the riemann hilbert approach to strong asymptotics for orthogonal polynomials on 1 1 abstract we consider polynomials that are orthogonal on 1 1 with respect to a modified jacobi weight 1 x 1 x h x with 1 and h real analytic and strictly positive on 1 1 we obtain full asymptotic expansions for the monic and orthonormal polynomials outside the interval 1 1 for the recurrence coefficients and for the leading coefficients of the orthonormal polynomials we also deduce asymptotic behavior for the hankel determinants and for the monic orthogonal polynomials on the interval 1 1 for the asymptotic analysis we use the steepest descent technique for riemann hilbert problems developed by deift and zhou and applied to orthogonal polynomials on the real line by deift kriecherbauer mclaughlin venakides and zhou in the steepest descent method we will use the szeg function associated with the weight and for the local analysis around the endpoints 1 we use bessel functions of appropriate order whereas deift et al use airy functions

central limit theorem for linear eigenvalue statistics of random matrices with independent entries we consider n x n real symmetric and hermitian wigner random matrices n 1 2 w with independent modulo symmetry condition entries and the null sample covariance matrices n 1 x x with independent entries of m x n matrix x assuming first that the 4th cumulant excess 4 of entries of w and x is zero and that their 4th moments satisfy a lindeberg type condition we prove that linear statistics of eigenvalues of the above matrices satisfy the central limit theorem clt as n m m n c 0 oo with the same variance as for gaussian matrices if the test functions of statistics are smooth enough essentially of the class c 5 this is done by using a simple interpolation trick from the known results for the gaussian matrices and the integration by parts presented in the form of certain differentiation formulas then by using a more elaborated version of the techniques we prove the clt in the case of nonzero excess of entries again for essentially 5 test function here the variance of statistics contains an additional term proportional to 4 the proofs of all limit theorems follow essentially the same scheme

on the characteristic polynomial of a random unitary matrix we present a range of fluctuation and large deviations results for the logarithm of the characteristic polynomial z of a random n n unitary matrix as n first we show that evaluated at a finite set of distinct points is asymptotically a collection of i i d complex normal random variables this leads to a refinement of a recent central limit theorem due to keating and snaith and also explains the covariance structure of the eigenvalue counting function next we obtain a central limit theorem for ln z in a sobolev space of generalised functions on the unit circle in this limiting regime lower order terms which reflect the global covariance structure are no longer negligible and feature in the covariance structure of the limiting gaussian measure large deviations results for ln z a evaluated at a finite set of distinct points can be obtained for for higher order scalings we obtain large deviations results for ln z a evaluated at a single point there is a phase transition at a ln n which only applies to negative deviations of the real part reflecting a switch from global to local conspiracy

generalized fictitious methods for fluid structure interactions analysis and simulations we present a new fictitious pressure method for fluid structure interaction fsi problems in incompressible flow by generalizing the fictitious mass and damping methods we published previously in 1 the fictitious pressure method involves modification of the fluid solver whereas the fictitious mass and damping methods modify the structure solver we analyze all fictitious methods for simplified problems and obtain explicit expressions for the optimal reduction factor convergence rate index at the fsi interface 2 this analysis also demonstrates an apparent similarity of fictitious methods to the fsi approach based on robin boundary conditions which have been found to be very effective in fsi problems we implement all methods including the semi implicit robin based coupling method in the context of spectral element discretization which is more sensitive to temporal instabilities than low order methods however the methods we present here are simple and general and hence applicable to fsi based on any other spatial discretization in numerical tests we verify the selection of optimal values for the fictitious parameters for simplified problems and for vortex induced vibrations viv even at zero mass ratio for ever resonance we also develop an empirical a posteriori analysis for complex geometries and apply it to 3d patient specific flexible brain arteries with aneurysms for very large deformations we demonstrate that the fictitious pressure method enhances stability and convergence and is comparable or better in most cases to the robin approach or the other fictitious methods

a robin robin preconditioner for advection diffusion equations with discontinuous coefficients abstract we consider an advection diffusion problem with discontinuous viscosity coefficients we apply a substructuring technique and we extend to the resulting schur complement the robin robin preconditioner used for problems with constant viscosity a quasi optimal convergence analysis is performed in the case of uniform convection by means of fourier techniques the variational formulation in order to generalize the preconditioner to an arbitrary number of subdomains is also addressed as well as some numerical tests in 3d

finite element approximation of transmission conditions in fluids and solids introducing boundary subgrid scales terms involving jumps of stresses on boundaries are proposed for the finite element approximation of the stokes problem and the linear elasticity equations these terms are designed to improve the transmission conditions between subdomains at three different levels namely between the element domains between the interfaces in homogeneous domain interaction problems and at the interface between the fluid and the solid in fluid structure interaction problems the benefits in each case are respectively the possibility of using discontinuous pressure interpolations in a stabilized finite element approximation of the stokes problem a stronger enforcement of the stress continuity in homogeneous domain decomposition problems and a considerable improvement of the behavior of iterative schemes to couple the fluid and the solid in fluid structure integration algorithms the motivation to introduce these terms stems from a decomposition of the unknown into a conforming and a non conforming part a hybrid formulation for the latter and a simple approximation for the unknowns involved in the hybrid problem copyright 2011 john wiley sons ltd

random hermitian matrices and gaussian multiplicative chaos n berestycki s work is supported by epsrc grants ep l018896 1 and ep i03372x 1 m d wong is a phd student at the cambridge centre for analysis supported by epsrc grant ep l016516 1 some of this work was carried out while the first and third authors visited the university of helsinki funded in part by epsrc grant ep l018896 1 they also wish to thank the university of helsinki for its hospitality during this visit c webb wishes to thank the isaac newton institute for mathematical sciences for its hospitality during the random geometry program during which this project was initiated c webb was supported by the eemil aaltonen foundation grant stochastic dynamics on large random graphs and academy of finland grants 288318 and 308123

