development of high order taylor galerkin schemes for les in this paper we describe the implementation and development of a new taylor galerkin finite element scheme within an unstructured hybrid parallel solver the scheme has been specifically conceived for unsteady les it is third order in space and time and has a low dissipative error minimal additional cpu costs are achieved by using a new approximation of the finite element integrals and a simple iterative method for the approximate inversion of the modified mass matrix basic convective tests are carried out in 2 and 3 dimensions for arbitrary elements numerical estimates of the order of convergence are presented on regular and perturbed grids finally test cases that are relevant to les are carried out and these clearly demonstrate the important improvements that our new scheme offers relative to a selection of existing methods

the sensitivity of muscle force predictions to changes in physiologic cross sectional area abstract the mechanical effects of a muscle are related in part to the size of the muscle and to its location relative to the joint it crosses for more than a century researchers have expressed muscle size by its physiological cross sectional area pcsa researchers mathematically calculating muscle and joint forces typically use some expression of a muscle s pcsa to constrain the solution to one which is reasonable i e a solution in which small muscles may not have large forces and large muscles have large forces when expected or when there is significant electromyographic activity it is obvious that muscle mass and therefore any expression of pcsa varies significantly from person to person even in individuals of similar weight and height since it is not practical to predict the pcsa of each muscle in a living subject s limb or trunk it is important to generally understand the sensitivity of muscle force solutions to possible variations in pcsa we used nonlinear optimization techniques to predict 47 muscle forces and hip contact forces in a living subject the pcsa volume muscle fiber length of each of 47 lower limb muscle elements from two cadaver specimens and the 47 pcsa s reported by pierrynowski were input into an optimization algorithm to create three solution sets the three solutions were qualitatively similar but at times a predicted muscle force could vary as much as two to eight times in contrast the joint force solutions were within 11 of each other and therefore much less variable when using optimization techniques to predict muscle forces it must be recognized that the solution is sensitive to many assumptions and variables such as pcsa the muscle force solutions are therefore best used to determine relative values i e trends in parametric studies on the other hand the joint force solutions are less sensitive to such variations and the absolute values are more reliable

a high order time accurate loosely coupled solution algorithm for unsteady conjugate heat transfer problems abstract thermal interaction of fluids and solids or conjugate heat transfer cht is encountered in many engineering applications noting that time accurate computations of transient cht problems can be computationally expensive we consider the use of high order implicit time integration schemes which have the potential to be computationally more efficient relative to the commonly used second order implicit schemes for thermally weak couplings we present a loosely coupled solution algorithm where high order implicit explicit imex runge kutta schemes are employed for time integration the imex schemes consist of the explicit first stage singly diagonally implicit runge kutta esdirk schemes for advancing the solution in time within each separate fluid and solid subdomain and the explicit runge kutta erk schemes for explicit integration of part of the coupling terms by considering a numerical example an unsteady conjugate natural convection in an enclosure temporal order preservation of the coupling algorithm without subiterating is demonstrated in addition the stability of the loosely coupled algorithm is investigated numerically for the cht test case when the ratio of the thermal effusivities of the fluid and solid subdomains is much smaller than unity using large fourier numbers of the subdomains is possible indicating that time step size is restricted by accuracy rather than stability furthermore the computational work temporal precision character of several time integration schemes in solving the cht test case is compared over a range of accuracy requirements for time accurate solutions the fourth and fifth order imex schemes are 1 5 times more efficient than crank nicolson and 2 7 times more efficient than bdf2 the computational gain is higher for smaller tolerances

sensitivity of dynamic simulations of gait and dynamometer experiments to hill muscle model parameters of knee flexors and extensors we assessed and compared sensitivities of dynamic simulations to musculotendon mt parameters for gait and dynamometer experiments our aim with this comparison was to investigate whether dynamometer experiments could provide information about mt parameters that are important to reliably study mt function during gait this would mean that dynamometer experiments could be used to estimate these parameters muscle contribution to the joint torque mt torque rather than relative mt force primarily affects the resulting gait pattern and torque measured by the dynamometer in contrast to recent studies therefore we assessed the sensitivity of the mt torque rather than the sensitivity of the relative mt force based on sensitivity of the mt torque to a parameter perturbation mt parameters of the knee flexors and extensors were classified in three categories low medium and high for gait classification was based on the average sensitivity during a gait cycle for isometric and isokinetic dynamometer experiments classification was based on the highest sensitivity found in the experiments the calculated muscle contributions to the knee torque during gait and dynamometer experiments had a high sensitivity to only a limited number of mt parameters of the knee flexors and extensors suggesting that not all mt parameters need to be estimated in general the highest sensitivity was found for tendon slack length however for some muscles the sensitivity to the optimal fibre length or the maximal isometric muscle force was also high or medium the classification of the individual mt parameters for gait and dynamometer experiments was largely similar we therefore conclude that dynamometer experiments provide information about mt parameters important to reliably study mt function during gait so that subject specific estimates of mt parameters could be made based on dynamometer experiments

