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

a model for simulating the deterioration of structural scale material responses of microheterogeneous solids abstract in this paper we develop a model to characterize the deterioration of mechanical responses of microheterogeneous solids due to progressive microstructural failure with increased loading in the approach the effects of microscopic failure so called relaxation are described by a variational boundary value problem with constraints on the microfields the extent of the relaxation which is induced by reducing the eigenvalues of the elasticity tensor at a point in the heterogeneous body is dictated by the condition that the solution must satisfy the equations of equilibrium and simultaneously the constraints at that point theoretical properties of the model are determined and a computational algorithm is developed to simulate the deterioration of the material microstructure numerical simulations involving the finite element method are given to illustrate various aspects of the model

direct estimation of the fiber orientation density function from diffusion weighted mri data using spherical deconvolution diffusion weighted magnetic resonance imaging can provide information related to the arrangement of white matter fibers the diffusion tensor is the model most commonly used to derive the orientation of the fibers within a voxel however this model has been shown to fail in regions containing several fiber populations with distinct orientations a number of alternative models have been suggested such as multiple tensor fitting q space and q ball imaging however each of these has inherent limitations in this study we propose a novel method for estimating the fiber orientation distribution directly from high angular resolution diffusion weighted mr data without the need for prior assumptions regarding the number of fiber populations present we assume that all white matter fiber bundles in the brain share identical diffusion characteristics thus implicitly assigning any differences in diffusion anisotropy to partial volume effects the diffusion weighted signal attenuation measured over the surface of a sphere can then be expressed as the convolution over the sphere of a response function the diffusion weighted attenuation profile for a typical fiber bundle with the fiber orientation density function odf the fiber odf the distribution of fiber orientations within the voxel can therefore be obtained using spherical deconvolution the properties of the technique are demonstrated using simulations and on data acquired from a volunteer using a standard 1 5 t clinical scanner the technique can recover the fiber odf in regions of multiple fiber crossing and holds promise for applications such as tractography

strain driven homogenization of inelastic microstructures and composites based on an incremental variational formulation the paper investigates computational procedures for the treatment of a homogenized macro continuum with locally attached micro structures of inelastic constituents undergoing small strains the point of departure is a general internal variable formulation that determines the inelastic response of the constituents of a typical micro structure as a generalized standard medium in terms of an energy storage and a dissipation function consistent with this type of inelasticity we develop a new incremental variational formulation of the local constitutive response where a quasi hyperelastic micro stress potential is obtained from a local minimization problem with respect to the internal variables it is shown that this local minimization problem determines the internal state of the material for finite increments of time we specify the local variational formulation for a setting of smooth single surface inelasticity and discuss its numerical solution based on a time discretization of the internal variables the existence of the quasi hyperelastic stress potential allows the extension of homogenization approaches of elasticity to the incremental setting of inelasticity focusing on macro strain driven micro structures we develop a new incremental variational formulation of the global homogenization problem where a quasi hyperelastic macro stress potential is obtained from a global minimization problem with respect to the fine scale displacement fluctuation field it is shown that this global minimization problem determines the state of the micro structure for finite increments of time we consider three different settings of the global variational problem for prescribed linear displacements periodic fluctuations and constant stresses on the boundary of the micro structure and discuss their numerical solutions based on a spatial discretization of the fine scale displacement fluctuation field the performance of the proposed methods is demonstrated for the model problem of von mises type elasto visco plasticity of the constituents and applied to a comparative study of micro to macro transitions of inelastic composites copyright 2002 john wiley sons ltd

displacement structure of w weighted drazin inverse ad w and its perturbation it is well known that matrices with a uv displacement structure possess generalized inverse with a vu displacement structure estimations for the displacement rank of a d wu va d w are presented where a d w is the w weighted drazin inverse of a we extend the results for the drazin inverse and group inverse respectively in the end the perturbation of w weighted drazin inverse a d w is studied

