euler characteristic of coherent sheaves on simplicial torics via the stanley reisner ring we combine work of cox on the total coordinate ring of a toric variety and results of eisenbud musta stillman and musta on cohomology of toric and monomial ideals to obtain a formula for computing ox d for a weil divisor d on a complete simplicial toric variety x the main point is to use alexander duality to pass from the toric irrelevant ideal which appears in the computation of ox d to the stanley reisner ideal of which is used in defining the chow ring of x

the immersed boundary lattice boltzmann method for solving fluid particles interaction problems a new computational method the immersed boundary lattice boltzmann method is presented this method is a combination and utilizes the most desirable features of the lattice boltzmann and the immersed boundary methods the method uses a regular eulerian grid for the flow domain and a lagrangian grid to follow particles that are contained in the flow field the rigid body conditions for the fluid and the particles are enforced by a penalty method which assumes that the particle boundary is deformable with a high stiffness constant the velocity field of the fluid and particles is solved by adding a force density term into the lattice boltzmann equation this novel method preserves the advantages of lbm in tracking a group of particles and at the same time provides an alternative and better approach to treating the solid fluid boundary conditions the method also solves the problems of fluctuation of the forces and velocities on the particles when the bounce back boundary conditions are applied this method enables one to simulate problems with particle deformation and fluid structure deformation its results are validated by comparison with results from other methods

a coupled momentum method for modeling blood flow in three dimensional deformable arteries abstract blood velocity and pressure fields in large arteries are greatly influenced by the deformability of the vessel moreover wave propagation phenomena in the cardiovascular system can only be described considering wall deformability since blood is usually described as an incompressible fluid however computational methods for simulating blood flow in three dimensional models of arteries have either considered a rigid wall assumption for the vessel or significantly simplified or reduced geometries computing blood flow in deformable domains using standard techniques like the ale method remains a formidable problem for large realistic anatomic and physiologic models of the cardiovascular system we have developed a new method to simulate blood flow in three dimensional deformable models of arteries the method couples the equations of the deformation of the vessel wall at the variational level as a boundary condition for the fluid domain we consider a strong coupling of the degrees of freedom of the fluid and the solid domains and a linear membrane model enhanced with transverse shear for the vessel wall the effect of the vessel wall boundary is therefore added in a monolithic way to the fluid equations resulting in a remarkably robust scheme we present here the mathematical formulation of the method and discuss issues related to the fluid solid coupling membrane formulation time integration method and boundary and initial conditions implementation is discussed and results with simple geometries as well as large subject specific models are presented

a loosely coupled scheme for the interaction between a fluid elastic structure and poroelastic material abstract we model the interaction between an incompressible viscous fluid thin elastic structure and a poroelastic material the poroelastic material is modeled using the biot s equations of dynamic poroelasticity the fluid elastic structure and the poroelastic material are fully coupled giving rise to a nonlinear moving boundary problem with novel energy estimates we present a modular loosely coupled scheme where the original problem is split into the fluid sub problem elastic structure sub problem and poroelasticity sub problem an energy estimate associated with the stability of the scheme is derived in the case where one of the coupling parameters is equal to zero we present numerical tests where we investigate the effects of the material properties of the poroelastic medium on the fluid flow our findings indicate that the flow patterns highly depend on the storativity of the poroelastic material and cannot be captured by considering fluid structure interaction only

scalable parallel methods for monolithic coupling in fluid structure interaction with application to blood flow modeling we introduce and study numerically a scalable parallel finite element solver for the simulation of blood flow in compliant arteries the incompressible navier stokes equations are used to model the fluid and coupled to an incompressible linear elastic model for the blood vessel walls our method features an unstructured dynamic mesh capable of modeling complicated geometries an arbitrary lagrangian eulerian framework that allows for large displacements of the moving fluid domain monolithic coupling between the fluid and structure equations and fully implicit time discretization simulations based on blood vessel geometries derived from patient specific clinical data are performed on large supercomputers using scalable newton krylov algorithms preconditioned with an overlapping restricted additive schwarz method that preconditions the entire fluid structure system together the algorithm is shown to be robust and scalable for a variety of physical parameters scaling to hundreds of processors and millions of unknowns

incremental displacement correction schemes for incompressible fluid structure interaction in this paper we introduce a class of incremental displacement correction schemes for the explicit coupling of a thin structure with an incompressible fluid these methods enforce a specific robin neumann explicit treatment of the interface coupling we provide a general stability and convergence analysis that covers both the incremental and the non incremental variants their stability properties are independent of the added mass effect the superior accuracy of the incremental schemes with respect to the original non incremental variant is highlighted by the error estimates and then confirmed in a benchmark by numerical experiments

on the spectral side of arthur s trace formula combinatorial setup in arthur s trace formula a ubiquitous role is played by certain limiting expressions arising from piecewise smooth functions with respect to projections of the coxeter fan g m families these include terms resulting from intertwining operators on the spectral side and volumes of polytopes on the geometric side we introduce the combinatorial concept of a compatible family with respect to an arbitrary polyhedral fan and obtain new formulas for the corresponding limiting expressions in this general framework our formulas can be regarded as algebraic generalizations of certain volume formulas for convex polytopes in a companion paper the results are used to study the spectral side of the trace formula

counting lattice points of rational polyhedra abstract the generating function f p p zn x for a rational polytope p carries all essential information of p in this paper we show that for any positive integer n the generating function f p n of np nx x p can be written as f p n a p n x n where a is the set of all vertices of p and each p n is a certain periodic function of n the ehrhart reciprocity law follows automatically from the above formula we also present a formula for the coefficients of ehrhart polynomials in terms of elementary symmetric functions

