Spherical Coordinates Research Articles

Parity-time and anti-parity-time states of Bragg gratings and their representation in spherical coordinates

Parity-time and anti-parity-time states of Bragg gratings and their representation in spherical coordinates

Cooperative Path Planning for Multi-UAVs with Time-Varying Communication and Energy Consumption Constraints

In the field of Unmanned Aerial Vehicle (UAV) path planning, designing efficient, safe, and feasible trajectories in complex, dynamic environments poses substantial challenges. Traditional optimization methods often struggle to address the multidimensional nature of these problems, particularly when considering constraints like obstacle avoidance, energy efficiency, and real-time responsiveness. In this paper, we propose a novel algorithm, Dimensional Learning Strategy and Spherical Motion-based Particle Swarm Optimization (DLS-SMPSO), specifically designed to handle the unique constraints and requirements of cooperative path planning for Multiple UAVs (Multi-UAVs). By encoding particle positions as motion paths in spherical coordinates, the algorithm offers a natural and effective approach to navigating multidimensional search spaces. The incorporation of a Dimensional Learning Strategy (DLS) enhances performance by minimizing particle oscillations and allowing each particle to learn valuable information from the global best solution on a dimension-by-dimension basis. Extensive simulations validate the effectiveness of the DLS-SMPSO algorithm, demonstrating its capability to consistently generate optimal paths. The proposed algorithm outperforms other metaheuristic optimization algorithms, achieving a feasibility ratio as high as 97%. The proposed solution is scalable, adaptable, and suitable for real-time implementation, making it an excellent choice for a broad range of cooperative multi-UAV applications.

Magnetic dissipation in short gamma-ray-burst jets

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.

Moshinsky brackets for a wide range of quantum numbers using generating functions

We used a new Python code to reproduce the brackets for the Moshinsky harmonic oscillator, which was based on the generating function. We made these brackets by transforming the wave functions of two groups of coupled particle harmonic oscillators, Φn1l1,n2l2,Λm1,m2,λ(r→1,r→2) and Φnala,nblb,Λma,mb,λ(r→a,r→b). To convert between the supplied position and momentum coordinates in both frames, we performed orthogonal transformations on nuclei with both low and high angular momentum.In our derivation, we have used the expansion of the generating functions e2p→.r→−p2 and e2cpi.pj in spherical coordinates in terms of harmonic oscillator wave functions. When we modified the Moshinsky brackets for two-coupled oscillator states, we used generating functions with two variables. The number of indices has significantly decreased compared to the oscillator brackets in previous references; this reduction in the program code's iterative process has yielded influential results. Compared to the previous version of the Moshinsky brackets code, the new Python code is easier to use. Our approach utilizes this code to assess Moshinsky brackets across a broad spectrum of quantum numbers. According to the revelation, adding more variables to the generating function makes the number of Moshinsky brackets that work for the higher body interactions increase. Program summaryProgram Title: GFBRACKETSCPC Library link to program files:https://doi.org/10.17632/jvbnwp35rm.1Licensing provisions: MITProgramming language: PythonSupplementary material: AppendixNature of problem: The generating functions were used to obtain a concise representation of the oscillator states for single particles. This was done to formulate and compute the generalized version of the Moshinsky brackets and matrix elements of two-body operators. By enlarging sets of basis oscillator states, it becomes possible to cover interactions involving more than two bodies. This can be easily achieved using the expanded generating function to compute the Moshinsky brackets for high-quantum numbers.Solution method: The Python code requires fewer iterations than similar codes generated by the method of the generating functions.Additional comments including restrictions and unusual features: When calculating Moshinsky brackets for large quantum numbers, restrictions arise. There is no data for quantum numbers greater than 10 in the formation of reaction potential. Additionally, a transformation matrix can be used to switch from single-particle to centre-of-mass coordinates on a two-particle harmonic oscillator basis. This transformation is applicable even when the masses of the two particles are unequal.

