Data management study, volume 5. Appendix K - Contractor data package data management /DM/ Final report

Contractor data management system for Voyager projec

Wetting and Minimal Surfaces

We study minimal surfaces which arise in wetting and capillarity phenomena. Using conformal coordinates, we reduce the problem to a set of coupled boundary equations for the contact line of the fluid surface, and then derive simple diagrammatic rules to calculate the non-linear corrections to the Joanny-de Gennes energy. We argue that perturbation theory is quasi-local, i.e. that all geometric length scales of the fluid container decouple from the short-wavelength deformations of the contact line. This is illustrated by a calculation of the linearized interaction between contact lines on two opposite parallel walls. We present a simple algorithm to compute the minimal surface and its energy based on these ideas. We also point out the intriguing singularities that arise in the Legendre transformation from the pure Dirichlet to the mixed Dirichlet-Neumann problem.Comment: 22 page

Simulating the Mammalian Blastocyst - Molecular and Mechanical Interactions Pattern the Embryo

Mammalian embryogenesis is a dynamic process involving gene expression and mechanical forces between proliferating cells. The exact nature of these interactions, which determine the lineage patterning of the trophectoderm and endoderm tissues occurring in a highly regulated manner at precise periods during the embryonic development, is an area of debate. We have developed a computational modeling framework for studying this process, by which the combined effects of mechanical and genetic interactions are analyzed within the context of proliferating cells. At a purely mechanical level, we demonstrate that the perpendicular alignment of the animal-vegetal (a-v) and embryonic-abembryonic (eb-ab) axes is a result of minimizing the total elastic conformational energy of the entire collection of cells, which are constrained by the zona pellucida. The coupling of gene expression with the mechanics of cell movement is important for formation of both the trophectoderm and the endoderm. In studying the formation of the trophectoderm, we contrast and compare quantitatively two hypotheses: (1) The position determines gene expression, and (2) the gene expression determines the position. Our model, which couples gene expression with mechanics, suggests that differential adhesion between different cell types is a critical determinant in the robust endoderm formation. In addition to differential adhesion, two different testable hypotheses emerge when considering endoderm formation: (1) A directional force acts on certain cells and moves them into forming the endoderm layer, which separates the blastocoel and the cells of the inner cell mass (ICM). In this case the blastocoel simply acts as a static boundary. (2) The blastocoel dynamically applies pressure upon the cells in contact with it, such that cell segregation in the presence of differential adhesion leads to the endoderm formation. To our knowledge, this is the first attempt to combine cell-based spatial mechanical simulations with genetic networks to explain mammalian embryogenesis. Such a framework provides the means to test hypotheses in a controlled in silico environment

Mappings of least Dirichlet energy and their Hopf differentials

The paper is concerned with mappings between planar domains having least Dirichlet energy. The existence and uniqueness (up to a conformal change of variables in the domain) of the energy-minimal mappings is established within the class $\bar{\mathscr H}_2(X, Y)$ of strong limits of homeomorphisms in the Sobolev space $W^{1,2}(X, Y)$, a result of considerable interest in the mathematical models of Nonlinear Elasticity. The inner variation leads to the Hopf differential $h_z \bar{h_{\bar{z}}} dz \otimes dz$ and its trajectories. For a pair of doubly connected domains, in which $X$ has finite conformal modulus, we establish the following principle: A mapping $h \in \bar{\mathscr H}_2(X, Y)$ is energy-minimal if and only if its Hopf-differential is analytic in $X$ and real along the boundary of $X$. In general, the energy-minimal mappings may not be injective, in which case one observes the occurrence of cracks in $X$. Nevertheless, cracks are triggered only by the points in the boundary of $Y$ where $Y$ fails to be convex. The general law of formation of cracks reads as follows: Cracks propagate along vertical trajectories of the Hopf differential from the boundary of $X$ toward the interior of $X$ where they eventually terminate before making a crosscut.Comment: 51 pages, 4 figure

Strong-Segregation Theory of Bicontinuous Phases in Block Copolymers

We compute phase diagrams for $A_nB_m$ starblock copolymers in the strong-segregation regime as a function of volume fraction $\phi$, including bicontinuous phases related to minimal surfaces (G, D, and P surfaces) as candidate structures. We present the details of a general method to compute free energies in the strong segregation limit, and demonstrate that the gyroid G phase is the most nearly stable among the bicontinuous phases considered. We explore some effects of conformational asymmetry on the topology of the phase diagram.Comment: 14 pages, latex, 21 figures, to appear in Macromolecule

Reorganizing the Intrinsic Functional Architecture of the Human Primary Motor Cortex during Rest with Non-Invasive Cortical Stimulation

