a tqft from quantum teichmuller theory by using quantum teichmuller theory we construct a one parameter family of tqfts on the categroid of admissible leveled shaped 3 manifolds

ratio coordinates for higher teichmuller spaces we define new coordinates for fock goncharov s higher teichmuller spaces for a surface with holes which are the moduli spaces of representations of the fundamental group into a reductive lie group g some additional data on the boundary leads to two closely related moduli spaces the mathscr x space and the mathscr a space forming a cluster ensemble fock and goncharov gave nice descriptions of the coordinates of these spaces in the cases of g mathrm pgl m and g mathrm sl m together with poisson structures we consider new coordinates for higher teichmuller spaces given as ratios of the coordinates of the mathscr a space for g mathrm sl m which are generalizations of kashaev s ratio coordinates in the case m 2 using kashaev s quantization for m 2 we suggest a quantization of the system of these new ratio coordinates which may lead to a new family of projective representations of mapping class groups these ratio coordinates depend on the choice of an ideal triangulation decorated with a distinguished corner at each triangle and the key point of the quantization is to guarantee certain consistency under a change of such choices we prove this consistency for m 3 and for completeness we also give a full proof of the presentation of kashaev s groupoid of decorated ideal triangulations

moduli spaces and macromolecules techniques from moduli spaces are applied to biological macromolecules the first main result provides new a priori constraints on protein geometry discovered empirically and confirmed computationally the second main result identifies up to homotopy the natural moduli space of several interacting rna molecules with the riemann moduli space of a surface with several boundary components in each fixed genus applications to rna folding prediction are discussed the mathematical and biological frameworks are surveyed and presented from first principles

positive linear operators with equidistant nodes abstract in the present paper the approximation power of positive linear operators with equidistant nodes is investigated new pointwise estimates are given in terms of first and second order moduli of continuity showing that for positive operators having uniform jackson orders of approximation one may expect interpolation at the endopoints in particular the first solution to butzer s problem with equidistant nodes is given a negative result yields an explanation why bernstein operators and some of their modifications are optimal in a certain sense

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

universal constructions in teichmuller theory we study a new model tess of a universal teichmuller space which is defined to be the collection tess of all ideal tesselations of the poincare disk together with a distinguished oriented edge modulo the natural action of the modbius group mob applying arguments from the decorated teichmuller theory of punctured surfaces which was developed elsewhere we find that tess is an infinite dimensional frehet manifold with canonical global coordinates and there are a universal sympletic form on tess which generalizes the classical weil petersson kahler two forms and a group g which generalizes the classical mapping class groups acting on tess and preserving in fact tess is isomorphic to the right coset space of mob in the group homeo of all orientation preserving homeomorphisms of the circle and one sees easily that tess naturally generalizes the other well known models of a universal teichmuller space namely bers universal teichmuller space and the right coset space of mob in the subgroup of c smooth elements of homeo which is of interest in physics the latter model supports the kirillov kostant two form and we show that the universal symplectic form pulls back to this two form implicit in our discussion so far is the fact that homeo is isomorphic to tess and one is led to ask for the characterization of various families of homeomorphisms in terms of the corresponding tesselation reporting on joint work with dennis sullivan we partially solve one such problem here using the ahlfors bers theory furthermore as in the classical decorated teichmuller theory there is an associated universal decorated teichmuller space tess which is actually of central concern in this work tess is a frechet manifold on which g acts and there is a g invariant two form just above for tess there is moreover a g invariant cell decomposition of tess which generalizes the cell decompositions of the classical decorated teichmullerspaces thus truly all of the structure of the decorated teichmuller spaces of punctured surfaces which is known from previous work arises as the restriction of a corresponding universal structure on tess

a discrete uniformization theorem for polyhedral surfaces a notion of discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper this discrete conformality is shown to be computable it is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a unique hyperbolic polyhedral metric with a given discrete curvature satisfying gauss bonnet formula furthermore the hyperbolic polyhedral metric with given curvature can be obtained using a discrete yamabe flow with surgery in particular each hyperbolic polyhedral metric on a closed surface with negative euler characteristic is discrete conformal to a unique hyperbolic metric

zygmund vector fields hilbert transform and fourier coefficients in shear coordinates we parametrize the space cal z of zygmund vector fields on the unit circle in terms of infinitesimal shear functions on the farey tesselation then we express the hilbert transform and the fourier coefficients of the zygmund vector fields in terms of the above parametrization by infinitesimal shear functions finally we compute the weil petersson metric on the teichm uller space of a punctured surface in terms of shears

