Concentric Spheres Research Articles

A Three-Dimensional Model of a Spherically Symmetric, Compressible Micropolar Fluid Flow with a Real Gas Equation of State

In this work, we analyze a spherically symmetric 3D flow of a micropolar, viscous, polytropic, and heat-conducting real gas. In particular, we take as a domain the subset of R3 bounded by two concentric spheres that present solid thermoinsulated walls. Also, here, we consider the generalized equation of state for the pressure in the sense that the pressure depends, as a power function, on the mass density. The model is based on the conservation laws for mass, momentum, momentum moment, and energy, as well as the equation of state for a real gas, and it is derived first in the Eulerian and then in the Lagrangian description. Through the application of the Faedo–Galerkin method, a numerical solution to a corresponding problem is obtained, and numerical simulations are performed to demonstrate the behavior of the solutions under various parameters and initial conditions in order to validate the method. The results of the simulations are discussed in detail.

Enlargement of the localized resonant band gap by using multi-layer structures

Multi-layer structures possess highly geometrically tunable optical resonances to change the surface plasmon frequencies in the wide range. A simple analytic model is presented to describe the plasmon hybridization of multi-layer metamaterial structures with multipole resonances. We theoretically demonstrate that the number of plasmon modes increases with the number of layers, which results in the enlargement of the localized resonant optical band gap. To explore the interaction between incident fields and multi-layer structures, we derive the closed-form perturbed field in terms of a generalized polarization matrix, whose dimension matches the number of layers. This enables us to obtain the eigenmode frequencies and their corresponding eigenfunctions for three-dimensional multi-layer concentric spheres and two-dimensional multi-layer concentric cylinders in a vacuum setting. These findings offer nanoscientists a general design principle that can be applied to facilitate the proper selection of the metamaterial parameters, thereby inducing the desired resonance and enabling customized applications to be realized.

A generalized uniform placement of alters on spherical surface (U-PASS) for visualizing general weighted networks

Network visualization is an important tool for extracting information from the structure and configuration of a network, especially when the network includes weighted edges and nodes with attribute information. Previous studies have demonstrated an effective visualization method that projects the network onto a spherical surface. In this work, we extend this method, known as Uniform Placement of Alters on Spherical Surface (U-PASS), to general weighted networks. This extension enables the uniform distribution of network nodes across multiple layers of concentric spheres. In addition, we discuss the lower bound of a criterion called generalized spherical cap discrepancy, which is used to evaluate the uniformity of node distribution on a collapsed spherical surface.

Evaluation of Scatterer Parameters From Ultrasound Scattering Models Taking Into Account Scattering From Nuclei and Cells of Cell-Pellet Biophantoms and Ex Vivo Tumors.

The Quantitative Ultrasound backscatter coefficient provides the capability to evaluate tissue microstructure parameters. Tissue-based scatterer parameters are extracted using ultrasound scattering models. It is challenging to correlate ultrasound scatterer parameters of tissue structures from optical-measured histology, possibly because of inappropriate scattering models or the presence of multiple scatterers. The objective of this study is to pursue the quantification of pertinent scatterer parameters with scattering models that consider ultrasound scattering from nuclei and cells. The concentric sphere model (CSM) and the structure factor model adapted for two types of scatterers (SFM2) are evaluated for cell-pellet biophantoms and ex vivo tumors of four cell lines: 4T1, JC, LMTK, and MAT. The structure factor model (SFM) was used for comparison. CSM and SFM2 provided scatterer parameters closer to histology (lower relative errors) for nucleus and cell radii and volume fractions than SFM but were not always accompanied by lower dispersion of the scatterer distribution (lower coefficient of variation). CSM and SFM2 quantified cell and nucleus radius and volume fraction parameters with lower relative error compared to SFM. For tumors, CSM provided better results than SFM2.

