Isotropic Geometry Research Articles

Analysis of stress concentration in isotropic and orthotropic plates with hole under uniformly distributed loading conditions

The Behaviour of Stress Concentration Factor in rectangular and circular plates of Isotropic (Magnesium alloy) and Orthotropic material (E-glass/Epoxy) under static loading in transverse direction (UDL) has been studied. Aim of this work was to analyse the effect of D/A (From 0.1 to 0.9) and D/t ratio (From 0 to 90) upon Stress Concentration Factor (SCF) for Isotropic and Orthotropic material under given boundary conditions. To solve this problem, Finite Element Method (i.e. FEM Software) ‘ANSYS’ was used. Element length of 2mm was adopted. For design, a quarter rectangular plate and a complete circular plate were considered. Orthotropic material of rectangular plate for given boundary conditions achieved more Stress Concentration Factor than Isotropic Material. In Orthotropic Material, circular plate, Stress concentration was observed less than Rectangular Plate, whereas in Isotropic circular plate, SCF is almost similar to rectangular plate. Material properties of Orthotropic material has vital role for this behaviour when compared with Isotropic material and Geometry of the plate was also a reason to get SCF for Rectangular plate.

Isotropic geometry of graph surfaces associated with product production functions in economics

A production function is a mathematical formalization in economics which denotes the relations between the output generated by a firm, an industry or an economy and the inputs that have been used in obtaining it. In this paper, we study the product production functions of 2 variables in terms of the geometry of their associated graph surfaces in the isotropic $3-$space $\mathbb{I}^{3}$. In particular, we derive several classification results for the graph surfaces of product production functions in $\mathbb{I}^{3}$ with constant curvature.

Implementation of ICRP 116 Dose Conversion Coefficients for Reconstructing Organ Dose in a Radiation Compensation Program.

Since 2000, National Institute for Occupational Safety and Health (NIOSH) has used dose conversion coefficients published by the International Commission on Radiation Protection in report 74 (ICRP 74) to determine organ dose from external radiation sources. In 2010, the ICRP issued publication 116 using more realistic phantoms than ICRP 74. NIOSH has developed a Monte Carlo method to sample the energy-organ-specific distribution of the ICRP 116 conversion coefficients to determine the organ dose and the associated uncertainty. Using Monte Carlo methods, irradiation geometry factors (IGFs) were developed to convert the measured dosemeter dose on the front of the body to values that are compatible with ICRP 116 organ dose conversion coefficients. Specific IGFs were developed for (1) both neutrons and photon exposures, (2) to male and female workers and (3) for rotational and isotropic exposure geometries. The computed mean organ dose and the associated uncertainty are used in the probability of causation calculation for compensation.

Anisotropic Shape-Memory Alginate Scaffolds Functionalized with Either Type I or Type II Collagen for Cartilage Tissue Engineering.

Regenerating articular cartilage and fibrocartilaginous tissue such as the meniscus is still a challenge in orthopedic medicine. While a range of different scaffolds have been developed for joint repair, none have facilitated the development of a tissue that mimics the complexity of soft tissues such as articular cartilage. Furthermore, many of these scaffolds are not designed to function in mechanically challenging joint environments. The overall goal of this study was to develop a porous, biomimetic, shape-memory alginate scaffold for directing cartilage regeneration. To this end, a scaffold was designed with architectural cues to guide cellular and neo-tissue alignment, which was additionally functionalized with a range of extracellular matrix cues to direct stem cell differentiation toward the chondrogenic lineage. Shape-memory properties were introduced by covalent cross-linking alginate using carbodiimide chemistry, while the architecture of the scaffold was modified using a directional freezing technique. Introducing such an aligned pore structure was found to improve the mechanical properties of the scaffold, and promoted higher levels of sulfated glycosaminoglycans (sGAG) and collagen deposition compared to an isotropic (nonaligned) pore geometry when seeded with adult human stem cells. Functionalization with collagen improved stem cell recruitment into the scaffold and facilitated more homogenous cartilage tissue deposition throughout the construct. Incorporating type II collagen into the scaffolds led to greater cell proliferation, higher sGAG and collagen accumulation, and the development of a stiffer tissue compared to scaffolds functionalized with type I collagen. The results of this study demonstrate how both scaffold architecture and composition can be tailored in a shape-memory alginate scaffold to direct stem cell differentiation and support the development of complex cartilaginous tissues.

Conversion Coefficients for Proton Beams using Standing and Sitting Male Hybrid Computational Phantom Calculated in Idealized Irradiation Geometries.

