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Time functions with asymptotically hyperbolic geometry play an increasingly important role in many areas of relativity, from computing black hole perturbations to analyzing wave equations. Despite their significance, many of their properties remain underexplored. In this expository article, I discuss hyperbolic time functions by considering the hyperbola as the relativistic analog of a circle in two-dimensional Minkowski space and argue that suitably defined hyperboloidal coordinates are as natural in Lorentzian manifolds as spherical coordinates are in Riemannian manifolds. Editor's Note: The finite spacetime manifold in which outgoing waves reach infinity in a finite spacetime interval was introduced in the 1960s by Roger Penrose. It plays an important role in the analysis of gravitational waves. In this work the author shows how to construct a temporal foliation using spacelike slices with hyperbolic geometry in compactified Minkowski space. Instructors in special relativity will be able to make these ideas accessible to their students, including an application to massless fields in flat spacetime. [ABSTRACT FROM AUTHOR]

Cloud computing is an emerging technology in the field of distributed computing with the flexibility to pay per usage based on user needs and requirements. Task scheduling is considered to be a NP-hard problem, which directly affects the operational efficiency of the whole system, load balancing and system energy consumption, so it is challenging to find the best solution. A honey badger algorithm (HBA) based on improved density factor and Foucault pendulum motion is proposed to improve the efficiency of task execution in cloud computing systems. It improves the digging phase of the honey badger's foraging strategy using representations of Foucault pendulum motion in a right-angle coordinate system and a spherical coordinate system, respectively, and improves the density factor by using a variable-order sinusoidal curve. The performance of the proposed improvement scheme is tested by using 23 benchmark functions. Simulation experiments are conducted for the total cost, time cost, load cost and price cost of the system under large-scale and small-scale tasks. Compared to traditional scheduling algorithms such as ACO, PSO, WOA, AOA, RSO, SOA, CDO, RIME and GGO, HBA-Z (10) reduces about 15%, 39% and 12% in total, load and price costs over the next best algorithm in the small-scale task case, and about 25%, 51% and 27% over the worst algorithm. In the case of large-scale tasks, HBA-Z (10) reduces the total cost, load cost and price cost by about 16%, 40% and 14% compared to the next best algorithm, and reduces about 25%, 52% and 26% compared to the worst algorithm. Experimental results show that the proposed HBA-Z (10) has significant advantages in efficiently searching for optimal task scheduling policy. [ABSTRACT FROM AUTHOR]

We find the solution to the two-dimensional Laplace equation on a given set of three independent variables in the three-dimensional Euclidean space. The problem is solved by transforming the two-dimensional Laplace equation into some equation with the sought function of three independent variables. This turns out possible by introducing a spherical coordinate system. The proposed method allows us to find a solution to the two-dimensional Laplace equation in the form of a function of three independent variables. By way of example, we consider the problem of an incompressible fluid flow around a three-dimensional body shaped as an "iron." For this problem, we give the detailed arguments that reduce the three-dimensional Laplace equation describing the distribution of the scalar potential of the flow velocities near the surface of the body which depends on three independent coordinates to some two-dimensional Laplace equation whose solution is strictly justified by analysis. We also observe that similar problems arise not only in hydrodynamics but also in elasticity and electromagnetism theories. The described technique, namely, the possibility of passing from two to three independent variables by a given transformation enables us to find purely physical solutions for a wide range of problems from the various areas of natural sciences. [ABSTRACT FROM AUTHOR]

Aims. Short gamma-ray bursts originate when relativistic jets emerge from the remnants of binary neutron star (BNS) mergers, as observed in the first multi-messenger event GW170817–GRB 170817A, which coincided with a gravitational wave signal. Both the jet and the remnant are believed to be magnetized, and the presence of magnetic fields is known to influence the jet propagation across the surrounding post-merger environment. In the magnetic interplay between the jet and the environment itself, effects due to a finite plasma conductivity may be important, especially in the first phases of jet propagation. We aim to investigate these effects, from jet launching to its final breakout from the post-merger environment. Methods. We used the PLUTO numerical code to perform 2D axisymmetric and full 3D resistive relativistic magnetohydrodynamic (MHD) simulations, employing spherical coordinates with spatial radial stretching. We considered and compared different models for physical resistivity, which must be small but still dominating over the intrinsic numerical dissipation (which yields unwanted smearing of structures in any ideal MHD code). Stiff terms in the current density are treated with IMplicit-EXplicit Runge Kutta algorithms for time-stepping. A Synge-like gas (Taub equation of state) is also considered. All simulations were performed using an axisymmetric analytical model for both the jet propagation environment and the jet injection; we leave the case of jet propagation in a realistic environment (i.e., imported from an actual BNS merger simulation) to a future study. Results. As expected, no qualitative differences are detected due to the effect of a finite conductivity, but significant quantitative differences in the jet structure and induced turbulence are clearly seen in 2D axisymmetric simulations, and we also compare different resistivity models. We see the formation of regions with a resistive electric field parallel to the magnetic field, and nonthermal particle acceleration may be enhanced there. The level of dissipated Ohmic power is also dependent on the various recipes for resistivity. Most of the differences arise before the breakout from the inner environment, whereas once the jet enters the external weakly magnetized environment region, these differences are preserved during further propagation despite the lower grid refinement. Finally, we show and discuss the 3D evolution of the jet within the same environment in order to highlight the emergence of nonaxisymmetric features. [ABSTRACT FROM AUTHOR]

In the limit of very low Reynolds numbers, the steady translation of a fluid sphere situated at a non‐concentric position in a second immiscible fluid bounded by spherical cavity is investigated using boundary collocation technique. The flow inside and outside the fluid sphere is governed by Stokes equations. Boundary conditions at the fluid sphere are continuity of velocity and shear stress. Zero shear stress and zero vorticity are used on spherical cavity. By using superposition principle, a general solution is constructed from the basic solutions in the two spherical coordinate systems based on both the fluid sphere and spherical cavity. The normalized drag force exerted on the fluid sphere contained in a cavity is depended on the ratio of fluid sphere and cavity radii, viscosity ratio of fluid sphere and cavity, relative distance between the centers of fluid sphere and cavity. The results are in good agreement with previously published work in the limiting cases. The numerical results of the drag force are good agreement with the solutions of the translation of the fluid sphere in a concentric cavity and the translation of a solid sphere in a non‐concentric cavity. The drag force is increasing function of the viscosity ratio, volume fraction, and the relative distance. This work is extension of the previous work of Keh and Lee for the fluid sphere using Happel's and Kuwabara's models. [ABSTRACT FROM AUTHOR]