computational homogenization of microfractured continua using weakly periodic boundary conditions computational homogenization of elastic media with stationary cracks is considered whereby the macroscale stress is obtained by solving a boundary value problem on a statistical volume element sve and the cracks are represented by means of the extended finite element method xfem with the presence of cracks on the microscale conventional bcs dirichlet neumann strong periodic perform poorly in particular when cracks intersect the sve boundary as a remedy we herein propose to use a mixed variational format to impose periodic boundary conditions in a weak sense on the sve within this framework we develop a novel traction approximation that is suitable when cracks intersect the sve boundary our main result is the proposition of a stable traction approximation that is piecewise constant between crack boundary intersections in particular we prove analytically that the proposed approximation is stable in terms of the lbb inf sup condition and illustrate the stability properties with a numerical example we emphasize that the stability analysis is carried out within the setting of weakly periodic boundary conditions but it also applies to other mixed problems with similar structure e g contact problems the numerical examples show that the proposed traction approximation is more efficient than conventional boundary conditions dirichlet neumann strong periodic in terms of convergence with increasing sve size

comment on condition number of drazin inverse and their condition numbers of singular linear systems abstract in this paper we establish the condition number of drazin inverse of a singular matrix a where r a k r a k and k index a by the schur decomposition based on this form the spectral norm and frobenius norm of relative condition number for the drazin inverse and level 2 condition number of the drazin inverse are characterized the sensitivity for the drazin inverse solution of singular systems is also presented we obtain several formulas for the condition number of the drazin inverse by spectral norm instead of the p norm where p is a transformation matrix of the jordan canonical form of a thereby improving the earlier work y wei g wang d wang condition number of drazin inverse and their condition numbers of singular linear systems appl math comput 146 2003 455 467

mapping the orientation of intravoxel crossing fibers based on the phase information of diffusion circular spectrum a new method is presented to map the orientation of intravoxel crossing fibers by using the phase of the diffusion circular spectrum harmonics in a previous study zhan w gu h xu s silbersweig d a stern e yang y 2003 circular spectrum mapping for intravoxel fiber structures based on high angular resolution apparent diffusion coefficients magn reson med 49 1077 1088 we demonstrated that the magnitude of the 4th order harmonic of the diffusion circular spectrum can be used to identify the existence of fiber crossings however the orientation of the intravoxel crossing fibers remained unknown this study extends the diffusion circular spectrum mapping method so that it is able to identify the orientation of the intravoxel crossing fibers by utilizing the phase information of the circular spectrum in general the phase of the circular harmonic determines the rotation of the apparent diffusion coefficient adc profile on the sampling circle that is spanned by the major and medium eigenvector of the diffusion tensor and thus can be used to determine the orientation of the crossing fibers simulation results show that the regular tensor based major eigenvector maps have obvious artifacts in the fiber crossing area whereas the estimated crossing fibers by the proposed method are much more consistent with the orientation of the actual intravoxel fibers diffusion mri experiments were performed on five healthy human brains using a 3t scanner the brain regions with fiber crossings were selected by thresholding the magnitudes of the 4th order circular spectrum map intravoxel crossing fibers were estimated by the phase of the 4th order harmonic for each voxel within these areas the estimated intravoxel crossing fibers demonstrated a clear consistency with the orientations of fiber tracks in the surrounding tissues reducing the fiber orientation discontinuity of the regular major eigenvector map

the perturbation theory for the drazin inverse and its applications abstract let a and e be n n matrices and b a e denote the drazin inverse of a by ad we give an upper bound for the relative error b d a d a d under certain circumstances an error bound for the solution for the singular equations ax b b r a is also considered

a general framework for low level vision we introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented we consider intensity images as surfaces in the x i space the image is thereby a two dimensional 2 d surface in three dimensional 3 d space for gray level images and 2 d surfaces in five dimensions for color images the new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast and results in new and efficient schemes extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms

condition number of the w weighted drazin inverse abstract in this paper we get the explicit condition number formulas for the w weighted drazin inverse of a rectangular matrix using the schur decomposition and the spectral norm we characterize the spectral norm and the frobenius norm of the relative condition number of the w weighted drazin inverse and the level 2 condition number of the w weighted drazin inverse the sensitivity for the w weighted drazin inverse solution of linear systems is presented we also present the structured perturbation of the w weighted drazin inverse