Fuzzy onionlike space as a matrix model

We propose a matrix model realization of a three-dimensional quantum space. It has an onionlike structure composed of concentric fuzzy spheres of increasing radius. The angular part of the Laplace operator is inherited from that of the fuzzy sphere. The radial part is constructed using operators that relate matrices of various sizes using the matrix harmonic expansion. As an example of this approach, we produce a numerical simulation of a scalar quantum field theory, the classical heat transfer, study the quantum-mechanical hydrogen atom, and consider some analytical aspects of the scalar field theory on this space. Published by the American Physical Society 2024

Hydrophobic effects on a solid sphere translating in a Brinkman couple stress fluid covered by a concentric spherical cavity

In this study, a fluid flow with an incompressible axisymmetric steady couple stress translated through a porous media is analyzed between a hollow sphere and a concentric rigid sphere. In the permeable region, the flow field is regulated by Brinkman's equation. The slip and spin slip conditions are applied on both the rigid sphere and spherical cavity surfaces. Modified Bessel functions provide a systematic approach to the problem by utilizing the principle of a stream function. On the inner sphere, the wall correction factor that an incompressible couple stress fluid encounters is calculated. The effects of the slip, spin slip, coupling stress parameter, separation distance, and permeability parameter on the field functions and the normalized drag force are also graphically shown. The corresponding results are contrasted with the outcomes reported for particular cases of couple stress fluid and viscous fluid flow in two permeability-free concentric circles. Furthermore, graphs of the streamlines for various values of the relevant parameters have been included.

MHD Couple stress fluid between two concentric spheres with slip regime

The problem of the axisymmetric steady flow of an incompressible couple stress fluid within two concentric spheres is analyzed analytically in this study. In the interior of the solid sphere, translation takes place with a uniform velocity, and in the exterior, translation takes place with a fixed velocity. A study of slip conditions was carried out on the surfaces of the two spheres. In terms of stream functions, modified Bessel functions provide an analytical solution to the problem. As the outer sphere remains stationary, the inner sphere experiences the normalized drag force. A graphic representation of drag is provided based on the slip and spin slip parameters, the couple stress parameter, the separation distance, and the MHD parameter. In addition, the results are compared with earlier results for special cases of translation of one rigid sphere through an unbounded magnetic medium, viscous fluid flow, and Couple stress fluid without MHD between two concentric spheres.

FPGA-Based Hardware Implementation of a Stable Inverse Source Problem Algorithm in a Non-Homogeneous Circular Region

Objective: This work presents an implementation of a stable algorithm that recovers sources located at the boundary separating two homogeneous media in field-programmable gate arrays. Two loop unrolling architectures were developed and analyzed for this purpose. This inverse source problem is ill-posed due to numerical instability, i.e., small errors in the measurement can produce significant changes in the source location. Methodology: To handle the numerical instability when recovering these sources, the Tikhonov regularization method in combination with the Fourier series truncation method are applied in the stable algorithm. This stable algorithm is implemented in two different architectures developed in this work: The first architecture (Mode 1) allows for different operating speeds, which is an advantage depending on whether we work with fast or slow signals. The second one (Mode 2) reduces resource consumption by exploiting the characteristics of the source identification algorithm, which is an advantage for multichannel problems such as inverse electrocardiography or electroencephalography. Results: The architectures were tested on four devices of the 7 Series of Xilinx: Spartan-7 xc7s100fgga484, Virtex-7 xc7v585tffg1157, Kintex-7 xc7k70tfbg484, and Artix-7 xc7a35tcpg236. The two hardware implementations of the stable algorithm were validated using synthetic examples implemented in MATLAB, which shows the advantages of each architecture. Contributions: We developed two efficient architectures based on a loop unrolling design for source identification problems. These are effective strategies to divide and assign tasks to the configurable hardware, and they appear as an appropriate technique for implementing the algorithm. The first one is simple and allows for different operating speeds. The second one uses a control system based on multiplexors that reduce resource consumption and complexity of the design and can be used for multichannel problems. From the numerical test, we found the regularization parameters. The synthetic examples developed here can be considered for similar problems and can be extended to concentric spheres.

