generalized parametric solutions in stokes flow abstract design optimization and uncertainty quantification among other applications of industrial interest require fast or multiple queries of some parametric model the proper generalized decomposition pgd provides a separable solution a computational vademecum explicitly dependent on the parameters efficiently computed with a greedy algorithm combined with an alternated directions scheme and compactly stored this strategy has been successfully employed in many problems in computational mechanics the application to problems with saddle point structure raises some difficulties requiring further attention this article proposes a pgd formulation of the stokes problem various possibilities of the separated forms of the pgd solutions are discussed and analyzed selecting the more viable option the efficacy of the proposed methodology is demonstrated in numerical examples for both stokes and brinkman models

dynamic correlations in domain growth a 1 n expansion the authors consider the dynamics of the n component ginzburg landau model with nonconserved order parameter model a following a quench from a high temperature equilibrium state to zero temperature the two time correlation function of the order parameter field is found in the 1 n expansion to have the asymptotic scaling form ck t t t d2 t t lambda 2 f k2t k2t for t t with f 0 0 constant the form of the new exponent lambda which is a non trivial function of n and d was given explicitly to o 1 n in a recent letter the purpose of this study is to present a more detailed account of the calculation leading to the o 1 n form for lambda they also examine the role of thermal fluctuations in the ordered phase and the effect of long range initial correlations on the ordering process

on the stability of the reduced basis method for stokes equations in parametrized domains we present an application of reduced basis method for stokes equations in domains with affine parametric dependence the essential components of the method are i the rapid convergence of global reduced basis approximations galerkin projection onto a space wn spanned by solutions of the governing partial differential equation at n selected points in parameter space ii the off line on line computational procedures decoupling the generation and projection stages of the approximation process the operation count for the on line stage in which given a new parameter value we calculate an output of interest depends only on n typically very small and the parametric complexity of the problem the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation design optimization and real time control particular attention is given i to the pressure treatment of incompressible stokes problem ii to find an equivalent inf sup condition that guarantees stability of reduced basis solutions by enriching the reduced basis velocity approximation space with the solutions of a supremizer problem iii to provide algebraic stability of the problem by reducing the condition number of reduced basis matrices using an orthonormalization procedure applied to basis functions iv to reduce computational costs in order to allow real time solution of parametrized problem

a priori model reduction through proper generalized decomposition for solving time dependent partial differential equations over the past years model reduction techniques have become a necessary path for the reduction of computational requirements in the numerical simulation of complex models a family of a priori model reduction techniques called proper generalized decomposition pgd methods are receiving a growing interest these methods rely on the a priori construction of separated variables representations of the solution of models defined in tensor product spaces they can be interpreted as generalizations of proper orthogonal decomposition pod for the a priori construction of such separated representations in this paper we introduce and study different definitions of pgd for the solution of time dependent partial differential equations we review classical definitions of pgd based on galerkin or minimal residual formulations and we propose and discuss several improvements for these classical definitions we give an interpretation of optimal decompositions as the solution of pseudo eigenproblems we also introduce a new definition of pgd called minimax pgd which can be interpreted as a petrov galerkin model reduction technique where test and trial reduced basis functions are related by an adjoint problem this new definition improves convergence properties of separated representations with respect to a chosen metric it coincides with a classical pod for degenerate time dependent partial differential equations for the numerical construction of each pgd we propose algorithms inspired from the solution of eigenproblems several numerical examples illustrate and compare the different definitions of pgd on transient advection diffusion reaction equations

multidimensional a priori hyper reduction of mechanical models involving internal variables this paper concerns the adaptation of reduced order models during simulations of series of elastoviscoplastic problems in continuation with previous works this paper aimed at extending the a priori hyper reduction method aphr method for nonlinear thermal problems to nonlinear mechanical problems involving internal variables this method is an a priori approach because full incremental responses of detailed models are not forecasted in order to build reduced order models the recent extension of the hyper reduction method to reduction of mechanical models involving internal variables makes possible the reduction of degrees of freedom and the reduction of integration points a multi level formulation is introduced to focus on the capability of the method to perform efficient parallel computations to adapt reduced order models