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

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 cohomological dimension of the moduli space of riemann surfaces the moduli space of riemann surfaces of genus g 2 is up to a finite etale cover a complex manifold and so it makes sense to speak of its dolbeault cohomological dimension the conjecturally optimal bound is g 2 this expectation is verified in low genus and supported by harer s computation of its de rham cohomological dimension and by vanishing results in the tautological intersection ring in this paper we prove that such dimension is at most 2g 2 we also prove an analogous bound for the moduli space of riemann surfaces with marked points the key step is to show that the dolbeault cohomological dimension of each stratum of translation surfaces is at most g in order to do that we produce an exhaustion function whose complex hessian has controlled index in the construction of such a function some basic geometric properties of flat surfaces come into play

margulis spacetimes via the arc complex we study strip deformations of convex cocompact hyperbolic surfaces defined by inserting hyperbolic strips along a collection of disjoint geodesic arcs properly embedded in the surface we prove that any deformation of the surface that uniformly lengthens all closed geodesics can be realized as a strip deformation in an essentially unique way the infinitesimal version of this result gives a parameterization by the arc complex of the moduli space of margulis spacetimes with fixed convex cocompact linear holonomy as an application we provide a new proof of the tameness of such margulis spacetimes m by establishing the crooked plane conjecture which states that m admits a fundamental domain bounded by piecewise linear surfaces called crooked planes the noninfinitesimal version gives an analogous theory for noncompact complete anti de sitter 3 manifolds

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

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

anosov flows surface groups and curves in projective space note that in 10 w goldman gives a complete description of these connected components in the case of finite covers of psl 2 r in the case of psl 2 r two homeomorphic components called teichmuller spaces play a central role these two components are well known to be homeomorphic to a ball of dimension 6g 6 n hitchin generalises this situation to psl n r indeed one of these components when n is odd and two when n is even has a very simple topology let us define an n fuchsian representation to be a representation which can be written as 0 where 0 is a cocompact representation with values in psl 2 r and is the irreducible representation of psl 2 r in psl n r we denote by reph 1 s psl n r a connected component that contains fuchsian representations and call it a hitchin component in fact when n is odd there is one hitchin component and when n is even two isomorphic ones n hitchin proves in 17

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

centrally extended mapping class groups from quantum teichmuller theory abstract the central extension of the mapping class groups of punctured surfaces of finite type that arises in quantum teichmuller theory is 12 times the meyer class plus the euler classes of the punctures this is analogous to the result obtained in 12 for the thompson groups

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

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

polyhedra inscribed in a quadric we study convex polyhedra in three space that are inscribed in a quadric surface up to projective transformations there are three such surfaces the sphere the hyperboloid and the cylinder our main result is that a planar graph gamma is realized as the 1 skeleton of a polyhedron inscribed in the hyperboloid or cylinder if and only if gamma is realized as the 1 skeleton of a polyhedron inscribed in the sphere and gamma admits a hamiltonian cycle this answers a question asked by steiner in 1832 rivin characterized convex polyhedra inscribed in the sphere by studying the geometry of ideal polyhedra in hyperbolic space we study the case of the hyperboloid and the cylinder by parameterizing the space of convex ideal polyhedra in anti de sitter geometry and in half pipe geometry just as the cylinder can be seen as a degeneration of the sphere and the hyperboloid half pipe geometry is naturally a limit of both hyperbolic and anti de sitter geometry we promote a unified point of view to the study of the three cases throughout

fock goncharov coordinates for rank two lie groups let g be a simply connected simple complex lie group of rank 2 we give explicit fock goncharov coordinates for configurations of triples and quadruples of affine flags in g we show that the action on triples by orientation preserving permutations corresponds to explicit quiver mutations and that the same holds for the flip changing the diagonal in a quadrilateral this gives explicit coordinates on higher teichmuller space and also coordinates for boundary unipotent representations of 3 manifold groups as an application we compute the generic boundary unipotent representations in mathrm sp 4 mathbb c langle i rangle for the figure eight knot complement