The primary motor cortex (M1) is the main effector structure implicated in the generation of voluntary movements and is directly involved in motor learning. The intrinsic horizontal neuronal connections of M1 exhibit short-term and long-term plasticity, which is a strong substrate for learning-related map reorganization. Transcranial direct current stimulation (tDCS) applied for few minutes over M1 has been shown to induce relatively long-lasting plastic alterations and to modulate motor performance. Here we test the hypothesis that the relatively long-lasting synaptic modification induced by tDCS over M1 results in the alteration of associations among populations of M1 neurons which may be reflected in changes of its functional architecture. fMRI resting-state datasets were acquired immediately before and after 10 minutes of tDCS during rest, with the anode/cathode placed over the left M1. For each functional dataset, grey-matter voxels belonging to Brodmann area 4 (BA4) were labelled and afterwards BA4 voxel-based synchronization matrices were calculated and thresholded to construct undirected graphs. Nodal network parameters which characterize the architecture of functional networks (connectivity degree, clustering coefficient and characteristic path-length) were computed, transformed to volume maps and compared before and after stimulation. At the dorsolateral-BA4 region cathodal tDCS boosted local connectedness, while anodal-tDCS enhanced long distance functional communication within M1. Additionally, the more efficient the functional architecture of M1 was at baseline, the more efficient the tDCS-induced functional modulations were. In summary, we show here that it is possible to non-invasively reorganize the intrinsic functional architecture of M1, and to image such alterations

Gas chemical investigation of hafnium and zirconium complexes with hexafluoroacetylacetone using preseparated short-lived radioisotopes

Volatile metal complexes of the group 4 elements Zr and Hf with hexafluoroacetylacetonate (hfa) have been studied using short-lived radioisotopes of the metals. The new technique of physical preseparation has been employed where reaction products from heavy-ion induced fusion reactions are isolated in a physical recoil separator - the Berkeley Gas-filled Separator in our work - and made available for chemistry experiments. Formation and decomposition of M(hfa)4 (M=Zr, Hf) has been observed and the interaction strength with a fluorinated ethylene propylene (FEP) Teflon surface has been studied. From the results of isothermal chromatography experiments, an adsorption enthalpy of -ΔHa=(57±3)kJ/mol was deduced. In optimization experiments, the time for formation of the complex and its transport to a counting setup installed outside of the irradiation cave was minimized and values of roughly one minute have been reached. The half-life of 165Hf, for which conflicting values appear in the literature, was measured to be (73.9±0.8)s. Provided that samples suitable for α-spectroscopy can be prepared, the investigation of rutherfordium (Rf), the transactinide member of group 4, appears possible. In the future, based on the studies presented here, it appears possible to investigate short-lived single atoms produced with low rates ( e.g. , transactinide isotopes) in completely new chemical systems, e.g. , as metal complexes with organic ligands as used here or as organometallic compound

Motion of a vortex sheet on a sphere with pole vortices

We cons i der the motion of a vortex sheet on the surface of a unit sphere in the presence of point vortices xed on north and south poles.Analytic and numerical research revealed that a vortex sheet in two-dimensional space has the following three properties.First,the vortex sheet is linearly unstable due to Kelvin-Helmholtz instability.Second,the curvature of the vortex sheet diverges in nite time.Last,the vortex sheet evolves into a rolling-up doubly branched spiral,when the equation of motion is regularized by the vortex method.The purpose of this article is to investigate how the curvature of the sphere and the presence of the pole vortices

Cross Section Limits for the 208^{208}Pb(86^{86}Kr,n)293^{293}118 Reaction

In April-May, 2001, the previously reported experiment to synthesize element 118 using the $^{208}$Pb($^{86}$Kr,n)$^{293}$118 reaction was repeated. No events corresponding to the synthesis of element 118 were observed with a total beam dose of 2.6 x 10$^{18}$ ions. The simple upper limit cross sections (1 event) were 0.9 and 0.6 pb for evaporation residue magnetic rigidities of 2.00 $T m$ and 2.12 $T m$, respectively. A more detailed cross section calculation, accounting for an assumed narrow excitation function, the energy loss of the beam in traversing the target and the uncertainty in the magnetic rigidity of the Z=118 recoils is also presented. Re-analysis of the primary data files from the 1999 experiment showed the reported element 118 events are not in the original data. The current results put constraints on the production cross section for synthesis of very heavy nuclei in cold fusion reactions.Comment: 7 pages, 2 figures. Submitted to EPJ

Analysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data

We prove the inf-sup stability of a discontinuous Galerkin scheme for second order elliptic operators in (unbalanced) mesh-dependent norms for quasi-uniform meshes for all spatial dimensions. This results in a priori error bounds in these norms. As an application we examine some problems with rough source term where the solution can not be characterised as a weak solution and show quasi-optimal error control