Application of the log-conformation tensor to three-dimensional time-dependent free surface flows

The numerical simulation of flows of highly elastic fluids has been the subject of intense research over the past decades with important industrial applications. Therefore, many efforts have been made to improve the convergence capabilities of the numerical methods employed to simulate viscoelastic fluid flows. An important contribution for the solution of the High-Weissenberg Number Problem has been presented by Fattal and Kupferman [J. Non-Newton. Fluid. Mech. 123 (2004) 281-285] who developed the matrix-logarithm of the conformation tensor technique, henceforth called log-conformation tensor. Its advantage is a better approximation of the large growth of the stress tensor that occur in some regions of the flow and it is doubly beneficial in that it ensures physically correct stress fields, allowing converged computations at high Weissenberg number flows. In this work we investigate the application of the log-conformation tensor to three-dimensional unsteady free surface flows. The log-conformation tensor formulation was applied to solve the Upper-Convected Maxwell (UCM) constitutive equation while the momentum equation was solved using a finite difference Marker-and-Cell type method. The resulting developed code is validated by comparing the log-conformation results with the analytic solution for fully developed pipe flows. To illustrate the stability of the log-conformation tensor approach in solving three-dimensional free surface flows, results from the simulation of the extrudate swell and jet buckling phenomena of UCM fluids at high Weissenberg numbers are presented. (C) 2012 Elsevier B.V. All rights reserved.

A new registration method based on Log-Euclidean tensor metrics and its application to genetic studies

In structural brain MRI, group differences or changes in brain structures can be detected using Tensor-Based Morphometry (TBM). This method consists of two steps: (1) a non-linear registration step, that aligns all of the images to a common template, and (2) a subsequent statistical analysis. The numerous registration methods that have recently been developed differ in their detection sensitivity when used for TBM, and detection power is paramount in epidemological studies or drug trials. We therefore developed a new fluid registration method that computes the mappings and performs statistics on them in a consistent way, providing a bridge between TBM registration and statistics. We used the Log-Euclidean framework to define a new regularizer that is a fluid extension of the Riemannian elasticity, which assures diffeomorphic transformations. This regularizer constrains the symmetrized Jacobian matrix, also called the deformation tensor. We applied our method to an MRI dataset from 40 fraternal and identical twins, to revealed voxelwise measures of average volumetric differences in brain structure for subjects with different degrees of genetic resemblance.

Numerical study of driven flows of shear thinning viscoelastic fluids in rectangular cavities

In this work, we present a numerical study of flow of shear thinning viscoelastic fluids in rectangular lid driven cavities for a wide range of aspect ratios (depth to width ratio) varying from 1/16 to 4. In particular, the effect of elasticity, inertia, model parameters and polymer concentration on flow features in rectangular driven cavity has been studied for two shear thinning viscoelastic fluids, namely, Giesekus and linear PTT. We perform numerical simulations using the symmetric square root representation of the conformation tensor to stabilize the numerical scheme against the high Weissenberg number problem. The variation in flow structures associated with merging and splitting of elongated vortices in shallow cavities and coalescence of corner eddies to yield a second primary vortex in deep cavities with respect to the variation in flow parameters is discussed. We discuss the effect of the dominant eigenvalues and the corresponding eigenvectors on the location of the primary eddy in the cavity. We also demonstrate, by performing numerical simulations for shallow and deep cavities, that where the Deborah number (based on convective time scale) characterizes the elastic behaviour of the fluid in deep cavities, Weissenberg number (based on shear rate) should be used for shallow cavities. (C) 2016 Elsevier B.V. All rights reserved.

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids. (C) 2010 Elsevier B.V. All rights reserved.

Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.

Clustering of web users using the tensor decomposed models

We propose to use the Tensor Space Modeling (TSM) to represent and analyze the user’s web log data that consists of multiple interests and spans across multiple dimensions. Further we propose to use the decomposition factors of the Tensors for clustering the users based on similarity of search behaviour. Preliminary results show that the proposed method outperforms the traditional Vector Space Model (VSM) based clustering.

Comparison of fractional and geodesic anisotropy in diffusion tensor images of 90 monozygotic and dizygotic twins

We used diffusion tensor magnetic resonance imaging (DTI) to reveal the extent of genetic effects on brain fiber microstructure, based on tensor-derived measures, in 22 pairs of monozygotic (MZ) twins and 23 pairs of dizygotic (DZ) twins (90 scans). After Log-Euclidean denoising to remove rank-deficient tensors, DTI volumes were fluidly registered by high-dimensional mapping of co-registered MP-RAGE scans to a geometrically-centered mean neuroanatomical template. After tensor reorientation using the strain of the 3D fluid transformation, we computed two widely used scalar measures of fiber integrity: fractional anisotropy (FA), and geodesic anisotropy (GA), which measures the geodesic distance between tensors in the symmetric positive-definite tensor manifold. Spatial maps of intraclass correlations (r) between MZ and DZ twins were compared to compute maps of Falconer's heritability statistics, i.e. the proportion of population variance explainable by genetic differences among individuals. Cumulative distribution plots (CDF) of effect sizes showed that the manifold measure, GA, comparably the Euclidean measure, FA, in detecting genetic correlations. While maps were relatively noisy, the CDFs showed promise for detecting genetic influences on brain fiber integrity as the current sample expands.