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

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

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

multiple edges in m kontsevich s graph complexes and computations of the dimensions and euler characteristics we provide a generating function for the graded dimensions of m kontsevich s graph complexes of ordinary graphs this generating function can be used to compute the euler characteristic in each loop order furthermore we show that graphs with multiple edges can be omitted from these graph complexes

finite type invariants and fatgraphs abstract we define an invariant g m of pairs m g where m is a 3 manifold obtained by surgery on some framed link in the cylinder i is a connected surface with at least one boundary component and g is a fatgraph spine of in effect g is the composition with the n maps of le murakami ohtsuki of the link invariant of andersen mattes reshetikhin computed relative to choices determined by the fatgraph g this provides a basic connection between 2d geometry and 3d quantum topology for each fixed g this invariant is shown to be universal for homology cylinders i e g establishes an isomorphism from an appropriate vector space h of homology cylinders to a certain algebra of jacobi diagrams via composition g g 1 for any pair of fatgraph spines g g of we derive a representation of the ptolemy groupoid i e the combinatorial model for the fundamental path groupoid of teichmuller space as a group of automorphisms of this algebra the space h comes equipped with a geometrically natural product induced by stacking cylinders on top of one another and furthermore supports related operations which arise by gluing a homology handlebody to one end of a cylinder or to another homology handlebody we compute how g interacts with all three operations explicitly in terms of natural products on jacobi diagrams and certain diagrammatic constants our main result gives an explicit extension of the lmo invariant of 3 manifolds to the ptolemy groupoid in terms of these operations and this groupoid extension nearly fits the paradigm of a tqft we finally re derive the morita penner cocycle representing the first johnson homomorphism using a variant generalization of g

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

on hilbert fourier and wavelet transforms several new families of wavelets which are derived from earlier work by the author on teichmuller theory are introduced and studied these wavelets are associated with the modular group rather than the affine group of the real line as for classical wavelets in further contrast to the usual setting there are explicit and essentially algebraic formulas relating wavelet and fourier expansions furthermore rather than relying on equally spaced multiscale sampling methods the wavelet expansions introduced here rely instead on an explicit nonuniformly spaced multiscale sampling method that depends upon the farey sequence of classical number theory these ingredients combine to give novel methods for calculating wavelet fourier and hilbert transforms with potential applications to myriad problems in electrical engineering by employing a new characteristic length associated to 2 2 matrices finiteness and convergence properties of the wavelet expansions are derived for functions with more than 5 2 derivatives in l2 one of our wavelet families forms a frame and the hilbert transform is calculable in hyperbolic coordinates 2002 wiley periodicals inc

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

on ramond decorations we impose constraints on the odd coordinates of super teichmuller space in the uniformization picture for the monodromies around ramond punctures thus reducing the overall odd dimension to be compatible with that of the moduli spaces of super riemann surfaces namely the monodromy of a puncture must be a true parabolic element of the canonical subgroup sl 2 mathbb r of osp 1 2

the dilogarithmic central extension of the ptolemy thompson group via the kashaev quantization abstract quantization of universal teichmuller space provides projective representations of the ptolemy thompson group which is isomorphic to the thompson group t this yields certain central extensions of t by z called dilogarithmic central extensions we compute a presentation of the dilogarithmic central extension t kash of t resulting from the kashaev quantization and show that it corresponds to 6 times the euler class in h 2 t z meanwhile the braided ptolemy thompson groups t t of funar kapoudjian are extensions of t by the infinite braid group b and by abelianizing the kernel b one constructs central extensions t ab t ab of t by z which are of topological nature we show t kash t ab our result is analogous to that of funar and sergiescu who computed a presentation of another dilogarithmic central extension t cf of t resulting from the chekhov fock goncharov quantization and thus showed that it corresponds to 12 times the euler class and that t cf t ab in addition we suggest a natural relationship between the two quantizations in the level of projective representations

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

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

laurent positivity of quantized canonical bases for quantum cluster varieties from surfaces in 2006 fock and goncharov constructed a nice basis of the ring of regular functions on the moduli space of framed pgl2 local systems on a punctured surface s the moduli space is birational to a cluster mathcal x variety whose positive real points recover the enhanced teichmuller space of s their basis is enumerated by integral laminations on s which are collections of closed curves in s with integer weights around ten years later a quantized version of this basis still enumerated by integral laminations was constructed by allegretti and kim for each choice of an ideal triangulation of s each quantum basis element is a laurent polynomial in the exponential of quantum shear coordinates for edges of the triangulation with coefficients being laurent polynomials in q with integer coefficients we show that these coefficients are laurent polynomials in q with positive integer coefficients our result was expected in a positivity conjecture for framed protected spin characters in physics and provides a rigorous proof of it and may also lead to other positivity results as well as categorification a key step in our proof is to solve a purely topological and combinatorial ordering problem about an ideal triangulation and a closed curve on s for this problem we introduce a certain graph on s which is interesting in its own right