Migration of a slip-spin solid spherical particle in a micropolar fluid-filled circular cylindrical tube

A combined study analytically and numerically for the axially symmetric creeping flow due to a slip-spin solid sphere surface moving in a microstructure fluid of micropolar type along the centreline of a circular cylindrical tube is introduced. This investigation was presented under low Reynolds number conditions. A general solution is obtained by superposing the essential solutions in both spherical and cylindrical coordinates to solve the Eringen micropolar field equations. The condition of the microrotation, along with couple stress, is used at the surface of the solid particle; while the microrotation is used at the inner cylindrical surface. Boundary conditions are imposed initially on the inner cylindrical surface using Fourier transforms and subsequently on the outer surface of the solid particle using a collocation technique. This paper aims to study the wall interaction problem of a translating slip-spin solid spherical particle in a micropolar fluid along the centreline of a circular cylindrical tube. The study also investigates the effect of the addition of slip conditions for velocity and microrotation on the surface of a solid particle. There is good convergence in the numerical findings obtained for the normalised hydrodynamic drag force (the tube-corrected factor) applying on the surface of the solid particle for several values of the micropolarity coefficient, slip-spin coefficients, and the ratio between the radius of the solid particle and tube. Regarding the flow of a solid spherical particle along the centreline of a cylindrical tube, our drag findings compare favourably to the solutions found in the literature. We found that the normalised drag force acting on the solid particle monotonically increases with the increase of the particle-to-tube radius ratio and reaches infinity in the limitless, with the increase of the micropolarity coefficient, and with the increase of the slip-spin coefficients for a steady ratio of particle-to-tube radius.

Direct numerical simulation of turbulent, generalized Couette–Poiseuille flow

We present direct numerical simulation (DNS) and modelling of incompressible, turbulent, generalized Couette–Poiseuille flow. A particular example is specified by spherical coordinates $(Re,\theta,\phi )$ , where $Re = 6000$ is a global Reynolds number, $\phi$ denotes the angle between the moving plate, velocity-difference vector and the volume-flow vector and $\tan \theta$ specifies the ratio of the mean volume-flow speed to the plate speed. The limits $\phi \to 0^\circ$ and $\phi \to 90^\circ$ give alignment and orthogonality, respectively, while $\theta \to 0^\circ,\ \theta \to 90^\circ$ correspond respectively to pure Couette flow in the $x$ direction and pure Poiseuille flow at angle $\phi$ to the $x$ axis. Competition between the Couette-flow shear and the forced volume flow produces a mean-velocity profile with directional twist between the confining walls. Resultant mean-speed profiles relative to each wall generally show a log-like region. An empirical flow model is constructed based on component log and log-wake velocity profiles relative to the two walls. This gives predictions of four independent components of shear stress and also mean-velocity profiles as functions of $(Re,\theta,\phi )$ . The model captures DNS results including the mean-flow twist. Premultiplied energy spectra are obtained for symmetric flows with $\phi =90^\circ$ . With increasing $\theta$ , the energy peak gradually moves in the direction of increasing $k_x$ and decreasing $k_z$ . Rotation of the energy spectrum produced by the faster moving velocity near the wall is also observed. Rapid weakening of a spike maxima in the Couette-type flow regime indicates attenuation of large-scale roll structures, which is also shown in the $Q$ -criterion visualization of a three-dimensional time-averaged flow.

On the non-flatness nature of noncommutative Minkowski spacetime and the singular behavior of probes

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.

A new Hilbert-type inequalities obtained via Cantor-type spherical coordinates

In this paper, we introduce a class of Hilbert-type inequalities on a fractal set [Formula: see text]. 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.

Modeling Pollutant Diffusion in the Ground Using Conformable Fractional Derivative in Spherical Coordinates with Complete Symmetry

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.

High-Efficiency Forward Modeling of Gravitational Fields in Spherical Harmonic Domain with Application to Lunar Topography Correction

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.

Flight Stability of Spinning Projectiles at High Angles of Attack

The flight behavior of the spin-stabilized 105 mm M1 artillery projectile, when fired with high quadrant elevation, is studied using six-degrees-of-freedom trajectory simulations and theoretical methods of stability analysis. Trajectory simulation results confirm the known effect of overstabilization at the apogee, leading to high angles of attack (AoA), drift to the left, and base-forward descent. For quadrant elevations between nose-forward and base-forward descent, a previously unknown descent mode was discovered, with projectiles performing a low-frequency coning motion at high angles of attack of 73 and 104 deg, respectively. An exhaustive theoretical description of such high-AoA limit cycles is given that overcomes the limitation to small angles of attack prevalent in traditional concepts of projectile stability. Based on a formulation of the angular motion in spherical coordinates, conditions for the existence of limit cycles are identified and stability criteria are derived using Lyapunov’s first method of linearization around equilibrium and eigenvalue analysis of the resulting Jacobian. The resulting criteria indicate that limit cycle flight is primarily governed by the Magnus moment coefficient. The method is applied to the 105 mm M1 projectile, and the coning motions observed in the trajectory simulations are accurately reproduced by the theory.

