Flexible polyhedral nets in isotropic geometry

Forces generated by the cytoskeleton can be transmitted to the nucleus and chromatin via physical links on the nuclear envelope and the lamin meshwork. Although the role of these active forces in modulating prestressed nuclear morphology has been well studied, the effect on nuclear and chromatin dynamics remains to be explored. To understand the regulation of nuclear deformability by these active forces, we created different cytoskeletal states in mouse fibroblasts using micropatterned substrates. We observed that constrained and isotropic cells, which lack long actin stress fibers, have more deformable nuclei than elongated and polarized cells. This nuclear deformability altered in response to actin, myosin, formin perturbations, or a transcriptional down-regulation of lamin A/C levels in the constrained and isotropic geometry. Furthermore, to probe the effect of active cytoskeletal forces on chromatin dynamics, we tracked the spatiotemporal dynamics of heterochromatin foci and telomeres. We observed increased dynamics and decreased correlation of the heterochromatin foci and telomere trajectories in constrained and isotropic cell geometry. The observed enhanced dynamics upon treatment with actin depolymerizing reagents in elongated and polarized geometry were regained once the reagent was washed off, suggesting an inherent structural memory in chromatin organization. We conclude that active forces from the cytoskeleton and rigidity from lamin A/C nucleoskeleton can together regulate nuclear and chromatin dynamics. Because chromatin remodeling is a necessary step in transcription control and its memory, genome integrity, and cellular deformability during migration, our results highlight the importance of cell geometric constraints as critical regulators in cell behavior.

UDC 515.12 We classify translation surfaces in isotropic geometry with arbitrary constant isotropic Gaussian and mean curvatures underthe condition that at least one of translating curves lies in a plane.

Meshes with planar quadrilateral faces are desirable discrete surface representations for architecture. The present paper introduces new classes of planar quad meshes, which discretize principal curvature lines of surfaces in so-called isotropic 3-space. Like their Euclidean counterparts, these isotropic principal meshes meshes are visually expressing fundamental shape characteristics and they can satisfy the aesthetical requirements in architecture. The close relation between isotropic geometry and Euclidean Laguerre geometry provides a link between the new types of meshes and the known classes of conical meshes and edge offset meshes. The latter discretize Euclidean principal curvature lines and have recently been realized as particularly suited for freeform structures in architecture, since they allow for a supporting beam layout with optimal node properties. We also present a discrete isotropic curvature theory which applies to all types of meshes including triangle meshes. The results are illustrated by discrete isotropic minimal surfaces and meshes computed by a combination of optimization and subdivision.

We classify translation surfaces in isotropic geometry with arbitrary constant isotropic Gaussian and mean curvatures under the condition that at least one translating curve lies in the plane.

The production function is one of the key concepts of mainstream neoclassical theories in economics. The study of the shape and properties of the production possibility frontier is a subject of great interest in economic analysis. In this respect, Cobb-Douglas and CES production functions with flat graph hyper-surfaces in Euclidean spaces are first studied in [20, 21]. Later, more general studies of production models were given in [5]-[9] and [11, 13, 22]. On the other hand, from visual-physical experiences [16, 17, 18], the second and third authors proposed in [15] to study production models via isotropic geometry as well. The purpose of this paper is thus to investigate important production models via isotropic geometry.

The generating rank of the symplectic grassmannians: Hyperbolic and isotropic geometry

An approximating formula recently proposed by the authors for gamma-ray buildup factors of multilayered shields is applied to point isotropic source problems.The formula, which is formulated in vector form with a four-group approximation, handles the gamma-ray energy spectrum directly and uses the transmission and albedo matrices to take gamma-ray transmission and back-scattering effects into consideration. The gamma-ray transmission and back-scattering probabilities through a 1-mean-free-path-(mfp-) thick shell depend on the shell curvature. This phenomenon plays an important role in simulating the gamma-ray buildup factor in point isotropic source geometry. In this model, the dependence is described by simplified expressions. The feasibility of the formula for systematically describing the point isotropic buildup factors was tested by using buildup factors calculated by the Monte Carlo method as reference data. The materials used in the tests were water, iron, and lead, and the source energies assumed were 0.5, 1, and 10MeV. Through the tests, the method was found to reproduce the reference data of double-layered shields of these materials very well. With the same parameters, the buildup factors of three-layered shields are also reproducible. Buildup factors computed with two different group structures were examined to test the adequacy of the energy group structure adopted. The group structure previously adopted was found to be adequate in the energy range of 0.5 to 10 MeV