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

reduced basis method for multi parameter dependent steady navier stokes equations applications to natural convection in a cavity this work focuses on the approximation of parametric steady navier stokes equations by the reduced basis method for a particular instance of the parameters under consideration we are able to solve the underlying partial differential equations compute an output and give sharp error bounds the computations are split into an offline part where the values of the parameters are not yet identified but only given within a range of interest and an online part where the problem is solved for an instance of the parameters the offline part is expensive and is used to build a reduced basis and prepare all the ingredients mainly matrix vector and scalar products but also eigenvalue computations necessary for the online part which is fast we provide a model problem describing natural convection phenomena in a laterally heated cavity characterized by three parameters grashof and prandtl numbers and the aspect ratio of the cavity we show the feasibility and efficiency of the a posteriori error estimation by the natural norm approach considering several test cases by varying two different parameters the gain in terms of cpu time with respect to a parallel finite element approximation is of three magnitude orders with an acceptable indeed less than 0 1 error on the selected outputs

some implications of renormalization group theoretical ideas to statistics renormalization group rg theory and statistical data analysis are obviously closely related reductive rg can provide a natural framework to understand asymptotic estimate problems some observations relevant to this problem and an example of a data mining algorithm inspired by the consideration are exhibited

advanced simulation of models defined in plate geometries 3d solutions with 2d computational complexity abstract many models in polymer processing and composites manufacturing are defined in degenerated three dimensional domains involving plate or shell geometries the reduction of models from 3d to 2d is not obvious when complex physics are involved the hypotheses to be introduced for reaching this dimensionality reduction are sometimes unclear and most of possible proposals will have a narrow interval of validity the only getaway is to explore new discretization strategies able to circumvent or at least alleviate the drawbacks related to mesh based discretizations of fully 3d models defined in plate or shell domains an in plane out of plane separated representation of the involved fields within the context of the proper generalized decomposition allows solving the fully 3d model by keeping a 2d characteristic computational complexity moreover the pgd features allow the introduction of many extra coordinates as for example the orientation of the different laminate plies without affecting the solvability of the resulting multidimensional model

estimation of rate and mean functions from truncated recurrent event data abstract this article investigates data on recurrent events that arise from sources such as warranty claims where the observation period for a unit is unknown until it experiences at least one event this creates a type of truncation in the data we consider nonparametric estimation of means and rates of the event occurrences with such zero truncated data and examine the case where the population size and the distribution of observation times across units are at least approximately known we study the behaviors of the proposed estimators by simulation we examine some car warranty data by applying the methodology developed here and considering the underlying assumptions

generalized spectral decomposition for stochastic nonlinear problems we present an extension of the generalized spectral decomposition method for the resolution of nonlinear stochastic problems the method consists in the construction of a reduced basis approximation of the galerkin solution and is independent of the stochastic discretization selected polynomial chaos stochastic multi element or multi wavelets two algorithms are proposed for the sequential construction of the successive generalized spectral modes they involve decoupled resolutions of a series of deterministic and low dimensional stochastic problems compared to the classical galerkin method the algorithms allow for significant computational savings and require minor adaptations of the deterministic codes the methodology is detailed and tested on two model problems the one dimensional steady viscous burgers equation and a two dimensional nonlinear diffusion problem these examples demonstrate the effectiveness of the proposed algorithms which exhibit convergence rates with the number of modes essentially dependent on the spectrum of the stochastic solution but independent of the dimension of the stochastic approximation space