localization in equivariant intersection theory and the bott residue formula we prove the localization theorem for torus actions in equivariant intersection theory using the theorem we give another proof of the bott residue formula for chern numbers of bundles on smooth complete varieties in addition our techniques allow us to obtain residue formulas for bundles on a certain class of singular schemes which admit torus actions this class is rather special but it includes some interesting examples such as complete intersections and schubert varieties 1 introduction the purpose of this paper is to prove the localization theorem for torus actions in equivariant intersection theory using the theorem we give another proof of the bott residue formula for chern numbers of bundles on smooth complete varieties in addition our techniques allow us to obtain residue formulas for bundles on a certain class of singular schemes which admit torus actions this class is rather special but it includes some interesting examples such as complete intersections cf bfq and schubert varieties let t be a split torus acting on a scheme x the 7 equivariant chow groups of x are a module over rt sym t where f is the character group of t the localization theorem states that up to torsion the equivariant chow groups of the fixed locus xt are isomorphic to those of x such a theorem is a hallmark of any equivariant theory the earliest version for equivariant cohomology is due to borel bo subsequently it theory versions were proved by segal se in topological a theory quart qu for actions of a cyclic group and thomason th2 for algebraic theory th2 for equivariant chow groups the localization isomorphism is given by the equivariant push forward induced by the inclusion of xt to x an interesting aspect of this theory is that the push forward is naturally defined on the level of cycles even in the singular case the closest topological analogue of this is equivariant borel moore homology see e g3 for a definition and a similar proof establishes localization in that theory for smooth spaces the inverse to the equivariant push forward can be written explicitly it was realized independently by several authors i n a b b v

a stable partitioned fsi algorithm for incompressible flow and deforming beams an added mass partitioned amp algorithm is described for solving fluid structure interaction fsi problems coupling incompressible flows with thin elastic structures undergoing finite deformations the new amp scheme is fully second order accurate and stable without sub time step iterations even for very light structures when added mass effects are strong the fluid governed by the incompressible navier stokes equations is solved in velocity pressure form using a fractional step method large deformations are treated with a mixed eulerian lagrangian approach on deforming composite grids the motion of the thin structure is governed by a generalized euler bernoulli beam model and these equations are solved in a lagrangian frame using two approaches one based on finite differences and the other on finite elements the key amp interface condition is a generalized robin mixed condition on the fluid pressure this condition which is derived at a continuous level has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers special treatment of the amp condition is required to couple the finite element beam solver with the finite difference based fluid solver and two coupling approaches are described a normal mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains and it is shown that the amp scheme is stable independent of the ratio of the mass of the fluid to that of the structure a traditional partitioned tp scheme using a dirichlet neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large a series of benchmark problems of increasing complexity are considered to illustrate the behavior of the amp algorithm and to compare the behavior with that of the tp scheme the results of all these benchmark problems verify the stability and accuracy of the amp scheme results for one benchmark problem modeling blood flow in a deforming artery are also compared with corresponding results available in the literature

a split step finite element method for incompressible navier stokes equations with high order accuracy up to the boundary abstract an efficient and accurate finite element algorithm is described for the numerical solution of the incompressible navier stokes ins equations the new algorithm that solves the ins equations in a velocity pressure reformulation is based on a split step scheme in conjunction with the standard finite element method the split step scheme employed for the temporal discretization of our algorithm completely separates the pressure updates from the solution of velocity variables when the pressure equation is formed explicitly the algorithm avoids solving a saddle point problem therefore our algorithm has more flexibility in choosing finite element spaces in contrast popular mixed finite element methods that solve the ins equations in the primitive variables or velocity divergence formulation lead to discrete saddle point problems whose solution depends on the choice of finite element spaces for velocity and pressure that is subject to the well known ladyzenskaja babuska brezzi lbb or inf sup condition for efficiency and robustness lagrange piecewise polynomial finite elements of equal order for both velocity and pressure are used accurate numerical boundary condition for the pressure equation is also investigated motivated by a post processing technique that calculates derivatives of a finite element solution with super convergent error estimates an alternative numerical boundary condition is proposed for the pressure equation at the discrete level the new numerical pressure boundary condition that can be regarded as a better implementation of the compatibility boundary condition improves the boundary layer errors of the pressure solution a normal mode analysis is performed using a simplified model problem on a uniform mesh to demonstrate the numerical properties of our methods convergence studies using p 1 elements support the analytical results and demonstrates that our algorithm with the new numerical boundary condition achieves the optimal second order accuracy for both velocity and pressure up to the boundary benchmark problems are also computed and carefully compared with existing studies finally as an example to illustrate that our approach can be easily adapted for higher order finite elements we solve the classical flow past a cylinder problem using p n finite elements with n 1

lattice points in simple polytopes in terms of fp h q x dx where the polytope p h is obtained from p by independent parallel motions of all facets this extends to simple lattice polytopes the eulermaclaurin summation formula of khovanskii and pukhlikov 8 valid for lattice polytopes such that the primitive vectors on edges through each vertex of p form a basis of the lattice as a corollary we recover results of pommersheim 9 and kantor khovanskii 6 on the coefficients of the ehrhart polynomial of p our proof is elementary in a subsequent article we will show how to adapt it to compute the equivariant todd class of any complete toric variety with quotient singularities the euler maclaurin summation formula for simple lattice polytopes has been obtained independently by ginzburg guillemin karshon 4 they used the dictionary between convex polytopes and projective toric varieties with an ample divisor class in combination with the riemann roch kawasaki formula 1 7 for complex manifolds with quotient singularities a counting formula for lattice points in lattice simplices has been announced by cappell and shaneson 2 as a consequence of their computation of the todd class of toric varieties with quotient singularities

optimal training sequence for mimo wireless systems in colored environments in this paper we design the training signal for a multi input multi output mimo communication system in a colored medium we assume that the known channel covariance matrix cm is a kronecker product of a transmit channel cm and a receive channel cm similarly the cm of the additive gaussian noise is modeled by a kronecker product of a temporal cm and a spatial cm we maximize the differential entropy gained by receiver for a limited energy budget for training at the transmitter using singular value decomposition of the involved cms we turn this problem into a convex optimization problem we prove that the left and right singular vectors of the optimal training matrix are eigenvectors of the channel transmit cm and the noise temporal cm in general case this problem can be solved numerically using efficient methods the impact of the optimal training is more significant in environments with larger eigenvalue spread the expression of the optimal solution is interesting for some specific cases for uncorrelated receive channel the optimal training looks like water filling i e more training power must be invested on the directions which have more impact for high signal to noise ratios snrs any orthogonal training is optimal this means that if large amount of energy is available it must be invested uniformly in all directions in low snr scenarios where low amount of energy is available for channel training all the energy must be allocated to the best mode of channel which has the highest ratio of the received channel variance to the received noise power