The aim of this study was the calculation of conversion coefficients for absorbed doses per fluence (DT/Φ) using the sitting and standing male hybrid phantom (UFH/NCI) exposure to monoenergetic protons with energy ranging from 2 MeV to 10 GeV. Sex-averaged effective dose per fluence (E/Φ) using the results of DT/Φ for the male and female hybrid phantom in standing and sitting postures were also calculated. Results of E/Φ of UFH/NCI standing phantom were also compared with tabulated effective dose conversion coefficients provided in ICRP publication 116. To develop an exposure scenario implementing the male UFH/NCI phantom in sitting and standing postures was used the radiation transport code MCNPX. Whole-body irradiations were performed using the recommended irradiation geometries by ICRP publication 116 antero-posterior (AP), postero-anterior (PA), right and left lateral, rotational (ROT) and isotropic (ISO). In most organs, the conversion coefficients DT/Φ were similar for both postures. However, relative differences were significant for organs located in the lower abdominal region, such as prostate, testes and urinary bladder, especially in the AP geometry. Results of effective dose conversion coefficients were 18% higher in the standing posture of the UFH/NCI phantom, especially below 100 MeV in AP and PA. In lateral geometry, the conversion coefficients values below 20 MeV were 16% higher in the sitting posture. In ROT geometry, the differences were below 10%, for almost all energies. In ISO geometry, the differences in E/Φ were negligible. The results of E/Φ of UFH/NCI phantom were in general below the results of the conversion coefficients provided in ICRP publication 116.

Cosmological implications of modified gravity induced by quantum metric fluctuations

We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a nonminimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the quantum correction tensor is given by the coupling of a scalar field and of a scalar function to the metric tensor, and by a term proportional to the matter energy-momentum tensor. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry. In some of these models the divergence of the matter energy-momentum tensor is non-zero, indicating a process of matter creation, which corresponds to an irreversible energy flow from the gravitational field to the matter fluid, and which is direct consequence of the nonminimal curvature-matter coupling. The cosmological evolution equations of these modified gravity models induced by the quantum fluctuations of the metric are investigated in detail by using both analytical and numerical methods, and it is shown that a large variety of cosmological models can be constructed, which, depending on the numerical values of the model parameters, can exhibit both accelerating and decelerating behaviors.

Cosmology with higher-derivative matter fields

We investigate the cosmological implications of a new class of modified gravity, where the field equations generically include higher-order derivatives of the matter fields, arising from the introduction of non-dynamical auxiliary fields in the action. Imposing a flat, homogeneous and isotropic geometry, we extract the Friedmann equations, obtaining an effective dark-energy sector containing higher-derivatives of the matter energy density and pressure. For the cases of dust, radiation and stiff matter, we analyze the cosmological behavior, finding accelerating, de Sitter and non-accelerating phases, dominated by matter or dark-energy. Additionally, the effective dark-energy equation-of-state parameter can be quintessence-like, cosmological-constant-like or even phantom-like. The detailed study of these scenarios may provide signatures, that could distinguish them from other candidates of modified gravity.

Tunable scattering cancellation cloak with plasmonic ellipsoids in the visible

The scattering cancellation technique is a powerful tool to reduce the scattered field from electrically small objects in a specific frequency window. The technique relies on covering the object of interest with a shell that scatters light into the far field of equal strength as the object, but $\pi$ out-of-phase. The resulting destructive interference prohibits its detection in measurements that probe the scattered light. Whereas at radio or microwave frequencies feasible designs have been proposed that allow to tune the operational frequency upon request, similar capabilities have not yet been explored in the visible. However, such ability is decisive to capitalize on the technique in many envisioned applications. Here, we solve the problem and study the use of small metallic nanoparticles with an ellipsoidal shape as the material from which the shell is made to build an isotropic geometry. Changing the aspect ratio of the ellipsoids allows to change the operational frequency. The basic functionality is explored with two complementary analytical approaches. Additionally, we present a powerful multiscattering algorithm that can be used to perform full wave simulations of clusters of arbitrary particles. We utilize this method to analyze the scattering of the presented designs numerically. Hereby we provide useful guidelines for the fabrication of this cloak with self-assembly methods by investigating the effects of disorder.

Design of lattice structures with controlled anisotropy

Recent advances in additive manufacturing make it possible to fabricate periodic lattice structures with complex configurations. However, a proper design strategy to achieve lattice structures with controlled anisotropy is still unavailable. There is an urgent need to fill this knowledge gap in order to develop mechanical metamaterials with prescribed properties. Here we propose two different methodologies to design lattice structures with controlled anisotropy. As examples, we created two new families of lattice structures with isotropic elasticity and cubic symmetric geometry. The findings of this work provide simple and effective strategies for exploring lightweight metamaterials with desired mechanical properties.

Nuclear deformability and telomere dynamics are regulated by cell geometric constraints

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.