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

response of non equilibrium systems with long range initial correlations the long time dynamics of the d dimensional spherical model with a non conserved order parameter and quenched from an initial state with long range correlations is studied through the exact calculation of the two time autocorrelation and autoresponse functions in the ageing regime these are given in terms of non trivial universal scaling functions of both time variables at criticality five distinct types of ageing are found depending on the form of the initial correlations while at low temperatures only a single type of ageing exists the autocorrelation and autoresponse exponents are shown to be generically different and to depend on the initial conditions the scaling form of the two time response functions agrees with a recent prediction coming from conformal invariance

a reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for burgers equation in this article a reduced optimizing finite difference scheme fds based on singular value decomposition svd and proper orthogonal decomposition pod for burgers equation is presented also the error estimates between the usual finite difference solution and the pod solution of reduced optimizing fds are analyzed it is shown by considering the results obtained for numerical simulations of cavity flows that the error between the pod solution of reduced optimizing fds and the solution of the usual fds is consistent with theoretical results moreover it is also shown that the reduced optimizing fds is feasible and efficient

nonparametric estimation of a lifetime distribution when censoring times are missing we consider datasets for which lifetimes associated with the units in a population are observed if they occur within certain time intervals but for which lengths of the time intervals or censoring times of unfailed units are missing we consider nonparametric estimation of the lifetime distribution for the population from such data a maximum likelihood estimator and a simple moment estimator are obtained an example involving automobile warranty data is discussed at some length

an optimal projection method for the reduced order modeling of incompressible flows a new method to build reduced order models roms for incompressible flows is addressed in this paper proper orthogonal decompositions pods are used to efficiently represent both the fluid velocity and pressure fields with a small number of spatial modes a minimum residual projection is then developed for building the reduced models in which the velocity and pressure temporal coefficients are fully coupled comparisons of numerical calculations based on the proposed approach with results arising from the classical galerkin projection are exposed on three fluid flows a transient ventilated cavity a periodic lid driven cavity and a transient mixed convection flow it is shown that both stability and accuracy of the roms are strongly enhance when the minimum residual projection is used

how super rough is the glassy phase of a crystalline surface with a disordered substrate we discuss the behaviour of a crystalline surface with a disordered substrate we focus on the possible existence of a super rough glassy phase with height height correlation functions which vary as the square logarithm of the distance with numerical simulations we establish the presence of such a behaviour that does not seem to be connected to finite size effects we comment on the variational approach and suggest that a more general extension of the method could be needed to fully explain the behaviour of the model

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

on the verification of model reduction methods based on the proper generalized decomposition in this work we introduce a consistent error estimator for numerical simulations performed by means of the proper generalized decomposition pgd approximation this estimator which is based on the constitutive relation error enables to capture all error sources i e those coming from space and time numerical discretizations from the truncation of the pgd decomposition etc and leads to guaranteed bounds on the exact error the specificity of the associated method is a double approach i e a kinematic approach and a unusual static approach for solving the parameterized problem by means of pgd this last approach makes straightforward the computation of a statically admissible solution which is necessary for robust error estimation an attractive feature of the error estimator we set up is that it is obtained by means of classical procedures available in finite element codes it thus represents a practical and relevant tool for driving algorithms carried out in pgd being possibly used as a stopping criterion or as an adaptation indicator numerical experiments on transient thermal problems illustrate the performances of the proposed method for global error estimation

a galerkin free model reduction approach for the navier stokes equations galerkin projection of the navier stokes equations on proper orthogonal decomposition pod basis is predominantly used for model reduction in fluid dynamics the robustness for changing operating conditions numerical stability in long term transient behavior and the pressure term consideration are generally the main concerns of the galerkin reduced order models rom in this article we present a novel procedure to construct an off reference solution state by using an interpolated pod reduced basis a linear interpolation of the pod reduced basis is performed by using two reference solution states the pod basis functions are optimal in capturing the averaged flow energy the energy dominant pod modes and corresponding base flow are interpolated according to the change in operating parameter the solution state is readily built without performing the galerkin projection of the navier stokes equations on the reduced pod space modes as well as the following time integration of the resulted ordinary differential equations ode to obtain the pod time coefficients the proposed interpolation based approach is thus immune from the numerical issues associated with a standard pod galerkin rom in addition a posteriori error estimate and a stability analysis of the obtained rom solution are formulated a detailed case study of the flow past a cylinder at low reynolds numbers is considered for the demonstration of proposed method the rom results show good agreement with the high fidelity numerical flow simulation