a third order boundary value problem with jumping nonlinearities abstract a third order boundary value problem with jumping nonlinearities is studied some results obtained for second order boundary value problems with jumping nonlinearities are shown to hold also for the third order case

sensitivity of a hill based muscle model to perturbations in model parameters abstract musculoskeletal simulations of human movement commonly use hill muscle models to predict muscle forces but their sensitivity to model parameter values is not well understood the purpose of this study was to evaluate muscle model sensitivity to perturbations in 14 hill muscle model parameters in forward dynamic simulations of running and walking by varying each by 50 three evaluations of the muscle model were performed based on 1 calculating the sensitivity of the muscle model only 2 determining the continuous partial derivatives of the muscle equations with respect to each parameter and 3 evaluating the effects on the running and walking simulations model evaluations were found to be very sensitive percent change in outputs greater than parameter perturbation to parameters defining the series elastic component tendon force length curve of the contractile element and maximum isometric force for some parameters the range of literature values was larger than the model sensitivity model evaluations were insensitive to parameters defining the parallel elastic element force velocity curve of the contractile element and muscle activation time constants the derivative method provided similar results but also provided a generic continuous equation that can easily be applied to other motions the sensitivities of the running and walking simulations were reduced compared to the sensitivity of the muscle model alone results demonstrate the importance of evaluating sensitivity of a musculoskeletal simulation in a controlled manner and provide an indication of which parameters must be selected most carefully based on the sensitivity of a given movement

an abstract theorem in nonlinear analysis and two applications abstract we prove abstract multiplicity theorems for a class of nonlinear equations on the hilbert space l 2 then we use these theorems to deduce new results for two different types of nonlinear boundary value problems

optimal solutions of numerical interface conditions in fluid structure thermal analysis abstract this paper presents major and new results in the numerical treatment of conjugate heat transfer problems the stability analysis of a 1d implicit model problem for heat transfer between a fluid and a solid is performed in the traditional finite volume fluid finite element solid configuration the interface stability study is carried out according to the godunov ryabenkii theory normal mode analysis two interface boundary conditions are studied first the commonly used dirichlet robin algorithm is described in detail and to the best of our knowledge the exact expression of an optimal coupling coefficient is formulated for the first time it is shown that this optimal coefficient is the best choice in terms of stability and convergence rate the effect and impact on stability of various solid data are also discussed in the last section of this paper the same stability analysis is carried out for a general robin robin interface condition and an optimal relationship between the two coupling parameters is also provided no stability restrictions are introduced by these optimal interface treatments and some noteworthy expressions are provided

a single stable scheme for steady conjugate heat transfer problems abstract the goal of this paper is to propose a single interface treatment based on the dirichlet robin interface condition to deal with all steady cht scenarios these scenarios depend on the so called numerical biot number that controls the stability process and the optimal coefficient that ensures in theory unconditional stability it is shown that this coefficient is closely related to fundamental thermal quantities for very large thermal fluid solid interactions the dirichlet robin condition may result in profound stability issues a thorough examination of the stability behavior has highlighted a narrow and slow varying stable zone located around the optimal coefficient this allows us to determine coupling coefficients valid in any case and the reasonable value of these coefficients avoids significantly impairing the accuracy of cht solutions a flat plate partially protected by a thermal barrier coating is presented as a test case