Learning Spherical Radiance Field for Efficient 360° Unbounded Novel View Synthesis.

Novel view synthesis aims at rendering any posed images from sparse observations of the scene. Recently, neural radiance fields (NeRF) have demonstrated their effectiveness in synthesizing novel views of a bounded scene. However, most existing methods cannot be directly extended to 360° unbounded scenes where the camera orientations and scene depths are unconstrained with large variations. In this paper, we present a spherical radiance field (SRF) for efficient novel view synthesis in 360° unbounded scenes. Specifically, we represent a 3D scene as multiple concentric spheres with different radii. In particular, each sphere encodes its corresponding layered scene into implicit representations and is parameterized with an equirectangular projection image. A shallow multi-layer perceptron (MLP) is then used to infer the density and color from these sphere representations for volume rendering. Moreover, an occupancy grid is introduced to cache the density field and guide the ray sampling, which accelerates the training and rendering procedures by reducing the number of samples along the ray. Experiments show that our method can well fit 360° unbounded scenes and produces state-of-the-art results on three benchmark datasets with less than 30 minutes of training time on a 3090 GPU, surpassing Mip-NeRF 360 with a 400× speedup. In addition, our method achieves competitive performance in terms of both accuracy and efficiency on a bounded dataset. Project page: https://minglin-chen.github.io/SphericalRF.

Changes in the Impacts of COVID-19 over Time on Families with Older Adults Living on Remote Islands in Japan: A Study in Family Ethnographic Research

Coronavirus disease 2019 (COVID-19) affected not only individuals but also families. The purpose of this study was to clarify the temporal changes in the impact of the COVID-19 pandemic on entire families with older adults susceptible to infection living on small islands in Japan over the duration of the pandemic. Family ethnographic research was conducted from 2021 to 2023, using the Concentric Sphere Family Environment Theory as the theoretical framework. Formal interviews were conducted with 20 families. In addition, data from informal interviews, participant observation and other sources were compiled into field notes. All data on the impact on the entire family were extracted and content analysis was conducted. Six categories (family internal environmental system, family system unit, micro system, macro system, supra system, and family chrono-environment system) and a total of 85 subcategories were extracted. The results show that COVID-19 exerted not only negative but also positive impacts on the entire family, and their temporal changes are clarified. The impact on families is believed to have been influenced by the family external environment, such as increases and decreases of infection cases or events that occurred outside the family. The knowledge acquired from these studies will help healthcare professionals in providing appropriate family support.

Simulation study on high spatio-temporal resolution acousto-electrophysiological neuroimaging.

Objective.Acousto-electrophysiological neuroimaging (AENI) is a technique hypothesized to record electrophysiological activity of the brain with millimeter spatial and sub-millisecond temporal resolution. This improvement is obtained by tagging areas with focused ultrasound (fUS). Due to mechanical vibration with respect to the measuring electrodes, the electrical activity of the marked region will be modulated onto the ultrasonic frequency. The region's electrical activity can subsequently be retrieved via demodulation of the measured signal. In this study, the feasibility of this hypothesized technique is tested.Approach.This is done by calculating the forward electroencephalography response under quasi-static assumptions. The head is simplified as a set of concentric spheres. Two sizes are evaluated representing human and mouse brains. Moreover, feasibility is assessed for wet and dry transcranial, and for cortically placed electrodes. The activity sources are modeled by dipoles, with their current intensity profile drawn from a power-law power spectral density.Results.It is shown that mechanical vibration modulates the endogenous activity onto the ultrasonic frequency. The signal strength depends non-linearly on the alignment between dipole orientation, vibration direction and recording point. The strongest signal is measured when these three dependencies are perfectly aligned. The signal strengths are in the pV-range for a dipole moment of 5 nAm and ultrasonic pressures within Food and Drug Administration (FDA)-limits. The endogenous activity can then be accurately reconstructed via demodulation. Two interference types are investigated: vibrational and static. Depending on the vibrational interference, it is shown that millimeter resolution signal detection is possible also for deep brain regions. Subsequently, successful demodulation depends on the static interference, that at MHz-range has to be sub-picovolt.Significance.Our results show that mechanical vibration is a possible underlying mechanism of acousto-electrophyisological neuroimaging. This paper is a first step towards improved understanding of the conditions under which AENI is feasible.