the weighted drazin inverse of perturbed matrices with related support idempotents this paper deals with the perturbation of the w weighted drazin inverse a d w of rectangular matrices with related support idempotents a s w we characterize matrices b such that b s ww a s ww providing an algebraic structure for b and a formula for b d w similarly we obtain characterizations of rectangular matrices b such that wb s w wa s w we show two classes of perturbed matrices to which these results can be applied further we derive upper bounds for b d email protected and b d w a d email protected a d email protected finally we consider an application of our results to the perturbation of linear systems

a note on the perturbation of the w weighted drazin inverse the perturbation bound is presented for the w weighted drazin inverse for a rectangular matrix under the weaker condition the application to the singular linear equations is also given in this note

determinantal representations of the w weighted drazin inverse over the quaternion skew field within the framework of the theory of the column and row determinants we obtain new determinantal representations of the w weighted drazin inverse over the quaternion skew field we give determinantal representations of the w weighted drazin inverse by using previously introduced determinantal representations of the drazin inverse the moore penrose inverse and the limit representations of the w weighted drazin inverse in some special case

condition numbers and structured perturbation of the w weighted drazin inverse we give the explicit condition number formulas for the w weighted drazin inverse of a rectangular matrix we also present the structured perturbation of the w weighted drazin inverse and consider the perturbation for the w weighted drazin inverse of a rectangular matrix and give an explicit expression for the w weighted drazin inverse of a perturbed matrix under some certain conditions finally we discuss the minimum quality of the condition number

weighted g drazin inverses and a new pre order on rectangular matrices abstract this paper deals with weighted g drazin inverses which is a new class of matrices introduced to extend to the rectangular case g drazin inverses recently considered by wang and liu for square matrices first we define and characterize weighted g drazin inverses next we consider a new pre order defined on complex rectangular matrices based on weighted g drazin inverses finally we characterize this pre order and relate it to the minus partial order and to the weighted drazin pre order

mathematical methods for diffusion mri processing in this article we review recent mathematical models and computational methods for the processing of diffusion magnetic resonance images including state of the art reconstruction of diffusion models cerebral white matter connectivity analysis and segmentation techniques we focus on diffusion tensor images dti and q ball images qbi

segmentation of brain mr images through a hidden markov random field model and the expectation maximization algorithm the finite mixture fm model is the most commonly used model for statistical segmentation of brain magnetic resonance mr images because of its simple mathematical form and the piecewise constant nature of ideal brain mr images however being a histogram based model the fm has an intrinsic limitation no spatial information is taken into account this causes the fm model to work only on well defined images with low levels of noise unfortunately this is often not the the case due to artifacts such as partial volume effect and bias field distortion under these conditions fm model based methods produce unreliable results here the authors propose a novel hidden markov random field hmrf model which is a stochastic process generated by a mrf whose state sequence cannot be observed directly but which can be indirectly estimated through observations mathematically it can be shown that the fm model is a degenerate version of the hmrf model the advantage of the hmrf model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites although mrf modeling has been employed in mr image segmentation by other researchers most reported methods are limited to using mrf as a general prior in an fm model based approach to fit the hmrf model an em algorithm is used the authors show that by incorporating both the hmrf model and the em algorithm into a hmrf em framework an accurate and robust segmentation can be achieved more importantly the hmrf em framework can easily be combined with other techniques as an example the authors show how the bias field correction algorithm of guillemaud and brady 1997 can be incorporated into this framework to achieve a three dimensional fully automated approach for brain mr image segmentation

on the implementation of rate independent standard dissipative solids at finite strain variational constitutive updates this paper is concerned with an efficient variationally consistent implementation for rate independent dissipative solids at finite strain more precisely focus is on finite strain plasticity theory based on a multiplicative decomposition of the deformation gradient adopting the formalism of standard dissipative solids which allows to describe constitutive models by means of only two potentials being the helmholtz energy and the yield function or equivalently a dissipation functional finite strain plasticity is recast into an equivalent minimization problem in contrast to previous models the presented framework covers isotropic and kinematic hardening as well as isotropic and anisotropic elasticity and yield functions based on this approach a novel numerical implementation representing the main contribution of the paper is given in sharp contrast to by now classical approaches such as the return mapping algorithm and analogously to the theoretical part the numerical formulation is variationally consistent i e all unknown variables follow naturally from minimizing the energy of the considered system consequently several different numerically efficient and robust optimization schemes can be directly employed for solving the resulting minimization problem extending previously published works on variational constitutive updates the advocated model does not rely on any material symmetry and therefore it can be applied to a broad range of different plasticity theories as two examples an anisotropic hill type and a barlat type model are implemented numerical examples demonstrate the applicability and the performance of the proposed implementation