A linear model for predicting the ignition delay time of hypergolic ignition is presented based on thermal diffusion theory. The heat released by the hypergolic reaction is assumed to diffuse through a given length scale while being governed by a heat source in the form of an Arrhenius equation. A linearized approach is used to reach analytical expressions for the ignition delay times, defined when the temperature change at the reactants interface drastically increases, diverges, or tends toward infinity. Ignition delay times for three different geometries, cartesian, cylindrical, and spherical, are derived and compared. The results show that, for spherical coordinates, the ignition depends on a critical condition, which is based on material and chemical properties and geometry. A prediction of the ignition condition for all cases where one of the reactants is a droplet/particle is given. The ignition process is analyzed based on non-dimensional parameters in order to understand the behavior of the temperature change during ignition. The results obtained are consistent with results presented in the literature. In addition, a prediction for ignition delay times is provided. [ABSTRACT FROM AUTHOR]

It is more than a century-old concept that the Minkowski spacetime is flat. From the pure geometric point of view, we explicitly address the issue of whether a noncommutative Minkowski spacetime is flat or not. In the framework of the twisted-diffeomorphism approach to noncommutative gravity with canonical type noncommutative (NC) coordinate structure, one important result that we get is that the NC Minkowski spacetime parametrized either with spherical polar coordinates or with parabolic coordinates has nontrivial NC corrections to Riemann curvature tensor, Ricci tensor and curvature scalars. Another crucial result is that the curvature scalars have singular behavior at certain points, and these singularities are not coordinate singularities. The nature of these singularities clearly points towards the idea of high-energetic probes turning into black holes. The absence of any such noncommutative corrections, and thus any such singularities, in the cases of Cartesian coordinates and cylindrical coordinates leads to the conclusion that high-energetic probes do not turn into black holes when the canonical NC structure is considered for these coordinates. [ABSTRACT FROM AUTHOR]

In a gas–water interaction problem, the nonlinear relationship between shock wave velocity is introduced into a Hugoniot curve, and a Mie–Grüneisen Equation of state (EOS) is established by setting the Hugoiot curve as the reference state. Unlike other simple EOS based on the thermodynamics laws of gas (such as the Tait EOS), the Mie–Grüneisen EOS uses reference states to cover an adiabatic impact relationship and considers the thermodynamics law separately. However, the expression of the EOS becomes complex, and it is not adaptive to many methods. A multicomponent Mie–Grüneisen mixture model is employed in this study to conquer the difficulty of the complex form of an EOS. In this model, some coefficients in the Mie–Grüneisen EOS are regarded as variables and solved using newly constructed equations. The performance of the Mie–Grüneisen mixture model in the gas–water problem is tested by low-compression cases and high-compression cases. According to these two tests, it is found that the numerical solutions of the shock wave under the Mie–Grüneisen EOS agrees with empirical data. When compared to other simple-form EOSs, it is seen that the Mie–Grüneisen EOS has slight advantages in the low-compression case, but it plays an important role in the high-compression case. The comparison results show that the solution of the simple-form EOS clearly disagrees with the empirical data. A further study shows that the gap between the Mie–Grüneisen EOS and other simple-form EOSs becomes larger as the initial pressure and particle velocity increase. The impact effects on the pressure, density and particle velocity are studied. Moreover, the gas–water interaction in a spherical coordinate plane and a two-dimensional coordinate is a significant part of our work. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of Hilbert-type inequalities on a fractal set (ℝ+αn)k. Establishing higher-dimensional Cantor-type spherical coordinates is an essential step in our results. We also impose the corresponding requirements that lead to the best constants obtained in the fractal Hilbert-type inequalities. Our results are applied by comparing them with previous results that are well known from the literature. [ABSTRACT FROM AUTHOR]

A quasi-steady flow due to a solid sphere moving in a micropolar fluid inside a concentric cavity is analyzed, where on the particle's external surface and the cavity's internal surface, the fluid can slip-spin. The solid particle translates upon the diameter connecting their centers when the Reynolds numbers are low. A general solution, to resolve the Stokesian equations for the fluid velocity field, is obtained according to the spherical coordinates, depending on the concentric position between the particle and cavity. Boundary conditions are satisfied, on the particle's external surface and the cavity's internal surface. Moreover, a tangential couple stress is used on both surfaces. The normalized drag force affecting a translating particle is determined to be a function that increases monotonically for the ratio of the solid-to-cavity radii, becoming infinite when the particle surface touches the cavity surface. Numerical outcomes for the normalized force affecting the particle's surface are gained at different values for the ratio of the particle-to-cavity radii and also the slip-spin surface coefficients of the particle and cavity. Our outcomes are in a high level of precision with the solutions available in the literature. The current study is significant for the domains of industrial, natural, biological, and medical processes, like the production of raindrops, the flow of blood cells in arteries and veins, sedimentation, coagulation, suspension rheology, and liquid–liquid extraction. [ABSTRACT FROM AUTHOR]

