Minimal surfaces in nuclear pasta with the Time-Dependent Hartree-Fock approach

In continuation to the studies of the whole variety of pasta shapes in [1], we present here calculations performed with the Hartree-Fock and time-dependent Hartree- Fock method concerning the mid-density range of pasta shapes: The slab-like, connected rod-like (p-surface) and the gyroidal shapes. On the one hand we present simulations of the dynamic formation of these shapes at fi- nite temperature. On the other hand we calculate the binding energies of these shapes for varying simulation box lengths and mean densities. All of these shapes are found to be at least metastable. The slab shape has a slightly lower energy because of the lack of curvature, but among these three configurations the gyroidal shape is metastable for the widest range in mean density

Choline: The Neurocognitive Essential Nutrient of Interest to Obstetricians and Gynecologists

Choline is an essential nutrient for proper liver, muscle, and brain functions as well as for lipid metabolism and cellular membrane composition and repair. Humans can produce small amounts of choline via the hepatic phosphatidylethanolamine N-methyltransferase pathway; however, most individuals must consume this vitamin through the diet to prevent deficiency. An individual’s dietary requirement for choline is dependent on common genetic variants in genes required for choline, folate, and one-carbon metabolism. Both the American Academy of Pediatrics and American Medical Association have recently reinforced the importance of maternal choline intake during pregnancy and lactation and recognize that failure to provide choline and other key essential nutrients during the first 1,000 days postconception may result in lifelong deficits in brain function despite subsequent nutrient repletion. Given that dietary intake for the majority of the US population, including subpopulations such as pregnant women, women of childbearing age, and vegetarians, falls well below the current adequate intake, there is a need to develop better policies and improve consumer education around the importance of this essential nutrient for human health. This comprehensive expert review summarizes the current scientific evidence on choline and health in relation to interests of obstetricians and gynecologists

Universal hidden order in amorphous cellular geometries

Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile space are preferred. We employ Lloyd’s centroidal Voronoi diagram algorithm to solve this problem and find that it converges to disordered states associated with deep local minima. These states are universal in the sense that their structure factors are characterised by a complete independence of a wide class of initial conditions they evolved from. They moreover exhibit an anomalous suppression of long-wavelength density fluctuations and quickly become effectively hyperuniform. Our findings warrant the search for novel amorphous hyperuniform phases and cellular materials with unique physical properties

The underconsumed and underappreciated essential nutrient

Choline has been recognized as an essential nutrient by the Food and Nutrition Board of the National Academies of Medicine since 1998. Its metabolites have structural, metabolic, and regulatory roles within the body. Humans can endogenously produce small amounts of choline via the hepatic phosphatidylethanolamine N-methyltransferase pathway. However, the nutrient must be consumed exogenously to prevent signs of deficiency. The Adequate Intake (AI) for choline was calculated at a time when dietary intakes across the populationwere unknown for the nutrient. Unlike the traditional National Academy of Medicine approach of calculating an AI based on observed or experimentally determined approximations or estimates of intake by a group (or groups) of healthy individuals, calculation of the AI for choline was informed in part by a depletionrepletion study in adultmen who, upon becoming deficient, developed signs of liver damage. The AI for other gender and life-stage groups was calculated based on standard reference weights, except for infants 0 to 6 months, whose AI reflects the observedmean intake from consuming human breast milk. Recent analyses indicate that large portions of the population (ie, approximately 90% of Americans), including most pregnant and lactating women, are well below the AI for choline. Moreover, the food patterns recommended by the 2015-2020 Dietary Guidelines for Americans are currently insufficient to meet the AI for choline in most age-sex groups. An individual's requirement for choline is dependent on common genetic variants in genes required for choline, folate, and 1-carbon metabolism, potentially increasing more than one-third of the population's susceptibly to organ dysfunction. The American Medical Association and American Academy of Pediatrics have both recently reaffirmed the importance of choline during pregnancy and lactation. Newand emerging evidence suggests that maternal choline intake during pregnancy, and possibly lactation, has lasting beneficial neurocognitive effects on the offspring. Because choline is found predominantly in animal-derived foods, vegetarians and vegans may have a greater risk for inadequacy. With the 2020-2025 Dietary Guidelines for Americans recommending expansion of dietary information for pregnant women, and the inclusion of recommendations for infants and toddlers 0 to 2 years, better communication of the role that choline plays, particularly in the area of neurocognitive development, is critical. This narrative review summarizes the peer-reviewed literature and discussions from the 2018 Choline Science Summit, held in Washington, DC, in February 2018

Second order analysis of geometric functionals of Boolean models

This paper presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of stationary Boolean models. Special focus is put on the anisotropic case. In the (anisotropic) example of aligned rectangles, we provide explicit analytic formulae and compare them with simulation results. We discuss which information about the grain distribution second moments add to the mean values.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jensen. (The second version mainly resolves minor LaTeX problems.