1 f α noise in the fluctuations of the spectra of tridiagonal random matrices from the β hermite ensemble the 1 f ensuremath alpha noise displayed by the fluctuation of the n th unfolded eigenvalue where n plays the role of a discrete time was recently characterized for the classical gaussian ensembles of n ifmmode times else texttimes fi n random matrices it is investigated here for the ensuremath beta hermite ensemble by wavelet analysis of monte carlo simulated series both as a function of ensuremath beta and of n when ensuremath beta decreases from 1 to 0 for a given and large enough n the evolution from a 1 f noise at ensuremath beta 1 gaussian orthogonal ensemble goe to a 1 f 2 noise at ensuremath beta 0 gaussian diagonal ensemble gde is heterogeneous with a ensuremath sim 1 f 2 noise at the finest scales and a ensuremath sim 1 f noise at the coarsest ones

iterative strong coupling of dimensionally heterogeneous models in this article we address decomposition strategies especially tailored to perform strong coupling of dimensionally heterogeneous models under the hypothesis that one wants to solve each submodel separately and implement the interaction between subdomains by boundary conditions alone the novel methodology takes full advantage of the small number of interface unknowns in this kind of problems existing algorithms can be viewed as variants of the natural staggered algorithm in which each domain transfers function values to the other and receives fluxes or forces and vice versa this natural algorithm is known as dirichlet to neumann in the domain decomposition literature essentially we propose a framework in which this algorithm is equivalent to applying gauss seidel iterations to a suitably defined linear or nonlinear system of equations it is then immediate to switch to other iterative solvers such as gmres or other krylov based method which we assess through numerical experiments showing the significant gain that can be achieved indeed the benefit is that an extremely flexible automatic coupling strategy can be developed which in addition leads to iterative procedures that are parameter free and rapidly converging further in linear problems they have the finite termination property copyright 2009 john wiley sons ltd

coupling biot and navier stokes equations for modelling fluid poroelastic media interaction the interaction between a fluid and a poroelastic structure is a complex problem that couples the navier stokes equations with the biot system the finite element approximation of this problem is involved due to the fact that both subproblems are indefinite in this work we first design residual based stabilization techniques for the biot system motivated by the variational multiscale approach then we state the monolithic navier stokes biot system with the appropriate transmission conditions at the interface for the solution of the coupled system we adopt both monolithic solvers and heterogeneous domain decomposition strategies different domain decomposition methods are considered and their convergence is analyzed for a simplified problem we compare the efficiency of all the methods on a test problem that exhibits a large added mass effect as it happens in hemodynamics applications

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

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

regularity conditions in the clt for linear eigenvalue statistics of wigner matrices abstract we show that the variance of centred linear statistics of eigenvalues of gue matrices remains bounded for large n for some classes of test functions less regular than lipschitz functions this observation is suggested by the limiting form of the variance which has previously been computed explicitly but it does not seem to appear in the literature we combine this fact with comparison techniques following tao vu and erdos yau et al and a littlewood paley type decomposition to extend the central limit theorem for linear eigenvalue statistics to functions in the holder class c 1 2 in the case of matrices of gaussian convolution type we also give a variance bound which implies the clt for test functions in the sobolev space h 1 and c 1 for general wigner matrices satisfying moment conditions if the additional assumption of the test function being supported away from the edge of the spectrum is made we prove the clt for test functions of regularity h 1 2 l and h 1 2 for gue and johansson matrices respectively previous results on the clt impose the existence and continuity of at least one classical derivative

some comments on six inequalities associated with the inefficiency of ordinary least squares with one regressor abstract the study of the inefficiency of the ordinary least squares estimator olse with one regressor by watson 1951 required a lower bound for the efficiency defined as the ratio of the variance of the best linear unbiased estimator blue to the variance of the olse such a lower bound was provided by the cassels inequality 1951 which we note is closely related to five other inequalities including the well known inequality usually attributed to kantorovich 1948 but which was established already by frucht 1943 the main purpose in this paper is to show how these six inequalities are related with a historical perspective we present some proofs and conclude that all six inequalities are essentially equivalent in the sense that any one inequality implies the other five we identify conditions for equality in each inequality and present the six continuous integral analogues we end the paper with english translations of the seminal papers by frucht 1943 and schweitzer 1914 respectively from the spanish and hungarian and a fairly extensive bibliography

a stabilized finite element method for generalized stationary incompressible flows abstract in this paper we describe a finite element formulation for the numerical solution of the stationary incompressible navier stokes equations including coriolis forces and the permeability of the medium the stabilized method is based on the algebraic version of the sub grid scale approach we first describe this technique for general systems of convection diffusion reaction equations and then we apply it to the linearized flow equations the important point is the design of the matrix of stabilization parameters that the method has this design is based on the identification of the stability problems of the galerkin method and a scaling of variables argument to determine which coefficients must be included in the stabilization matrix this together with the convergence analysis of the linearized problem leads to a simple expression for the stabilization parameters in the general situation considered in the paper the numerical analysis of the linearized problem also shows that the method has optimal convergence properties

exact solution of the six vertex model with domain wall boundary conditions disordered phase the six vertex model or the square ice model with domain wall boundary conditions dwbc has been introduced and solved for finite n by korepin and izergin the solution is based on the yang baxter equations and it represents the free energy in terms of an n n hankel determinant paul zinn justin observed that the izergin korepin formula can be re expressed in terms of the partition function of a random matrix model with a nonpolynomial interaction we use this observation to obtain the large n asymptotics of the six vertex model with dwbc in the disordered phase the solution is based on the riemann hilbert approach and the deift zhou nonlinear steepest descent method as was noticed by kuperberg the problem of enumeration of alternating sign matrices the asm problem is a special case of the six vertex model we compare the obtained exact solution of the six vertex model with known exact results for the 1 2 and 3 enumerations of asms and also with the exact solution on the so called free fermion line we prove the conjecture of zinn justin that the partition function of the six vertex model with dwbc has the asymptotics z n sim cn kappa e n 2 f as n and we find the exact value of the exponent