values of zeta functions at negative integers dedekind sums and toric geometry in the present paper we study relations among special values of zeta functions of real quadratic fields properties of generalized dedekind sums and todd classes of toric varieties the main theme of the paper is the use of toric geometry to explain in a conceptual way properties of the values of zeta functions and dedekind sums as well as to provide explicit computations both toric varieties and zeta functions associate numerical invariants to cones in lattices with different motivations and applications though we will focus on the case of two dimensional cones in the present paper we introduce notation and definitions that are valid for cones of arbitrary dimension the reason for this added generality is clarity as well as preparation for the results of a subsequent publication

an adaptive formally second order accurate version of the immersed boundary method like many problems in biofluid mechanics cardiac mechanics can be modeled as the dynamic interaction of a viscous incompressible fluid the blood and a visco elastic structure the muscular walls and the valves of the heart the immersed boundary method is a mathematical formulation and numerical approach to such problems that was originally introduced to study blood flow through heart valves and extensions of this work have yielded a three dimensional model of the heart and great vessels in the present work we introduce a new adaptive version of the immersed boundary method this adaptive scheme employs the same hierarchical structured grid approach but a different numerical scheme as the two dimensional adaptive immersed boundary method of roma et al a multilevel self adaptive version of the immersed boundary method ph d thesis courant institute of mathematical sciences new york university 1996 an adaptive version of the immersed boundary method j comput phys 153 2 1999 509 534 and is based on a formally second order accurate i e second order accurate for problems with sufficiently smooth solutions version of the immersed boundary method that we have recently described b e griffith c s peskin on the order of accuracy of the immersed boundary method higher order convergence rates for sufficiently smooth problems j comput phys 208 1 2005 75 105 actual second order convergence rates are obtained for both the uniform and adaptive methods by considering the interaction of a viscous incompressible flow and an anisotropic incompressible viscoelastic shell we also present initial results from the application of this methodology to the three dimensional simulation of blood flow in the heart and great vessels the results obtained by the adaptive method show good qualitative agreement with simulation results obtained by earlier non adaptive versions of the method but the flow in the vicinity of the model heart valves indicates that the new methodology provides enhanced boundary layer resolution differences are also observed in the flow about the mitral valve leaflets

the jacobian conjecture reduction of degree and formal expansion of the inverse introduction i the jacobian conjecture 1 statement of the jacobian problem first observations 2 some history of the jacobian conjecture 3 faulty proofs 4 the use of stabilization and of formal methods ii the reduction theorem 1 notation 2 statement of the reduction theorem 3 reduction to degree 3 4 proof of the reduction theorem 5 r linearization and unipotent reduction 6 nilpotent rank 1 jacobians iii the formal inverse 1 notation 2 abhyankar s inversion formula 3 the terms gj 4 the tree expansion g lt a t lfptf 5 calculations references

stabilization of explicit coupling in fluid structure interaction involving fluid incompressibility abstract in this work we propose a stabilized explicit coupling scheme for fluid structure interaction problems involving a viscous incompressible fluid the coupled discrete formulation is based on nitsche s method with a time penalty term giving l 2 control on the fluid pressure variations at the interface for a linear model problem we prove that the scheme is stable in the energy norm irrespectively of the so called added mass effect namely the fluid structure density ratio and the geometry of the domain numerical experiments in the linear and non linear case show that optimal time accuracy can be obtained by performing one defect correction iteration

residue formulae vector partition functions and lattice points in rational polytopes we obtain residue formulae for certain functions of several vari ables as an application we obtain closed formulae for vector partition func tions and for their continuous analogs they imply an euler maclaurin sum mation formula for vector partition functions and for rational convex poly topes as well we express the sum of values of a polynomial function at all lattice points of a rational convex polytope in terms of the variation of the integral of the function over the deformed polytope institut fourier b p 74 38402 saint martin d heres cedex france e mail address mbrion fourier ujf grenoble fr ecole normale superieure 45 rue d ulm 75005 paris cedex 05 france e mail address vergne dmi ens fr

random polynomials with prescribed newton polytope the newton polytope pf of a polynomial f is well known to have a strong impact on its zeros as in the kouchnirenko bernstein theorem on the number of simultaneous zeros of m polynomials with given newton polytopes in this article we show that pf also has a strong impact on the distribution of zeros of one or several polynomials we equip the space of holomorphic polynomials of degreen in m complex variables with its usual su m 1 invariant gaussian measure and then consider the conditional measures np induced on the subspace of polynomials whose newton polytope pfnp when p the unit simplex then it is obvious and well known that the expected distribution of zeros zf1 fk regarded as a current of k polynomials f1 fk of degree n is uniform relative to the fubini study form our main results concern the conditional expectation e np zf1 fk of zeros of k polynomials with newton polytope npnp where p deg p these results are asymptotic as the scaling factor n 1 we show that e np zf1 fk is asymptotically uniform on the inverse image ap of the open scaled polytope 1 p via the moment map cp m for projective space however the zeros have an exotic distribution outside of ap and when k m the case of the kouchnirenko bernstein theorem the percentage of zeros outside ap approaches 0 as n 1

cohomology of regular embeddings we give in this paper an explicit description of the rational cohomology ring of a complete symmetric variety or regular compactification of an algebraic symmetric variety the motivation for this computation comes from the desire to describe an explicit schubert calculus for these varieties which have been considered since the work of chasles and schubert in several special cases the technique we use is the result of our attempts to understand better the work of jurkiewicz and danilov in the case of torus embeddings the combinatorial presentation of the cohomology ring of a smooth torus embedding finds a natural explanation and proof using the language of equivariant cohomology the key point is that the reisner stanley algebra of the torus embedding coincides with its equivariant cohomology ring we consider a class of spaces regular embeddings that contains both complete symmetric varieties and smooth torus embeddings by suitably generalizing the notion of reisner stanley algebra we are able to compute the rational equivariant cohomology ring of these spaces in an explicit way

fluid structure interaction with large structural displacements the calculation of viscous flows inside deformable structures faces major difficulties when enforcing the kinematic compatibility at the fluid structure interface and updating the geometry of the domain this paper proposes to overcome these problems by considering the fluid and the structure as a unique continuous medium to be studied in a fixed reference configuration the resulting problem is then split into a fluid and a structural part through an additive decomposition of the space of kinematically admissible test functions this approach treats the structure in a fully lagrangian way and uses an associated arbitrary lagrangian eulerian ale formulation for the fluid such a strategy has three advantages which are detailed in the present paper it can be discretised in time by implicit stable energy conserving time integration schemes and solved by simple iterative uncoupled algorithms the fluid and the structural problems can be approximated by independent finite element spaces the most recent geometrically exact nonlinear shell models can be used for the structures the full strategy has been implemented into an industrial cfd code results obtained in the simulation of industrial hydraulic shock absorbers are presented at the end of the paper