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

approximation theory and functional analysis part 1 research and survey articles on bernstein durrineyer polynomials with jacob weights h berens and y xu an overview of wavelets c chui a note on weak inequalities in orlicz and lorentz spaces g a edgar and l sucheston bivariate birkhoff interpolation a survey r a lorentz linear approximations of functions with several restricted derivatives y makovoz some characterizations theorems for measures associated with orthogonal polynomials on the unit circle k pan and e b saff box splines cardinal series and wavelets s d reimenschneider and z shen some aspects of the subspace structure of infinite dimensional banach space h rosenthal fairness and monotone curvature j roulier et al projections on 2 dimensional spaces n tomczak jacgermann real versus complex best rational approximation r s varga and a ruttan

rigidity of polyhedral surfaces ii we study the rigidity of polyhedral surfaces using variational principles the action functionals are derived from the cosine laws the main focus of this paper is on the cosine law for a nontriangular region bounded by three possibly disjoint geodesics several of these cosine laws were first discovered and used by fenchel and nielsen by studying the derivative of the cosine laws we discover a uniform approach to several variational principles on polyhedral surfaces with or without boundary as a consequence the work of penner bobenko and springborn and thurston on rigidity of polyhedral surfaces and circle patterns are extended to a very general context

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

teichmuller spaces as degenerated symplectic leaves in dubrovin ugaglia poisson manifolds abstract in this paper we study the goldman bracket between geodesic length functions both on a riemann surface g s 0 of genus g with s 1 2 holes and on a riemann sphere 0 1 n with one hole and n orbifold points of order two we show that the corresponding teichmuller spaces t g s 0 and t 0 1 n are realised as real slices of degenerated symplectic leaves in the dubrovin ugaglia poisson algebra of upper triangular matrices s with 1 on the diagonal

perturbative series and the moduli space of riemann surfaces on utilise des techniques de la theorie quantique des champs pour calculer des quantites reliees aux groupes de symetrie de paires f g ou f est une surface et g une epine de f

canonical extensions of the johnson homomorphisms to the torelli groupoid abstract we prove that every trivalent marked bordered fatgraph comes equipped with a canonical generalized magnus expansion in the sense of kawazumi this magnus expansion is used to give canonical extensions of the higher johnson homomorphisms m for m 1 to the torelli groupoid and we provide a recursive combinatorial formula for tensor representatives of these extensions in particular we give an explicit 1 cocycle in the dual fatgraph complex which extends 2 and thus answer affirmatively a question of morita and penner to illustrate our techniques for calculating higher johnson homomorphisms in general we give explicit examples calculating m for m 3

endomorphic presentations of branch groups we introduce endomorphic presentations or l presentations group presentations whose relations are iterated under a set of substitutions on the generating set and show that a broad class of groups acting on rooted trees admit explicitly constructible finite l presentations generalising results by igor lysionok and said sidki

a new approach to the word and conjugacy problems in the braid groups abstract a new presentation of the n string braid group b n is studied using it a new solution to the word problem in b n is obtained which retains most of the desirable features of the garside thurston solution and at the same time makes possible certain computational improvements we also give a related solution to the conjugacy problem but the improvements in its complexity are not clear at this writing

the virtual cohomological dimension of the mapping class group of an orientable surface let f f r be the mapping class group of a surface f of genus g with s punctures and r boundary components the purpose of this paper is to establish cohomology properties of f parallel to those of the arithmetic groups if g is a linear algebraic group defined over q x is the symmetric space associated to g and a is an arithmetic subgroup of g then a is virtually torsion free and acts properly discontinuously on x the rational homology of a is the same as that of x a furthermore there is a bordification of x bs to a manifold with corners 3 and an extension of the action of a to a properly discontinuous action on jf so that the quotient x a is compact the boundary of jf is homotopy equivalent to a wedge of spheres say of dimension d and the virtual cohomological dimension of a is n d 1 where n is the dimension of x in the case of the mapping class group there is no analog for g ivanov unpublished has proven that f is not arithmetic nevertheless f acts properly discontinuously on teichmiiller space r which is homeomorphic to euclidean space of dimension 6 g 6 2 s 3 will play the role of the symmetric space the quotient of 9by f is the moduli space of curves whose rational homology is then identified with that of e harvey har has constructed a borel serre bordification j of 3 by analytic methods in the case where f has punctures we will build g by a different combinatorial method in addition we will explicitly describe inside y a cell complex y of dimension 4 g 4 s onto which j may be f equivariantly retracted thus establishing an analog of the constructions for sl n by serre soul6 sol and ash a this complex will be of the lowest possible dimension because we will use j to prove our main result

