computational plasticity for composite structures based on mathematical homogenization theory and practice abstract this paper generalizes the classical mathematical homogenization theory for heterogeneous medium to account for eigenstrains starting from the double scale asymptotic expansion for the displacement and eigenstrain fields we derive a close form expression relating arbitrary eigenstrains to the mechanical fields in the phases the overall structural response is computed using an averaging scheme by which phase concentration factors are computed in the average sense for each micro constituent and history data is updated at two points reinforcement and matrix in the microstructure one for each phase macroscopic history data is stored in the database and then subjected in the post processing stage onto the unit cell in the critical locations for numerical examples considered the cpu time obtained by means of the two point averaging scheme with variational micro history recovery with 30 seconds on sparc 10 51 as opposed to 7 hours using classical mathematical homogenization theory at the same time the maximum error in the microstress field in the critical unit cell was only 3 5 in comparison with the classical mathematical homogenization theory

wilcoxon type generalized bayesian information criterion we develop a generalized bayesian information criterion for regression model selection the new criterion relaxes the usually strong distributional assumption associated with schwarz s bic by adopting a wilcoxon type dispersion function and appropriately adjusting the penalty term we establish that the wilcoxon type generalized bic preserves the consistency of schwarz s bic without the need to assume a parametric likelihood we also show that it outperforms schwarz s bic with heavier tailed data in the sense that asymptotically it can yield substantially smaller l 2 risk on the other hand when the data are normally distributed both criteria have similar l 2 risk the new criterion function is convex and can be conveniently computed using existing statistical software our proposal provides a flexible yet highly efficient alternative to schwarz s bic at the same time it broadens the scope of wilcoxon inference which has played a fundamental role in classical nonparametric analysis

subset clustering of binary sequences with an application to genomic abnormality data this article develops a model based approach to clustering multivariate binary data in which the attributes that distinguish a cluster from the rest of the population may depend on the cluster being considered the clustering approach is based on a multivariate dirichlet process mixture model which allows for the estimation of the number of clusters the cluster memberships and the cluster specific parameters in a unified way such a clustering approach has applications in the analysis of genomic abnormality data in which the development of different types of tumors may depend on the presence of certain abnormalities at subsets of locations along the genome additionally such a mixture model provides a nonparametric estimation scheme for dependent sequences of binary data

approximate bayes factors and accounting for model uncertainty in generalised linear models summary ways of obtaining approximate bayes factors for generalised linear models are described based on the laplace method for integrals we propose a new approximation which uses only the output of standard computer programs for estimating generalised linear models this appears to be quite accurate a reference set of proper priors is suggested both to represent the situation where there is not much prior information and to assess the sensitivity of the results to the prior distribution the methods can be used when the dispersion parameter is unknown when there is overdispersion to compare link functions and to compare error distributions and variance functions the methods can be used to implement the bayesian approach to accounting for model uncertainty we describe an application to inference about relative risks in the presence of control factors where model uncertainty is large and important software to implement the methods is available at no cost from statlib

effective properties of composite materials with periodic microstructure a computational approach abstract this study reviews several problems which are specific of composites with periodic microstructure composed of linear or nonlinear constituents the theoretical background of the method is recalled first two different families of numerical methods are considered to solve the problem the first is based on the finite element method the concept of macroscopic degrees of freedom is presented the implementation of periodicity conditions is discussed a general framework permitting either a strain or stress control is proposed the second numerical method is based on fast fourier transforms it considers first the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain the solution of this problem is based on the explicit form of the periodic green s function of the reference medium the relative merits of the two methods are compared and several examples are discussed both methods give very comparable results on test examples and their domains of applications appear to be complementary