A preliminary study on the application of the two-space nonperiodic asymptotic homogenization method to the EEG forward problem with continuously differentiable coefficient

The knowledge on the Electroencephalogram (EEG) forward problem is important to improve the imaging of the neural activity, that is an inverse problem. This paper introduces the study of the EEG forward problem via a nonperiodic homogenization technique: the two-space method. Considering a concentric spheres head model for the brain-skull-scalp medium as an micro-heterogeneous medium, a simplification consisting of a 1D problem in spherical coordinates with continuously differentiable coefficient is considered. The two-space method is applied successfully, and a numerical example shows the convergence of the micro-heterogeneous solution to the one obtained by the two-space method, as was expected. The preliminary conclusion is that this approach for the EEG forward problem with homogenization techniques shows itself as very promising. More experiments should be executed, considering more realistic models for the head.

Numerical solutions to an inverse problem for a non-linear Helmholtz equation

In this work, we develop numerical methods to solve forward and inverse wave problems for a nonlinear Helmholtz equation defined in a spherical shell between two concentric spheres centred at the origin. A spectral method is developed to solve the forward problem while a combination of a finite difference approximation and the least squares method are derived for the inverse problem. Numerical examples are given to verify the method.

Effects of slippage and permeability of couple stress fluid squeezed between two concentric rotating spheres

This study investigates the rotation of two concentric spheres saturated by creeping single-phase couple stress fluid flow under the impacts of permeability and slippage. The slippage conditions are applied on the surfaces of the spheres. In addition, the couple stresses on the boundary are assumed to vanish. Moreover, the analytical solution to the problem is used to obtain the field functions velocity, tangential stress, and couple stresses. The torque experienced by the fluid on the inner solid sphere is evaluated and plotted. The contour lines of fluid velocity are sketched at specific values of the parameters. The results presented that the torque acting on the inside sphere decreases monotonically with the permeability and slippage parameters at certain values of the relevant parameters. Also, the rise of couple stresses inclined the torque.

Emission of Energetic Neutral Atoms From the Magnetosphere‐Atmosphere Interactions at Callisto and Europa

AbstractWe analyze the emission of energetic neutral atom (ENA) flux from charge exchange between Jovian magnetospheric ions and the atmospheres of Callisto and Europa. For this purpose, we combine the draped electromagnetic fields from a hybrid plasma model with a particle tracing tool for the energetic ions. We determine the ENA flux through a concentric sphere located just outside of each moon's atmosphere, thereby capturing the complete physics imprinted in these emission patterns. In order to constrain the modifications to the ENA emissions that arise from the periodic change of the ambient plasma conditions, we calculate the emission morphology at multiple positions during a Jovian synodic rotation. To isolate the influence of field line draping, we compare to the emission patterns in uniform fields. Our major results are: (a) At Europa and Callisto, the majority of detectable ENA emissions are concentrated into a band normal to the Jovian magnetospheric field. (b) The fraction of observable ENA flux that contributes to this band depends on the number of complete gyrations that the parent ions can complete within the moon's atmosphere. (c) Field line draping partially deflects impinging parent ions around both moons, thereby attenuating the ENA flux and driving significant morphological changes to the emission patterns. (d) The band of elevated ENA flux is locally maximized on the opposite (antipodal) side of the moon where the flux is locally minimized. At Europa, detectable ENA emissions are maximized slightly west of the ramside apex. At Callisto, they maximize near the Jupiter‐facing apex.