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

a composite grid solver for conjugate heat transfer in fluid structure systems we describe a numerical method for modeling temperature dependent fluid flow coupled to heat transfer in solids this approach to conjugate heat transfer can be used to compute transient and steady state solutions to a wide range of fluid solid systems in complex two and three dimensional geometry fluids are modeled with the temperature dependent incompressible navier stokes equations using the boussinesq approximation solids with heat transfer are modeled with the heat equation appropriate interface equations are applied to couple the solutions across different domains the computational region is divided into a number of sub domains corresponding to fluid domains and solid domains there may be multiple fluid domains and multiple solid domains each fluid or solid sub domain is discretized with an overlapping grid the entire region is associated with a composite grid which is the union of the overlapping grids for the sub domains a different physics solver fluid solver or solid solver is associated with each sub domain a higher level multi domain solver manages the entire solution process we propose and analyze some centered discrete approximations to the interface equations that have some desirable stability properties the coupled interface equations may be solved directly when using explicit time stepping methods in the sub domains resulting in a strongly coupled approach the stability of the interface treatment in this case is independent of the relative sizes of the material properties in the two domains with the time step only depending on the usual von neumann conditions for each sub domain for implicit time stepping methods we solve the interface equations in a weakly coupled fashion to avoid forming a coupled implicit system across all sub domains the convergence of this approach does depend on the relative sizes of the thermal conductivities and diffusivities we analyze different iteration strategies for solving these implicit equations including the use of mixed robin approximations at the interface numerical results are presented to illustrate the method the accuracy of the technique is verified using the method of analytic solutions and by computing the solution to some heat exchanger problems where the exact solution is known the technique is also applied to the modeling of an inertial confinement fusion hohlraum target and the flow of coolant past an hexagonal array of heated fuel rods the multi domain solver runs in parallel on distributed memory computers and some parallel results are provided

multiple solutions for a semilinear boundary value problem a computational multiplicity proof abstract we prove the first genuine partial differential equation result on a conjecture concerning the number of solutions of second order elliptic boundary value problems with a nonlinearity which grows superlinearly at the proof makes massive use of computer assistance after approximate solutions have been computed by a numerical mountain pass algorithm combined with a newton iteration to improve accuracy a fixed point argument is used to show the existence of exact solutions close to the approximations

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 three dimensional computational method for blood flow in the heart 1 immersed elastic fibers in a viscous incompressible fluid abstract this paper describes the numerical solution of the 3 dimensional equations of motion of a viscous incompressible fluid that contains an immersed system of elastic fibers implementation details such as vectorization and the efficient use of external memory are discussed the method is applied to the damped vibrations of a fiber wound toroidal tube and empirical evidence of convergence is presented

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

kalman smoothing improves the estimation of joint kinematics and kinetics in marker based human gait analysis we developed a kalman smoothing algorithm to improve estimates of joint kinematics from measured marker trajectories during motion analysis kalman smoothing estimates are based on complete marker trajectories this is an improvement over other techniques such as the global optimisation method gom kalman filtering and local marker estimation lme where the estimate at each time instant is only based on part of the marker trajectories we applied gom kalman filtering lme and kalman smoothing to marker trajectories from both simulated and experimental gait motion to estimate the joint kinematics of a ten segment biomechanical model with 21 degrees of freedom three simulated marker trajectories were studied without errors with instrumental errors and with soft tissue artefacts sta two modelling errors were studied increased thigh length and hip centre dislocation we calculated estimation errors from the known joint kinematics in the simulation study compared with other techniques kalman smoothing reduced the estimation errors for the joint positions by more than 50 for the simulated marker trajectories without errors and with instrumental errors compared with gom kalman smoothing reduced the estimation errors for the joint moments by more than 35 compared with kalman filtering and lme kalman smoothing reduced the estimation errors for the joint accelerations by at least 50 our simulation results show that the use of kalman smoothing substantially improves the estimates of joint kinematics and kinetics compared with previously proposed techniques gom kalman filtering and lme for both simulated with and without modelling errors and experimentally measured gait motion

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

partitioned procedures for the transient solution of coupled aroelastic problems part i model problem theory and two dimensional application abstract in order to predict the dynamic response of a flexible structure in a fluid flow the equations of motion of the structure and the fluid must be solved simultaneously in this paper we present several partitioned procedures for time integrating this focus coupled problem and discuss their merits in terms of accuracy stability heterogeneous computing i o transfers subcycling and parallel processing all theoretical results are derived for a one dimensional piston model problem with a compressible flow because the complete three dimensional aeroelastic problem is difficult to analyze mathematically however the insight gained from the analysis of the coupled piston problem and the conclusions drawn from its numerical investigation are confirmed with the numerical simulation of the two dimensional transient aeroelastic response of a flexible panel in a transonic non linear euler flow regime