bifurcation analysis of multiple steady flow patterns for rayleigh benard convection in a cubical cavity at pr 130 the bifurcation diagram of steady convective flow patterns inside a cubical cavity with adiabatic lateral walls heated from below and filled with silicone oil pr 130 was determined for values of the rayleigh number ra up to 1 5 x 10 5 a continuation procedure based on the galerkin spectral method was used to determine the steady convective solutions as a function of ra bifurcations leading to either new steady or time dependent solutions were identified and new steady solution branches were also continued a total of fifteen steady solutions were tracked and the stability analysis predicted that six flow patterns were stable and that two three or even four of these patterns coexisted over certain ranges of ra in the studied domain predicted flow patterns and transitions are in agreement with flow visualizations previously reported in the literature the variation of the nusselt number nu as a function of pr was investigated for three of the stable flow patterns identified a x or y roll a diagonal oriented roll and a pattern formed by four connected half rolls it was found that whereas the nusselt changes within the region 0 71 or pr or 10 it tends to an asymptotic value with increasing pr

the intrinsic bayes factor for model selection and prediction abstract in the bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions it is typically not possible to utilize standard noninformative or default prior distributions this has led bayesians to use conventional proper prior distributions or crude approximations to bayes factors in this article we introduce a new criterion called the intrinsic bayes factor which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual bayes factors the criterion can be used for nested or nonnested models and for multiple model comparison and prediction from another perspective the development suggests a general definition of a reference prior for model comparison

a computational scheme for linear and non linear composites with arbitrary phase contrast a numerical method making use of fast fourier transforms has been proposed in moulinec and suquet 1994 1998 to investigate the effective properties of linear and non linear composites this method is based on an iterative scheme the rate of convergence of which is proportional to the contrast between the phases composites with high contrast typically above 104 or infinite contrast those containing voids or rigid inclusions or highly non linear materials cannot be handled by the method this paper presents two modified schemes the first one is an accelerated scheme for composites with high contrast which extends to elasticity a scheme initially proposed in eyre and milton 1999 its rate of convergence varies as the square root of the contrast the second scheme adequate for composites with infinite contrast is based on an augmented lagrangian method the resulting saddle point problem involves three steps the first step consists of solving a linear elastic problem using the fast fourier transform method in the second step a non linear problem is solved at each individual point in the volume element the third step consists of updating the lagrange multiplier applications of this scheme to rigidly reinforced and to voided composites are shown copyright 2001 john wiley sons ltd

inverse groundwater modeling for hydraulic conductivity estimation using bayesian model averaging and variance window 1 this study proposes a bayesian model averaging bma method to address parameter estimation uncertainty arising from nonuniqueness in parameterization methods bma is able to incorporate multiple parameterization methods for prediction through the law of total probability and to obtain an ensemble average of hydraulic conductivity estimates two major issues in applying bma to hydraulic conductivity estimation are discussed the first problem is using occam s window in usual bma applications to measure approximated posterior model probabilities occam s window only accepts models in a very narrow range tending to single out the best method and discard other good methods we propose a variance window to replace occam s window to cope with this problem the second problem is the kashyap information criterion kic in the approximated posterior model probabilities which tends to prefer highly uncertain parameterization methods by considering the fisher information matrix with sufficient amounts of observation data the bayesian information criterion bic is a good approximation and is able to avoid controversial results from using kic this study adopts multiple generalized parameterization gp methods such as the bma models to estimate spatially correlated hydraulic conductivity numerical examples illustrate the issues of using kic and occam s window and show the advantages of using bic and the variance window in bma application finally we apply bma to the hydraulic conductivity estimation of the 1500 foot sand in east baton rouge parish louisiana

assessing a mixture model for clustering with the integrated completed likelihood we propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood for this purpose the observed data are assigned to unknown clusters using a maximum a posteriori operator then the integrated completed likelihood icl is approximated using the bayesian information criterion bic numerical experiments on simulated and real data of the resulting icl criterion show that it performs well both for choosing a mixture model and a relevant number of clusters in particular icl appears to be more robust than bic to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data