The conformal fractional derivative (CFD) has become a hot research topic since it has a physical interpretation and is easier to grasp and apply to problems compared with other fractional derivatives. Its application to heat transfer, diffusion, diffusion-advection, and wave propagation problems can be found in the literature. Fractional diffusion equations have received great attention recently due to their applicability in physical, chemical, and biological processes and engineering. The diffusion of the pollutants within the ground, which is an important environmental problem, can be modeled with a diffusion equation. Diffusion in some porous materials or soil can be modeled more accurately with fractional derivatives or the conformal fractional derivative. In this study, the diffusion problem of a spilled pollutant leaking into the ground modeled with the conformal fractional time derivative in spherical coordinates has been solved analytically using the Fourier series for a constant mass flow rate and complete symmetry under the assumptions of homogeneous and isotropic soil, constant soil temperature, and constant permeability. The solutions have been simulated spatially and in time. A parametric analysis of the problem has been performed for several values of the CFD order. The simulation results are interpreted. It has also been suggested how to find the parameters of the soil to see whether the CFD can be used to model the soil or not. The approach described here can also be used for modeling pollution problems involving different boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, an analytical and numerical technique are examined in order to analyse the Stokes flow determination problem due to a viscous sphere droplet moving at a concentric instantaneous position inside a spherical interface separating finite and semi-infinite immiscible fluid phases. Here, when only one of the three phases of the fluid (micropolar fluid) has a microstructure, attention is focused on this case. The motion is considered when Reynolds- and capillary-numbers are low, and the droplet surface and the fluid-fluid interface have insignificant deformation. A general solution is obtained in a spherical coordinate system based on a concentric position to analyse the slow axisymmetric movement of the micropolar fluid, considering microrotation and velocity components. Boundary conditions are initially fulfilled at the fluid-fluid interface and subsequently at the droplet surface. The normalised hydrodynamic drag force applying to a moving viscous droplet appears to be a function of the droplet-to-interface radius ratio, which increases monotonically and becomes unbounded when the droplet surface touches the fluid-fluid interface. The numerical outcomes of the normalised drag force acting on the viscous droplet are derived for different values of the parameters, and are presented in a tabular and graphical framework. A comparison was made between our numerical outcomes for the drag force and the pertinent data for the special cases found in the literature. [ABSTRACT FROM AUTHOR]

When an activated complex, as defined in transition state theory (TST), has a polyhedral shape, its kinetic energy is found to be diagonal in a system of spherical polar coordinates. If, in addition, the polyhedron is characterized by a high symmetry, then its dynamics considerably simplifies. An application of this approach to the most symmetrical TS known to date, i.e., that which controls the Cl− + CH3Cl → ClCH3 + Cl− SN2 nucleophilic substitution, is presented and an analytical expression of its potential energy surface is provided. In a substantial range around the saddle point, approximate equations of motion for the two components of the reaction coordinate, i.e., the antisymmetrical stretching motion of the ClCCl core and the wagging motion of the hydrogen triad, can be derived in an analytical form. During an extensive period of time, the main component of the reaction coordinate is governed by an unexpectedly simple equation of motion that depends on a single initial condition, irrespective of the other ones and of the internal energy. Reactive trajectories are observed to form a perfectly collimated bundle characterized by undetectable dispersion, thereby giving a spectacular example of regular dynamics in an anharmonic potential. Regularity and collimation are brought about by local symmetry, which is a widespread feature of potential energy surfaces. Anharmonicity is observed to influence the dynamics only at a late stage. As energy increases, trajectories tend to fan out and to deviate from the analytical equation. For the wagging motion, chaos sets in at much lower energies. [ABSTRACT FROM AUTHOR]

Historical measurements, such as the measurement of the size of our Galaxy and distance to its center, are based on relatively simple assumptions that allow high-school students and undergraduate college students to explore and replicate the basic analysis of astronomical data. Here, I present a practical data analysis exercise that was developed to select Slovenian participants to the International Olympiad on Astronomy and Astrophysics (IOAA). The exercise guides students to discover the globular cluster distribution within our Galaxy, use basic knowledge of spherical astronomy and coordinate transformation, explore the night sky and develop basic skills for the analysis of astronomical data. [ABSTRACT FROM AUTHOR]

A 5-DoF fully parallel machining robot (PMR) with attitude coupling motion property holds the potential to realize the high-efficiency and high-quality machining of complex parts with curved surfaces. Mechanistically, this type of 5-DoF fully PMR can achieve no singularity in the workspace after optimum design, allowing the mobile platform to be adjusted to an arbitrary orientation directly and flexibly. To full leverage these mechanical characteristics, the concept of planning orientation paths in a unit spherical coordinate system was proposed in our previous work, thereby enhancing orientation adjustment efficiency. However, challenges in toolpath continuity and computational simplicity still persist. In light of this concern, constraint equations were formulated to ensure continuity between two adjacent B-splines, and a configuration of control points was established to maintain controllable curvature. Building on this, a symmetrical arrangement strategy was introduced to set shape limits for fitted B-splines to achieve high-order continuity, and a corresponding toolpath planning method was developed. To decrease computational complexity during feedrate scheduling, a system of linear constraints was utilized to calculate the feedrate for each point, with the feedrate calculation and interpolation occurring concurrently to generate the motion trajectory in real time. Trajectory planning for S-shaped toolpaths was conducted using the proposed method and the commercial ISG CNC kernel, with comparison results demonstrating that our method significantly improves motion efficiency, reduces computational complexity, and mitigates feedrate and acceleration fluctuations. This study offers a more efficient and effective trajectory planning approach, significantly contributing to the advancement of 5-DoF PMR technology. [ABSTRACT FROM AUTHOR]

Gravity forward modeling as a basic tool has been widely used for topography correction and 3D density inversion. The source region is usually discretized into tesseroids (i.e., spherical prisms) to consider the influence of the curvature of planets in global or large-scale problems. Traditional gravity forward modeling methods in spherical coordinates, including the Taylor expansion and Gaussian–Legendre quadrature, are all based on spatial domains, which mostly have low computational efficiency. This study proposes a high-efficiency forward modeling method of gravitational fields in the spherical harmonic domain, in which the gravity anomalies and gradient tensors can be expressed as spherical harmonic synthesis forms of spherical harmonic coefficients of 3D density distribution. A homogeneous spherical shell model is used to test its effectiveness compared with traditional spatial domain methods. It demonstrates that the computational efficiency of the proposed spherical harmonic domain method is improved by four orders of magnitude with a similar level of computational accuracy compared with the optimized 3D GLQ method. The test also shows that the computational time of the proposed method is not affected by the observation height. Finally, the proposed forward method is applied to the topography correction of the Moon. The results show that the gravity response of the topography obtained with our method is close to that of the optimized 3D GLQ method and is also consistent with previous results. [ABSTRACT FROM AUTHOR]