a partitioned scheme for fluid composite structure interaction problems we present a benchmark problem and a loosely coupled partitioned scheme for fluid structure interaction with composite structures the benchmark problem consists of an incompressible viscous fluid interacting with a structure composed of two layers a thin elastic layer with mass which is in contact with the fluid and modeled by the koiter membrane shell equations and a thick elastic layer with mass modeled by the equations of linear elasticity an efficient modular partitioned operator splitting scheme is proposed to simulate solutions to the coupled nonlinear fsi problem without the need for sub iterations at every time step an energy estimate associated with unconditional stability is derived for the fully nonlinear fsi problem defined on moving domains two instructive numerical benchmark problems are presented to test the performance of numerical fsi schemes involving composite structures it is shown numerically that the proposed scheme is at least first order accurate both in time and space this work reveals a new physical property of fsi problems involving thin interfaces with mass the inertia of the thin fluid structure interface regularizes solutions to the full fsi problem

the nilpotence conjecture in k theory of toric varieties it is shown that all nontrivial elements in higher k groups of toric varieties are annihilated by iterations of the natural frobenius type endomorphisms this is a higher analog of the triviality of vector bundles on affine toric varieties

algebraic birkhoff factorization and the euler maclaurin formula on cones we equip the space of lattice cones with a coproduct which makes it a cograded coaugmented connnected coalgebra the exponential generating sum and exponential generating integral on lattice cones can be viewed as linear maps on this space with values in the space of meromorphic germs with linear poles at zero we investigate the subdivision properties reminiscent of the inclusion exclusion principle for the cardinal on finite sets of such linear maps and show that these properties are compatible with the convolution quotient of maps on the coalgebra implementing the algebraic birkhoff factorization procedure on the linear maps under consideration we factorize the exponential generating sum as a convolution quotient of two maps with each of the maps in the factorization satisfying a subdivision property a direct computation shows that the polar decomposition of the exponential generating sum on a smooth lattice cone yields an euler maclaurin formula the compatibility with subdivisions of the convolution quotient arising in the algebraic birkhoff factorization then yields the euler maclaurin formula for any lattice cone this provides a simple formula for the interpolating factor by means of a projection formula

an effective fluid structure interaction formulation for vascular dynamics by generalized robin conditions in this work we focus on the modeling and numerical simulation of the fluid structure interaction mechanism in vascular dynamics we first propose a simple membrane model to describe the deformation of the arterial wall which is derived from the koiter shell equations and is applicable to an arbitrary geometry secondly we consider a reformulation of the fluid structure problem in which the newly derived membrane model thanks to its simplicity is embedded into the fluid equations and will appear as a generalized robin boundary condition the original problem is then reduced to the solution of subsequent fluid equations defined on a moving domain and may be achieved with a fluid solver only we also derive a stability estimate for the resulting numerical scheme finally we propose new outflow absorbing boundary conditions which are easy to implement and allow us to reduce significantly the spurious pressure wave reflections that typically appear in artificially truncated computational domains we present several numerical results showing the effectiveness of the proposed approaches

special values of partial zeta functions of real quadratic fields at nonpositive integers and the euler maclaurin formula we compute the special values at nonpositive integers of the partial zeta function of an ideal of a real quadratic field applying an asymptotic version of euler maclaurin formula to the lattice cone associated to the ideal considered the euler maclaurin formula in volved is obtained by applying the todd series of differential opera tors to an integral of a small perturbation of the cone the additive property of todd series w r t the cone decomposition enables us to express the partial zeta values in terms of the continued fraction of the reduced element of the ideal the expression obtained uses the positive continued fraction which yields a virtual decomposition of the cone we apply the expression to some indexed families of real quadratic fields satisfying certain condition on the shape of the continued frac tions the families considered include those appeared in 20 and 21 as well as the richaud degert types we show that the partial zeta values at a given nonpositive integerk in the family indexed by n is a polynomial of n finally we compute explicitly the polynomials producing the par tial zeta values at s k for small k of some chosen families and compare these with some previously known results

new polytope decompositions and euler maclaurin formulas for simple integral polytopes abstract we give new weighted decompositions for simple polytopes generalizing previous results of lawrence varchenko and brianchon gram we start with witten s non abelian localization principle in equivariant cohomology for the norm square of the moment map in the context of toric varieties to obtain a decomposition for delzant polytopes then by a purely combinatorial argument we show that this formula holds for any simple polytope as an application we study euler maclaurin formulas

how to integrate a polynomial over a simplex this paper starts by settling the computational complexity of the problem of integrating a polynomial function f over a rational simplex we prove that the problem is np hard for arbitrary polynomials via a generalization of a theorem of motzkin and straus on the other hand if the polynomial depends only on a fixed number of variables while its degree and the dimension of the simplex are allowed to vary we prove that integration can be done in polynomial time as a consequence for polynomials of fixed total degree there is a polynomial time algorithm as well we explore our algorithms with some experiments we conclude the article with extensions to other polytopes and discussion of other available methods 1

fluid structure interaction in blood flow capturing non zero longitudinal structure displacement we present a new model and a novel loosely coupled partitioned numerical scheme modeling fluid structure interaction fsi in blood flow allowing non zero longitudinal displacement arterial walls are modeled by a linearly viscoelastic cylindrical koiter shell model capturing both radial and longitudinal displacement fluid flow is modeled by the navier stokes equations for an incompressible viscous fluid the two are fully coupled via kinematic and dynamic coupling conditions our numerical scheme is based on a new modified lie operator splitting that decouples the fluid and structure sub problems in a way that leads to a loosely coupled scheme which is unconditionally stable this was achieved by a clever use of the kinematic coupling condition at the fluid and structure sub problems leading to an implicit coupling between the fluid and structure velocities the proposed scheme is a modification of the recently introduced kinematically coupled scheme for which the newly proposed modified lie splitting significantly increases the accuracy the performance and accuracy of the scheme were studied on a couple of instructive examples including a comparison with a monolithic scheme it was shown that the accuracy of our scheme was comparable to that of the monolithic scheme while our scheme retains all the main advantages of partitioned schemes such as modularity simple implementation and low computational costs