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 physiologically based criterion of muscle force prediction in locomotion abstract the inversely nonlinear relationship of muscle contraction force and the possible contraction duration i e endurance is utilized in a method to mathematically predict individual muscle forces the method uses a nonlinear optimization scheme to solve the redundant distribution problem at the joints of interest the method is demonstrated at the elbow during isometric contraction and in the lower extremity during locomotion during gait the observed muscle activity pattern in the lower extremity as determined by emg shows substantial agreement with that activity pattern predicted when endurance is used as the optimization criterion the importance of selecting muscle prediction criteria based on sound physiological bases rather than on an arbitrary or mathematically convenient basis is emphasized

remarks and generalizations related to a recent multiplicity result of a lazer and p mckenna we will show here that this result has a natural generalization to the case that u 5 ai to state the result we consider the model problem lu au autel 2 where 0 0 and set t 0 we have a nonlinear eigenvalue problem lu yu au 4 the following proposition is known cf fueik 3 dancer 2 and also lo where the result appears in the formulation given below

existence and multiplicity of solutions for elliptic equations with jumping nonlinearities abstract in this paper we are concerned with a semilinear elliptic dirichlet problem with jumping nonlinearity and using a completely variational method we show that the number of solutions may be arbitrarily large provided the number of jumped eigenvalues is large enough in order to prove this fact we show that for every positive integer k when a suitable parameter is large enough there exists a solution which presents k peaks under the assumptions we consider in this paper new unexpected phenomena are observed in the study of this problem and new methods are required to construct the k peaks solutions and describe their asymptotic behavior weak limits of the rescaled solutions localization of the concentration points of the peaks asymptotic profile of the rescaled peaks etc

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 new approach to numerical solution of defective boundary value problems in incompressible fluid dynamics we consider the incompressible navier stokes equations where on a part of the boundary flow rate and mean pressure boundary conditions are prescribed there are basically two strategies for solving these defective boundary problems the variational approach see j heywood r rannacher and s turek internat j numer methods fluids 22 1996 pp 325 352 and the augmented formulation see l formaggia j f gerbeau f nobile and a quarteroni siam j numer anal 40 2002 pp 376 401 and a veneziani and c vergara internat j numer methods fluids 47 2005 pp 803 816 however both of these approaches present some drawbacks for the flow rate problem the former resorts to nonstandard functional spaces which are quite difficult to discretize on the other hand for the mean pressure problem it yields exact solutions only in very special cases the latter is applicable only to the flow rate problem since for the mean pressure problem it provides unfeasible boundary conditions in this paper we propose a new strategy based on a reformulation of the problems at hand in terms of the minimization of an appropriate functional this approach allows us to treat the two kinds of problems flow rate and mean pressure successfully within the same framework which can be useful in view of a mixed problem where the two conditions are simultaneously prescribed on different artificial boundaries moreover it is more versatile being prone to be extended to other kinds of defective conditions we analyze the problems obtained with this approach and propose some algorithms for their numerical solution several numerical results are presented supporting the effectiveness of our approach

sensitivity of subject specific models to errors in musculo skeletal geometry subject specific musculo skeletal models of the lower extremity are an important tool for investigating various biomechanical problems for instance the results of surgery such as joint replacements and tendon transfers the aim of this study was to assess the potential effects of errors in musculo skeletal geometry on subject specific model results we performed an extensive sensitivity analysis to quantify the effect of the perturbation of origin insertion and via points of each of the 56 musculo tendon parts contained in the model we used two metrics namely a local sensitivity index lsi and an overall sensitivity index osi to distinguish the effect of the perturbation on the predicted force produced by only the perturbed musculo tendon parts and by all the remaining musculo tendon parts respectively during a simulated gait cycle results indicated that for each musculo tendon part only two points show a significant sensitivity its origin or pseudo origin point and its insertion or pseudo insertion point the most sensitive points belong to those musculo tendon parts that act as prime movers in the walking movement insertion point of the achilles tendon lsi 15 56 osi 7 17 origin points of the rectus femoris lsi 13 89 osi 2 44 and as hip stabilizers insertion points of the gluteus medius anterior lsi 17 92 osi 2 79 insertion point of the gluteus minimus lsi 21 71 osi 2 41 the proposed priority list provides quantitative information to improve the predictive accuracy of subject specific musculo skeletal models

on the number of solutions of two classes of sturm liouville boundary value problems abstract we employ global bifurcation theory of p h rabinowitz together with sturm comparison theorem to establish multiplicity results for some classes of sturm liouville boundary value problems

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

a stable and high order accurate conjugate heat transfer problem this paper analyzes well posedness and stability of a conjugate heat transfer problem in one space dimension we study a model problem for heat transfer between a fluid and a solid the energy method is used to derive boundary and interface conditions that make the continuous problem well posed and the semi discrete problem stable the numerical scheme is implemented using 2nd 3rd and 4th order finite difference operators on summation by parts sbp form the boundary and interface conditions are implemented weakly we investigate the spectrum of the spatial discretization to determine which type of coupling that gives attractive convergence properties the rate of convergence is verified using the method of manufactured solutions