the isomonodromy approach to matric models in 2d quantum gravity we consider the double scaling limit in the hermitian matrix model for 2d quantum gravity associated with the measure exp sum limits j 1 n t j z 2j n geqq 3 we show that after the appropriate modification of the contour of integration the cross migdal douglas shenker limit to the painleve i equation in the generic case of the pure gravity is valid and calculate the nonperturbative parameters of the corresponding painleve function our approach is based on the wkb analysis of the l a pair corresponding to the discrete string equation in the framework of the inverse monodromy method here we extend our results which were obtained before for the particular casesn 2 3 our analysis complements the isomonodromy approach proposed by g moore to the general string equations that come from the matrix model in the continuous limit and differ in that we apply the isomonodromy technique to investigate the double scaling limit itself

strong asymptotics of orthogonal polynomials with respect to exponential weights we consider asymptotics of orthogonal polynomials with respect to weights w x dx e q x dx on the real line where q x 2m k 0 qkx k q2m 0 denotes a polynomial of even order with positive leading coefficient the orthogonal polynomial problem is formulated as a riemann hilbert problem following 22 23 we employ the steepest descent type method introduced in 18 and further developed in 17 19 in order to obtain uniform plancherel rotach type asymptotics in the entire complex plane as well as asymptotic formulae for the zeros the leading coefficients and the recurrence coefficients of the orthogonal polynomials c 1999 john wiley sons inc

partitioned solution algorithms for fluid structure interaction problems with hyperelastic models in this work we consider fluid structure interaction simulation with nonlinear hyperelastic models in the solid part we use a partitioned approach to deal with the coupled nonlinear fluid structure interaction problems we focus on handling the nonlinearity of the fluid and structure sub problems using adaptive newton s method the near incompressibility of materials the stabilization of employed finite element discretization and the robustness and efficiency of krylov subspace and algebraic multigrid methods for the linearized algebraic equations

sensitivity analysis in kinematically incompatible models abstract a natural question that arises when working with the so called kinematically incompatible models is about the positioning of the internal artificial boundary that splits the domain of analysis into the sub domains for which the different incompatible models are established although the experience in modeling might provide an ad hoc solution to such matter it may also draw misleading conclusions here the sensitivity analysis furnishes a systematic and reliable framework to study the impact of the positioning of the artificial boundary over the solution of the problem in this sense the present work is concerned with the sensitivity analysis of the variational formulation corresponding to the kinematically incompatible models when the boundary over which the incompatibility between the models takes place is changed assuming the presence of a discontinuity in the fields over a given interface between two incompatible models this analysis allows to measure the sensitivity of a given cost functional when the location of such interface is changed the application for which this analysis is envisaged is to assess the correctness or incorrectness in the definition of the positioning of such coupling interface between dimensionally heterogeneous domains also some numerical results are provided to give numerical evidence of the usefulness of the present tool

on the potentialities of 3d 1d coupled models in hemodynamics simulations this work comprises a step towards the quantitative and qualitative analysis of coupled local and global hemodynamics phenomena in the arterial system the aim of this work is to present some numerical examples to put in evidence the importance of the use of 3d 1d coupled models in hemodynamics problems when carrying out simulations of rather complex situations accordingly some cases for which classical modeling cannot be applied are identified and solved the results obtained here allow us to assess some interrelations between local pointwise quantities defined at the level of the 3d model and global mean quantities defined at the level of the 1d model

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

flow rate boundary problems for an incompressible fluid in deformable domains formulations and solution methods in this paper we consider the numerical solution of the interaction of an incompressible fluid and an elastic structure in a truncated computational domain as well known in this case there is the problem of prescribing realistic boundary data on the artificial sections when only partial data are available this problem has been investigated extensively for the rigid case in this work we start considering the compliant case by focusing on the flow rate conditions for the fluid we propose three formulations of this problem different algorithms for its numerical solution and carry out several 2d numerical simulations with the aim of comparing the performances of the different algorithms

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

correlations of the characteristic polynomials in the gaussian unitary ensemble or a singular hankel determinant we obtain large n asymptotics for products of powers of the absolute values of the characteristic polynomials in the gaussian unitary ensemble gue of n n matrices our results can also be interpreted as asymptotics of the determinant of a hankel matrix whose symbol is supported on the real line and possesses power like fisher hartwig singularities

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

fixed energy universality for generalized wigner matrices we prove the wigner dyson mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and hermitian wigner matrices previous results concerning the universality of random matrices either require an averaging in the energy parameter or they hold only for hermitian matrices if the energy parameter is fixed we develop a homogenization theory of the dyson brownian motion and show that microscopic universality follows from mesoscopic statistics 2015 wiley periodicals inc

inexact accurate partitioned algorithms for fluid structure interaction problems with finite elasticity in haemodynamics in this paper we consider the numerical solution of the three dimensional fluid structure interaction problem in haemodynamics in the case of real geometries physiological data and finite elasticity vessel deformations we study some new inexact schemes obtained from semi implicit approximations which treat exactly the physical interface conditions while performing just one or few iterations for the management of the interface position and of the fluid and structure non linearities we show that such schemes allow to improve the efficiency while preserving the accuracy of the related exact implicit scheme to do this we consider both a simple analytical test case and two real cases of clinical interest in haemodynamics we also provide an error analysis for a simple differential model problem when a bdf method is considered for the time discretization and only few newton iterations are performed at each temporal instant

inequalities involving powers of generalized inverses abstract converses of matrix inequalities corresponding to ratios and differences of means are extended to the positive semidefinite case this is done by the use of generalized inverses of powers of positive semidefinite matrices similar extensions for converses of matrix forms of holder s inequality are also given