a priori reduction method for solving the two dimensional burgers equations abstract the two dimensional burgers equations are solved here using the a priori reduction method this method is based on an iterative procedure which consists in building a basis for the solution where at each iteration the basis is improved the method is called a priori because it does not need any prior knowledge of the solution which is not the case if the standard karhunen loeve decomposition is used the accuracy of the apr method is compared with the standard newton raphson scheme and with results from the literature the apr basis is also compared with the karhunen loeve basis

estimation from truncated lifetime data with supplementary information on covariates and censoring times summary in epidemiology reliability and other areas one encounters situations where response times and covariates for individuals in a population are observed only if the response time does not exceed an associated censoring time methods for obtaining supplementary information about covariates and censoring times for nonresponding individuals are considered estimation procedures are developed for the resulting combination of truncated data and supplementary data theoretical and simulation results are given and the methodology illustrated on some automobile failure data collected under a warranty plan

recent advances on the use of separated representations separated representations based on finite sum decompositions constitute an appealing strategy for reducing the computer resources and the calculation costs by reducing drastically the number of degrees of freedom that the functional approximations involve the number of degrees of freedom scale linearly with the dimension of the space in which the model is defined instead of the exponential growing characteristic of mesh based discretization strategies in our knowledge the use of separated representations is the only possibility for circumventing the terrific curse of dimensionality related to some highly multidimensional models involving hundreds of dimensions as we proved in some of our former works its application is not restricted to multidimensional models obviously separated representation can also be applied in standard 2d or 3d models allowing for high resolution computations because its early life numerous issues persist many of them attracting the curiosity of many research groups within the computational mechanics community in this paper we are focusing in two issues never until now addressed i the imposition of non homogenous essential boundary conditions and ii the consideration of complex geometries copyright 2009 john wiley sons ltd

a generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations we propose a new robust technique for solving stochastic partial differential equations the solution is approximated by a series of terms each of which being the product of a scalar stochastic function by a deterministic function none of these functions are fixed a priori but determined by solving a problem which can be interpreted as an extended eigenvalue problem this technique generalizes the classical spectral decomposition namely the karhunen loeve expansion ad hoc iterative techniques to build the approximation inspired by the power method for classical eigenproblems then transform the problem into the resolution of a few uncoupled deterministic problems and stochastic equations this method drastically reduces the calculation costs and memory requirements of classical resolution techniques used in the context of galerkin stochastic finite element methods finally this technique is particularly suitable to non linear and evolution problems since it enables the construction of a relevant reduced basis of deterministic functions which can be efficiently reused for subsequent resolutions

an error estimator for separated representations of highly multidimensional models fine modeling of the structure and mechanics of materials from the nanometric to the micrometric scales uses descriptions ranging from quantum to statistical mechanics most of these models consist of a partial differential equation defined in a highly multidimensional domain e g schrodinger equation fokker planck equations among many others the main challenge related to these models is their associated curse of dimensionality we proposed in some of our former works a new strategy able to circumvent the curse of dimensionality based on the use of separated representations also known as finite sums decomposition this technique proceeds by computing at each iteration a new sum that consists of a product of functions each one defined in one of the model coordinates the issue related to error estimation has never been addressed this paper presents a first attempt on the accuracy evaluation of such a kind of discretization techniques

