Analysis of and workarounds for element reversal for a finite element-based algorithm for warping triangular and tetrahedral meshes

We consider an algorithm called FEMWARP for warping triangular and tetrahedral finite element meshes that computes the warping using the finite element method itself. The algorithm takes as input a two- or three-dimensional domain defined by a boundary mesh (segments in one dimension or triangles in two dimensions) that has a volume mesh (triangles in two dimensions or tetrahedra in three dimensions) in its interior. It also takes as input a prescribed movement of the boundary mesh. It computes as output updated positions of the vertices of the volume mesh. The first step of the algorithm is to determine from the initial mesh a set of local weights for each interior vertex that describes each interior vertex in terms of the positions of its neighbors. These weights are computed using a finite element stiffness matrix. After a boundary transformation is applied, a linear system of equations based upon the weights is solved to determine the final positions of the interior vertices. The FEMWARP algorithm has been considered in the previous literature (e.g., in a 2001 paper by Baker). FEMWARP has been succesful in computing deformed meshes for certain applications. However, sometimes FEMWARP reverses elements; this is our main concern in this paper. We analyze the causes for this undesirable behavior and propose several techniques to make the method more robust against reversals. The most successful of the proposed methods includes combining FEMWARP with an optimization-based untangler.Comment: Revision of earlier version of paper. Submitted for publication in BIT Numerical Mathematics on 27 April 2010. Accepted for publication on 7 September 2010. Published online on 9 October 2010. The final publication is available at http://www.springerlink.co

Universal Scaling of Optimal Current Distribution in Transportation Networks

Transportation networks are inevitably selected with reference to their global cost which depends on the strengths and the distribution of the embedded currents. We prove that optimal current distributions for a uniformly injected d-dimensional network exhibit robust scale-invariance properties, independently of the particular cost function considered, as long as it is convex. We find that, in the limit of large currents, the distribution decays as a power law with an exponent equal to (2d-1)/(d-1). The current distribution can be exactly calculated in d=2 for all values of the current. Numerical simulations further suggest that the scaling properties remain unchanged for both random injections and by randomizing the convex cost functions.Comment: 5 pages, 5 figure

Associations among parental feeding styles and children's food intake in families with limited incomes

<p>Abstract</p> <p>Background</p> <p>Although general parenting styles and restrictive parental feeding practices have been associated with children's weight status, few studies have examined the association between feeding styles and proximal outcomes such as children's food intake, especially in multi-ethnic families with limited incomes. The purpose of this study was to evaluate the association of parental feeding styles and young children's evening food intake in a multiethnic sample of families in Head Start.</p> <p>Methods</p> <p>Participants were 715 Head Start children and their parents from Texas and Alabama representing three ethnic groups: African-American (43%), Hispanic (29%), and White (28%). The Caregivers Feeding Styles Questionnaire (Hughes) was used to characterize authoritative, authoritarian (referent), indulgent or uninvolved feeding styles. Food intake in several food groups was calculated from 3 days of dietary recalls for the child for evening food intakes from 3 PM until bedtime.</p> <p>Results</p> <p>Compared to children of authoritarian parents, intakes of fruits, juice and vegetables were lowest among children of indulgent or uninvolved parents (1.77 ± 0.09 vs 1.45 ± 0.09 and 1.42 ± 0.11 cups) as were intakes of dairy foods (0.84 ± 0.05 vs 0.67 ± 0.05 and 0.63+0.06 cups), respectively.</p> <p>Conclusion</p> <p>Findings suggest that permissive parent feeding styles like indulgent or uninvolved relate negatively to children's intake of nutrient-rich foods fruit, 100% fruit juice, vegetables and dairy foods from 3 PM until bedtime.</p

Assessment of surface roughness and blood rheology on local coronary hemodynamics: a multi-scale computational fluid dynamics study

The surface roughness of the coronary artery is associated with the onset of atherosclerosis. The study applies, for the first time, the micro-scale variation of the artery surface to a 3D coronary model, investigating the impact on haemodynamic parameters which are indicators for atherosclerosis. The surface roughness of porcine coronary arteries have been detailed based on optical microscopy and implemented into a cylindrical section of coronary artery. Several approaches to rheology are compared to determine the benefits/limitations of both single and multiphase models for multi-scale geometry. Haemodynamic parameters averaged over the rough/smooth sections are similar; however, the rough surface experiences a much wider range, with maximum wall shear stress greater than 6 Pa compared to the approximately 3 Pa on the smooth segment. This suggests the smooth-walled assumption may neglect important near-wall haemodynamics. While rheological models lack sufficient definition to truly encompass the micro-scale effects occurring over the rough surface, single-phase models (Newtonian and non-Newtonian) provide numerically stable and comparable results to other coronary simulations. Multiphase models allow for phase interactions between plasma and red blood cells which is more suited to such multi-scale models. These models require additional physical laws to govern advection/aggregation of particulates in the near-wall region

Whirling Hexagons and Defect Chaos in Hexagonal Non-Boussinesq Convection

We study hexagon patterns in non-Boussinesq convection of a thin rotating layer of water. For realistic parameters and boundary conditions we identify various linear instabilities of the pattern. We focus on the dynamics arising from an oscillatory side-band instability that leads to a spatially disordered chaotic state characterized by oscillating (whirling) hexagons. Using triangulation we obtain the distribution functions for the number of pentagonal and heptagonal convection cells. In contrast to the results found for defect chaos in the complex Ginzburg-Landau equation and in inclined-layer convection, the distribution functions can show deviations from a squared Poisson distribution that suggest non-trivial correlations between the defects.Comment: 4 mpg-movies are available at http://www.esam.northwestern.edu/~riecke/lit/lit.html submitted to New J. Physic

Robust Poisson Surface Reconstruction

Abstract. We propose a method to reconstruct surfaces from oriented point clouds with non-uniform sampling and noise by formulating the problem as a convex minimization that reconstructs the indicator func-tion of the surface’s interior. Compared to previous models, our recon-struction is robust to noise and outliers because it substitutes the least-squares fidelity term by a robust Huber penalty; this allows to recover sharp corners and avoids the shrinking bias of least squares. We choose an implicit parametrization to reconstruct surfaces of unknown topology and close large gaps in the point cloud. For an efficient representation, we approximate the implicit function by a hierarchy of locally supported basis elements adapted to the geometry of the surface. Unlike ad-hoc bases over an octree, our hierarchical B-splines from isogeometric analysis locally adapt the mesh and degree of the splines during reconstruction. The hi-erarchical structure of the basis speeds-up the minimization and efficiently represents clustered data. We also advocate for convex optimization, in-stead isogeometric finite-element techniques, to efficiently solve the min-imization and allow for non-differentiable functionals. Experiments show state-of-the-art performance within a more flexible framework.

The effect of tightly-bound water molecules on scaffold diversity in computer-aided de novo ligand design of CDK2 inhibitors

We have determined the effects that tightly bound water molecules have on the de novo design of cyclin-dependent kinase-2 (CDK2) ligands. In particular, we have analyzed the impact of a specific structural water molecule on the chemical diversity and binding mode of ligands generated through a de novo structure-based ligand generation method in the binding site of CDK2. The tightly bound water molecule modifies the size and shape of the binding site and we have found that it also imposed constraints on the observed binding modes of the generated ligands. This in turn had the indirect effect of reducing the chemical diversity of the underlying molecular scaffolds that were able to bind to the enzyme satisfactorily