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

analysis and optimization of the generalized schwarz method for elliptic problems with application to fluid structure interaction we propose a unified convergence analysis of the generalized schwarz method applied to a linear elliptic problem for a general interface flat cylindrical or spherical in any dimension in particular we provide the exact convergence set of the interface symbols related to the operators involved in the transmission conditions we also provide a general procedure to obtain estimates of the optimized interface symbols within the constants we apply such general results to a simple fluid structure interaction model problem given by the interaction between an incompressible inviscid fluid and the wave equation finally we assess the effectiveness of the theoretical findings through three dimensional numerical experiments in the haemodynamic context obtained by solving the coupling between the navier stokes equations and the linear infinitesimal elasticity

robin robin domain decomposition methods for the stokes darcy coupling in this paper we consider a coupled system made of the stokes and darcy equations and we propose some iteration by subdomain methods based on robin conditions on the interface we prove the convergence of these algorithms and for suitable finite element approximations we show that the rate of convergence is independent of the mesh size h special attention is paid to the optimization of the performance of the methods when both the kinematic viscosity nu of the fluid and the hydraulic conductivity tensor k of the porous medium are very small

a convergence study of a new partitioned fluid structure interaction algorithm based on fictitious mass and damping we develop analyze and validate a new method for simulating fluid structure interactions fsis which is based on fictitious mass and fictitious damping in the structure equation we employ a partitioned method for the fluid and structure motions in conjunction with sub iteration and aitken relaxation in particular the use of such fictitious parameters requires sub iterations in order to reduce the induced error in addition to the local temporal truncation error to this end proper levels of tolerance for terminating the sub iteration procedure have been obtained in order to recover the formal order of temporal accuracy for the coupled fsi problem these fictitious terms have a significant effect leading to better convergence rate and hence substantially smaller number of sub iterations through analysis we identify the proper range of these parameters which we then verify by corresponding numerical tests we implement the method in the context of spectral element discretization which is more sensitive than low order methods to numerical instabilities arising in the explicit fsi coupling however the method we present here is simple and general and hence applicable to fsi based on any other discretization we demonstrate the effectiveness of the method in applications involving 2d vortex induced vibrations viv and in 3d flexible arteries with structural density close to blood density we also present 3d results for a patient specific aneurysmal flow under pulsatile flow conditions examining in particular the sensitivity of the results on different values of the fictitious parameters

regularized fractional ornstein uhlenbeck processes and their relevance to the modeling of fluid turbulence motivated by the modeling of the temporal structure of the velocity field in a highly turbulent flow we propose and study a linear stochastic differential equation that involves the ingredients of an ornstein uhlenbeck process supplemented by a fractional gaussian noise of parameter h regularized over a small time scale e 0 a peculiar correlation between these two plays a key role in the establishment of the statistical properties of its solution we show that this solution reaches a stationary regime which marginals including variance and increment variance remain bounded when e 0 in particular in this limit for any h 0 1 we show that the increment variance behaves at small scales as the one of a fractional brownian motion of same parameter h from the theoretical side this approach appears especially well suited to deal with the very rough case h 1 2 including the boundary value h 0 and to design simple and efficient numerical simulations

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

factorization methods for the numerical approximation of navier stokes equations we investigate a general approach for the numerical approximation of incompressible navier stokes equations based on splitting the original problem into successive subproblems which are cheaper to solve the splitting is obtained through an algebraic approximate factorization of the matrix arising from space and time discretization of the original equations several schemes based on approximate factorization are investigated for some of these methods a formal analogy with well known time advancing schemes such as the projection chorin temam s can be pointed out features and limits of this analogy that was earlier introduced in b perot j comp phys 108 1993 51 8 are addressed other new methods can also be formulated starting from this approach in particular we introduce the so called yosida method which can be investigated in the framework of quasi compressibility schemes numerical results illustrating the different performances of the different methods addressed are presented for a couple of test cases

stochastic calculus for fractional brownian motion with hurst exponent h a rough path method by analytic extension the d dimensional fractional brownian motion fbm for short b t b 1 t b d t t r with hurst exponent 0 1 is a d dimensional centered self similar gaussian process with covariance e b i s b i t 1 2 i j lsl 2 ltl 2 t s 2 the long standing problem of defining a stochastic integration with respect to fbm and the related problem of solving stochastic differential equations driven by fbm has been addressed successfully by several different methods although in each case with a restriction on the range of either d or the case corresponds to the usual stochastic integration with respect to brownian motion while most computations become singular when gets under various threshhold values due to the growing irregularity of the trajectories as 0 we provide here a new method valid for any d and for 1 4 by constructing an approximation e t e 0 of fbm which allows to define iterated integrals and then applying the geometric rough path theory the approximation relies on the definition of an analytic process z on the cut plane z c r of which fbm appears to be a boundary value and allows to understand very precisely the well known see 5 but as yet a little mysterious divergence of levy s area for 1 4

modeling dimensionally heterogeneous problems analysis approximation and applications in the present work a general theoretical framework for coupled dimensionally heterogeneous partial differential equations is developed this is done by recasting the variational formulation in terms of coupling interface variables in such a general setting we analyze existence and uniqueness of solutions for both the continuous problem and its finite dimensional approximation this approach also allows the development of different iterative substructuring solution methodologies involving dimensionally homogeneous subproblems numerical experiments are carried out to test our theoretical results