asymptotic euler maclaurin formula over lattice polytopes abstract formulas for the riemann sums over lattice polytopes determined by the lattice points in the polytopes are often called euler maclaurin formulas an asymptotic euler maclaurin formula by which we mean an asymptotic expansion formula for riemann sums over lattice polytopes was first obtained by guillemin and sternberg 2007 11 then the problem is to find a concrete formula for each term of the expansion in this paper an asymptotic euler maclaurin formula of the riemann sums over general lattice polytopes is given the formula given here is an asymptotic form of the so called local euler maclaurin formula of berline and vergne 2007 3 for delzant polytopes our proof given here is independent of the local euler maclaurin formula furthermore a concrete description of differential operators which appear in each term of the asymptotic expansion for delzant lattice polytopes is given by using this description when the polytopes are delzant lattice a concrete formula for each term of the expansion in two dimension and a formula for the third term of the expansion in arbitrary dimension are given

a penalty projection algorithm for a monolithic fluid structure interaction solver in this paper we propose a new iterative penalty projection algorithm for a monolithic fluid structure interaction solver projection methods that split the computation of the velocity from the pressure are very popular in fluid dynamics since the boundary errors generated by the projection method are localized mainly near the boundary layers where the incorrect pressure boundary conditions are imposed however when solid regions are taken into account the pressure projected field cannot satisfy fully coupled boundary constraints imposed on external solid surfaces such as stress free conditions and due to the rigidity of the medium the boundary errors propagate deeply in the interior in order to reduce the projection errors we propose a one step penalty projection method in the fluid domain and an iterative penalty projection method in the solid region this technique decouples the pressure velocity degrees of freedom and as a consequence the computational cost in order to verify the accuracy and robustness of the proposed method we compare the results between this splitting velocity pressure algorithm and the coupled one these numerical results show stability and robustness of the proposed algorithm with a strong reduction of the computational effort a new penalty projection algorithm for a monolithic fsi solver is proposed projection method error is localized where pressure boundary conditions are imposed a one step penalty together with an iterative projection algorithm is used this technique reduces the problem degrees of freedom and the computational cost numerical results show stability and reduction of cpu effort for large problems

fourth order spatial correlation coefficient across the uplink receiver s spatial aperture analytically derived in closed form this paper is first in the open literature to the authors best knowledge on wireless channel fading to derive the uplink received signal s fourth order spatial correlation coefficient function across a receiving sensor array s aperture this derivation is mathematically rigorous and is based on idealized geometric relationships among the mobile transmitter the base station s receiving antennas and the scatterers of the channel the scatterers spatial locations are modeled as poisson distributed with a gaussian intensity over a two dimensional space this scatterer model has previously been empirically verified to produce faithful expressions for the second order spatial correlation coefficient the final formula is in closed form explicit in terms of the simple geometric model s few independent parameters

lattice boltzmann method for simulating the viscous flow in large distensible blood vessels a lattice boltzmann method for simulating the viscous flow in large distensible blood vessels is presented by introducing a boundary condition for elastic and moving boundaries the mass conservation for the boundary condition is tested in detail the viscous flow in elastic vessels is simulated with a pressure radius relationship similar to that of the pulmonary blood vessels the numerical results for steady flow agree with the analytical prediction to very high accuracy and the simulation results for pulsatile flow are comparable with those of the aortic flows observed experimentally the model is expected to find many applications for studying blood flows in large distensible arteries especially in those suffering from atherosclerosis stenosis aneurysm etc

fluid structure partitioned procedures based on robin transmission conditions in this article we design new partitioned procedures for fluid structure interaction problems based on robin type transmission conditions the choice of the coefficient in the robin conditions is justified via simplified models the strategy is effective whenever an incompressible fluid interacts with a relatively thin membrane as in hemodynamics applications we analyze theoretically the new iterative procedures on a model problem which represents a simplified blood vessel system in particular the robin neumann scheme exhibits enhanced convergence properties with respect to the existing partitioned procedures the theoretical results are checked using numerical experimentation

euler maclaurin with remainder for a simple integral polytope we give an euler maclaurin formula with remainder for the sum of the values of a smooth function on the integral points in a simple integral polytope we prove this formula by elementary methods

a note on optimal regularity and regularizing effects of point mass coupling for a heat wave system abstract we consider a coupled 1d heat wave system which serves as a simplified fluid structure interaction problem the system is coupled in two different ways the first when the interface does not have mass and the second when the interface does have mass we prove an optimal regularity result in sobolev spaces for both cases the main idea behind the proof is to reduce the coupled problem to a single nonlocal equation on the interface by using neummann to diriclet operator furthermore we show that point mass coupling regularizes the problem and quantify this regularization in the sense of sobolev spaces

wellposedness spectral analysis and asymptotic stability of a multilayered heat wave wave system abstract in this work we consider a multilayered heat wave system where a 3 d heat equation is coupled with a 3 d wave equation via a 2 d interface whose dynamics is described by a 2 d wave equation this system can be viewed as a simplification of a certain fluid structure interaction fsi pde model where the structure is of composite type namely it consists of a thin layer and a thick layer we associate the wellposedness of the system with a strongly continuous semigroup and establish its asymptotic decay our first result is semigroup well posedness for the fsi pde dynamics utilizing here a lumer phillips approach we show that the fluid structure system generates a c 0 semigroup on a chosen finite energy space of data as our second result we prove that the solution to the fsi dynamics generated by the c 0 semigroup tends asymptotically to the zero state for all initial data that is the semigroup of the fsi system is strongly stable for this stability work we analyze the spectrum of the generator a and show that the spectrum of a does not intersect the imaginary axis

the equivariant todd genus of a complete toric variety with danilov condition we write the equivariant todd class of a general complete toric variety as an explicit combination of the orbit closures the coefficients being analytic functions on the lie algebra of the torus which satisfy danilov s requirement 2007 published by elsevier inc