nonparametric bayes modeling of multivariate categorical data modeling of multivariate unordered categorical nominal data is a challenging problem particularly in high dimensions and cases in which one wishes to avoid strong assumptions about the dependence structure commonly used approaches rely on the incorporation of latent gaussian random variables or parametric latent class models the goal of this article is to develop a nonparametric bayes approach which defines a prior with full support on the space of distributions for multiple unordered categorical variables this support condition ensures that we are not restricting the dependence structure a priori we show this can be accomplished through a dirichlet process mixture of product multinomial distributions which is also a convenient form for posterior computation methods for nonparametric testing of violations of independence are proposed and the methods are applied to model positional dependence within transcription factor binding motifs

a numerical spectral approach for solving elasto static field dislocation and g disclination mechanics a spectral approach is developed to solve the elasto static equations of field dislocation and g disclination mechanics in periodic media given the spatial distribution of nye s dislocation density and or g disclination density tensors in heterogeneous or homogenous linear elastic media the incompatible and compatible elastic distortions are respectively obtained from the solutions of poisson and navier type equations in the fourier space intrinsic discrete fourier transforms solved by the fast fourier transform fft method which are consistent with the pixel grid for the calculation of first and second order spatial derivatives are preferred and compared to the classical discrete approximation of continuous fourier transforms when deriving elastic fields of defects numerical examples are provided for homogeneous linear elastic isotropic solids for various defects a regularized defect density in the core is considered and smooth elastic fields without gibbs oscillations are obtained when using intrinsic discrete fourier transforms the results include the elastic fields of single screw and edge dislocations standard wedge disclinations and associated dipoles as well as twinning g disclinations in order to validate the present spectral approach comparisons are made with analytical solutions using the riemann graves integral operator and with numerical simulations using the finite element approximation

numerical computation of algorithmic consistent tangent moduli in large strain computational inelasticity abstract an algorithm for the numerical computation of so called algorithmic or consistent tangent moduli in finite inelasticity is presented these moduli determine the sensitivity of algorithmic expressions for stresses with respect to the change in total deformation they serve as iteration operators by application of newton type solvers for the iterative solution of non linear initial boundary value problems in finite inelasticity the underlying concept of the numerical computation is a perturbation technique based on a forward difference approximation which reduces the computation of the tangent moduli to a multiple stress computation the algorithmic procedure is material independent and surprisingly simple it is outlined for a lagrangian as well as an eulerian geometric setting and applied to model problems of finite elasticity and finite elastoplasticity

trend and fluctuations analysis and design of population dynamics measurements in replicate ecosystems the dynamical evolution of complex systems is often intrinsically stochastic and subject to external random forces in order to study the resulting variability in dynamics it is essential to make measurements on replicate systems and to separate arbitrary variation of the average dynamics of these replicates from fluctuations around the average dynamics here we do so for population time series data from replicate ecosystems sharing a common average dynamics or common trend we explain how model parameters including the effective interactions between species and dynamical noise can be estimated from the data and how replication reduces errors in these estimates for this it is essential that the model can fit a variety of average dynamics we then show how one can judge the quality of a model compare alternate models and determine which combinations of parameters are poorly determined by the data in addition we show how replicate population dynamics experiments could be designed to optimize the acquired information of interest about the systems our approach is illustrated on a set of time series gathered from replicate microbial closed ecosystems

a reference bayesian test for nested hypotheses and its relationship to the schwarz criterion abstract to compute a bayes factor for testing h 0 0 in the presence of a nuisance parameter priors under the null and alternative hypotheses must be chosen as in bayesian estimation an important problem has been to define automatic or reference methods for determining priors based only on the structure of the model in this article we apply the heuristic device of taking the amount of information in the prior on equal to the amount of information in a single observation then after transforming to be null orthogonal to we take the marginal priors on to be equal under the null and alternative hypotheses doing so and taking the prior on to be normal we find that the log of the bayes factor may be approximated by the schwarz criterion with an error of order o p n rather than the usual error of order o p 1 this result suggests the schwarz criterion should provide sensible approximate solutions to bayesian testing problems at least when the hypotheses are nested when