additive results for the wg drazin inverse abstract in this paper we prove the formula for the expression a b d w in terms of a b w a d w b d w assuming some conditions for a b and w here s d w denotes the generalized w weighted drazin inverse of a linear bounded operator s on a banach space

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

single and multiple shell uniform sampling schemes for diffusion mri using spherical codes in diffusion mri dmri a good sampling scheme is important for efficient acquisition and robust reconstruction diffusion weighted signal is normally acquired on single or multiple shells in q space signal samples are typically distributed uniformly on different shells to make them invariant to the orientation of structures within tissue or the laboratory coordinate frame the electrostatic energy minimization eem method originally proposed for single shell sampling scheme in dmri was recently generalized to multi shell schemes called generalized eem geem geem has been successfully used in the human connectome project however eem does not directly address the goal of optimal sampling i e achieving large angular separation between sampling points in this paper we propose a more natural formulation called spherical code sc to directly maximize the minimal angle between different samples in single or multiple shells we consider not only continuous problems to design single or multiple shell sampling schemes but also discrete problems to uniformly extract sub sampled schemes from an existing single or multiple shell scheme and to order samples in an existing scheme we propose five algorithms to solve the above problems including an incremental sc isc a sophisticated greedy algorithm called iterative maximum overlap construction imoc an 1 opt greedy method a mixed integer linear programming method and a constrained non linear optimization method to our knowledge this is the first work to use the sc formulation for single or multiple shell sampling schemes in dmri experimental results indicate that sc methods obtain larger angular separation and better rotational invariance than the state of the art eem and geem the related codes and a tutorial have been released in dmritool 1 1 https diffusionmritool github io tutorial qspacesampling html

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

localization aligned weakly periodic boundary conditions when computing the homogenized response of a representative volume element rve a popular choice is to impose periodic boundary conditions on the rve despite their popularity it is well known that standard periodic boundary conditions lead to inaccurate results if cracks or localization bands in the rve are not aligned with the periodicity directions a previously proposed remedy is to use modified strong periodic boundary conditions that are aligned with the dominating localization direction in the rve in the present work we show that alignment of periodic boundary conditions can also conveniently be performed on weak form starting from a previously proposed format for weak micro periodicity that does not require a periodic mesh we show that aligned weakly periodic boundary conditions may be constructed by only modifying the mapping mirror function between the associated parts of the rve boundary in particular we propose a modified mirror function that allows alignment with an identified localization direction this modified mirror function corresponds to a shifted stacking of rves and thereby ensures compatibility of the dominating discontinuity over the rve boundaries the proposed method leads to more accurate results compared to using unaligned periodic boundary conditions as demonstrated by the numerical examples

stabilized lagrange multiplier methods for bilateral elastic contact with friction in most finite element fe codes contact is checked only at the nodes corresponding to the use of pointwise constraints however this approach might not be stable in case the bodies coming into contact have non matching grids at the contact interface to alleviate this problem we propose a stabilized lagrange multiplier method based on a global polynomial multiplier for the finite element solution of non linear elastic contact problems with non matching grids in particular our approach allows us to avoid integrating products of different finite element basis functions on the surface meshes at the contact zone