a new partitioned staggered scheme for flexible multibody interactions with strong inertial effects abstract in generic flexible multibody interaction problems the differences in the mass damping and stiffness of the bodies can be very large of particular interest is a small change in the higher mass structure which triggers relatively large inertial effects on the lower mass structure in this work a new partitioned staggered time integration scheme is developed and its applicability is extended to the problems involving low mass ratios in coupled multibody problems the equation of motion of body with larger inertia is integrated by implicit newmark method whereas the smaller inertia is solved using a robust self starting explicit integration procedure the coupled formulation includes explicit correction terms that adjusts the amount of interfacial velocity which plays a key role in the stability and accuracy of the simulations a wide range of mass 10 6 10 1 damping and stiffness 10 3 10 3 ratios are chosen to assess the stability and accuracy characteristics of the proposed scheme the closed form expressions for the coupling parameter have been constructed for both matching and non matching time stepping through the godunov ryabenkii normal mode analysis the stability of the proposed method is observed as a function of the relative properties and temporal discretisation of the coupled system the time step of the heavier body significantly influences the stability more than the lighter body to maintain the staggering error minimal an optimal range of the coupling parameter is identified the error computed with uniform variation in the time step revealed that the present method is more accurate than the existing methods the partitioned method is an energy preserving integration method for the dynamic analysis of multibody systems as a potential application of this scheme flexible multibody problems in the field of offshore engineering viz wave energy converter and floater mooring systems are presented and validated with experimental measurements

fluid structure algorithms based on steklov poincare operators in this paper we review some classical algorithms for fluid structure interaction problems and we propose an alternative viewpoint mutuated from the domain decomposition theory this approach yields preconditioned richardson iterations on the steklov poincare nonlinear equation at the fluid structure interface

the algebra of continuous piecewise polynomials abstract for a triangulated d dimensional region r d we consider the algebra c 0 of all continuous piecewise polynomial functions on we find generators for c 0 as an r algebra and use these to give an isomorphism between c 0 and a quotient of the face ring a of we then study the structure of c 0 as a module over r r y 1 y d the polynomial ring in d indeterminates giving generators for c 0 as an r module these form a free basis when is a shellable complex in general we show that c 0 is a free r module whenever is a disk

the euler maclaurin formula for simple integral polytopes we give a euler maclaurin formula with remainder for the sum of a smooth function on the integral points in a simple integral lattice polytope our proof uses elementary methods

the ehrhart polynomial of a lattice polytope the problem of counting the number of lattice points inside a convex lattice polytope in r a polytope whose vertices have integer coordinates has been studied from a variety of perspectives here we use the poisson summation formula and related techniques in fourier analysis to obtain a formula for the number of lattice points inside all integral dilates of a lattice polytope we show that an associated generating function has an explicit representation in terms of sums of cotangents which are higher dimensional generalizations of dedekind sums let en denote the n dimensional integer lattice in r and let p be an n dimensional lattice polytope in r which is a compact simplicial complex of pure dimension n whose vertices lie on the lattice consider the function of an integer valued variable t that describes the number of lattice points that lie inside the dilated polytope tp

exact controllability and stabilization of a vibrating string with an interior point mass in this article we examine the problems of boundary control and stabilization for a one dimensional wave equation with interior point masses we show that singularities in waves are smoothed one order as they cross a point mass thus in the case of one interior point mass with e g l 2 dirichlet control at the left end the most general reachable space from 0 that one can expect is l 2 times h 1 to the left of the mass and h 1 times l 2 to the right of the mass we show that this is in fact the optimal result modulo certain compatibility conditions several related results for both control and stabilization of such systems are also given

numerical approximation schemes for multi dimensional wave equations in asymmetric spaces we develop finite difference numerical schemes for a model arising in multi body structures previously analyzed by h koch and e zuazua 13 constituted by two n dimensional wave equations coupled with a n 1 dimensional one along a flexible interface that model under suitable assumptions on the speed of propagation in each media is well posed in asymmetric spaces in which the regularity of solutions differs by one derivative from one medium to the other here we consider a flat interface and analyze this property at a discrete level for finite difference and mixed finite element methods on regular meshes parallel to the interface we prove that those methods are well posed in such asymmetric spaces uniformly with respect to the mesh size parameters and we prove the convergence of the numerical solutions towards the continuous ones in these spaces in other words these numerical methods that are well behaved in standard energy spaces preserve the convergence properties in these asymmetric spaces too these results are illustrated by several numerical experiments

the impact of non isotropic scattering and directional antennas on mimo multicarrier mobile communication channels in outdoor environments waves propagate non isotropically because of non uniform distribution of scatterers in addition directional antennas which are efficient for communication applications have considerable impact on the response of the communication channel the impact of non isotropic propagation and directional antennas is more significant when the system employs multiple antennas in this paper we propose a space time frequency cross correlation function ccf for multiple input multiple output multicarrier channels in a two dimensional 2d random scattering medium the expression of the ccf turns out to be a multiplication of three ccfs two of these terms characterize the impact of mobile station and base station respectively and are linear bessel expansions where the coefficients are given by the linear convolution of the fourier series coefficients fsc s of the employed antenna patterns and the fscs of the probability density function describing 2d non isotropic environment the third expression characterizes the impact of the wireless channel in the stationary case we derive the expression of the fading channel power spectrum cps in terms of the non isotropic pdf and antenna patterns using the expression of the ccf we also calculate coherence bandwidth cb coherence time ct as a function of carrier frequency time separations our numerical results show a good fit to the available experimental results obtained for the cb ct of realistic outdoor channels

splitting methods based on algebraic factorization for fluid structure interaction we discuss in this paper the numerical approximation of fluid structure interaction fsi problems dealing with strong added mass effect we propose new semi implicit algorithms based on inexact block lu factorization of the linear system obtained after the space time discretization and linearization of the fsi problem as a result the fluid velocity is computed separately from the coupled pressure structure velocity system at each iteration reducing the computational cost we investigate explicit implicit decomposition through algebraic splitting techniques originally designed for the fsi problem this approach leads to two different families of methods which extend to fsi the algebraic pressure correction method and the yosida method two schemes that were previously adopted for pure fluid problems furthermore we have considered the inexact factorization of the fluid structure system as a preconditioner the numerical properties of these methods have been tested on a model problem representing a blood vessel system

