is an artin stack with quasi compact and separated diagonal