The thermal–electric bifunctional devices with isotropic and anisotropic geometries are designed in this paper, which can realize different control functions (invisible sensors and cloaks) of thermal and electric fields. We first theoretically achieve the bifunctions of invisible sensors and cloaks with isotropic and anisotropic geometries. When the material parameters of the core and matrix and the geometric parameters of the core, inner shell, and outer shell are determined, the thermal–electric invisible sensors could be realized. Meanwhile, the invisible sensors will degrade to invisible cloaks as the inner shell material is insulating. The simulations applying the derived material parameters have also been conducted to verify the thermal–electric bifunctions of different circular and confocal elliptical devices. The results show that the thermal–electric bifunctional devices can effectively control the thermal and electric fields, and these devices exhibit perfect performance of the thermal–electric functions of invisible sensors and cloaks. This work presents a new method to realize thermal–electric bifunctional devices and opens a new window to the development of multi-physics field.

The sacrificed-QD-layer method can well control the indium deposition amount to grow InAs quantum dots (QDs) with isotropic geometry. Individual Si dopant above an (001)-based InAs QD proves a new method to build a local electric field to reduce fine structure splitting (FSS = X1−X2) and show D3h symmetric excitons. The lowest FSS obtained is 3.9 μeV with the lowest energy X state (LX) anticlockwise rotate from [1–10] (i.e., zero FSS will be crossed in a proper field). The lateral field projection induces a large eh separation and various FSS, LX, and emission intensity polarization. The lateral field along [1–10] breaks the X1–X2 wavefunction degeneracy for independent HH and VV cascade emissions with robust polarization correlation. With FSS ~4 μeV and T1 ~0.3 ns fastened in a distributed Bragg reflector cavity, polarization-resolved XX–X cross-correlations show fidelity ~0.55 to a maximal entangled state |HH> + |VV>. A higher fidelity and zero FSS will be obtained in the hybrid QD structure with a junction field integrated to tune the FSS and a sub-bandgap excitation to avoid influences from electrons in the barrier.

Complex material surfaces can reduce secondary electron emission (SEE) and sputtering via geometric trapping. In this work, the SEE yields for a range of open-cell reticulated carbon foam geometries are characterized using scanning electron microscopy. The total reduction in the SEE yield from carbon foams with a 3% volume fill density and 10–100 pores per inch (PPI) is shown to be between 23.5% and 35.0%. Contributions of a foam backplate are assessed by experimentally and analytically defining the critical parameter, transparency. The transparency of a foam is quantified and is shown to affect the primary electron angular dependence on the SEE yield. For the same thickness of 6 mm, it is found that higher PPI decreases foam transparency from 32% to 0% and reduces the SEE yield. The SEE yield from carbon foams is also shown to have weaker dependence on the morphology of the surface compared with fuzzes and velvets and less variation across individual sample surfaces due to the rigidity of their ligament structures and isotropic geometries.

Solutions of Einstein’s equations are examined when a particular class of closed three-form fields is taken as a source. The choice of source is motivated by developments in particle physics indicating the possible existence of physical fields described by three-forms. After summarizing basic dynamical equations and some properties, attention is focused on two particular configurations: (1) static, spherically symmetric, self-gravitating, three-form fields; and (2) homogeneous and isotropic geometries coupled to three-forms. For the spherically symmetric case, there exists two mutually exclusive sets of effective equations, solutions which describe static, spherically symmetric, self-gravitating axion fields. For the one class of the effective equations, a two-parameter family of asymptotically flat solutions of the Einstein axion field equations have been constructed. The axionic black hole solution of Bowick et al. [Phys. Rev. Lett. 61, 2823 (1988)] is also recovered as a special case of this class. For the other set of equations, only a special solution has been constructed. Its properties and global structure are discussed at length. For the case of axions coupled to homogeneous and isotropic geometries, explicit solutions of the relevant equations have also been constructed. In particular, for the case where the hypersurfaces of homogeneity are either flat or characterized by negative curvature, a global solution is obtained. It represents an ever expanding universe originating from a spacelike curvature singularity. For the case of a closed universe, local solutions have been constructed, which in principle can be patched to yield a global solution. Nevertheless, by employing them, the singularity structure of this solution was able to be analyzed. It behaves in the same manner as the previous two cases.

