interpreting proper orthogonal modes of randomly excited vibration systems proper orthogonal modes poms of displacements are interpreted for linear vibration systems under random excitation excitations are considered for which the fourier transform is convergent meaning that the input must have zero mean and no sustained sinusoidal component in such a case the poms in undamped discrete linear symmetric systems can represent linear natural modes if the mass distribution is known poms in one dimensional distributed parameter self adjoint systems can approximately represent the linear normal modes if the mass distribution is known simulation examples are presented simulations show that these ideas are also applicable under light modal damping

convergence and local equilibrium for the one dimensional nonzero mean exclusion process we consider finite range nonzero mean one dimensional exclusion processes on we show that if the initial configuration has density then the process converges in distribution to the product bernoulli measure with mean density from this we deduce the strong form of local equilibrium in the hydrodynamic limit for non product initial measures

quenched convergence and strong local equilibrium for asymmetric zero range process with site disorder we study asymmetric zero range processes on z with nearest neighbour jumps and site disorder the jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles we prove quenched strong local equilibrium at subcritical and critical hydrodynamic densities and dynamic local loss of mass at supercritical hydrodynamic densities our results do not assume starting from local gibbs states as byproducts of these results we prove convergence of the process from given initial configurations with an asymptotic density of particles to the left of the origin in particular we relax the weak convexity assumption of 7 8 for the escape of mass property 1 msc 2010 subject classification 60k35 82c22

quadratic loss of order restricted estimators for treatment means with a control we consider an experiment which consists of k treatment groups and a control group let the sample means yo y1 yk be independent normal variates with expected values a ml uk and with variances u2 no o2 n1 02 nk let ub wl wk be positive weights and let uo t be the weighted least squares estimators subject to the constraints yl fi i 1 k we establish that for large k e 1 mo 2 e yo mo 2 when wi ni i 0 1 k under suitable conditions we show that e a ai 2 e yi mi 2 i 0 1 k

the behavior of the specific entropy in the hydrodynamic scaling limit the paper studies the behavior of the specific entropyfor onedimensional simple exclusion processes under the hydrodynamic scaling of time and space it is shown that if the initial configurations possess a macroscopic profile then for each positive macroscopic time the specific microscopic entropyconverges to the macroscopic entropy the latter is defined in terms of the solution of the corresponding hydrodynamic equation 1 introduction the paper concerns simple exclusion models on the periodic integer lattice the symmetric simple exclusion process is reversible and we studyit under diffusive parabolic scaling of time and space the corresponding hydrodynamic equation describing the behavior of the limiting macroscopic densityis the heat equation it has smooth solutions uniquely defined bythe initial data asy mmetric simple exclusion models are nonreversible and require euler hyperbolic scaling which leads to inviscid burgers type equations solutions of such equations are not unique and may develop shocks relevant solutions are known to be the entropic solutions of these equations we studythe behavior of the microscopic entropyrelative to uniform measures and to local gibbs measures in words a version of the main result can be stated as follows let the initial configurations be deterministic and possess a macroscopic profile then under the appropriate scaling of time and space for anypositive macroscopic time the specific microscopic entropyconverges to the macroscopic entropycalculated from the relevant solution of the hydrodynamic equation the main emphasis is placed on the asymmetric case when the solution of the hydrodynamic equation develops shocks and the macroscopic entropy is lost at each shock our results show that in the scaling limit the particle system closely follows the hydrodynamic equation and loses the same amount of the specific entropyat the same macroscopic time the keyidea of this paper is presented in lemma a 1 it is a rather general statement which could be adopted for applications to other models one of the important ingredients of the proof of lemma a 1 is the logarithmic sobolev inequality theorem a 1 let us stress that we do not need an estimate on the constant in the logarithmic sobolev inequality the main difficulty in apply ing

fast low rank modifications of the thin singular value decomposition this paper develops an identity for additive modivations of a singular value decomposition svd to reflect updates downdates shifts and edits of the data matrix this sets the stage for fast and ememory efficient sequential algorithms for tracking singular values and subspaces in conjunction with a fast solution for the pseudo inverse of a submatrix of an orthogonal matrix we develop a scheme for computing a thin svd of streaming data in a single pass with linear time complexity a rank r think svd of a p x q matrix can be computed in o pqr time for r less than or equal sqroot min p q linear algebra and its applications

arlequin framework for multi model multi time scale and heterogeneous time integrators for structural transient dynamics this paper presents a general framework for performing spatio temporal multi scale multi model coupling based on displacement continuity this approach guarantees a global energy balance of the system in the context of the arlequin method it introduces specific interpolation of the lagrange multipliers and parameters of time integration operators in the overlapping zone a dual schur implementation is then used to illustrate the efficiency and robustness of the method convergence analysis with numerical experiments is performed finally 1d 1d and 2d 1d coupling applications are presented in which each subdomain is integrated in time using different time steps and different schemes this approach gives the user more ways of controlling computational behaviour via newmark parameters time steps and sizing the overlapping zones