a priori space time separated representation for the reduced order modeling of low reynolds number flows abstract reduced order models roms in fluid dynamics are nowadays mostly developed by performing a projection of the navier stokes equations onto a low dimensional space basis this basis is usually obtained through proper orthogonal decomposition pod which remains one the most efficient techniques to compress precomputed data the main drawback of a posteriori pod based roms is however their lacks of reliability as their parameters are varied preventing their direct uses within optimization algorithms the goal of the present article is to obtain an a priori low dimensional space time separated representation of the fluid fields without precomputed data the approach is based on the use of space time proper generalized decomposition pgd definitions which are successfully applied in several fields but whose uses in fluid dynamics remain scarce their applications to the navier stokes equations are indeed not straightforward due to the pressure velocity coupling the divergence free constraint and the non linear convective term the roms are built here from a space time weak formulation of the chorin temam prediction correction scheme more particularly a priori space time separated representations are obtained by applying the galerkin based progressive pgd definition the minimax pgd definition is moreover experimented on a linear stokes simplified case the related algorithms are explicitly given and illustrated on a transient lid driven cavity flow it is shown that the a priori space time separated representations converge to the full model solution as the decomposition order increases the ability of the resulting rom to learn iteratively from its own error is highlighted the progressive pgd algorithm can be used to effectively enrich incomplete pod and pgd precomputed space bases such as those obtained with different parameter values this may allow to ensure the accuracy of a rom as the parameter is varied which is of crucial interest for optimization problems

proper general decomposition pgd for the resolution of navier stokes equations in this work the pgd method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions in the first stage the equations of stokes and burgers will be solved then we will solve the navier stokes problem in the case of the lid driven cavity for different reynolds numbers re 100 1000 and 10 000 finally the pgd method will be compared to the standard resolution technique both in terms of cpu time and accuracy

functional renormalization group and the field theory of disordered elastic systems we study elastic systems such as interfaces or lattices pinned by quenched disorder to escape triviality as a result of dimensional reduction we use the functional renormalization group difficulties arise in the calculation of the renormalization group functions beyond one loop order even worse observables such as the two point correlation function exhibit the same problem already at one loop order these difficulties are due to the nonanalyticity of the renormalized disorder correlator at zero temperature which is inherent to the physics beyond the larkin length characterized by many metastable states as a result two loop diagrams which involve derivatives of the disorder correlator at the nonanalytic point are naively ambiguous we examine several routes out of this dilemma which lead to a unique renormalizable field theory at two loop order it is also the only theory consistent with the potentiality of the problem the beta function differs from previous work and the one at depinning by novel anomalous terms for interfaces and random bond disorder we find a roughness exponent zeta 0 208 298 04epsilon 0 006 858epsilon 2 epsilon 4 d for random field disorder we find zeta epsilon 3 and compute universal amplitudes to order o epsilon 2 for periodic systems we evaluate the universal amplitude of the two point function we also clarify the dependence of universal amplitudes on the boundary conditions at large scale all predictions are in good agreement with numerical and exact results and are an improvement over one loop finally we calculate higher correlation functions which turn out to be equivalent to those at depinning to leading order in epsilon

an overview of projection methods for incompressible flows a series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper these methods are often referred to in the literature as projection methods and can be classified into three classes namely the pressure correction methods the velocity correction methods and the consistent splitting methods for each class of schemes theoretical and numerical convergence results available in the literature are reviewed and open questions are discussed the essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners published by elsevier b v msc 65n35 65n22 65f05 35j05

an efficient method of solving the navier stokes equations for flow control a new method of solving the navier stokes equations efficiently by reducing their number of modes is proposed in the present paper it is based on the karhunen loeve decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system employing these empirical eigenfunctions as basis functions of a galerkin procedure one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena and consequently reduce the navier stokes equation defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom the present algorithm is well suited for the problems of flow control or optimization where one has to compute the flow field repeatedly using the navier stokes equation but one can also estimate the approximate solution space of the flow field based on the range of control variables the low dimensional dynamic model of viscous fluid flow derived by the present method is shown to produce accurate flow fields at a drastically reduced computational cost when compared with the finite difference solution of the navier stokes equation 1998 john wiley sons ltd

universal amplitudes of power law tails in the asymptotic structure factor of systems with topological defects we compute the asymptotic structure factor s k t of the o n model for n ensuremath le d where d and n are the dimensions of space and of the order parameter respectively topological defects in the field lead to the power law tail s k t a n d ensuremath rho t mathit k mathrm ensuremath mathit d mathit n where ensuremath rho is the defect density the amplitude a n d is calculated exactly using purely geometrical arguments based on the defect field