How many gods and how many spheres? Aristotle misunderstood as a monotheist and an astronomer in Metaphysics Λ 8

Abstract Although Aristotle’s Metaphysics received much attention in the nineteenth and the twentieth centuries, scholars and historians of science were not particularly interested in clarifying the aim of Aristotle’s appeal to astronomy in Λ 8. Read with monotheistic prejudices, this chapter was quickly abandoned by Aristotelian scholars as a gratuitous insertion, which downgrades Aristotle’s God for the sake of some supplementary principles, whose existence was dictated by celestial mechanics. On the other hand, historians of astronomy read the astronomical excursus as providing a picture of Aristotle as an able astronomer, who made an important contribution to the theory of concentric celestial spheres of Eudoxus and Callippus by adding the counteracting spheres. The present article argues (a) that Aristotle purposefully turned to astronomy as the only mathematical science whose objects were correlative to the immaterial first substances or gods, the number of which had to be precisely determined by his own project of first philosophy; and (b) that he had no aspiration of improving the astronomical theory of his peers, contrary to an interpretation that first emerged with the Peripatetic exegete Sosigenes in the second century A.D.

One Definition to Join Them All: The N-Spherical Solution for the EEG Lead Field.

Albeit its simplicity, the concentric spheres head model is widely used in EEG. The reason behind this is its simple mathematical definition, which allows for the calculation of lead fields with negligible computational cost, for example, for iterative approaches. Nevertheless, the literature shows contradictory formulations for the electrical solution of this head model. In this work, we study several different definitions for the electrical lead field of a four concentric spheres conduction model, finding that their results are contradictory. A thorough exploration of the mathematics used to build these formulations, provided in the original works, allowed for the identification of errors in some of the formulae, which proved to be the reason for the discrepancies. Moreover, this mathematical review revealed the iterative nature of some of these formulations, which allowed us to develop a formulation to solve the lead field in a head model built from an arbitrary number of concentric, homogeneous, and isotropic spheres.

Impact of slippage on the wall correction rotation factor of MHD couple stress fluid between two concentric spheres

The creeping rotational motion of a magnetohydrodynamic couple stress fluid between two concentric spheres under the impact of slippages. The slippage conditions are applied on the surface of the inside sphere. In addition, the couple stresses on the boundary are assumed to vanish. The analytical solution to the problem is used to obtain the field functions of velocity, tangential stress, and couple stresses. The wall correction factor experienced by the fluid on the inner solid sphere is evaluated and plotted. However, in the presence of a magnetic field, the eddy current caused by rotating particles produces a torque that tends to rise because the assumption of the torque direction is the opposite direction of magnetic induction. Also, the first couple stress parameter, the angular velocity ratio, and slip condition did an improvement in the torque. On the other side, the wall correction factor slows down with slippage on the inner sphere and the size parameter. All results give limiting cases with no slippage and viscous fluid.

The Spherical Retractable Bubble Space: An Egocentric Graph Visualization throughout a Retractable Visualization Space

In this paper, we present a new egocentric metaphor for graph visualization that consists in positioning a graph between two concentric spheres of different radii. It improves the expansion of nodes in space, contrary to 3D spatialization algorithms. The edge drawing is optimized by pushing all the edges into the area delimited by our two concentric spheres so that a user can move freely without being encumbered by edges. Our new metaphor also makes it possible to reduce the display angles in order to have a global view of the graph without leaving the egocentricity.

On the Gehring Type Condition and Properties of Mappings

The goal of this work is to obtain an analytical description of mappings satisfying some capacity inequality (so called $G_p$-condition): we study mappings for which the $G_p$-condition holds for a cubical ring. In other words, we replace rings with concentric spheres in the $G_p$-condition by rings with concentric cubes. We obtain new analytic properties of homeomophisms in $\mathbb R^n$ meeting Gehring type capacity inequality. In this paper the capacity inequality means that the capacity of the image of a cubical ring is controlled by the capacity of the given ring. From the analytic properties we conclude some geometric properties of mappings under consideration. The method is new and is based on an equivalent analytical description of such mappings previously established by the author. Our arguments are based on assertions and methods discovered in author's recent papers [2] and [3] (see also some references inside). Then we obtain geometric properties of these mappings.