Cell shape analysis of random tessellations based on Minkowski tensors

To which degree are shape indices of individual cells of a tessellation characteristic for the stochastic process that generates them? Within the context of stochastic geometry and the physics of disordered materials, this corresponds to the question of relationships between different stochastic models. In the context of image analysis of synthetic and biological materials, this question is central to the problem of inferring information about formation processes from spatial measurements of resulting random structures. We address this question by a theory-based simulation study of shape indices derived from Minkowski tensors for a variety of tessellation models. We focus on the relationship between two indices: an isoperimetric ratio of the empirical averages of cell volume and area and the cell elongation quantified by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for these quantities, as well as for distributions thereof and for correlations of cell shape and volume, are presented for Voronoi mosaics of the Poisson point process, determinantal and permanental point processes, and Gibbs hard-core and random sequential absorption processes as well as for Laguerre tessellations of polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data are complemented by mechanically stable crystalline sphere and disordered ellipsoid packings and area-minimising foam models. We find that shape indices of individual cells are not sufficient to unambiguously identify the generating process even amongst this limited set of processes. However, we identify significant differences of the shape indices between many of these tessellation models. Given a realization of a tessellation, these shape indices can narrow the choice of possible generating processes, providing a powerful tool which can be further strengthened by density-resolved volume-shape correlations.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jense

Special Libraries, April 1933

Volume 24, Issue 3https://scholarworks.sjsu.edu/sla_sl_1933/1002/thumbnail.jp

Mean-intercept anisotropy analysis of porous media. I. Analytic formulae for anisotropic Boolean models

Purpose Structure-property relations, which relate the shape of the microstructure to physical properties such as transport or mechanical properties, need sensitive measures of structure. What are suitable fabric tensors that quantify the shape of anisotropic heterogeneous materials? The mean intercept length is among the most commonly used characteristics of anisotropy in porous media, for example, of trabecular bone in medical physics. Methods We analyze the orientation-biased Boolean model, a versatile stochastic model that represents microstructures as overlapping grains with an orientation bias towards a preferred direction. This model is an extension of the isotropic Boolean model, which has been shown to truthfully reproduce multi-functional properties of isotropic porous media. We explain the close relationship between the concept of intersections with test lines to the elaborate mathematical theory of queues, and how explicit results from the latter can be directly applied to characterize microstructures. Results In this series of two papers, we provide analytic formulas for the anisotropic Boolean model and demonstrate often overlooked conceptual shortcomings of this approach. Queuing theory is used to derive simple and illustrative formulas for the mean intercept length. It separates into an intensity-dependent and an orientation-dependent factor. The global average of the mean intercept length can be expressed by local characteristics of a single grain alone. Conclusions We thus identify which shape information about the random process the mean intercept length contains. The connection between global and local quantities helps to interpret observations and provides insights into the possibilities and limitations of the analysis. In the second paper of this series, we discuss, based on the findings in this paper, short-comings of the mean intercept analysis for (bone-)microstructure characterization. We will suggest alternative and better defined sensitive anisotropy measures from integral geometry

Anisotropy in finite continuum percolation: threshold estimation by Minkowski functionals

We examine the interplay between anisotropy and percolation, i.e. the spontaneous formation of a system spanning cluster in an anisotropic model. We simulate an extension of a benchmark model of continuum percolation, the Boolean model, which is formed by overlapping grains. Here we introduce an orientation bias of the grains that controls the degree of anisotropy of the generated patterns. We analyze in the Euclidean plane the percolation thresholds above which percolating clusters in x- and in y-direction emerge. Only in finite systems, distinct differences between effective percolation thresholds for different directions appear. If extrapolated to infinite system sizes, these differences vanish independent of the details of the model. In the infinite system, the uniqueness of the percolating cluster guarantees a unique percolation threshold. While percolation is isotropic even for anisotropic processes, the value of the percolation threshold depends on the model parameters, which we explore by simulating a score of models with varying degree of anisotropy. To which precision can we predict the percolation threshold without simulations? We discuss analytic formulas for approximations (based on the excluded area or the Euler characteristic) and compare them to our simulation results. Empirical parameters from similar systems allow for accurate predictions of the percolation thresholds (with deviations of <5% in our examples), but even without any empirical parameters, the explicit approximations from integral geometry provide, at least for the systems studied here, lower bounds that capture well the qualitative dependence of the percolation threshold on the system parameters (with deviations of -). As an outlook, we suggest further candidates for explicit and geometric approximations based on second moments of the so-called Minkowski functionals

Low-temperature statistical mechanics of the Quantizer problem: Fast quenching and equilibrium cooling of the three-dimensional Voronoi liquid

The quantizer problem is a tessellation optimization problem where point configurations are identified such that the Voronoi cells minimize the second moment of the volume distribution. While the ground state (optimal state) in 3D is almost certainly the body-centered cubic lattice, disordered and effectively hyperuniform states with energies very close to the ground state exist that result as stable states in an evolution through the geometric Lloyd’s algorithm [M. A. Klatt et al. Nat. Commun. 10, 811 (2019)]. When considered as a statistical mechanics problem at finite temperature, the same system has been termed the “Voronoi liquid” by Ruscher, Baschnagel, and Farago [Europhys. Lett. 112, 66003 (2015)]. Here, we investigate the cooling behavior of the Voronoi liquid with a particular view to the stability of the effectively hyperuniform disordered state. As a confirmation of the results by Ruscher et al., we observe, by both molecular dynamics and Monte Carlo simulations, that upon slow quasi-static equilibrium cooling, the Voronoi liquid crystallizes from a disordered configuration into the body-centered cubic configuration. By contrast, upon sufficiently fast non-equilibrium cooling (and not just in the limit of a maximally fast quench), the Voronoi liquid adopts similar states as the effectively hyperuniform inherent structures identified by Klatt et al. and prevents the ordering transition into a body-centered cubic ordered structure. This result is in line with the geometric intuition that the geometric Lloyd’s algorithm corresponds to a type of fast quenc