This study investigates the iterative learning control method for discrete‐time systems with data quantization, and it employs a quantizer based on spherical polar coordinates. The quantizer uses spherical polar coordinates to transform an unquantized signal into one with a predetermined quantization level. The quantization capability is dependent on the size of the support sphere, which is dynamically adjustable. In the scenarios of system output quantization, general quantization, and tracking error quantization, the learning control schemes are developed with consideration of the smallest sphere quantization features. The radii of the support spheres are designed independently based on the characteristics of the quantized signals (system output, control input, tracking error). The findings suggest that the system can achieve a bounded error convergence in the scenarios of system output and general quantization. In the context of quantization in tracking error, it is achievable to attain tracking performance with zero error. The example of a permanent magnet synchronous motor is provided to illustrate the findings of the study. [ABSTRACT FROM AUTHOR]

Industrial computed tomography (CT) is widely used in the measurement field owing to its advantages such as non-contact and high precision. To obtain accurate size parameters, fitting parameters can be obtained rapidly by processing volume data in the form of point clouds. However, due to factors such as artifacts in the CT reconstruction process, many abnormal interference points exist in the point clouds obtained after segmentation. The classic least squares algorithm is easily affected by these points, resulting in significant deviation of the solution of linear equations from the normal value and poor robustness, while the random sample consensus (RANSAC) approach has insufficient fitting accuracy within a limited timeframe and the number of iterations. To address these shortcomings, we propose a spherical point cloud fitting algorithm based on projection filtering and K-Means clustering (PK-RANSAC), which strategically integrates and enhances these two methods to achieve excellent accuracy and robustness. The proposed method first uses RANSAC for rough parameter estimation, then corrects the deviation of the spherical center coordinates through two-dimensional projection, and finally obtains the spherical center point set by sampling and performing K-Means clustering. The largest cluster is weighted to obtain accurate fitting parameters. We conducted a comparative experiment using a three-dimensional ball-plate standard. The sphere center fitting deviation of PK-RANSAC was 1.91 μm, which is significantly better than RANSAC's value of 25.41 μm. The experimental results demonstrate that PK-RANSAC has higher accuracy and stronger robustness for fitting geometric parameters. [ABSTRACT FROM AUTHOR]

Copyright of Remote Sensing for Natural Resources is the property of Remote Sensing for Natural Resources Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Coffee consumption could provide various benefits for human health, but also could contribute to several health problems. The growing trend of coffee consumption has created a rising demand for decaffeinated coffee that is safe for consumers with low caffeine tolerance. Decaffeination process, however, can result in the alteration of several properties of coffee which affect overall coffee taste. This review discussed current decaffeination methods such as water decaffeination, solvent decaffeination, supercritical decaffeination, and biodecaffeination which includes their mechanisms, benefits, and drawbacks as well as their effect in the physicochemical and sensory characteristics of coffee. Solvent decaffeination has showed potential improvements in the future such as the incorporation of membrane and ultrasonic technology. In addition, the mathematical model for caffeine diffusion has been arranged according to Fick's second law of diffusion, based upon spherical and rectangular coordinates with several assumptions. Further research should be aimed to maintain the properties of coffee after decaffeination process. Furthermore, utilizing new solvents that are safe and non-toxic will potentially be favorable research in the development of decaffeination methods in the future. [ABSTRACT FROM AUTHOR]

The objective of this research paper is to propose an exact solution for resolving the transient conduction in a 2D sphere. The coefficients of governing equation are varied according to the material properties. The thermo‐physical properties are regarded as functions that follow a power‐law relationship concerning the radial direction. Both radial and angular thermal conductivity coefficients change with radius. Thermal boundary conditions are considered in a general state, which can cover different thermal conditions, including Dirichlet, Neumann, and Convection surface conditions. Laplace transform and Meromorphic function methods are used in the solution approach to the current unsteady problem. Two unsteady case studies with complex boundary conditions have been considered to show the credibility of the current solution. The results of both case studies have been successfully validated. The results confirm the high capability of the present solution in solving unsteady thermal problems of functionally graded materials in spherical coordinates. [ABSTRACT FROM AUTHOR]

In this paper, we analyse the computational advantages of the spherical parametrisation for correlation matrices in the context of Maximum Likelihood estimation via numerical optimisation. By using the special structure of correlation matrices, it is possible to define a bijective transformation of an n × n correlation matrix R into a vector of n (n - 1) / 2 angles between 0 and π . After discussing the algebraic aspects of the problem, we provide examples of the use of the technique we propose in popular econometric models: the multivariate DCC-GARCH model, widely used in applied finance for large-scale problems, and the multivariate probit model, for which the computation of the likelihood is typically accomplished by simulated Maximum Likelihood. Our analysis reveals the conditions when the spherical parametrisation is advantageous; numerical optimisation algorithms are often more robust and efficient, especially when R is large and near-singular. [ABSTRACT FROM AUTHOR]

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this research, a streamlined numerical approach designed for the quick estimation of temperature profiles across the finite thickness of a hemispherical dome subjected to aerodynamic heating is introduced. Hemispherical domes, with their advantageous aerodynamic, structural, and optical properties, are frequently utilized in the front sections of objects traveling at supersonic velocities, including missiles or vehicles. The proposed method relies on one-dimensional analyses of fluid dynamics and flow characteristics to approximate the local heat flux across the exterior surface of the dome. By calculating these local heat flux values, it is also possible to predict the temperature variations within the thickness of the dome by employing the finite difference technique, to solve the heat conduction equation in spherical coordinates. This process is iterated over successive time intervals, to simulate the entire flight duration. Unlike traditional Computational Fluid Dynamics (CFD) simulations, the proposed strategy offers the benefits of significantly lower computational time and resource demands. The primary objective of this work is to provide an efficient numerical tool for evaluating aerodynamic heating impact and temperature gradients on hemispherical domes under specific conditions. The effectiveness of the proposed method will be validated by comparing the temperature profiles derived for a standard flight scenario against those obtained from 2-D axisymmetric transient CFD simulations performed using ANSYS-Fluent 2022 R2. [ABSTRACT FROM AUTHOR]