penalized model based clustering with application to variable selection variable selection in clustering analysis is both challenging and important in the context of model based clustering analysis with a common diagonal covariance matrix which is especially suitable for high dimension low sample size settings we propose a penalized likelihood approach with an l1 penalty function automatically realizing variable selection via thresholding and delivering a sparse solution we derive an em algorithm to fit our proposed model and propose a modified bic as a model selection criterion to choose the number of components and the penalization parameter a simulation study and an application to gene function prediction with gene expression profiles demonstrate the utility of our method

from steady solutions to chaotic flows in a rayleigh benard problem at moderate rayleigh numbers abstract the dynamics of a rayleigh benard convection problem in a cubical cavity at moderate values of the rayleigh number ra 10 5 and a prandtl number of pr 0 71 with extensions to pr 0 75 and 0 80 was investigated the cubical cavity was heated from below and had perfectly conducting sidewalls and uniform temperature distributions on the two horizontal walls a system of ordinary differential equations with a dimension of typically n 11 000 was obtained when the conservation equations were discretized by means of a galerkin method previous knowledge of the bifurcation diagram of steady solutions reported in the literature was used to identify the origin of several branches of periodic orbits that were continued with ra half a dozen of such periodic orbits were found to be stable within narrow ranges of ra at most some 5000 units wide an attracting two torus restricted to a very narrow region of ra was also identified it was found that the instabilization of periodic orbits quite often resulted into the development of complex dynamics such as the creation of homoclinic and heteroclinic orbits instances of both types of global bifurcations were analyzed in some detail one particular instance of chaotic dynamics a strange attractor was also identified chaotic dynamics has been found at pr 0 71 in a flow invariant subspace which can be interpreted as a fixed point subspace in terms of equivariant theory this subspace is not attracting however some regions of attracting chaotic dynamics for moderate rayleigh numbers 9 10 4 r a 10 5 were found at values of pr slightly above 0 71 the role of a particular homoclinic solution found at pr 0 71 in the generation of these chaotic regions was analyzed

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

mixtures of g priors for bayesian model averaging with economic application this paper examines the issue of variable selection in linear regression modeling where there is a potentially large amount of possible covariates and economic theory offers insufficient guidance on how to select the appropriate subset in this context bayesian model averaging presents a formal bayesian solution to dealing with model uncertainty the main interest here is the effect of the prior on the results such as posterior inclusion probabilities of regressors and predictive performance the authors combine a binomial beta prior on model size with a g prior on the coefficients of each model in addition they assign a hyperprior to g as the choice of g has been found to have a large impact on the results for the prior on g they examine the zellner siow prior and a class of beta shrinkage priors which covers most choices in the recent literature the authors propose a benchmark beta prior inspired by earlier findings with fixed g and show it leads to consistent model selection inference is conducted through a markov chain monte carlo sampler over model space and g the authors examine the performance of the various priors in the context of simulated and real data for the latter they consider two important applications in economics namely cross country growth regression and returns to schooling recommendations for applied users are provided

benchmark priors for bayesian model averaging in contrast to a posterior analysis given a particular sampling model posterior model probabilities in the context of model uncertainty are typically rather sensitive to the speciflcation of the prior in particular difiuse priors on model speciflc parameters can lead to quite unexpected consequences here we focus on the practically relevant situation where we need to entertain a large number of sampling models and we have or wish to use little or no subjective prior information we aim at providing an automatic or benchmark prior structure that can be used in such cases we focus on the normal linear regression model with uncertainty in the choice of re gressors we propose a partly noninformative prior structure related to a natural conjugate g prior speciflcation where the amount of subjective information requested from the user is limited to the choice of a single scalar hyperparameter g0j the consequences of difierent choices for g0j are examined we investigate theoretical properties such as consistency of the implied bayesian procedure links with classical information criteria are provided in addition we examine the flnite sample implications of several choices of g0j in a simulation study the use of the mc 3 algorithm of madigan and york 1995 combined with e cient coding in fortran makes it feasible to conduct large simulations in addition to posterior criteria we shall also compare the predictive performance of difierent priors a classic exam ple concerning the economics of crime will also be provided and contrasted with results in the literature the main flndings of the paper will lead us to propose a benchmark prior speciflcation in a linear regression context with model uncertainty