Simplified gravitational collapse with an interacting vacuum energy density

The gravitational collapse of a spherical core, in which the fluid component interact with a growing vacuum energy density, filling an homogeneous and isotropic geometry with an arbitrary curvature parameter, is investigated. The complete set of exact solutions for all values of the free parameters are obtained, and the influence of the curvature term on the collapsing time, black hole mass and other physical quantities are also discussed in detail. We show that for the same initial conditions the total black hole mass depends only on the effective matter density parameter (including the vacuum component). It is also shown that the analytical condition to form a black hole, i.e. the formation of an apparent horizon, is not altered by the contribution of the curvature terms, however, the remaining physical quantities are quantitatively modified.

Cosmic fluctuations from a quantum effective action

Does the observable spectrum of cosmic fluctuations depend on detailed initial conditions? This addresses the question if the general inflationary paradigm is sufficient to predict within a given model the spectrum and amplitude of cosmic fluctuations, or if additional particular assumptions about the initial conditions are needed. The answer depends on the number of e-foldings $N_{in}$ between the beginning of inflation and horizon crossing of the observable fluctuations. We discuss an interacting inflaton field in an arbitrary homogeneous and isotropic geometry, employing the quantum effective action $\Gamma$. An exact time evolution equation for the correlation function involves the second functional derivative $\Gamma^{(2)}$. The operator formalism and quantum vacua for interacting fields are not needed. Use of the effective action also allows one to address the change of frames by field transformations (field relativity). Within the approximation of a derivative expansion for the effective action we find the most general solution for the correlation function, including mixed quantum states. For not too large $N_{in}$ the memory of the initial conditions is preserved. In this case the cosmic microwave background cannot disentangle between the initial spectrum and its processing at horizon crossing. The inflaton potential cannot be reconstructed without assumptions about the initial state of the universe. We argue that for very large $N_{in}$ a universal scaling form of the correlation function is reached for the range of observable modes. This can be due to symmetrization and equilibration effects, not yet contained in our approximation, which drive the short distance tail of the correlation function towards the Lorentz invariant propagator in flat space.

Quantum cosmology of multifield scalar matter: Some exact solutions

We consider the gravity interacting with matter scalar fields and quantized in the minisuperspace approach in which the wave functional is described by the Wheeler-DeWitt equations (WdW). Assuming the domination of the homogeneous and isotropic geometry the leading contributions to the wave functional in the approximation of the minisuperspace with Friedmann-Robertson-Walker metric (FRW) and spatially uniform scalar fields are considered. The model of several scalar fields with exponential potentials and kinetic terms admitting such a special mixing that ultimately it is possible to separate the variables in the WdW equation and to find its exact solution in terms of the special functions is proposed. The semiclassical approximation is thoroughly investigated and the boundary conditions permitting the physical solution selection for classical cosmologies are chosen.

Superconducting dark energy

Based on the analogy with superconductor physics we consider a scalar-vector-tensor gravitational model, in which the dark energy action is described by a gauge invariant electromagnetic type functional. By assuming that the ground state of the dark energy is in a form of a condensate with the U(1) symmetry spontaneously broken, the gauge invariant electromagnetic dark energy can be described in terms of the combination of a vector and of a scalar field (corresponding to the Goldstone boson), respectively. The gravitational field equations are obtained by also assuming the possibility of a non-minimal coupling between the cosmological mass current and the superconducting dark energy. The cosmological implications of the dark energy model are investigated for a Friedmann-Robertson-Walker homogeneous and isotropic geometry for two particular choices of the electromagnetic type potential, corresponding to a pure electric type field, and to a pure magnetic field, respectively. The time evolution of the scale factor, matter energy density and deceleration parameter are obtained for both cases, and it is shown that in the presence of the superconducting dark energy the Universe ends its evolution in an exponentially accelerating vacuum de Sitter state. By using the formalism of the irreversible thermodynamic processes for open systems we interpret the generalized conservation equations in the superconducting dark energy model as describing matter creation. The particle production rates, the creation pressure and the entropy evolution are explicitly obtained.

Acto-Myosin Contractility Regulates Nuclear and Chromatin Plasticity

The cytoskeleton can exert forces on the nucleus and chromatin via direct physical links on the nuclear envelope. Such forces provide prestress on the nucleus thereby governing its morphology. However, the role of these forces in modulating nucleus and chromatin plasticity has not yet been explored. In this project, we used micro-contact printing of fibronectin to create different substrate geometries for culturing NIH3T3 cells so as to obtain specific cytoskeletal organization and then measured the nuclear and chromatin dynamics in these cells. We observed that nuclei of cells on constrained isotropic geometry (small circle) were much more plastic than those on elongated anisotropic geometry (big rectangle). This nuclear plasticity, measured as projected nuclear area fluctuations, showed a non-monotonous relation to actin polymerization state. Also, myosin contractility was determined to be necessary for such nucleus plasticity. The effect of cytoskeletal organization and their active forces on chromatin plasticity was further quantified by tracking the dynamics of condensed chromatin regions, which showed increased dynamics corresponding to enhanced nuclear plasticity. In summary, using cells of defined geometries to specify cytoskeletal organization, our work demonstrates the role of active cytoskeletal forces in regulating nuclear and chromatin plasticity.