fibertract segmentation in position orientation space from high angular resolution diffusion mri in diffusion mri standard approaches for fibertract identification are based on algorithms that generate lines of coherent diffusion currently known as tractography a tract is then identified as a set of such lines selected on some criteria in the present study we investigate whether fibertract identification can be formulated as a segmentation task that recognizes a fibertract as a region where diffusion is intense and coherent indeed we show that it is possible to segment efficiently well known fibertracts with classical image processing methods provided that the problem is formulated in a five dimensional space of position and orientation as an example we choose to adapt to this newly defined high dimensional non euclidean space called position orientation space an algorithm based on the hidden markov random field framework structures such as the cerebellar peduncles corticospinal tract association bundles can be identified and represented in three dimensions by a back projection technique similar to maximum intensity projection potential advantages and drawbacks as compared to classical tractography are discussed for example it appears that our formulation handles naturally crossing tracts and is not biased by human intervention

vector least squares solutions for coupled singular matrix equations the weighted least squares solutions of coupled singular matrix equations are too difficult to obtain by applying matrices decomposition in this paper a family of algorithms are applied to solve these problems based on the kronecker structures subsequently we construct a computationally efficient solutions of coupled restricted singular matrix equations furthermore the need to compute the weighted drazin and weighted moore penrose inverses and the use of tian s work and lev ari s results are due to appearance in the solutions of these problems the several special cases of these problems are also considered which includes the well known coupled sylvester matrix equations finally we recover the iterative methods to the weighted case in order to obtain the minimum d norm g vector least squares solutions for the coupled sylvester matrix equations and the results lead to the least squares solutions and invertible solutions as a special case

non convex potentials and microstructures in finite strain plasticity a mathematical model for a finite strain elastoplastic evolution problem is proposed in which one time step of an implicit time discretization leads to generally non convex minimization problems the elimination of all internal variables enables a mathematical and numerical analysis of a reduced problem within the general framework of calculus of variations and nonlinear partial differential equations the results for a single slip system and von mises plasticity illustrate that finite strain elastoplasticity generates reduced problems with non quasiconvex energy densities and so allows for non attainment of energy minimizers and microstructures

computational homogenization based on a weak format of micro periodicity for rve problems computational homogenization with a priori assumed scale separation is considered whereby the macroscale stress is obtained via averaging on representative volume elements rve s a novel variational formulation of the rve problem based on the assumption of weak micro periodicity of the displacement fluctuation field is proposed notably independent fe discretization of boundary tractions lagrange multipliers allows for a parameterized transition between the conventional strong periodicity and neumann boundary conditions in this paper the standard situation of macroscale strain control is considered numerical results demonstrate the convergence properties with respect to 1 the approximation of displacement and tractions and 2 the rve size for random realizations of the microstructure

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

variationally consistent computational homogenization of transient heat flow a framework for variationally consistent homogenization combined with a generalized macrohomogeneity condition is exploited for the analysis of non linear transient heat conduction within this framework the classical approach of model based first order homogenization for stationary problems is extended to transient problems homogenization is then carried out in the spatial domain on representative volume elements rve which are in practice introduced in quadrature points in standard fashion along with the classical averages a higher order conservation quantity is obtained an iterative fe2 algorithm is devised for the case of non linear diffusion and storage coefficients and it is applied to transient heat conduction in a strongly heterogeneous particle composite parametric studies are carried out in particular with respect to the influence of the internal length associated with the second order conservation quantity copyright c 2009 john wiley sons ltd

a weighted drazin inverse and applications abstract in this paper the notation of the cline greville w weighted drazin inverse of a rectangular matrix is extended to bounded linear operators between banach spaces we give new characterizations of the w weighted drazin inverse and we study the perturbations and the the continuity of the w weighted drazin inverse

a characterization for the w weighted drazin inverse and a cramer rule for the w weighted drazin inverse solution we establish characterization for the w weighted drazin inverse of an arbitrary rectangular matrix which reduces to the well known result if the matrix is nonsingular also a cramer rule for finding the unique w weighted drazin inverse solution x r aw k 1 of special restricted linear equationswawx b b r wa k 2 is presented and reduces to the classical cramer rule if a is invertible

integral representation of the w weighted drazin inverse two integral representations are presented for the w weighted drazin inverse a d w of rectangular matrices a w the first one has some restriction on the eigenvalues of aw or wa the second one holds without any restriction on the eigenvalues