variable selection in penalized model based clustering via regularization on grouped parameters penalized model based clustering has been proposed for high dimensional but small sample sized data such as arising from genomic studies in particular it can be used for variable selection a new regularization scheme is proposed to group together multiple parameters of the same variable across clusters which is shown both analytically and numerically to be more effective than the conventional l 1 penalty for variable selection in addition we develop a strategy to combine this grouping scheme with grouping structured variables simulation studies and applications to microarray gene expression data for cancer subtype discovery demonstrate the advantage of the new proposal over several existing approaches

the effect of cluster size dimensionality and the number of clusters on recovery of true cluster structure an evaluation of four clustering methods and four external criterion measures was conducted with respect to the effect of the number of clusters dimensionality and relative cluster sizes on the recovery of true cluster structure the four methods were the single link complete link group average upgma and ward s minimum variance algorithms the results indicated that the four criterion measures were generally consistent with each other of which two highly similar pairs were identified the tirst pair consisted of the rand and corrected rand statistics and the second pair was the jaccard and the fowlkes and mallows indexes with respect to the methods recovery was found to improve as the number of clusters increased and as the number of dimensions increased the relative cluster size factor produced differential performance effects with ward s procedure providing the best recovery when the clusters were of equal size the group average method gave equivalent or better recovery when the clusters were of unequal size

fractional bayes factors for model comparison bayesian comparison of models is achieved simply by calculation of posterior probabilities of the models themselves however there are difficulties with this approach when prior information about the parameters of the various models is weak partial bayes factors offer a resoiution of the problem by setting aside part of the data as a training sampie the training sampie is used to obtain an initiai informative posterior distribution of the parameters in each model model comparison is then based on a bayes factor calculated from the remaining data properties of partial bayes factors are discussed particularly in the context of weak prior information and they are found to have advantages over other proposed methods of model comparison a new variant of the partial bayes factor the fractional bayes factor is advocated on grounds of consistency simplicity robustness and coherence

on the computation of the macroscopic tangent for multiscale volumetric homogenization problems in this contribution methods of computing the macroscopic tangent that is required in multiscale volumetric homogenization problems are investigated a condensation procedure that employs the tangent information from the microscale finite element analysis is derived within a special framework where deformation controlled boundary conditions in micromechanical testing are enforced via the penalty method the developed methodology is demonstrated by sample macroscale problems in the context of the multilevel finite element strategy due to the high memory allocation costs that the condensation procedure induces a perturbation procedure is developed based on a minimal number of micromechanical tests results from the condensation and perturbation procedures are compared for sample infinitesimal and finite deformation inelasticity problems and the algorithmic consistency of the macroscopic tangent with the evolution of the macroscopic stress is discussed it is shown that the ability to compute the macroscopic tangent can also be employed to construct a stress controlled micromechanical testing procedure

practical bayesian density estimation using mixtures of normals abstract mixtures of normals provide a flexible model for estimating densities in a bayesian framework there are some difficulties with this model however first standard reference priors yield improper posteriors second the posterior for the number of components in the mixture is not well defined if the reference prior is used third posterior simulation does not provide a direct estimate of the posterior for the number of components we present some practical methods for coping with these problems finally we give some results on the consistency of the method when the maximum number of components is allowed to grow with the sample size