modular vs non modular preconditioners for fluid structure systems with large added mass effect in this article we address the numerical simulation of fluid structure interaction fsi problems featuring large added mass effect we analyze different preconditioners for the coupled system matrix obtained after space time discretization and linearization of the fsi problem the classical dirichlet neumann preconditioner has the advantage of modularity because it allows to reuse existing fluid and structure codes with minimum effort simple interface communication unfortunately its performance is very poor in case of large added mass effects alternatively we consider two non modular approaches the first one consists in preconditioning the coupled system with a suitable diagonal scaling combined with an ilut preconditioner the system is then solved by a krylov method the drawback of this procedure is that the combination of fluid and structure codes to solve the coupled system is not straightforward the second non modular approach we consider is a splitting technique based on an inexact block lu factorization of the linear fsi system the resulting algorithm computes the fluid velocity separately from the coupled pressure structure system at each iteration reducing the computational cost independently of the preconditioner the efficiency of semi implicit algorithms i e those that treat geometric and fluid nonlinearities in an explicit way is highlighted and their performance compared to the one of implicit algorithms all the methods are tested on three dimensional blood vessel systems the algorithm combining the non modular ilut preconditioner with krylov methods proved to be the fastest

a characterisation of the gaussian free field we prove that a random distribution in two dimensions which is conformally invariant and satisfies a natural domain markov property is a multiple of the gaussian free field this result holds subject only to a fourth moment assumption

freezing transition characteristic polynomials of random matrices and the riemann zeta function we argue that the freezing transition scenario previously explored in the statistical mechanics of 1 f noise random energy models also determines the value distribution of the maximum of the modulus of the characteristic polynomials of large n ifmmode times else texttimes fi n random unitary matrices we postulate that our results extend to the extreme values taken by the riemann zeta function ensuremath zeta s over sections of the critical line s 1 2 it of constant length and present the results of numerical computations in support our main purpose is to draw attention to possible connections between the statistical mechanics of random energy landscapes random matrix theory and the theory of the riemann zeta function

analysis and optimization of robin robin partitioned procedures in fluid structure interaction problems in the solution of fluid structure interaction fsi problems partitioned procedures are modular algorithms that involve separate fluid and structure solvers that interact in an iterative framework through the exchange of suitable transmission conditions at the fs interface in this work we study using fourier analysis the convergence of partitioned algorithms based on robin transmission conditions we derive for different models of the fluid and the structure a frequency dependent reduction factor at each iteration of the partitioned algorithm which is minimized by choosing optimal values of the coefficients in the robin transmission conditions two dimensional numerical results are also reported which highlight the effectiveness of the optimization procedure

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

a unified variational approach for coupling 3d 1d models and its blood flow applications in this work we propose an extended variational formulation in order to handle the problem of the flow of an incompressible fluid in compliant vessels with discontinuous fields this approach makes possible to tackle in a consistent variational manner problems like the coupling between models of different dimensionality the main ideas of the work are presented for a simple heat transfer problem and then are used in the context of modelling blood flow in large vessels a computational implementation of the proposed formulation is also shown and discussed by presenting examples of practical applications

random conformal weldings we construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle the homeomorphism is constructed using the exponential of x where x is the restriction of the 2 dimensional free field on the circle and the parameter is in the high temperature regime beta sqrt 2 the welding problem is solved by studying a non uniformly elliptic beltrami equation with a random complex dilatation for the existence a method of lehto is used this requires sharp probabilistic estimates to control conformal moduli of annuli and they are proven by decomposing the free field as a sum of independent fixed scale fields and controlling the correlations of the complex dilatation restricted to dyadic cells of various scales for the uniqueness we invoke a result by jones and smirnov on conformal removability of holder curves our curves are closely related to sle for 4

fractional brownian motion with hurst index h 0 and the gaussian unitary ensemble the goal of this paper is to establish a relation between characteristic polynomials of n n gue random matrices h as n and gaussian processes with logarithmic correlations we introduce a regularized version of fractional brownian motion with zero hurst index which is a gaussian process with stationary increments and logarithmic increment structure then we prove that this process appears as a limit of d n z log det h zi on mesoscopic scales as n by employing a fourier integral representation we use this to prove a continuous analogue of a result by diaconis and shahshahani j appl probab 31a 1994 49 62 on the macroscopic scale d n x gives rise to yet another type of gaussian process with logarithmic correlations we give an explicit construction of the latter in terms of a chebyshev fourier random series

on jessen s inequality for convex functions ii on etablit quelques resultats lies a l integralite de b jessen pour les fonctions convexes

an analysis of the fractional step method the fractional step method for solving the incompressible navier stokes equations in primitive variables is analyzed as a block lu decomposition in this formulation the issues involving boundary conditions for the intermediate velocity variables and the pressure are clearly resolved in addition it is shown that poor temporal accuracy first order is not due to boundary conditions but due to the method itself a generalized block lu decomposition that overcomes this difficulty is presented allowing arbitrarily high temporal order of accuracy the generalized decomposition is shown to be useful for a wide range of problems including steady problems technical issues such as stability and the appropriate pressure update scheme are also addressed numerical simulations of the steady incompressible navier stokes equations in a square domain confirm the theoretical results 18 refs 4 figs

on barnes beta distributions and applications to the maximum distribution of the 2d gaussian free field a new family of barnes beta distributions on 0 infty is introduced and its infinite divisibility moment determinacy scaling and factorization properties are established the morris integral probability distribution is constructed from barnes beta distributions of types 1 0 and 2 2 and its moment determinacy and involution invariance properties are established for application the maximum distributions of the 2d gaussian free field on the unit interval and circle with a non random logarithmic potential are conjecturally related to the critical selberg and morris integral probability distributions respectively and expressed in terms of sums of barnes beta distributions of types 1 0 and 2 2