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

a fictitious domain method for external incompressible viscous flow modeled by navier stokes equations abstract in this article we discuss a fictitious domain method for the numerical solutions of three dimensional elliptic problems with dirichlet boundary conditions and also of the navier stokes equations modeling incompressible viscous flow the methodology for the navier stokes equations described here takes a systematic advantage of time discretization by operator splitting in order to treat separately advection imbedding and incompressibility due to the decoupling fast elliptic solvers can be used to treat the incompressibility condition even if the original problem is taking place on a nonregular geometry the resulting methodology is applied to two dimensional unsteady external incompressible viscous flow problems and three dimensional stokes problems

an approximate method for solving incompressible navier stokes problems with flow rate conditions we consider the incompressible navier stokes problem with flow rate boundary conditions this problem has been investigated in j heywood r rannacher s turek artificial boundaries and flux and pressure conditions for the incompressible navier stokes equations int j numer methods fluids 22 1996 325 352 l formaggia j f gerbeau f nobile a quarteroni numerical treatment of defective boundary conditions for the navier stokes equation siam j numer anal 40 1 2002 376 401 a veneziani c vergara flow rate defective boundary conditions in haemodynamics simulations int j numer methods fluids 47 2005 803 816 in the latter two papers a feasible numerical formulation of this problem based on a lagrange multiplier approach has been investigated this approach has the drawback of high computational costs in this paper we propose an approximate formulation of this problem yielding a strong reduction of the computational costs the error analysis shows that the error introduced by this approximate formulation is confined in a small region of the boundary this is confirmed by the numerical simulations

the exact number of solutions for a class of ordinary differential equations through morse index computation we consider a class of second order ordinary differential equations with jumping nonlinearities that cross the first k eigenvalues under zero boundary conditions and by means of a morse index computation show the existence of exactly 2 k solutions

a variational approach for estimating the compliance of the cardiovascular tissue an inverse fluid structure interaction problem estimation of the stiffness of a biological soft tissue is useful for the detection of pathologies such as tumors or atherosclerotic plaques elastography is a method based on the comparison between two images before and after a forced deformation of the tissue of interest an inverse elasticity problem is then solved for young s modulus estimation in the case of arteries no forced deformation is required since vessels naturally move under the action of blood young s modulus can therefore be estimated by solving a coupled inverse fluid structure interaction problem in this paper we focus on the mathematical properties of this problem and its numerical solution we give some well posedness analysis and some preliminary results based on a synthetic data set i e test cases where the exact young s modulus is known and the displacement dataset is numerically generated by solving a forward fluid structure interaction problem we address the problem of the presence of the noise in the measured displacement and of the proper sampling frequency for obtaining reliable estimates

on the superlinear lazer mckenna conjecture abstract we prove the lazer mckenna conjecture for a superlinear elliptic problem of ambrosetti prodi type by constructing solutions with sharp peaks

on the uniqueness of solution for a class of semilinear elliptic problems we shall discuss here the uniqueness of solution of the dirichlet problem updelta u f u rho h x quad text in upomega text u 0 quad text on partial upomega for large values of the real parameter rho

comparative study of coupling coefficients in dirichlet robin procedure for fluid structure aerothermal simulations this paper tests the performance of coupling coefficients of a dirichlet robin transmission procedure in the context of steady conjugate heat transfer cht particular emphasis is put on the optimal coefficients highlighted recently in a theoretical study based on a normal mode stability analysis this work can be seen as the logical continuation of that study in order to assess the relevance of the coefficients provided by the model problem in a realistic aerothermal computation first the numerical and physical cht modeling methodologies are presented then the optimal procedure applied to a dirichlet robin algorithm one coefficient method is briefly described in order to gauge the ability of this model to predict the stability and convergence properties of a realistic case it is compared on a heated cylinder in a flowfield test case a series of five coupling coefficients and three fourier numbers are considered these parameters are introduced into the model problem as data to compute the amplification factor and the stability limits the stability and convergence properties predicted by the model problem are then compared to those obtained in the cht computation this comparison shows an excellent overall agreement moreover for all the fourier numbers considered the numerical solution is stable and oscillation free when the optimal coefficient of the model problem is used this would suggest that the one dimensional normal mode analysis can provide relevant coefficients directly applicable to real cht problems