Tensor-based analysis of genetic influences on brain integrity using DTI in 100 twins

Information from the full diffusion tensor (DT) was used to compute voxel-wise genetic contributions to brain fiber microstructure. First, we designed a new multivariate intraclass correlation formula in the log-Euclidean framework. We then analyzed used the full multivariate structure of the tensor in a multivariate version of a voxel-wise maximum-likelihood structural equation model (SEM) that computes the variance contributions in the DTs from genetic (A), common environmental (C) and unique environmental (E) factors. Our algorithm was tested on DT images from 25 identical and 25 fraternal twin pairs. After linear and fluid registration to a mean template, we computed the intraclass correlation and Falconer's heritability statistic for several scalar DT-derived measures and for the full multivariate tensors. Covariance matrices were found from the DTs, and inputted into SEM. Analyzing the full DT enhanced the detection of A and C effects. This approach should empower imaging genetics studies that use DTI.

Best individual template selection from deformation tensor minimization

We study the influence of the choice of template in tensor-based morphometry. Using 3D brain MR images from 10 monozygotic twin pairs, we defined a tensor-based distance in the log-Euclidean framework [1] between each image pair in the study. Relative to this metric, twin pairs were found to be closer to each other on average than random pairings, consistent with evidence that brain structure is under strong genetic control. We also computed the intraclass correlation and associated permutation p-value at each voxel for the determinant of the Jacobian matrix of the transformation. The cumulative distribution function (cdf) of the p-values was found at each voxel for each of the templates and compared to the null distribution. Surprisingly, there was very little difference between CDFs of statistics computed from analyses using different templates. As the brain with least log-Euclidean deformation cost, the mean template defined here avoids the blurring caused by creating a synthetic image from a population, and when selected from a large population, avoids bias by being geometrically centered, in a metric that is sensitive enough to anatomical similarity that it can even detect genetic affinity among anatomies.

Water regulation of actinomycin-D binding to DNA: the interplay among drug affinity, DNA long-range conformation, and hydration

Actiaomycin-D (actD) binds to natural DNA at two different classes of binding sites, weak and strong. The affinity for these sites is highly dependent on DNA se(sequence and solution conditions, and the interaction appears to be purely entropic driven Although the entropic character of this reaction has been attributed to the release of water molecules upon drug to DNA complex formation, the mechanism by which hydration regulates actD binding and discrimination between different classes of binding sites on natural DNA is still unknown. In this work, we investigate the role of hydration on this reaction using the osmotic stress method. We skew that the decrease of solution water activity, due to the addition of sucrose, glycerol ethylene glycol, and betaine, favors drug binding to the strong binding sites on DNA by increasing both the apparent binding affinity Delta G, and the number of DNA base pairs apparently occupied by the bound drug n(bp/actD). These binding parameters vary linearly with the logarithm of the molar fraction of water in solution log(X-w), which indicates the contribution of water binding to the energetic of the reaction. It is demonstrated that the hydration change measured upon binding increases proportionally to the apparent size of the binding site n(bp/uctD). This indicates that n(bp/actD) measured from the Scatchard plod is a measure of the size of the DNA molecule changing conformation due to ligand binding. We also find that the contribution of DNA deformation, gauged by n(bp/act) to the total free energy of binding Delta G, is given by Delta G = Delta G(local) + n(bp/actD) x delta G(DNA), where Delta G(local), = -8020 +/- 51 cal/mol of actD bound and delta G(DNa) = -24.1 +/- 1.7cal/mol of base pair at 25 degrees C. We interpret Delta G(local), as the energetic contribution due to the direct interactions of actD with the actual tetranucleotide binding site, and it n(bp/actB) X delta G(DNA) as that due to change inconformation, induced by binding, of it n(bp/actD) DNA base pairs flanking the local site. This interpretation is supported by the agreement found between the value of delta G(DNA) and the torsional free energy change measured independently. We conclude suggesting an allosteric model for ligand binding to DNA, such that the increase in binding affinity is achieved by increasing the relaxation of the unfavorable free energy of binding storage at the local site through a larger number of DNA base pairs. The new aspect on this model is that the size of the complex is not fixed but determined by solutions conditions, such as water activity, which modulate the energetic barrier to change helix conformation. These results may suggest that long-range allosteric transitions of duplex DNA are involved in the inhibition of RNA synthesis by actD, and more generally, in the regulation of transcription. (C) 2000 John Wiley & Sons, Inc.

Time series analysis of a Web search engine transaction log

In this paper, we use time series analysis to evaluate predictive scenarios using search engine transactional logs. Our goal is to develop models for the analysis of searchers’ behaviors over time and investigate if time series analysis is a valid method for predicting relationships between searcher actions. Time series analysis is a method often used to understand the underlying characteristics of temporal data in order to make forecasts. In this study, we used a Web search engine transactional log and time series analysis to investigate users’ actions. We conducted our analysis in two phases. In the initial phase, we employed a basic analysis and found that 10% of searchers clicked on sponsored links. However, from 22:00 to 24:00, searchers almost exclusively clicked on the organic links, with almost no clicks on sponsored links. In the second and more extensive phase, we used a one-step prediction time series analysis method along with a transfer function method. The period rarely affects navigational and transactional queries, while rates for transactional queries vary during different periods. Our results show that the average length of a searcher session is approximately 2.9 interactions and that this average is consistent across time periods. Most importantly, our findings shows that searchers who submit the shortest queries (i.e., in number of terms) click on highest ranked results. We discuss implications, including predictive value, and future research.