the central limit theorem for local linear statistics in classical compact groups and related combinatorial identities author s soshnikov alexander abstract we discuss clt for the global and local linear statistics of random matrices from classical compact groups the main part of our proofs are certain combinatorial identities much in the spirit of works by kac and spohn

error amplification analysis of subiteration preconditioned gmres for fluid structure interaction the customary subiteration method for solving fluid structure interaction problems exhibits several deficiencies viz only conditional stability potential convergence difficulties due to non normality induced divergence and the inability to reuse information from previously solved similar problems to overcome these deficiencies a novel solution method is considered in which subiteration is used as a preconditioner to gmres this paper treats the linear algebra aspects of the subiteration method and of the subiteration preconditioned gmres method on the basis of properties of the error amplification matrix for the aggregated fluid structure system an analysis of the error amplification matrix of subiteration establishes that subiteration condenses errors into a low dimensional subspace which can be associated with the interface degrees of freedom therefore the gmres acceleration of subiteration can be confined to the interface degrees of freedom the error amplification analysis provides a clear explanation of the relation between the local gmres acceleration i e on the interface degrees of freedom and the global error amplification properties i e for the aggregated system moreover we show that the subiteration iterates span a krylov space corresponding to a preconditioned aggregated system we then address the implications of the non normality of the subiteration preconditioner for the convergence of gmres the subiteration preconditioned gmres method enables the optional reuse of krylov vectors in subsequent invocations of gmres which can substantially enhance the efficiency of the method to assess the potential and the limitations of the reuse option we analyse the error amplification matrix of the gmres method with reuse furthermore we establish that the gmres acceleration on the interface degrees of freedom generates an approximation to the schur complement for the aggregated system the gmres acceleration and the reuse of krylov vectors are then assessed in terms of the approximation properties for the schur complement and in terms of the properties of the corresponding error amplification matrices numerical experiments on a model fluid structure interaction problem illustrate the developed theory in particular we analyse the convergence of the respective methods in terms of spectral radii matrix norms and sharp convergence upper bounds

numerical treatment of defective boundary conditions for the navier stokes equations we present a formulation for accommodating defective boundary conditions for the incompressible navier stokes equations where only averaged values are prescribed on measurable portions of the boundary in particular we consider the case where the flow rate is imposed on several domain sections this methodology has an interesting application in the numerical simulation of flow in blood vessels when only a reduced set of boundary data are generally available for the upstream and downstream sections

multidimensional modelling for the carotid artery blood flow abstract in this work a multidimensional 3d 1d fem model of the whole arterial tree is implemented it comprises a 3d compliant model of the carotid bifurcation coupled with a 1d model for the remaining part of the arterial tree with this approach difficulties arising from the treatment of boundary conditions for the 3d model are naturally handled the navier stokes equations are used as the governing equations for the blood flow while an elastic compliant model is implemented for the arterial wall also the a l e formulation is considered within the 3d blood regions taking into account the domain deformations produced by the moving artery wall this 3d model is complemented with a 1d model of the entire arterial tree in order to appropriately set inflow and outflow boundary conditions for the former the reduced 1d model solves the momentum and continuity equations in compliant tubes so as to reproduce the propagation of the pressure pulse in the arterial network also a volumetric flow rate is imposed at the inlet to model the systolic work of the heart the peripheral arteriole beds are simulated with the well known lumped windkessel model a standard geometry of the carotid bifurcation is discretized with p1 bubble p1 tetrahedral elements the obtained results properly reproduce the general flow patterns reported in the literature very good agreement between the outcomes of a pure 1d model and those of the combined multidimensional model was obtained it is worth noting that this kind of model may provide useful information to gain understanding in the genesis and development of arterial diseases

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

on the moments of the moments of the characteristic polynomials of random unitary matrices denoting by p n a theta det i ae i theta the characteristic polynomial on the unit circle in the complex plane of an n times n random unitary matrix a we calculate the kth moment defined with respect to an average over a in u n of the random variable corresponding to the 2 beta th moment of p n a theta with respect to the uniform measure frac d theta 2 pi for all k beta in mathbb n these moments of moments have played an important role in recent investigations of the extreme value statistics of characteristic polynomials and their connections with log correlated gaussian fields our approach is based on a new combinatorial representation of the moments using the theory of symmetric functions and an analysis of a second representation in terms of multiple contour integrals our main result is that the moments of moments are polynomials in n of degree k 2 beta 2 k 1 this resolves a conjecture of fyodorov and keating philos trans r soc a 372 2007 20120503 2014 concerning the scaling of the moments with n as n rightarrow infty for k beta in mathbb n indeed it goes further in that we give a method for computing these polynomials explicitly and obtain a general formula for the leading coefficient

subcritical multiplicative chaos for regularized counting statistics from random matrix theory for an n times n haar distributed random unitary matrix u n we consider the random field defined by counting the number of eigenvalues of u n in a mesoscopic arc centered at the point u on the unit circle we prove that after regularizing at a small scale epsilon n 0 the renormalized exponential of this field converges as n to infty to a gaussian multiplicative chaos measure in the whole subcritical phase we discuss implications of this result for obtaining a lower bound on the maximum of the field we also show that the moments of the total mass converge to a selberg like integral and by taking a further limit as the size of the arc diverges we establish part of the conjectures in ostrovsky nonlinearity 29 2 426 464 2016 by an analogous construction we prove that the multiplicative chaos measure coming from the sine process has the same distribution which strongly suggests that this limiting object should be universal our approach to the l1 phase is based on a generalization of the construction in berestycki electron commun probab 22 27 12 2017 to random fields which are only asymptotically gaussian in particular our method could have applications to other random fields coming from either random matrix theory or a different context

artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows this note investigates the so called arti cial added mass e ect which is responsible for devastating instabilities within sequentially staggered fluid structure interaction fsi simulations where incompressible fluids are considered a discrete representation of the added mass operatorma is given and instability conditions are evaluated for different temporal discretisation schemes it is proven that for every sequentially staggered scheme and given spatial discretisation of a problem a mass ratio between fluid and structural mass density can be found at which the coupled system becomes unstable the analysis is quite general and does not depend upon the particular spatial discretisation schemes used however here special attention is put on stabilised finite elements employed on the fluid partition numerical investigations further highlight the results

testing in high dimensional spiked models we consider ve dierent classes of multivariate statistical problems iden ti ed by james 1964 each of these problems is related to the eigenvalues of e 1 h where h and e are proportional to high dimensional wishart ma trices under the null hypothesis both wisharts are central with identity covariance under the alternative the non centrality or the covariance pa rameter of h has a single eigenvalue a spike that stands alone when the spike is larger than a case speci c phase transition threshold one of the eigenvalues of e 1 h separates from the bulk this makes the alternative easily detectable so that reasonable statistical tests have asymptotic power one in contrast when the spike is sub critical that is lies below the thresh old none of the eigenvalues separates from the bulk which makes the testing problem more interesting from the statistical perspective in such cases we show that the log likelihood ratio processes parameterized by the value of the sub critical spike converge to gaussian processes with logarithmic corre lation we use this result to derive the asymptotic power envelopes for tests for the presence of a spike in the data representing each of the ve cases in james classi cation

facsi a block parallel preconditioner for fluid structure interaction in hemodynamics modeling fluid structure interaction fsi in the vascular system is mandatory to reliably compute mechanical indicators in vessels undergoing large deformations in order to cope with the computational complexity of the coupled 3d fsi problem after discretizations in space and time a parallel solution is often mandatory in this paper we propose a new block parallel preconditioner for the coupled linearized fsi system obtained after space and time discretization we name it facsi to indicate that it exploits the factorized form of the linearized fsi matrix the use of static condensation to formally eliminate the interface degrees of freedom of the fluid equations and the use of a simple preconditioner for saddle point problems facsi is built upon a block gauss seidel factorization of the fsi jacobian matrix and it uses ad hoc preconditioners for each physical component of the coupled problem namely the fluid the structure and the geometry in the fluid subproblem after operating static condensation of the interface fluid variables we use a simple preconditioner on the reduced fluid matrix moreover to efficiently deal with a large number of processes facsi exploits efficient single field preconditioners e g based on domain decomposition or the multigrid method we measure the parallel performances of facsi on a benchmark cylindrical geometry and on a problem of physiological interest namely the blood flow through a patient specific femoropopliteal bypass we analyze the dependence of the number of linear solver iterations on the cores count scalability of the preconditioner and on the mesh size optimality c 2016 elsevier inc all rights reserved

a variational approach for coupling kinematically incompatible structural models abstract in this work an extended variational framework aimed at properly addressing the coupling of kinematically incompatible structural models is presented the main goal is to variationally state the theoretical bases to deal with the coupling of structural models with different dimensionality in this approach the coupling conditions are naturally derived from the governing variational principle formulated at the continuous level furthermore by means of a real parameter we manage to build different continuous mechanical models that have different mechanical and mathematical features in particular the coupling of 3d solid models and 2d shell models under naghdi hypothesis is treated by introducing the corresponding kinematical assumptions into the proposed extended variational principle also the coupling between 3d solid and 1d beam models under bernoulli hypothesis is presented moreover for the continuous 3d 2d coupled problem a numerical approximation is addressed via the finite element method and some numerical results are given comparing the responses of the system when the discrete model varies by changing the value of the parameter finally a discussion comprising the main conclusions of the work is given

universality for eigenvalue correlations at the origin of the spectrum we establish universality of local eigenvalue correlations in unitary random matrix ensembles frac 1 z n det m 2 alpha e n rm tr v m dm near the origin of the spectrum if v is even and if the recurrence coefficients of the orthogonal polynomials associated with x 2 e nv x have a regular limiting behavior then it is known from work of akemann et al and kanzieper and freilikher that the local eigenvalue correlations have universal behavior described in terms of bessel functions we extend this to a much wider class of confining potentials v our approach is based on the steepest descent method of deift and zhou for the asymptotic analysis of riemann hilbert problems this method was used by deift et al to establish universality in the bulk of the spectrum a main part of the present work is devoted to the analysis of a local riemann hilbert problem near the origin

a domain decomposition method for advection diffusion processes with application to blood solutes in the present paper we consider a heterogeneous model for the dynamics of a blood solute both in the vascular lumen and inside the arterial wall in the lumen we consider an advection diffusion equation where the convective field is provided by the velocity of blood which is in turn obtained by solving the navier stokes equations inside the arterial wall we consider a pure diffusive dynamics since the endothelial layer at the interface between the lumen and the wall acts as a permeable membrane whose permeability depends on the shear rate exerted by the blood the solute concentration is discontinuous across this membrane a possible approach for the numerical study of this kind of problem is inspired by domain decomposition techniques in particular we introduce a splitting in the computation and alternate the solution of the advection diffusion equation in the lumen with that of the diffusion equation in the wall we set up an efficient iterative method based on a suitable reformulation of the problem in terms of a steklov poincare interface equation this formulation is a nonstandard one because of the concentration discontinuity at the lumen wall interface and plays a key role in the proof of convergence of our method in particular we prove that the convergence rate performed by the proposed method is independent of the finite element space discretization and provides a criterion for the selection of an acceleration parameter several numerical results referred to as biomedical applications support our theoretical conclusions and illustrate the efficiency of this algorithm