Diffusion chronometry is a technique gaining interest in the scientific community related to volcanology and petrology; however, modelling can be challenging for non-expert users. Here, we present DiffSim, a user-friendly standalone freeware that allows users to calculate magmatic timescales simulating 1D diffusion of major elements in olivine, orthopyroxene, titanomagnetite, and melt (inclusions). The freeware works solving the Fick's second law equation (for both Cartesian and spherical polar coordinates, depending on the phase) using finite differences through the Crank-Nicolson method. Users must specify the initial composition vs. distance profile, the time resolution, and the intensive conditions (such as temperature, pressure, and oxygen fugacity). For orthorhombic phases, such as olivine and orthopyroxene, users must also specify the plunge and the trend of the (001)-axis and the angle traverse of the 2D section being studied. The best-fitting profile, comparing the natural (measured) and the modelled (calculated) profiles, is obtained using the least-squares fitting method in accordance with the total time specified by the user for performing the diffusion modelling. To determine the uncertainties of the timescale calculation, DiffSim propagates errors based on the uncertainties associated with each intensive condition and the experimental diffusivity measurements. DiffSim is available as executable freeware, allowing researchers and students to use diffusion chronometry to elucidate information about crustal processes with ease and precision. [ABSTRACT FROM AUTHOR]

Several decades after the invention of the rechargeable Li‐ion battery, countless innovations from both the research and industry communities have led to placing the secondary battery at the heart of the electrification revolution in recent years. Mathematical and numerical models have been trusted companions in advancing the technology to help guide design improvements or to gain insight when physical measurements are impossible to perform. Starting with the breakthrough porous electrode theory (PET) model proposed by Newman and co‐workers in 1975 (Newman and Tiedemann, AIChE Journal, 1975, 21, 25–41), many authors have improved the formulation from a variety of perspectives. The novel aspects of the model we propose in this paper expand on this long stream of PET formulations and aim to address modeling needs that, to the authors' knowledge, have not been yet considered. The proposed formulation is characterized by the following concurrent features: (1) a full 3D description of the macroscale behavior and 1D microscale in spherical coordinates (Pseudo 4D formulation [P4D]) accounting for geometric details of the cell architecture such as imperfect spiral jellyrolls in cylindrical cells; (2) multiple concurrent particle chemistries to model the microscale lithiation/delithiation behavior at every macroscale element integration point, leading to a multiscale (FE2$$ {\mathrm{FE}}^2 $$) approach; (3) a fully coupled thermal‐electrochemical‐mechanical stress interaction due to lithiation/delithiation induced swelling and external confinement; (4) spatially‐dependent porosity evolutions due to swelling of the particles in the porous electrodes; (5) electrolyte flow in the porous regions and overfill spaces via Darcy‐based flow including partial saturation of the active regions; (6) detailed descriptions of individual battery components such as the electrodes, separator, and current collectors with the possibility of "connecting" the different components through contact definitions; (7) fully linearized macro‐microscale coupling behavior allowing for large time increments in an implicit time integration scheme for a scalable and computationally effective numerical solution. A number of numerical examples including validation against experimental data are performed to demonstrate the predictive power of the proposed model and its efficiency for industrial applications. [ABSTRACT FROM AUTHOR]

Spherical piezoelectric motors (SPMs) represent a promising actuator technology applicable to the development of motion control systems with multiple degrees of freedom. However, few SPMs have made it successfully to market, as an effective and systematic rotor orientation analysis and manipulation technique has yet to be developed. This study thus developed a novel triplet-stator SPM design that integrates electrode configuration to excite lateral vibrations and offers two fundamental rotor orientations for each set of piezoelectric plates by changing the contact position between the rotor and stator. To accomplish omnidirectional orientations for the proposed SPM system, we present a systematic orientation analysis based on spherical coordinates. We further apply the concept of vector composition to derive new composite orientations by adjusting the magnitude ratio of the provided torques between three stators. An orientation angle representation accounting for the rotor dynamics is used to validate the correctness of the synthesized orientation vectors both in simulation and experiments. The orientation analysis results in a three-dimensional sphere containing eight vector spaces corresponding to eight stator actuation modes, in which an arbitrary rotor orientation reference command can be generated under the designed actuation modes. Experimental results were well correlated with simulations, thereby verifying the effectiveness of the proposed SPM system design and orientation analysis. [ABSTRACT FROM AUTHOR]

The principle of independence is a fundamental yet often disregarded assumption in statistical inference. It is observed that the implications of correlations, if not considered, can lead to a conservative estimation of Type I error in the presence of positive linear correlations when utilizing the Kolmogorov-Smirnov (KS) test. Conversely, negative linear correlations may engender a liberal estimation of Type I error. To address the impact of spatial autocorrelation in the analysis of Positron Emission Tomography (PET) images, we have proposed an innovative methodology to reconstruct a grid map of human heart scans using spherical coordinates. We have examined the distribution of the KS test statistic under spatial autocorrelation through Monte Carlo (MC) simulation and have introduced a KS test with a spatial adjustment. The newly proposed KS test with spatial adjustment demonstrates a controlled Type I error and power that is not inferior when compared to the original KS test. This suggests its potential utility in the analysis of spatially autocorrelated data. [ABSTRACT FROM AUTHOR]

This semi-analytical study is presented examining the quasi-steady creeping flow caused by a soft (composite) spherical particle, which is a hard (impermeable) sphere core covered by a porous (permeable) layer, translating in an incompressible Newtonian fluid within a non-concentric spherical cavity along the line joining their centers. To solve the Brinkman and Stokes equations for the flow fields inside and outside the porous layer, respectively, general solutions are constructed in two spherical coordinate systems attached to the particle and cavity individually. The boundary conditions at the cavity wall and particle surface are fulfilled through a collocation method. Numerical results of the normalized drag force exerted by the fluid on the particle are obtained for numerous values of the ratios of core-to-particle radii, particle-to-cavity radii, the distance between the centers to the radius difference of the particle and cavity, and the particle radius to porous layer permeation length. For the translation of a soft sphere within a concentric cavity or near a small-curvature cavity wall, our drag results agree with solutions available in the literature. The cavity effect on the drag force of a translating soft sphere is monotonically increasing functions of the ratios of core-to-particle radii and the particle radius to porous layer permeation length. While the drag force generally rises with an increase in the ratio of particle-to-cavity radii, a weak minimum (surprisingly, smaller than that for an unconfined soft sphere) may occur for the case of low ratios of core-to-particle radii and of the particle radius to permeation length. This drag force generally increases with an increase in the eccentricity of the particle position, but in the case of low ratios of core-to-particle radii and particle radius to permeation length, the drag force may decrease slightly with increasing eccentricity. [ABSTRACT FROM AUTHOR]