nonlinear model order reduction based on local reduced order bases summary a new approach for the dimensional reduction via projection of nonlinear computational models based on the concept of local reduced order bases is presented it is particularly suited for problems characterized by different physical regimes parameter variations or moving features such as discontinuities and fronts instead of approximating the solution of interest in a fixed lower dimensional subspace of global basis vectors the proposed model order reduction method approximates this solution in a lower dimensional subspace generated by most appropriate local basis vectors to this effect the solution space is partitioned into subregions and a local reduced order basis is constructed and assigned to each subregion offline during the incremental solution online of the reduced problem a local basis is chosen according to the subregion of the solution space where the current high dimensional solution lies this is achievable in real time because the computational complexity of the selection algorithm scales with the dimension of the lower dimensional solution space because it is also applicable to the process of hyper reduction the proposed method for nonlinear model order reduction is computationally efficient its potential for achieving large speedups while maintaining good accuracy is demonstrated for two nonlinear computational fluid and fluid structure electric interaction problems copyright 2012 john wiley sons ltd

the latin multiscale computational method and the proper generalized decomposition this paper deals with the synergy between the latin multiscale method and what is called the proper generalized decomposition pgd which is the key of its performances

model order reduction and domain decomposition strategies for the solution of the dynamic elastic plastic structural problem abstract a new strategy for the efficient solution of highly nonlinear structural problems is proposed based on the combined use of domain decomposition dd and snapshots version of the proper orthogonal decomposition pod techniques the formulation here presented is tailored for applications in elastic plastic structural dynamics in this context the pod is applied to domains that remain elastic and a double strategy to update the reduced basis is adopted first the singular value decomposition svd proposed allows to update the reduced basis as soon as a new snapshot is stored secondly an online adaptation technique of the reduced space is performed through a plastic check during the reduced analysis the applications show that the computation time necessary for solving elastic plastic problems can be reduced of approximately 50 while keeping accuracy comparable to that obtained for the full model with a classical monolithic method

hydrodynamical limit for space inhomogeneous one dimensional totally asymmetric zero range processes we consider totally asymmetric attractive zero range processes with bounded jump rates on z in order to obtain a lower bound for the large deviations from the hydrodynamical limit of the empirical measure we perturb the process in two ways we first choose a finite number of sites and slow down the jump rate at these sites we prove a hydrodynamical limit for this perturbed process and show the appearance of dirac measures on the sites where the rates are slowed down the second type of perturbation consists of choosing a finite number of particles and making them jump at a slower rate in these cases the hydrodynamical limit is described by nonentropy weak solutions of quasilinear first order hyperbolic equations these two results prove that the large deviations for asymmetric processes with bounded jump rates are of order at least e cn all these results can be translated to the context of totally asymmetric simple exclusion processes where a finite number of particles or a finite number of holes jump at a slower rate

a pgd based homogenization technique for the resolution of nonlinear multiscale problems abstract this paper deals with the offline resolution of nonlinear multiscale problems leading to a pgd reduced model from which one can derive microinformation which is suitable for design here we focus on an improvement to the proper generalized decomposition pgd technique which is used for the calculation of the homogenized operator and which plays a central role in our multiscale computational strategy this homogenized behavior is calculated offline using the latin multiscale strategy and pgd leads to a drastic reduction in cpu cost indeed the multiscale aspect of the latin method is based on splitting the unknowns between a macroscale and a microcomplement this macroscale is used to capture the homogenized behavior of the structure and then to accelerate the convergence of the iterative algorithm the novelty of this work lies in the reduction of the computation cost of building the homogenized operator in order to do that the problems defined within each subdomain are solved using a new pgd representation of the unknowns in which the separation of the unknowns is performed not only in time and in space but also in terms of the interface macrodisplacements the numerical example presented shows that the convergence rate of the approach is not affected by this new representation and that a significant reduction in computation cost can be achieved particularly in the case of nonlinear behavior the technique used herein is then particularly important to enhance the performances of the latin strategy but is not limited to this method the more general path which is followed in this paper is to solve the microproblems arising in the homogenization for all the configurations that can be encountered in the calculation an additional and novel benefit of this approach is that it includes the calculation of the homogenized tangent operator which gives over the whole time interval and for any cell the relation between the perturbation in terms of macroforces and the perturbation in terms of macrodisplacements in linear viscoelasticity this operator represents the homogenized behavior of the structure exactly