truly monolithic algebraic multigrid for fluid structure interaction the coupling of flexible structures to incompressible fluids draws a lot attention during the last decade many different solution schemes have been proposed in this contribution we concentrate on strong coupling fluid structure interaction by means of monolithic solution schemes therein a newton krylov method is applied to the monolithic set of nonlinear equations such schemes require good preconditioning to be efficient we propose two preconditioners that apply algebraic multigrid techniques to the entire fluid structure interaction system of equations the first is based on a standard block gauss seidel approach where approximate inverses of the individual field blocks are based on a algebraic multigrid hierarchy tailored for the type of the underlying physical problem the second is based on a monolithic coarsening scheme for the coupled system that makes use of prolongation and restriction projections constructed for the individual fields the resulting nonsymmetric monolithic algebraic multigrid method therefore involves coupling of the fields on coarse approximations to the problem yielding significantly enhanced performance

a projection semi implicit scheme for the coupling of an elastic structure with an incompressible fluid we address the numerical simulation of fluid structure systems involving an incompressible viscous fluid this issue is particularly difficult to face when the fluid added mass acting on the structure is strong as it happens in hemodynamics for example indeed several works have shown that in such situations implicit coupling seems to be necessary in order to avoid numerical instabilities although significant improvements have been achieved during the last years solving implicit coupling often exhibits a prohibitive computational cost in this work we introduce a semi implicit coupling scheme which remains stable for a reasonable range of the discretization parameters the first idea consists in treating implicitly the added mass effect whereas the other contributions geometrical non linearities viscous and convective effects are treated explicitly the second idea relies on the fact that this kind of explicit implicit splitting can be naturally performed using a chorin temam projection scheme in the fluid we prove conditional stability of the scheme for a fully discrete formulation several numerical experiments point out the efficiency of the present scheme compared to several implicit approaches

coercive domain decomposition algorithms for advection diffusion equations and systems abstract two families of non overlapping coercive domain decomposition methods are proposed for the numerical approximation of advection dominated advection diffusion equations and systems convergence is proven for both the continuous and the discrete problem the rate of convergence of the first method is shown to be independent of the total number of degrees of freedom several numerical results are presented showing the efficiency and robustness of the proposed interative algorithms

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

an adaptive fixed mesh ale method for free surface flows in this work we present a fixed mesh ale method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain this mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required some of the main ingredients of the formulation are the use of an arbitrary lagrangian eulerian formulation for computing temporal derivatives the use of stabilization terms for stabilizing convection stabilizing the lack of compatibility between velocity and pressure interpolation spaces and stabilizing the ill conditioning introduced by the cuts on the background finite element mesh and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved the method is tested in several numerical examples the expected convergence rates both in space and time are observed smooth solution fields for both velocity and pressure are obtained as a result of the contribution of the stabilization terms finally a good agreement between the numerical results and the reference experimental data is obtained

random matrix theory and ζ 1 2 it we study the characteristic polynomials z u of matrices u in the circular unitary ensemble cue of random matrix theory exact expressions for any matrix size n are derived for the moments of z and z z and from these we obtain the asymptotics of the value distributions and cumulants of the real and imaginary parts of log z as n in the limit we show that these two distributions are independent and gaussian costin and lebowitz 15 previously found the gaussian limit distribution for im log z using a different approach and our result for the cumulants proves a conjecture made by them in this case we also calculate the leading order n asymptotics of the moments of z and z z these cue results are then compared with what is known about the riemann zeta function s on its critical line re s 1 2 assuming the riemann hypothesis equating the mean density of the non trivial zeros of the zeta function at a height t up the critical line with the mean density of the matrix eigenvalues gives a connection between n and t invoking this connection our cue results coincide with a theorem of selberg for the value distribution of log 1 2 it in the limit t they are also in close agreement with numerical data computed by odlyzko 29 for large but finite t this leads us to a conjecture for the moments of 1 2 it finally we generalize our random matrix results to the circular orthogonal coe and circular symplectic cse ensembles

rigidity and a mesoscopic central limit theorem for dyson brownian motion for general beta β and potentials we study dyson brownian motion with general potential v and for general beta ge 1 for short times t o 1 and under suitable conditions on v we obtain a local law and corresponding rigidity estimates on the particle locations that is with overwhelming probability the particles are close to their classical locations with an almost optimal error estimate under the condition that the density of states of the initial data is bounded below and above down to the scale eta ll t ll 1 we prove a mesoscopic central limit theorem for linear statistics at all scales eta with n 1 ll eta ll t

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

an analysis of a new stable partitioned algorithm for fsi problems part i incompressible flow and elastic solids stable partitioned algorithms for fluid structure interaction fsi problems are developed and analyzed in this two part paper part i describes an algorithm for incompressible flow coupled with compressible elastic solids while part ii discusses an algorithm for incompressible flow coupled with structural shells importantly these new added mass partitioned amp schemes are stable and retain full accuracy with no sub iterations per time step even in the presence of strong added mass effects e g for light solids the numerical approach described here for bulk compressible solids extends the scheme of banks et al 1 2 for inviscid compressible flow and uses robin mixed boundary conditions with the fluid and solid solvers at the interface the basic amp robin conditions involving a linear combination of velocity and stress are determined from the outgoing solid characteristic relation normal to the fluid solid interface combined with the matching conditions on the velocity and traction two alternative forms of the amp conditions are then derived depending on whether the fluid equations are advanced with a fractional step method or not the stability and accuracy of the amp algorithm is evaluated for linearized fsi model problems the full nonlinear case being left for future consideration a normal mode analysis is performed to show that the new amp algorithm is stable for any ratio of the solid and fluid densities including the case of very light solids when added mass effects are large in contrast it is shown that a traditional partitioned algorithm involving a dirichlet neumann coupling for the same fsi problem is formally unconditionally unstable for any ratio of densities exact traveling wave solutions are derived for the fsi model problems and these solutions are used to verify the stability and accuracy of the corresponding numerical results obtained from the amp algorithm for the cases of light medium and heavy solids