On the lower bound on the exchange-correlation energy in two dimensions

We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature. (c) 2009 Elsevier B.V. All rights reserved.

A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.

On E-functions of semisimple Lie groups

We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group G as their expansions into series of special functions that are invariant under the action of the even subgroup of the Weyl group of G. We distinguish two cases of even Weyl groups-one is the direct product of even Weyl groups of simple components of G and the second is the full even Weyl group of G. The problem is rather simple in two dimensions. It is much richer in dimensions greater than two-we describe in detail E-transforms of semisimple Lie groups of rank 3.

Comparison between two surgical techniques for root coverage with an acellular dermal matrix graft

Aim: The aim of this randomized, controlled, clinical study was to compare two surgical techniques with the acellular dermal matrix graft (ADMG) to evaluate which technique could provide better root coverage. Material and Methods: Fifteen patients with bilateral Miller Class I gingival recession areas were selected. In each patient, one recession area was randomly assigned to the control group, while the contra-lateral recession area was assigned to the test group. The ADMG was used in both groups. The control group was treated with a broader flap and vertical-releasing incisions, and the test group was treated with the proposed surgical technique, without releasing incisions. The clinical parameters evaluated before the surgeries and after 12 months were: gingival recession height, probing depth, relative clinical attachment level and the width and thickness of keratinized tissue. Results: There were no statistically significant differences between the groups for all parameters at baseline. After 12 months, there was a statistically significant reduction in recession height in both groups, and there was no statistically significant difference between the techniques with regard to root coverage. Conclusions: Both surgical techniques provided significant reduction in gingival recession height after 12 months, and similar results in relation to root coverage.

Longitudinal Study of Growth of Children With Unilateral Cleft-Lip Palate From Birth to Two Years of Age

Objective: To study the growth of children with complete unilateral cleft lip and palate (UCLP) from birth to 2 years of age and to construct specific UCLP growth curves. Design: Physical growth was a secondary outcome measure of a National Institutes of Health-sponsored longitudinal, prospective clinical trial involving the University of Florida (United States) and the University of Sao Paulo (Brazil). Patients: Six hundred twenty-seven children with UCLP, nonsyndromic, both genders. Methods: Length, weight, and head circumference were prospectively measured for a group of children enrolled in a clinical trial. Median growth curves for the three parameters (length, weight, head circumference) were performed and compared with the median for the National Center for Health Statistics (NCHS) curves. The median values for length, weight, and head circumference at birth and 6, 12, 18, and 24 months of age were plotted against NCHS median values and statistically compared at birth and 24 months. Setting: Hospital de Reabilitacao de Anomalias Craniofaciais, Universidade de Sao Paulo, Bauru, Brazil (HRAC-USP). Results: At birth, children of both genders with UCLP presented with smaller body dimensions in relation to NCHS median values, but the results suggest a catch-up growth for length, weight, and head circumference for girls and for weight (to some degree) and head circumference for boys. Conclusions: Weight was the most compromised parameter for both genders, followed by length and then head circumference. There was no evidence of short stature. This study established growth curves for children with UCLP.

THE VORONOI TESSELLATION CLUSTER FINDER IN 2+1 DIMENSIONS

We present a detailed description of the Voronoi Tessellation (VT) cluster finder algorithm in 2+1 dimensions, which improves on past implementations of this technique. The need for cluster finder algorithms able to produce reliable cluster catalogs up to redshift 1 or beyond and down to 10(13.5) solar masses is paramount especially in light of upcoming surveys aiming at cosmological constraints from galaxy cluster number counts. We build the VT in photometric redshift shells and use the two-point correlation function of the galaxies in the field to both determine the density threshold for detection of cluster candidates and to establish their significance. This allows us to detect clusters in a self-consistent way without any assumptions about their astrophysical properties. We apply the VT to mock catalogs which extend to redshift 1.4 reproducing the ACDM cosmology and the clustering properties observed in the Sloan Digital Sky Survey data. An objective estimate of the cluster selection function in terms of the completeness and purity as a function of mass and redshift is as important as having a reliable cluster finder. We measure these quantities by matching the VT cluster catalog with the mock truth table. We show that the VT can produce a cluster catalog with completeness and purity > 80% for the redshift range up to similar to 1 and mass range down to similar to 10(13.5) solar masses.

On the superfield effective potential in three dimensions

We develop the superfield approach to the effective potential in three dimensions and calculate the one-loop and two-loop Kahlerian effective potential in commutative and noncommutative cases. (C) 2009 Published by Elsevier B.V.

Two- and three-dimensional shape fabric analysis by the intercept method in grey levels

The count intercept is a robust method for the numerical analysis of fabrics Launeau and Robin (1996). It counts the number of intersections between a set of parallel scan lines and a mineral phase, which must be identified on a digital image. However, the method is only sensitive to boundaries and therefore supposes the user has some knowledge about their significance. The aim of this paper is to show that a proper grey level detection of boundaries along scan lines is sufficient to calculate the two-dimensional anisotropy of grain or crystal distributions without any particular image processing. Populations of grains and crystals usually display elliptical anisotropies in rocks. When confirmed by the intercept analysis, a combination of a minimum of 3 mean length intercept roses, taken on 3 more or less perpendicular sections, allows the calculation of 3-dimensional ellipsoids and the determination of their standard deviation with direction and intensity in 3 dimensions as well. The feasibility of this quick method is attested by numerous examples on theoretical objects deformed by active and passive deformation, on BSE images of synthetic magma flow, on drawing or direct analysis of thin section pictures of sandstones and on digital images of granites directly taken and measured in the field. (C) 2010 Elsevier B.V. All rights reserved.

Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation

We investigate several two-dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed. We first present two dynamic programming based algorithms for the Rectangular Knapsack (RK) problem and its variants in which the patterns must be staged. The first algorithm solves the recurrence formula proposed by Beasley; the second algorithm - for staged patterns - also uses a recurrence formula. We show that if the items are not so small compared to the dimensions of the bin, then these algorithms require polynomial time. Using these algorithms we solved all instances of the RK problem found at the OR-LIBRARY, including one for which no optimal solution was known. We also consider the Two-dimensional Cutting Stock problem. We present a column generation based algorithm for this problem that uses the first algorithm above mentioned to generate the columns. We propose two strategies to tackle the residual instances. We also investigate a variant of this problem where the bins have different sizes. At last, we study the Two-dimensional Strip Packing problem. We also present a column generation based algorithm for this problem that uses the second algorithm above mentioned where staged patterns are imposed. In this case we solve instances for two-, three- and four-staged patterns. We report on some computational experiments with the various algorithms we propose in this paper. The results indicate that these algorithms seem to be suitable for solving real-world instances. We give a detailed description (a pseudo-code) of all the algorithms presented here, so that the reader may easily implement these algorithms. (c) 2007 Elsevier B.V. All rights reserved.