framed sheaves on root stacks and supersymmetric gauge theories on ale spaces we develop a new approach to the study of supersymmetric gauge theories on ale spaces using the theory of framed sheaves on root toric stacks which illuminates relations with gauge theories on r 4 and with two dimensional conformal field theory we construct a stacky compactification of the minimal resolution xk of the ak 1 toric singularity c 2 zk which is a projective toric orbifold xk such that xknxk is a zk gerbe we construct moduli spaces of tor sion free sheaves on xk which are framed along the compactification gerbe we prove that this moduli space is a smooth quasi projective variety compute its dimension and classify its fixed points under the natural induced toric action we use this construction to compute the partition functions and correlators of chiral bps operators forn 2 quiver gauge theories on xk with nontrivial holonomies at infinity the partition functions are computed with and without cou plings to bifundamental matter hypermultiplets and expressed in terms of toric blowup formulas which relate them to the corresponding nekrasov partition functions on the affine toric subsets of xk we compare our new partition functions with previous computations explore their con nections to the representation theory of affine lie algebras and find new constraints on fractional instanton charges in the coupling to fundamental matter we show that the partition functions in the low energy limit are characterised by the seiberg witten curves and in some cases also by suitable blowup equations involving riemann theta functions on the seiberg witten curve with characteristics related to the nontrivial holonomies

long time behavior of a coupled heat wave system arising in fluid structure interaction this paper is devoted to the analysis of the long time behavior of a coupled wave heat system in which a wave and a heat equation evolve in two bounded domains with natural transmission conditions at a common interface these conditions couple in particular the heat unknown with the velocity of the wave solution this model may be viewed as a simplified version of linearized models which arise in fluid structure interaction first we show the strong asymptotic stability of solutions to this system then based on the construction of ray like solutions by means of geometric optics expansions and a careful analysis of the transfer of energy at the interface we show the lack of uniform decay in general domains further we obtain a polynomial decay result for smooth solutions of the system under a suitable geometric assumption which guarantees that the heat domain envelopes the wave domain finally in the absence of geometric conditions we show a logarithmic decay result for the same system but with simplified transmission conditions at the interface we also analyze the difficulty there is to extend this result to the more natural transmission conditions

homogeneous coordinates for algebraic varieties abstract we associate to every divisorial e g smooth variety x with only constant invertible global functions and finitely generated picard group a pic x graded homogeneous coordinate ring this generalizes the usual homogeneous coordinate ring of the projective space and constructions of cox and kajiwara for smooth and divisorial toric varieties we show that the homogeneous coordinate ring defines in fact a fully faithful functor for normal complex varieties x with only constant global functions we even obtain an equivalence of categories finally the homogeneous coordinate ring of a locally factorial complete irreducible variety with free finitely generated picard group turns out to be a krull ring admitting unique factorization

characteristic classes of singular toric varieties in this paper we compute the motivic chern classes and homology hirzebruch characteristic classes of possibly singular toric varieties which in the context of complete toric varieties fit nicely with a generalized hirzebruch riemann roch theorem as important special cases we obtain new or recover well known formulae for the baum fulton macpherson todd or macpherson s chern classes of toric varieties as well as for the thom milnor l classes of simplicial projective toric varieties we present two different perspectives for the computation of these characteristic classes of toric varieties first we take advantage of the torus orbit decomposition and the motivic properties of the motivic chern and respectively homology hirzebruch classes to express the latter in terms of dualizing sheaves and respectively the dual todd classes of closures of orbits this method even applies to torus invariant subspaces of a given toric variety the obtained formula is then applied to weighted lattice point counting in lattice polytopes and their subcomplexes yielding generalized pick type formulae second in the case of simplicial toric varieties we compute our characteristic classes by using the lefschetz riemann roch theorem of edidin graham in the context of the geometric quotient description of such varieties in this setting we define mock hirzebruch classes of simplicial toric varieties which specialize to the mock chern mock todd and mock l classes of such varieties and investigate the difference between the actual homology hirzebruch class and the mock hirzebruch class we show that this difference is localized on the singular locus and we obtain a formula for it in which the contribution of each singular cone is identified explicitly finally the two methods of computing characteristic classes are combined for proving several characteristic class formulae originally obtained by cappell and shaneson in the early 1990s 2015 wiley periodicals inc

simulations of the whirling instability by the immersed boundary method when an elastic filament spins in a viscous incompressible fluid it may undergo a whirling instability as studied asymptotically by wolgemuth powers and goldstein phys rev lett 84 2000 pp 16 23 we use the immersed boundary ib method to study the interaction between the elastic filament and the surrounding viscous fluid as governed by the incompressible navier stokes equations this allows the study of the whirling motion when the shape of the filament is very different from the unperturbed straight state

products of cycles and the todd class of a toric variety the purpose of this paper is to show that the todd class of a simplicial toric variety has a canonical expression in terms of products of torus invariant divisors the coefficients in this expression which are generalizations of the classical dedekind sum are shown to satisfy a reciprocity relation which characterizes them uniquely we achieve these results by giving an explicit formula for the push forward of a product of cycles under a proper birational map of simplicial toric varieties since the introduction of toric varieties in the 1970s finding formulas for their todd class has been an interesting and important problem this is partly due to a well known application of the riemann roch theorem which allows a formula for the todd class of a toric variety to be translated directly into a formula for the number of lattice points in a lattice polytope cf dan an example of this application is contained in pom where a formula for the todd class of a toric variety in terms of dedekind sums is used to obtain new lattice point formulas danilov dan posed the problem of finding a formula for the todd class of a toric variety in terms of the orbit closures under the torus action specifically he asked if it is possible given a lattice to assign a rational number to each cone in the lattice such that given any fan in the lattice the todd class of the corresponding toric variety equals the sum of the orbit closures with coefficients given by these assigned rational numbers morelli mor showed that such an assignment is indeed possible in a natural way if the coefficients instead of being rational numbers are allowed to take values in the field of rational functions on a grassmannian of linear subspaces of the lattice however if it is required that the coefficients be rational numbers invariant under lattice automorphisms such an assignment is clearly impossible for example the nonsingular cone a in 22 generated by 1 0 and 0 1 when subdivided by the ray through 1 1 yields two cones a and o2 which are both lattice equivalent to a by additivity a consequence of the fact that the todd class pushes forward we deduce that the coefficient assigned to a must equal 0 which is absurd in this paper we show that there is a canonical expression for the todd class of a simplicial toric variety in terms of products of the torus invariant divisors furthermore this expression is invariant under lattice automorphisms that is the coefficient of each product depends only on the set of rays with multiplicities