This paper aims to achieve bedrock geologic mapping in the overburden area using big data, distributed computing, and deep learning techniques. First, the satellite Bouguer gravity anomaly with a resolution of 2'x2' in the range of E66°E96°, N40°-N55° and 1:5000000 Asia-European geological map are used to design a dataset for bedrock prediction. Then, starting from the gravity anomaly formula in the spherical coordinate system, we deduce the non-linear functional between rock density ρ and rock mineral composition m, content p, buried depth h, diagenesis time t and other variables. We analyze the feasibility of using deep neural network to approximate the above nonlinear generalization. The problem of solving deep neural network parameters is transformed into a non-convex optimization problem. We give an iterative, gradient descentbased solution algorithm for the non-convex optimization problem. Utilizing neural architecture search (NAS) and human-designed approach, we propose a geological-geophysical mapping network (GGMNet). The dataset for the network consists of both gravity anomaly and a priori geological information. The network has fast convergence speed and stable iteration during the training process. It also has better performance than a single neural network search or human-designed architectures, with the mean pixel accuracy (MAP) = 63.1% and the frequency weighted intersection over union (FWIoU) = 42.88. Finally, the GGMNet is used to predict the rock distribution of the Junggar Basin. [ABSTRACT FROM AUTHOR]

Magnetic materials find wide applications in modern technology. For further materials design and optimization, physics-grounded micromagnetic simulations play a critical role, as predictions of properties, regarding the materials to be examined, can be made on the basis of in silico characterizations. However, micromagnetism, in particular, the Landau–Lifshitz–Gilbert equation, poses an interesting but challenging numerical issue, particularly the constraint of the preserved magnetization magnitude far below Curie temperature. Since this requirement is not fulfilled a priori, additional measures must be considered. In this work, four different methods for conserving the length of the magnetization vector in the framework of the finite element method are compared, namely, a projection method, penalty method, a Lagrange multiplier, and the approximation of the magnetization vectors using arithmetical and circular spherical coordinates. By applying the described methods to appropriate numerical examples, the different advantages and disadvantages are worked out so that a clear recommendation for the perturbed Lagrange method can be derived. [ABSTRACT FROM AUTHOR]

This paper investigates the electromagnetic fields being scattered by a metal spherical object in a vacuum environment, providing a numerical implementation of the obtained analytical results. A time-harmonic magnetic dipole source, far enough, emits the incident field at low frequencies, oriented arbitrarily in the three-dimensional space. The aim is to find a detailed solution to the scattering problem at spherical coordinates, which is useful for data inversion. Based on the theory of low frequencies, the Maxwell-type problem is transformed into Laplace's or Poisson's interconnected equations, accompanied by the proper boundary conditions on the perfectly conducting sphere and the radiation conditions at infinity, which are solved gradually. Broadly, the static and the first three dynamic terms are sufficient, while the terms of a higher order are negligible, which is confirmed by the field graphical representation. [ABSTRACT FROM AUTHOR]

The governing equations for a viscous, incompressible fluid, in the thin-shell approximation, written in a coordinate frame which ensures validity at the North Pole, is simplified by invoking the f-plane approximation. Together with suitable stress conditions at the surface, describing the interaction of wind over ice and ice over water, a solution is developed for the Transpolar Drift current. This involves prescribing the near-surface geostrophic ocean flow and also, for ease of calculation, a simple version of the Ekman flow. Then, via the stress conditions at the surface, the near-surface wind consistent with these flows is obtained. An example, which exhibits the reduction in ice thickness as the flow moves over the North Pole towards the Fram Strait, and also describes the relative directions and speeds of the wind, ice and water, is presented in graphical form; this solution recovers what is observed. The considerable freedom available in this approach, allowing choices to be made for the geostrophic flow and the wind (both variable), and the ice profile at some initial position, is explained, opening the way to further, extensive investigations. [ABSTRACT FROM AUTHOR]

This research focuses mainly on the spherical asymmetric multiple traveling salesman problem (AMTSP). Three-dimension AMTSP is an extension of the AMTSP, it arranges all cities and paths on the three-dimension sphere. Therefore, the AMTSP is more challenging but also has more research value. An improved hybrid algorithm called spherical vector-based artificial gorilla troops optimization (SGTO) with a discrete state transition strategy to deal with the three-dimension sphere asymmetric multiple traveling salesman problem. The proposed algorithm updates positions in spherical coordinates instead of Cartesian coordinates. By combining the discrete state transition algorithm's swap, shift, symmetric, and substitute operators, it enriches the population's diversity and enhances the efficiency of local searches. Numerical simulation results show that SGTO outperformed the basic GTO and other classical metaheuristic algorithms in solving the spherical AMTSP. [ABSTRACT FROM AUTHOR]

We examine the basic matrix equation for a spin-2 field in spherical coordinates and a tetrad of Minkowski spacetime. The technique of Wigner D-functions is used to separate the variables. The operators of energy, the square and the third projection of the total angular momentum, and the space reflection operators are then diagonalized on the solutions. The separation of the variables is done, the problem reduces to 11 radial second-order differential equations for 11 variables related to the scalar and symmetric tensors. We then consider the case of a massless field. The four gauge solutions for the massless spin-2 field have been found in explicit form. These gauge solutions do not contribute to physically observable quantities such as the energy–momentum tensor. They are derived according to Pauli–Fierz theory from four independent spherical solutions for a spin-1 massless particle. We have also constructed two types of solutions, related to opposite parities, which are not the gauge solutions. These solutions describe physically observable states with spherical symmetry for the spin-2 massless field. [ABSTRACT FROM AUTHOR]