a multiscale approach for modeling progressive damage of composite materials using fast fourier transforms abstract composite materials possess a highly complex material behavior and thus advanced simulation techniques are necessary to compute their mechanical response in this regard especially modeling failure and progressive damage presents a challenging task conventional macro mechanical methods and even closed form estimates are in many cases not sufficient to predict the appropriate mechanical material response full field simulations must be resorted to but these are known to be very expensive from the computational point of view in this contribution we propose a more efficient multiscale approach similar to fe2 nonlinear material effects caused by progressive damage behavior are captured directly on the discretized material level using simple isotropic continuum damage laws in contrast to conventional fe2 methods which use the finite element method fem to solve both scales numerically the fine scale problem material level is rewritten in an integral form of lippmann schwinger type and solved efficiently using the fast fourier transformation fft the calculation is carried out on a regular voxel grid that can be obtained from 3d images like tomographies the fine scale problem is integrated in a standard finite element framework which is used to solve the macroscopic bvp component level in the work at hand the scale coupling technique and the computation of the macroscopic tangent are described and in some numerical examples the convergence behavior of the macroscopic newton algorithm is investigated thereby the simulations were considered until localization and softening on the material scale occurred it is shown that the proposed method presents an effective way to determine the exact physical macroscopic response considering arbitrary microstructures and loading conditions

a marching cubes based failure surface propagation concept for three dimensional finite elements with non planar embedded strong discontinuities of higher order kinematics summary this paper presents an advanced failure surface propagation concept based on the marching cubes algorithm initially proposed in the field of computer graphics and applies it to the embedded finite element method when modeling three dimensional 3d solids at failure the propagation of the failure surface representing a crack or shear band should not exhibit a strong sensitivity to the details of the finite element discretization this results in the need for a propagation of the discrete failure zone through the individual finite elements which is possible for finite elements with embedded strong discontinuities whereas for two dimensional calculations the failure zone propagation location is easily predicted by the maximal principal stress direction more advanced strategies are needed to achieve a smooth failure surface in 3d simulations an example for such method is the global tracking algorithm which predicts the crack path by a scalar level set function computed on the basis of the solution of a simplified heat conduction like problem its prediction may though lead to various scenarios on how the failure surface may propagate through the individual finite elements in particular for a hexahedral eight node finite element 256 such cases exist to capture all those possibilities the marching cubes algorithm is combined with the global tracking algorithm and the finite elements with embedded strong discontinuities in this work in addition because many of the possible cases result in non planar failure surfaces within a single finite element and because the local quantities used to describe the kinematics of the embedded strong discontinuities are physically meaningful in a strict sense only for planar failure surfaces a remedy for such scenarios is proposed various 3d failure propagation simulations outline the performance of the proposed concept copyright 2013 john wiley sons ltd

nonuniform transformation field analysis the exact description of the overall behavior of composites with nonlinear dissipative phases requires an infinity of internal variables approximate models involving only a finite number of those can be obtained by considering a decomposition of the microscopic anelastic strain field on a finite set of transformation fields the transformation field analysis of dvorak proc r soc lond a 437 1992 311 corresponds to piecewise uniform transformation fields the present theory considers nonuniform transformation fields comparison with numerical simulations shows the accuracy of the proposed model

prediction of the mechanical behavior of nonlinear heterogeneous systems by multi level finite element modeling an accurate homogenization method that accounts for large deformations and viscoelastic material behavior on microscopic and macroscopic levels is presented this method is based on the classical homogenization theory assuming local spatial periodicity of the microstructure consequently the microstructure is identified by a representative volume element rve with conformity of opposite boundaries at any stage of the deformation process the local macroscopic stress is obtained by applying the local macroscopic deformation represented by the deformation tensor on a unique rve through imposing appropriate boundary conditions and averaging the resulting rve stress field if the assumption of local periodicity of the morphology is valid this homogenization procedure supplies a consistent objective relationship between the local macroscopic deformation and the microstructural deformation the homogenization method was implemented in a multi level finite element program with meshes on macroscopic level mesh of entire structure and microscopic level meshes of rves the performance was successfully verified by the comparison of the deformation of a perforated macroscopic sheet to the response of a homogenized sheet