atlas based fiber bundle segmentation using principal diffusion directions and spherical harmonic coefficients abstract purpose to develop an automatic atlas based method for segmentation of fiber bundles using high angular resolution diffusion imaging hardi data hypothesis quantitative evaluation of diffusion characteristics inside specific fiber bundles provides new insights into disease developments evolutions therapy effects and surgical interventions background most of previous segmentation methods use similarity measures and strategies that do not lead to accurate segmentation results they also suffer from subjectivity of initial seeds and regions of interest roi defined by operator materials and methods we propose a novel method that uses spherical harmonic coefficients shc of hardi diffusion signals to compute orientation distribution function odf and to extract principal diffusion directions pdds the proposed method selects most collinear pdd of neighbors of each voxel then based on shc and selected pdd a similarity measure is proposed and used as a speed function in the level set framework that segments fiber bundles to automate the process an atlas based method is used to select initial seeds for fiber bundles to generate data for evaluation of the proposed method an artificial pattern consisting of three crossing bundles intersected by a circular bundle is created also two normal controls are imaged by two different hardi protocols results segmentation results for different fiber bundles in simulated data and normal control data are presented influence of threshold selection on the proposed segmentation method is evaluated using dice coefficient also effect of increasing the number of gradient directions on accuracy of extracted pdds is evaluated conclusion the proposed segmentation method has advantages over previous methods especially those that use similarity measures based on diffusion tensor imaging dti data these advantages are achieved by proper propagation of a hyper surface in fiber crossing areas without making assumptions about diffusivity profile and selection of initial seeds or roi

an error analysis of white matter tractography methods synthetic diffusion tensor field simulations white matter tractography using diffusion tensor mr images is a promising method for estimating the pathways of white matter tracts in the human brain the success of this method ultimately depends upon the accuracy of the white matter tractography algorithms in this study a monte carlo simulation was used to investigate the impact of snr tensor anisotropy and diffusion tensor encoding directions on the accuracy of six tractography algorithms the accuracy was assessed in straight and curved tracts and tract geometries with divergence properties in general the tract dispersion increased with distance and decreased with snr and anisotropy the tract orientation with respect to the encoding scheme also influenced tract dispersion divergent tract geometries increased tract dispersion whereas convergent tract geometries reduced dispersion analytic models of tract dispersion were constructed as a function of the tract distance snr eigenvalues of the tracts voxel size and the relationship between the tract direction and the diffusion tensor encoding directions in certain cases the mean tract trajectory was found to deviate from the ideal pathway for curved trajectories analytical models of mean displacement were constructed as a function of the curvature tract distance step size and tensor eigenvalues these models may be used in future studies to assess the level of confidence associated with a tractography result

multi scale constitutive modelling of heterogeneous materials with a gradient enhanced computational homogenization scheme a gradient enhanced computational homogenization procedure that allows for the modelling of microstructural size effects is proposed within a general non linear framework in this approach the macroscopic deformation gradient tensor and its gradient are imposed on a microstructural representative volume element rve this enables us to incorporate the microstructural size and to account for non uniform macroscopic deformation fields within the microstructural cell every microstructural constituent is modelled as a classical continuum and the rve problem is formulated in terms of standard equilibrium and boundary conditions from the solution of the microstructural boundary value problem the macroscopic stress tensor and the higher order stress tensor are derived based on an extension of the hill mandel condition this automatically delivers the microstructurally based constitutive response of the higher order macro continuum and deals with the microstructural size in a natural way several examples illustrate the approach particularly the microstructural size effects

the variational formulation of viscoplastic constitutive updates we present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as finite elastic and plastic deformations non newtonian viscosity rate sensitivity and arbitrary flow and hardening rules the distinguishing characteristic of the proposed constitutive updates is that by construction the corresponding incremental stress strain relations derive from a pseudo elastic strain energy density this in turn confers the incremental boundary value problem a variational structure in particular the incremental deformation mapping follows from a minimum principle this minimum principle may conveniently be taken as a basis for error estimation and mesh adaption the accuracy and robustness of the variational constitutive updates is demonstrated with the aid of convergence tests involving the finitely deforming mises solid and ductile single crystals the ability of the updates to resolve the complex patterns of slip activity which arise in the latter application is particularly noteworthy