Fluence-to-effective dose conversion coefficients from a Saudi population based phantom for monoenergetic photon beams from 10 keV to 20 MeV

Fluence-to-dose conversion coefficients are important quantities for radiation protection, derived from Monte Carlo simulations of the radiation particles through a stylised phantom or voxel based phantoms. The voxel phantoms have been developed for many ethnic groups for their accurate reflection of the anatomy. In this study, we used the Monte Carlo code MCNPX to calculate the photon fluence-to-effective dose conversion coefficients with a voxel phantom based on the Saudi Arabian male population. Six irradiation geometries, anterior–posterior (AP), posterior–anterior (PA), left lateral (LLAT), right lateral (RLAT), rotational (ROT) and isotropic (ISO) were simulated for monoenergetic photon beams from 10 keV to 20 MeV. We compared the coefficients with the reference values in ICRP Publication 116. The coefficients in the AP and PA geometries match the reference values to 9% and 12% on average as measured by root mean square while those in the LLAT, RLAT ROT and ISO geometries differ, mostly below, from the reference by 23, 22, 15 and 16%, respectively. The torso of the Saudi phantom is wider than the ICRP reference male phantom and likely to cause more attenuation to the lateral beam. The ICRP reference coefficients serve well for the Saudi male population as conservative estimations for the purpose of radiation protection.

Colloidosomes formed by nonpolar/polar/nonpolar nanoball amphiphiles.

Fullerene-based amphiphiles are able to form bilayer vesicles in aqueous solution. In this study, the self-assembly behavior of polymer-tethered nanoballs (NBs) with nonpolar/polar/nonpolar (n-p-n') motif in a selective solvent is investigated by dissipative particle dynamics. A model NB bears two hydrophobic polymeric arms (n'-part) tethered on an extremely hydrophobic NB (n-part) with hydrophilic patch (p-part) patterned on its surface. Dependent on the hydrophobicity and length of tethered arms, three types of aggregates are exhibited, including NB vesicle, core-shell micelle, and segmented-worm. NB vesicles are developed for a wide range of hydrophobic arm lengths. The presence of tethered arms perturbs the bilayer structure formed by NBs. The structural properties including the order parameter, membrane thickness, and area density of the inner leaflet decrease with increasing the arm length. These results indicate that for NBs with longer arms, the extent of interdigitation in the membrane rises so that the overcrowded arms in the inner corona are relaxed. The transport and mechanical properties are evaluated as well. As the arm length grows, the permeability increases significantly because the steric bulk of tethered arms loosens the packing of NBs. By contrast, the membrane tension decreases owing to the reduction of NB/solvent contacts by the polymer corona. Although fusion can reduce membrane tension, NB vesicles show strong resistance to fusion. Moreover, the size-dependent behavior observed in small liposomes is not significant for NB vesicles due to isotropic geometry of NB. Our simulation results are consistent with the experimental findings.

Macromolecule loading into spherical, elliptical, star-like and cubic calcium carbonate carriers.

We fabricated calcium carbonate particles with spherical, elliptical, star-like and cubical morphologies by varying relative salt concentrations and adding ethylene glycol as a solvent to slow down the rate of particle formation. The loading capacity of particles of different isotropic (spherical and cubical) and anisotropic (elliptical and star-like) geometries is investigated, and the surface area of such carriers is analysed. Potential applications of such drug delivery carriers are highlighted.

Notes on isotropic geometry of production models

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.

Lattice Symmetry-Breaking Perturbations for Spiral Waves

Spiral waves in two-dimensional excitable media have been observed experimentally and studied extensively. It is now well known that the symmetry properties of the medium of propagation drives many of the dynamics and bifurcations which are experimentally observed for these waves. Also, symmetry-breaking induced by boundaries, inhomogeneities, and anisotropy have all been shown to lead to different dynamical regimes from that which is predicted for mathematical models that assume infinite homogeneous and isotropic planar geometry. Recent mathematical analyses incorporating the concept of forced symmetry-breaking from the Euclidean group of all planar translations and rotations have given model-independent descriptions of the effects of media imperfections on spiral wave dynamics. In this paper, we continue this program by considering rotating waves in dynamical systems which are small perturbations of a Euclidean-equivariant dynamical system, but for which the perturbation preserves only the symmetry of a regular square lattice.