toric varieties with huge grothendieck group abstract in each dimension n 3 there are many projective simplicial toric varieties whose grothendieck groups of vector bundles are at least as big as the ground field in particular the conjecture that the grothendieck groups of locally trivial sheaves and coherent sheaves on such varieties are rationally isomorphic fails badly

wall crossings for double hurwitz numbers abstract double hurwitz numbers count covers of p 1 by genus g curves with assigned ramification profiles over 0 and and simple ramification over a fixed branch divisor goulden jackson and vakil have shown double hurwitz numbers are piecewise polynomial in the orders of ramification goulden et al 2005 10 and shadrin shapiro and vainshtein have determined the chamber structure and wall crossing formulas for g 0 shadrin et al 2008 15 this paper gives a unified approach to these results and strengthens them in several ways the most important being the extension of the results of shadrin et al 2008 15 to arbitrary genus the main tool is the authors previous work cavalieri et al 2010 6 expressing double hurwitz number as a sum over certain labeled graphs we identify the labels of the graphs with lattice points in the chambers of certain hyperplane arrangements which give rise to piecewise polynomial functions our understanding of the wall crossing for these functions builds on the work of varchenko 1987 17 and could have broader applications

kinematic splitting algorithm for fluid structure interaction in hemodynamics abstract in this paper we study a kinematic splitting algorithm for fluid structure interaction problems this algorithm belongs to the class of loosely coupled fluid structure interaction schemes we will present stability analysis for a coupled problem of non newtonian shear dependent fluids in moving domains with viscoelastic boundaries fluid flow is described by the conservation laws with nonlinearities in convective and diffusive terms for simplicity of presentation the structure is modelled by the generalized string equation but the results presented in the paper may be generalized to more complex structure models the arbitrary lagrangian eulerian approach is used in order to take into account moving computational domain numerical experiments including numerical error analysis and comparison of hemodynamic parameters for newtonian and non newtonian fluids demonstrate reliability of the proposed scheme

robin based semi implicit coupling in fluid structure interaction stability analysis and numerics in this paper we propose a semi implicit coupling scheme for the numerical simulation of fluid structure interaction systems involving a viscous incompressible fluid the scheme is stable irrespective of the so called added mass effect and allows for conservative time stepping within the structure the efficiency of the scheme is based on the explicit splitting of the viscous effects and geometrical convective nonlinearities through the use of the chorin temam projection scheme within the fluid stability comes from the implicit pressure solid coupling and a specific robin treatment of the explicit viscous solid coupling derived from nitsche s method

existence of a solution to a fluid multi layered structure interaction problem abstract we study a nonlinear unsteady moving boundary fluid structure interaction fsi problem in which the structure is composed of two layers a thick layer and a thin layer which serves as a fluid structure interface with mass the fluid flow which is driven by the time dependent dynamic pressure data is modeled by the navier stokes equations for an incompressible viscous fluid defined on a 2d cylinder the elastodynamics of the cylinder wall is governed by the 1d linear wave equation modeling the thin structural layer and by the 2d equations of linear elasticity modeling the thick structural layer we prove existence of a weak solution to this nonlinear fsi problem as long as the cylinder radius is greater than zero the spaces of weak solutions presented in this manuscript reveal a striking new feature the presence of a thin fluid structure interface with mass regularizes solutions of the coupled problem

stable loosely coupled type algorithm for fluid structure interaction in blood flow we introduce a novel loosely coupled type algorithm for fluid structure interaction between blood flow and thin vascular walls this algorithm successfully deals with the difficulties associated with the added mass effect which is known to be the cause of numerical instabilities in fluid structure interaction problems involving fluid and structure of comparable densities our algorithm is based on a time discretization via operator splitting which is applied in a novel way to separate the fluid sub problem from the structure elastodynamics sub problem in contrast with traditional loosely coupled schemes no iterations are necessary between the fluid and structure sub problems this is due to the fact that our novel splitting strategy uses the added mass effect to stabilize rather than to destabilize the numerical algorithm this stabilizing effect is obtained by employing the kinematic lateral boundary condition to establish a tight link between the velocities of the fluid and of the structure in each sub problem the stability of the scheme is discussed on a simplified benchmark problem and we use energy arguments to show that the proposed scheme is unconditionally stable due to the crucial role played by the kinematic lateral boundary condition the proposed algorithm is named the kinematically coupled scheme

robin robin preconditioned krylov methods for fluid structure interaction problems in this work we propose a robin robin preconditioner combined with krylov iterations for the solution of the interface system arising in fluid structure interaction fsi problems it can be seen as a partitioned fsi procedure and in this respect it generalizes the ideas introduced in s badia f nobile c vergara j comput phys 227 2008 7027 7051 we analyze the convergence of gmres iterations with the robin robin preconditioner on a model problem and compare its efficiency with some existing algorithms the method is shown to be very efficient for many challenging fluid structure interaction problems such as those characterized by a large added mass effect or by enclosed fluids in particular the possibility to solve balloon type problems without any special treatment makes this algorithm very appealing compared to the computationally intensive existing approaches c 2009 elsevier b v all rights reserved

existence of a weak solution to a nonlinear fluid structure interaction problem modeling the flow of an incompressible viscous fluid in a cylinder with deformable walls we study a nonlinear unsteady moving boundary fluid structure interaction fsi problem arising in modeling blood flow through elastic and viscoelastic arteries the fluid flow which is driven by the time dependent pressure data is governed by two dimensional incompressible navier stokes equations while the elastodynamics of the cylindrical wall is modeled by the one dimensional cylindrical koiter shell model two cases are considered the linearly viscoelastic and the linearly elastic koiter shell the fluid and structure are fully coupled two way coupling via the kinematic and dynamic lateral boundary conditions describing continuity of velocity the no slip condition and the balance of contact forces at the fluid structure interface we prove the existence of weak solutions to the two fsi problems the viscoelastic and the elastic case as long as the cylinder radius is greater than zero the proof is based on a novel semi discrete operator splitting numerical scheme known as the kinematically coupled scheme introduced in guidoboni et al j comput phys 228 18 6916 6937 2009 to numerically solve the underlying fsi problems the backbone of the kinematically coupled scheme is the well known marchuk yanenko scheme also known as the lie splitting scheme we effectively prove convergence of that numerical scheme to a solution of the corresponding fsi problem