computational homogenization of elasticity on a staggered grid summary in this article we propose to discretize the problem of linear elastic homogenization by finite differences on a staggered grid and introduce fast and robust solvers our method shares some properties with the fft based homogenization technique of moulinec and suquet which has received widespread attention recently because of its robustness and computational speed these similarities include the use of fft and the resulting performing solvers the staggered grid discretization however offers three crucial improvements firstly solutions obtained by our method are completely devoid of the spurious oscillations characterizing solutions obtained by moulinec suquet s discretization secondly the iteration numbers of our solvers are bounded independently of the grid size and the contrast in particular our solvers converge for three dimensional porous structures which cannot be handled by moulinec suquet s method thirdly the finite difference discretization allows for algorithmic variants with lower memory consumption more precisely it is possible to reduce the memory consumption of the moulinec suquet algorithms by 50 we underline the effectiveness and the applicability of our methods by several numerical experiments of industrial scale copyright 2015 john wiley sons ltd

multiscale aggregating discontinuities a method for circumventing loss of material stability new methods for the analysis of failure by multiscale methods that invoke unit cells to obtain the subscale response are described these methods called multiscale aggregating discontinuities are based on the concept of perforated unit cells which exclude subdomains that are unstable i e exhibit loss of material stability using this concept it is possible to compute an equivalent discontinuity at the coarser scale including both the direction of the discontinuity and the magnitude of the jump these variables are then passed to the coarse scale model along with the stress in the unit cell the discontinuity is injected at the coarser scale by the extended finite element method analysis of the procedure shows that the method is consistent in power and yields a bulk stress strain response that is stable applications of this procedure to crack growth in heterogeneous materials are given copyright 2007 john wiley sons ltd

three dimensional continuation study of convection in a tilted rectangular enclosure a continuation method developed from a three dimensional spectral finite element code is used to study natural convection in a tilted rectangular cavity the cavity has its length equal to two times the side of its square cross section and it contains a fluid with a prandtl number mathrm pr 1 a detailed bifurcation diagram is first obtained in the case without inclination in order to get the sequence of the different branches of solutions and determine the stable solutions the focus is then put on the stable solutions in the inclined cavity when the tilt occurs around its longest axis the subtle changes induced by the tilt on the convective system are clarified three different stable solutions are obtained the longitudinal roll l ensuremath solution with the same sense of rotation as the inclination angle which develops smoothly from zero rayleigh number on the leading branch the longitudinal roll l solution with a sense of rotation opposite to the inclination angle which is on a disconnected branch and is stabilized beyond a secondary bifurcation point the oblique roll o ifmmode pm else textpm fi solutions corresponding to transverse roll solutions perturbed by the longitudinal flow induced by the tilt which quickly appear beyond saddle node points on new disconnected branches the domain of existence of these stable solutions is eventually obtained and described in the rayleigh number inclination parameter space finally the nusselt number is determined as a function of the inclination at a constant rayleigh number for the different stable solutions the nusselt number is maximum at an inclination of 49 55 ensuremath circ for the leading longitudinal roll l ensuremath solution

clustering objects on subsets of attributes with discussion read before the royal statistical society at a meeting organized by the research section on wednesday may 5th 2004 professor j t kent in the chair summary a new procedure is proposed for clustering attribute value data when used in conjunction with conventional distance based clustering algorithms this procedure encourages those algorithms to detect automatically subgroups of objects that preferentially cluster on subsets of the attribute variables rather than on all of them simultaneously the relevant attribute subsets for each individual cluster can be different and partially or completely overlap with those of other clusters enhancements for increasing sensitivity for detecting especially low cardinality groups clustering on a small subset of variables are discussed applications in different domains including gene expression arrays are presented