We present a class of "ellipsoidal rotation matrices" which can be used to characterize tectonic plate motion; where geocentric Cartesian coordinates travel along paths tangential to the ellipsoid. We contrast them with conventional Euler pole plate motion models which are more closely aligned with spherical coordinate systems and inherently induce a change in geodetic ellipsoidal height. We demonstrate the use of each in the Indo‐Australian tectonic plate setting, which is known to move approximately 7 cm/year in a north‐northeast direction. Geocentric Datum of Australia 2020 (GDA2020) coordinates are "plate‐fixed" static coordinates obtained using a conventional Euler pole plate motion model to align time dependent coordinates with the 2014 realization of the International Terrestrial Reference Frame at the epoch 2020.0. We show that this Euler pole plate motion model can introduce ellipsoidal height velocities of up to −0.2 mm/year. This is small but systematic, so pertinent for consideration with high accuracy vertical land motion studies using GDA2020 coordinates and velocities. We further investigate the comparative statistical accuracy of conventional Euler pole and the ellipsoidal models with respect to characterizing plate motion captured in high quality Global Navigation Satellite System data. Plain Language Summary: We introduce a new way to study the movement of Earth's tectonic plates, using something called "ellipsoidal rotation matrices." These matrices help us understand how plates move along a path that agrees with the Earth's ellipsoidal shape. This is different to the traditional way of studying plate motion, which usually assumes the Earth is a perfect sphere. We tested both methods by looking at the Indo‐Australian tectonic plate, which is moving north‐northeast at about 7 cm per year. Our findings show that the traditional, spherical method could result in slightly misrepresenting how the land is moving vertically, by up to −0.2 mm per year, since the vertical motion signal cannot be separated from the tectonic plate motion adequately. While this might not seem like much, it could matter in studies that require very accurate measurements of land height changes over time. We verify how well each method is in capturing the real movement of the Indo‐Australian tectonic plate and demonstrate that the ellipsoidal method is more accurate. Key Points: We introduce "ellipsoidal rotation matrices," contrasting with the traditional Euler pole method, which assumes Earth is a perfect sphereIn the Indo‐Australian tectonic plate setting, the traditional method can misrepresent vertical land movement by up to −0.2 mm per yearThe new ellipsoidal method provides a more accurate way to study plate movements, where ellipsoidal coordinate systems are used [ABSTRACT FROM AUTHOR]

Six red-light-emitting Eu(III) complexes having a β-hydroxyketone as ligand and heterocyclic ring containing compounds as ancillary ligands were synthesized to explore their use in displays and optoelectronics. The coordinating behavior of complexes was determined by various techniques such as FTIR (Fourier transform infrared), 1H-NMR (Nuclear magnetic resonance), and 13C-NMR that establishes a bonding of ligand and ancillary ligand with the Eu(III) ion. Morphology and purity were investigated through XRD (X-ray diffraction), SEM (scanning electron microscopy) and EDS (energy-dispersive X-ray spectroscopy) analyses that suggest semicrystalline and pure complex formation. Thermal analysis of complexes by TGA/DTG (thermogravimetric/derivative thermogravimetric) indicates that complexes are stable upto 200 ºC temperature making them suitable for use in display devices. Analysis of the photophysical properties was carried out in both solid and solution states using PL (photoluminescence) studies, color parameters, J–O (Judd–Ofelt) analysis and bandgap. Most emissive transition (5D0 → 7F2) is responsible for the red emission in the complexes. The CIE (Commission International de I'Eclairage) coordinates of complexes also indicate the red emission on UV excitation. The bandgap which was obtained in the range of 2.54–3.02 eV reveals the semiconducting behavior of complexes. Values of J–O parameters and Ω2 in the complexes reflect asymmetric chemical environment around Eu (III) and less covalence and the Ω4 indicates that complexes are less rigid. Bandgap calculated through DFT (density function theory) for complexes is in range of 2.37–2.77 eV, and intensity parameters (J–O), energy transfer rates, and spherical coordinates were determined by LUMPAC software. The computational data are in good harmony with the experimental data. Further biological aspects of complexes were studied using antioxidant and antimicrobial studies. [ABSTRACT FROM AUTHOR]

The heat transport that takes place in living tissue during magnetic tumor hyperthermia is described in this study using the nonlocal bioheat model in spherical coordinates. In magnetic fluid hyperthermia, it is crucial to regulate the therapeutic temperature. This paper suggests a hybrid numerical approach that employs the Laplace transforms, change of variables, and modified discretization techniques, coupled with nonlocal hyperbolic shape function, to tackle the present problem. This study investigates the impacts of nonlocal parameter and the disparity in thermophysical properties between diseased and healthy tissue. A graph is displayed to represent the numerical temperature results. The validity of the numerical findings is demonstrated by comparing them with the results reported in previous literature. [ABSTRACT FROM AUTHOR]

Analogue space-times (and in particular metamaterial analogue space-times) have a long varied and rather complex history. Much of the previous related work to this field has focused on spherically symmetric models; however, axial symmetry is much more relevant for mimicking astrophysically interesting systems that are typically subject to rotation. Now it is well known that physically reasonable stationary axisymmetric space-times can, under very mild technical conditions, be put into Boyer–Lindquist form. Unfortunately, a metric presented in Boyer–Lindquist form is not well adapted to the "quasi-Cartesian" metamaterial analysis that we developed in our previous articles on "bespoke analogue space-times". In the current article, we shall first focus specifically on various space-time metrics presented in Boyer–Lindquist form, and subsequently determine a suitable set of equivalent metamaterial susceptibility tensors in a laboratory setting. We shall then turn to analyzing generic space-times, not even necessarily stationary, again determining a suitable set of equivalent metamaterial susceptibility tensors. Perhaps surprisingly, we find that the well-known ADM formalism proves to be not particularly useful, and that it is instead the dual "threaded" (Kaluza–Klein–inspired) formalism that provides much more tractable results. While the background laboratory metric is (for mathematical simplicity and physical plausibility) always taken to be Riemann flat, we will allow for arbitrary curvilinear coordinate systems on the flat background space-time. Finally, for completeness, we shall reconsider spherically symmetric space-times, but now in general spherical polar coordinates rather than quasi-Cartesian coordinates. In summary, this article provides a set of general-purpose calculational tools that can readily be adapted for mimicking various interesting (curved) space-times by using nontrivial susceptibility tensors in general (background-flat) laboratory settings. [ABSTRACT FROM AUTHOR]