We consider the cosmological implications of the Weyl geometric gravity theory. The basic action of the model is obtained from the simplest conformally invariant gravitational action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and a matter term, respectively. The total action is linearized in the Weyl scalar by introducing an auxiliary scalar field. To maintain the conformal invariance of the action the trace condition is imposed on the matter energy–momentum tensor, thus making the matter sector of the action conformally invariant. The field equations are derived by varying the action with respect to the metric tensor, the Weyl vector field, and the scalar field, respectively. We investigate the cosmological implications of the theory, and we obtain first the cosmological evolution equations for a flat, homogeneous and isotropic geometry, described by Friedmann–Lemaitre–Robertson–Walker metric, which generalize the Friedmann equations of standard general relativity. In this context we consider two cosmological models, corresponding to the vacuum state, and to the presence of matter described by a linear barotropic equation of state. In both cases we perform a detailed comparison of the predictions of the theory with the cosmological observational data, and with the standard Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} CDM model. By assuming that the presence of the Weyl geometric effects induce small perturbations in the homogeneous and isotropic cosmological background, and that the anisotropy parameter is small, the equations of the cosmological perturbations due to the presence of the Weyl geometric effects are derived. The time evolution of the metric and matter perturbations are explicitly obtained. Therefore, if Weyl geometric effects are present, the Universe would acquire some anisotropic characteristics, and its geometry will deviate from the standard FLRW one.

Decoherence of Friedmann-Robertson-Walker geometries in the presence of massive vector fields with U(1) or SO(3) global symmetries

In epidemiological investigations of cancer risk from occupational exposure, it is important to obtain an organ-specific dose for each cohort member for accurate risk analysis. To date, dose conversion coefficients, which convert physical dose measurement to organ dose, are only available for individuals with reference body size, which can differentially bias the estimated organ dose depending on the body mass index of cohort members. In the current study, we calculated the organ dose coefficients applicable to adult males and females with various body weights by using the Monte Carlo radiation transport technique combined with a library of body size-dependent hybrid computational phantoms exposed in six idealised irradiation geometries. We adapted the eight adult male phantoms, 175 cm tall with weights of 60, 70, 80, 90, 100, 110, 120 and 130 kg, and the nine adult female phantoms, 165 cm tall with weights of 50, 60, 70, 80, 90, 100, 110, 120 and 130 kg. The radiation transport was simulated using MCNPX 2.7 Monte Carlo code. Phantoms were irradiated by external photon fields in anterior posterior (AP), posterior-anterior, right and left lateral, rotational, and isotropic geometries. The results showed that the 60 kg adult male phantom shows 1.33-, 1.43-, 1.44- and 1.52-fold greater dose coefficients for the lungs, heart, stomach, and liver, respectively, than the 120 kg adult male phantom at 0.1 MeV in AP geometry. We derived exponential correlation between organ dose coefficients and body weight to facilitate calculation of organ dose coefficients for a given weight. The comprehensive organ dose coefficients and exponential regression model can be used to estimate more accurate organ dose for individuals of the two genders with various body weights exposed to external photon radiation.

A group of Monte Carlo simulations has been performed for external neutron dosimetry calculation based on a whole-body mathematical model. The Chinese mathematical phantom (CMP) is a mathematical human body model developed based on methods of ORNL (Oak ridge National Laboratory) mathematical phantom series (OMPS), and data from Chinese reference man and reference Asian man. Fluence-to-absorbed dose conversion coefficients of 24 organs and tissues for monoenergetic neutron beams ranging from 10−9 to 102 MeV were calculated using the Monte Carlo code MCNPX. Irradiation conditions include anterior–posterior, posterior–anterior, right lateral, left lateral, rotational, and isotropic geometries. Results for the different organs are compared with those recommended in International Commission of Radiological Protection (ICRP) publication 74 and results obtained based on the visible Chinese human (VCH) phantom. Overall the consistency among the three sets of data was observed, but significant deviations up to 30–50% were also found in the AP, PA and lateral irradiation conditions. Since CMP represents the Chinese population, this work is helpful as a reference to investigate the difference of the neutron induced organ doses due to the anatomical variation between the Chinese and the Caucasians, and that between the average population and an individual.