approximation of constrained problems using the pgd method with application to pure neumann problems in this paper we introduce analyze and compare several approaches designed to incorporate a linear or affine constraint within the proper generalized decomposition framework we apply the considered methods and numerical strategies to two classes of problems the pure neumann case where the role of the constraint is to recover unicity of the solution and the robin case where the constraint forces the solution to move away from the already existing unique global minimizer of the energy functional

out of equilibrium properties of the semi infinite kinetic spherical model we study the ageing properties of the semi infinite kinetic spherical model at the critical point and in the ordered low temperature phase for both dirichlet and neumann boundary conditions the surface fluctuation dissipation ratio and the scaling functions of two time surface correlation and response functions are determined explicitly in the dynamical scaling regime in the low temperature phase our results show that for the case of dirichlet boundary conditions the value of the non equilibrium surface exponent b1 differs from the usual bulk value of systems undergoing phase ordering

proper generalized decomposition method for incompressible navier stokes equations with a spectral discretization proper generalized decomposition pgd is a method which consists in looking for the solution to a problem in a separate form this approach has been increasingly used over the last few years to solve mathematical problems the originality of this work consists in the association of pgd with a spectral collocation method to solve transfer equations as well as navier stokes equations in the first stage the pgd method and its association with spectral discretization is detailed this approach was tested for several problems the poisson equation the darcy problem navier stokes equations the taylor green problem and the lid driven cavity in the navier stokes problems the coupling between velocity and pressure was performed using a fractional step scheme and a p n p n 2 discretization for all problems considered the results from pgd simulations were compared with those obtained by a standard solver and or with the results found in the literature the simulations performed showed that pgd is as accurate as standard solvers pgd preserves the spectral behavior of the errors in velocity and pressure when the time step or the space step decreases moreover for a given number of discretization nodes pgd is faster than the standard solvers

ageing phenomena without detailed balance the contact process the long time dynamics of the 1d contact process suddenly brought out of an uncorrelated initial state is studied through a light cone transfer matrix renormalization group approach at criticality the system undergoes ageing which is characterized through the dynamical scaling of the two times autocorrelation and autoresponse functions the observed non equality of the ageing exponents a and b excludes the possibility of a finite fluctuation dissipation ratio in the ageing regime the scaling form of the critical autoresponse function is in agreement with the prediction of local scale invariance

aging in ferromagnetic systems at criticality near four dimensions we study the off equilibrium response and correlation functions and the corresponding fluctuation dissipation ratio for a purely dissipative relaxation of an o n symmetric vector model model a below its upper critical dimension the scaling behavior of these quantities is analyzed and the associated universal functions are determined at first order in ensuremath epsilon 4 ensuremath d in the high temperature phase and at criticality a nontrivial limit of the fluctuation dissipation ratio is found in the aging regime x ensuremath infty 1 2 1 ensuremath ensuremath epsilon 4 n 2 n 8 o ensuremath epsilon 2

exact multilocal renormalization of the effective action application to the random sine gordon model statics and nonequilibrium dynamics we extend the exact multilocal renormalization group rg method to study the flow of the effective action functional this important physical quantity satisfies an exact rg equation which is then expanded in multilocal components integrating the nonlocal parts yields a closed exact rg equation for the local part to a given order in the local part the method is illustrated on the o n model by straightforwardly recovering the ensuremath eta exponent and scaling functions then it is applied to study the glass phase of the cardy ostlund random phase sine gordon model near the glass transition temperature the static correlations and equilibrium dynamical exponent z are recovered and several results are obtained such as the equilibrium two point scaling functions the nonequilibrium finite momentum two time t t ensuremath response and correlations are computed they are shown to exhibit scaling forms characterized by exponents ensuremath lambda r ensuremath ne ensuremath lambda c as well as universal scaling functions that we compute the fluctuation dissipation ratio is found to be nontrivial and of the form x q z t ensuremath t ensuremath t t ensuremath analogies and differences with pure critical models are discussed