derivation of the hydrodynamical equation for the zero range interaction process small volume is so large compared with the distances between molecules that it contains an infinite number of them which are in equilibrium with given characteristics density temperature of course these parameters vary with x say p x t x if we look at the system after a time t the system will be still locally in equilibrium with other local characteristics p x t t x t varying slowly in time although each particle individually moves very rapidly we want to derive the equation of evolution of these macroscopical parameters however it is surprising that this derivation is almost never based on the analysis of the movement of the particles but rather on conservation laws the limiting procedure that we describe below has been used by various authors 2 8 in efforts to give rigorous treatment of the program alluded to above consider a system of infinitely many particles in rd or xd moving according

a unified set of single step algorithms part 1 general formulation and applications a general algorithm for a single step time marching scheme for use in dynamic or diffusion equations is presented this algorithm is easily programmed in its universal form for all orders of approximation and covers most of the currently used schemes as well as presenting many new possibilities in many cases it presents a computationally advantageous form over conventional procedures this is particularly so when compared with the newmark algorighm and its variants

interpolation method for adapting reduced order models and application to aeroelasticity reduced order models are usually thought of as computationally inexpensive mathematical representations that offer the potential for near real time analysis although most reduced order models can operate in near real time their construction can be computationally expensive as it requires accumulating a large number of system responses to input excitations furthermore reduced order models usually lack robustness with respect to parameter changes and therefore must often be rebuilt for each parameter variation together these two issues underline the need for a fast and robust method for adapting precomputed reduced order models to new sets of physical or modeling parameters to this effect this paper presents an interpolation method based on the grassmann manifold and its tangent space at a point that is applicable to structural aerodynamic aeroelastic and many other reduced order models based on projection schemes this method is illustrated here with the adaptation of computational fluid dynamics based aeroelastic reduced order models of complete fighter configurations to new values of the freestream mach number good correlations with results obtained from direct reduced order model reconstruction high fidelity nonlinear and linear simulations are reported thereby highlighting the potential of the proposed reduced order model adaptation method for near real time aeroelastic predictions using precomputed reduced order model databases

model order reduction for dynamic simulation of a flexible multibody system via absolute nodal coordinate formulation abstract the absolute nodal coordinate formulation ancf can be used to model a flexible multibody system subject to both overall motions and large deformations with an increasing number of finite elements of ancf to mesh flexible bodies however the computation cost will become extremely high to improve the computational efficiency of ancf for a large scaled flexible multibody system a systematic method is proposed in this study for the model order reduction based on the proper orthogonal decomposition and the galerkin projection at first an approach for the selection of reduced constraint equations is proposed to deal with the singularity of the coefficient matrix of the reduced order model rom then the computation of the reduced stiffness matrix and generalized force vector of the rom are parallelized via the openmp directives afterwards two parametric approaches are presented to make the rom be adaptive to the change of system parameters one is the interpolation approach of reduced order basis vectors on a manifold to obtain the parametric rom and the other is the fast to slow rom approach via the reduced order basis vectors extracted from the fast dynamic responses to simulate slow dynamic responses finally four numerical examples are given to validate the efficacy of the proposed method for the dynamic simulations of both rigid and flexible multibody systems

aerodynamic characteristics of pretensioned elastic membrane rectangular sailwings presented in the paper are the details of a method for obtaining aerodynamic characteristics of pretensioned elastic membrane rectangular sailwings this is a nonlinear problem governed by the membrane equation for the inflated sail and the lifting surface theory integral equation for aerodynamic loads on the sail assuming an admissible mode shape for the inflated elastic sail an iterative procedure based on a doublet lattice method is employed to determine the inflated configuration as well as various aerodynamic characteristics application of the method is made to a typical nylon cotton sailwing of ar 6 0 and results are presented graphically to show the effect of various parameters the results are found to tend to plane wing values when the pretensions are large in magnitude

multi time step explicit implicit method for non linear structural dynamics we present a method with domain decomposition to solve time dependent non linear problems this method enables arbitrary numeric schemes of the newmark family to be coupled with different time steps in each subdomain this coupling is achieved by prescribing continuity of velocities at the interface we are more specifically interested in the coupling of implicit explicit numeric schemes taking into account material and geometric non linearities the interfaces are modelled using a dual schur formulation where the lagrange multipliers represent the interfacial forces unlike the continuous formulation the discretized formulation of the dynamic problem is unable to verify simultaneously the continuity of displacements velocities and accelerations at the interfaces we show that within the framework of the newmark family of numeric schemes continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged to prove this stability we use an energy method i e a global method over the whole time interval in order to verify the algorithms properties then we propose to extend this to non linear situations in the following cases implicit linear explicit non linear explicit non linear explicit non linear and implicit non linear explicit non linear finally we present some examples showing the feasibility of the method copyright 2001 john wiley sons ltd