Nonhydrostatic models have proven their superiority in describing tsunami propagation over trans-oceanic distances and nearshore transformation because of their good dispersion and nonlinearity properties. The novel one-layer nonhydrostatic formulations proposed by Wang et al. [Phys. Fluids 35, 076610 (2023)] have been rederived in the spherical coordinate system incorporating Coriolis effects to enable the application of basin-wide tsunami propagation. The model was implemented using the fractional step method, where the hydrostatic step was solved by a Godunov-type finite-volume scheme, and the nonhydrostatic step was obtained with the finite-difference method. Additionally, a two-way grid-nesting scheme was employed to adapt the topographic features for efficient computation of tsunami propagation in deep ocean and coastal inundation. Furthermore, graphics processing unit (GPU)-parallelism technique was incorporated to further optimize the model performance. An idealized benchmark test as well as three experiments of regular and irregular waves, solitary, and N-waves transformations have been simulated to demonstrate the superior performance of the current GPU-accelerated grid-nesting nonhydrostatic model. Finally, the model has been applied to reproduce the 1964 Prince William Sound Tsunami, its propagation across the North Pacific and induced inundation in the Seaside. [ABSTRACT FROM AUTHOR]

The focus of this article is to study theoretically the steady‐axisymmetric creeping flow dynamics of a couple stress fluid external to a semi‐permeable sphere containing a solid core. This problem is motivated by emulsion hydrodynamics in chemical engineering where rheological behaviour often arises in addition to porous media effects. The non‐Newtonian Stokes' couple stress fluid model features couple stresses and body couples that are absent in the classical Navier–Stokes viscous model. It provides a robust framework for simulating emulsions, complex suspensions and other liquids which possess microstructure. The physical regime is delineated into two zones – the interior of the semi‐permeable zone (region II) which engulfs the solid core and the external couple stress fluid zone (region I). The model is formulated using a spherical polar coordinate system in terms of the stream function ψ. The Brinkman‐extended Darcy model is deployed for the porous medium hydrodynamics and isotropic permeability is considered. Analytical expressions are derived for dimensionless pressure, tangential stress and the couple stress components using the method of separation of variables and Gegenbauer functions of the first kind. The integration constants are evaluated with appropriate boundary conditions on the inner and outer boundary of the semi‐permeable zone with the aid of Mathematica symbolic software. Solutions for the drag force exerted by the couple stress fluid on the semi‐permeable sphere and volumetric flow rate are also derived with corresponding expressions for the drag coefficient and non‐dimensional volumetric flow rate. The influence of permeability (k), separation parameter (l), couple stress viscosity coefficient (η), couple stress inverse length dependent parameter (λ = √(μ/η)) and couple stress viscosity ratio (τ = η/η/) on all key variables is studied graphically. Additionally, streamline contours are computed for a range of parameters including inverse permeability parameter (α = 1/k). The computations show that increasing couple stress inverse length dependent parameter (λ) greatly reduces the dimensionless volumetric flow rate in particular at high values of separation parameter (l). Flow rate is, however, markedly enhanced with permeability (k) and also couple stress viscosity parameter (η). In the presence of the solid core, a much greater drag coefficient is observed at all values of couple stress inverse length dependent parameter (λ) relative to the case without a solid core. A significant distortion in streamlines is computed with increasing separation parameter (l) with a dual vortex structure emanating. With greater couple stress viscosity parameter (τ), no tangible modification is observed in the streamline contours. The present work generalizes the earlier study of Krishnan and Shukla to consider a semi‐permeable (porous medium) outer sphere and furthermore presents detailed streamline visualizations of the creeping flow for a range of emerging parameters of relevance to non‐Newtonian chemical engineering processes including emulsion droplet dynamics in porous materials. [ABSTRACT FROM AUTHOR]

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Sound source localization technology has gradually become one of the main methods for fault source target localization in dangerous and difficult-to-discover applications. In order to locate the target fault sound source more intuitively, accurately and in real time in practical applications, an audio-visual positioning system is developed. A 64-channel microphone array is designed, which is evenly distributed in a circular shape, and has a video acquisition target at the same time. The system uses GCC-PHAT to estimate the relative time delay between the signal source arriving at two microphones, and then uses SRP-PHAT algorithm to obtain weighted sum beamforming. A spatial grid search strategy based on spherical coordinate spatial contraction method is proposed. When the output power is maximum, the direction corresponding to the beam is regarded as the sound source direction. Using the same sound source signal, the proposed positioning method is compared with the direct Newton iterative method and the Cartesian coordinate scanning SRP-based maximum method. The simulation results show that the Cartesian coordinate value and spherical coordinate value of the positioning algorithm in this article are closer to the real coordinates of the sound source position than the other two methods, and the positioning operation time is the shortest. In addition, in the actual corona discharge power source positioning experiment, the system can accurately locate the insulator pollution discharge point, which is consistent with the infrared detection and positioning results and has good robustness. Therefore, the system location method can provide a new choice for sound source location applications. [ABSTRACT FROM AUTHOR]

The Gaussian product rule for two-electron wave functions is introduced. The two-electron Gaussian product rule enables a new way for solving two-electron integrals. The solution is demonstrated with an example of the two-center two-electron integral in solid harmonic Gaussian basis. The solution is obtained by expanding inverse inter-electron separation and integrating in spherical coordinates. The resulting integral separates into four integrals, three of which are straightforward to solve. The remaining integral can be solved with Boys-like functions. It is demonstrated that the solution can deliver results with accuracy comparable with that of the McMurchie–Davidson scheme. [ABSTRACT FROM AUTHOR]

This paper studies a control problem of continuous time Lur'e systems involving input quantization (for the output of the controller) and output quantization (for the output of the plant). When the output of one quantization operator becomes directly the input of the other one, the nested quantization is produced, which is difficult for the design of the systems. Based on spherical polar coordinate quantizer, a quantization method with finite data rate is proposed for handling the nested quantization. In addition, both the quantization errors and Lur'e‐type nonlinearity are converted to sector bound uncertainties that are modeled by norm bounded uncertain matrices, which facilitates the design of the systems. Owing to the quantization error the resulting closed‐loop system is described by a discontinuous right‐hand side differential equation and the notion of Krasovskii solution is adopted for the equation. By Krasovskii solution the update rule of the quantization region is designed to ensure the convergence to the origin of the system with the nested quantization and avoid the quantizer saturation. Further, since the quantizers cannot quantize the controller output and the system output directly, we develop an optimalization problem for each quantizer to obtain the estimates of the outputs of the plant and the controller. Finally, a method is presented to achieve the parameters of the controller. [ABSTRACT FROM AUTHOR]