noncommutative marked surfaces abstract the aim of the paper is to attach a noncommutative cluster like structure to each marked surface this is a noncommutative algebra a generated by noncommutative geodesics between marked points subject to certain triangle relations and noncommutative analogues of ptolemy plucker relations it turns out that the algebra a exhibits a noncommutative laurent phenomenon with respect to any triangulation of which confirms its cluster nature as a surprising byproduct we obtain a new topological invariant of which is a free or a 1 relator group easily computable in terms of any triangulation of another application is the proof of laurentness and positivity of certain discrete noncommutative integrable systems

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

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

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

quantisation of super teichmuller theory we construct a quantisation of the teichmuller spaces of super riemann surfaces using coordinates associated to ideal triangulations of super riemann surfaces a new feature is the non trivial dependence on the choice of a spin structure which can be encoded combinatorially in a certain refinement of the ideal triangulation by constructing a projective unitary representation of the groupoid of changes of refined ideal triangulations we demonstrate that the dependence of the resulting quantum theory on the choice of a triangulation is inessential

complete positive group presentations abstract a combinatorial property of positive group presentations called completeness is introduced with an effective criterion for recognizing complete presentations and an iterative method for completing an incomplete presentation we show how to directly read several properties of the associated monoid and group from a complete presentation cancellativity or existence of common multiples in the case of the monoid or isoperimetric inequality in the case of the group in particular we obtain a new criterion for recognizing that a monoid embeds in a group of fractions typical presentations eligible for the current approach are the standard presentations of the artin tits groups and the heisenberg group

the unstable integral homology of the mapping class groups of a surface with boundary we construct a graph complex calculating the integral homology of the bordered mapping class groups we compute the homology of the bordered mapping class groups of the surfaces s 1 1 s 1 2 and s 2 1 using the circle action on this graph complex we build a double complex and a spectral sequence converging to the homology of the unbordered mapping class groups we compute the homology of the punctured mapping class groups associated to the surfaces s 1 1 and s 2 1 finally we use miller s operad to get the first kudo araki and browder operations on our graph complex we also consider an unstable version of the higher kudo araki dyer lashoff operations

variation on butzer s problem characterization of the solutions abstract the so called butzer problem had been a challenge to the approximation community for decades until its first constructive solution was given by cao and gonska at the end of the 1980s butzer s original problem can be turned into a strong form namely a pointwise one in the present note we characterize among other things and in an easy way certain operators which solve butzer s problem in this strong and most demanding version

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

cyclic symmetries of an quiver representations abstract this note contains a combinatorial construction of symmetries arising in symplectic geometry partially wrapped or infinitesimal fukaya categories algebraic geometry derived categories of singularities and k theory waldhausen s s construction our specific motivation in the spirit of expectations of kontsevich is a combinatorial construction of categorical quantizations of lagrangian skeleta of symplectic manifolds the main result of this paper gives an immediate solution in the one dimensional case of ribbon graphs

enumeration of chord diagrams on many intervals and their non orientable analogs two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here the real segments may contain additional bivalent vertices in one model but not in the other in the former case we record in a generating function the number of fatgraph boundary cycles containing a fixed number of bivalent vertices while in the latter we instead record the number of boundary cycles of each fixed length second order non linear algebraic partial differential equations are derived which are satisfied by these generating functions in each case giving efficient enumerative schemes moreover these generating functions provide multi parameter families of solutions to the kp hierarchy for each model there is furthermore a non orientable analog and each such model likewise has its own associated differential equation the enumerative problems we solve are interpreted in terms of certain polygon gluings as specific applications we discuss models of several interacting rna molecules we also study a matrix integral which computes numbers of chord diagrams in both orientable and non orientable cases in the model with bivalent vertices and the large n limit is computed using techniques of free probability

the euler characteristic of the moduli space of curves let fg 1 g 1 be the mapping class group consisting of all isotopy classes of base point and orientation preserving homeomorphisms of a closed oriented surface f of genus g let 1 be its euler characteristic in the sense of wall that is z f i fgl f l z e f where f is any torsion free subgroup of finite index in f 1 and e is a contractible space on which f acts freely and properly discontinuously an example of such a space is the teichmiiller space 1 and g f can be interpreted as the orbifold euler characteristic of f i join the moduli space of curves of genus g with base point the purpose of this paper is to prove the following formula for f i

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