nonlinear model reduction via discrete empirical interpolation a dimension reduction method called discrete empirical interpolation is proposed and shown to dramatically reduce the computational complexity of the popular proper orthogonal decomposition pod method for constructing reduced order models for time dependent and or parametrized nonlinear partial differential equations pdes in the presence of a general nonlinearity the standard pod galerkin technique reduces dimension in the sense that far fewer variables are present but the complexity of evaluating the nonlinear term remains that of the original problem the original empirical interpolation method eim is a modification of pod that reduces the complexity of evaluating the nonlinear term of the reduced model to a cost proportional to the number of reduced variables obtained by pod we propose a discrete empirical interpolation method deim a variant that is suitable for reducing the dimension of systems of ordinary differential equations odes of a certain type as presented here it is applicable to odes arising from finite difference discretization of time dependent pdes and or parametrically dependent steady state problems however the approach extends to arbitrary systems of nonlinear odes with minor modification our contribution is a greatly simplified description of the eim in a finite dimensional setting that possesses an error bound on the quality of approximation an application of deim to a finite difference discretization of the one dimensional fitzhugh nagumo equations is shown to reduce the dimension from 1024 to order 5 variables with negligible error over a long time integration that fully captures nonlinear limit cycle behavior we also demonstrate applicability in higher spatial dimensions with similar state space dimension reduction and accuracy results

reduced basis approximation and a posteriori error estimation for stokes flows in parametrized geometries roles of the inf sup stability constants in this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady stokes flows in affinely parametrized geometries focusing on the role played by the brezzi s and babuska s stability constants the crucial ingredients of the methodology are a galerkin projection onto a low dimensional space of basis functions properly selected an affine parametric dependence enabling to perform competitive offline online splitting in the computational procedure and a rigorous a posteriori error estimation on field variables the combinatiofn of these three factors yields substantial computational savings which are at the basis of an efficient model order reduction ideally suited for real time simulation and many query contexts e g optimization control or parameter identification in particular in this work we focus on i the stability of the reduced basis approximation based on the brezzi s saddle point theory and the introduction of a supremizer operator on the pressure terms ii a rigorous a posteriori error estimation procedure for velocity and pressure fields based on the babuska s inf sup constant including residuals calculations iii the computation of a lower bound of the stability constant and iv different options for the reduced basis spaces construction we present some illustrative results for both interior and external steady stokes flows in parametrized geometries representing two parametrized classical poiseuille and couette flows a channel contraction and a simple flow control problem around a curved obstacle

existence of hydrodynamics for the totally asymmetric simple k exclusion process in a totally asymmetric simple k exclusion process particles take nearest neighbor steps to the right on the lattice z under the constraint that each site contain at most k particles we prove that such processes satisfy hydrodynamic limits under euler scaling and that the limit of the empirical particle profile is the entropy solution of a scalar conservation law with a concave flux function our technique requires no knowledge of the invariant measures of the process which is essential because the equilibria of asymmetric k exclusion are unknown but we cannot calculate the flux function precisely the proof proceeds via a coupling with a growth model on the two dimensional lattice in addition to the basic k exclusion with constant exponential jump rates we treat the site disordered case where each site has its own jump rate randomly chosen but frozen for all time the hydrodynamic limit under site disorder is new even for the simple exclusion process the case k 1 our proof makes no use of the markov property so at the end of the paper we indicate how to treat the case with arbitrary waiting times

hyper reduction of mechanical models involving internal variables we propose to improve the efficiency of the computation of the reduced state variables related to a given reduced basis this basis is supposed to be built by using the snapshot proper orthogonal decomposition pod model reduction method in the framework of non linear mechanical problems involving internal variables the local integration of the constitutive laws can dramatically limit the computational savings provided by the reduction of the order of the model this drawback is due to the fact that using a galerkin formulation the size of the reduced basis has no effect on the complexity of the constitutive equations in this paper we show how a reduced basis approximation and a petrov galerkin formulation enable to reduce the computational effort related to the internal variables the key concept is a reduced integration domain where the integration of the constitutive equations is performed the local computations being not made over the entire domain we extrapolate the computed internal variable over the full domain using pod vectors related to the internal variables this paper shows the improvement of the computational saving obtained by the hyper reduction of the elasto plastic model of a simple structure

physical interpretation of the proper orthogonal modes using the singular value decomposition abstract proper orthogonal decomposition is a statistical pattern analysis technique for finding the dominant structures called the proper orthogonal modes in an ensemble of spatially distributed data while the proper orthogonal modes are obtained through a statistical formulation they can be physically interpreted in the field of structural dynamics the purpose of this paper is thus to provide some insights into the physical interpretation of the proper orthogonal modes using the singular value decomposition