Impacts of fossil fuel thermophoretic convective heat transfer on climate change with variable viscosity and thermal conductivity

The main aim of the current study is to analyze the impacts of fossil fuel thermophoretic convective heat transfer on climate change with variable viscosity and thermal conductivity. Furthermore, the purpose of the proposed problem is to develop a mathematical model based on three regions: source region (in terms of rectangular coordinates), plume region (in terms of cylindrical coordinates), and atmospheric region (in terms of spherical coordinates). The fossil fuels release thermophoretic particles, such as carbon dioxide, methane, black carbon, and many others, during burning process in the source region, and then release through the plume region. These particles are then distributed into the atmosphere, where the impact of thermophoretic particles on climate change is analyzed. The modeled nonlinear partial differential equations are transformed into a dimensionless form using suitable non-dimensional scaling variables. The proposed model is solved using finite difference approach in order to analyze the impacts of fossil fuel thermophoretic particles in the atmosphere in terms of climate change. In this regard, the effect of dimensionless parameters, viscosity variation parameter γ, Schimdt number Sc, thermal conductivity variation parameter ε, coefficient of thermophoretic process k, and thermophoresis parameter Nt on the velocity, temperature, and thermophoretic concentration fields are discussed. The main novelty of current work is that three models in three regions are coupled via trans-boundaries in term of temperature differences. It is very interesting to note that the concentration of thermophoretic particles, along with temperature profile, is maximum at α=π rad and minimum at α=1.5 rad in the atmospheric region.

Double flame dynamics in hotspot ignition

Hotspot ignition is a key problem in fundamental flame initiation, combustion control and prevention of abnormal combustion phenomena. Depending on the characteristics of the hotspot and the thermochemical condition of the reactive mixture, subsequent reaction front initiated from a hotspot can vary substantially. The current paper focus on the dynamics and chemistry for one of the most complicated scenarios - hotspot induced double flames, which include a cool and a hot flame segment. This work adopts a recently developed compressible reacting flow simulation code COGNAC to investigate the initiation and propagation of double flame dynamics from hotspot ignition in a one-dimensional spherical coordinate. The results have shown that under atmospheric pressure, double flame initiation is not feasible for sufficiently small hotspot. Under elevated pressures, double flame can be initiated within a much wider hotspot window, exhibiting complex flame dynamics, such as variations in cool and hot flame bifurcation behaviors and their initiation locations. Analysis on thermochemical structure and dynamics of double flame has shown that the interaction of cool and hot flames in a double flame structure is inherently intermutual, in that the leading cool flame enhances trailing hot flame speed through reform of the unburnt mixture, while the trailing hot flame initiation affects the leading cool flame via thermal expansion effects.

Numerical Method for Predicting Transient Aerodynamic Heating in Hemispherical Domes

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.

Optical coherence tomography otoscope for imaging of tympanic membrane and middle ear pathology.

Pathologies within the tympanic membrane (TM) and middle ear (ME) can lead to hearing loss. Imaging tools available in the hearing clinic for diagnosis and management are limited to visual inspection using the classic otoscope. The otoscopic view is limited to the surface of the TM, especially in diseased ears where the TM is opaque. An integrated optical coherence tomography (OCT) otoscope can provide images of the interior of the TM and ME space as well as an otoscope image. This enables the clinicians to correlate the standard otoscopic view with OCT and then use the new information to improve the diagnostic accuracy and management. We aim to develop an OCT otoscope that can easily be used in the hearing clinic and demonstrate the system in the hearing clinic, identifying relevant image features of various pathologies not apparent in the standard otoscopic view. We developed a portable OCT otoscope device featuring an improved field of view and form-factor that can be operated solely by the clinician using an integrated foot pedal to control image acquisition. The device was used to image patients at a hearing clinic. The field of view of the imaging system was improved to a 7.4mm diameter, with lateral and axial resolutions of and , respectively. We developed algorithms to resample the images in Cartesian coordinates after collection in spherical polar coordinates and correct the image aberration. We imaged over 100 patients in the hearing clinic at USC Keck Hospital. Here, we identify some of the pathological features evident in the OCT images and highlight cases in which the OCT image provided clinically relevant information that was not available from traditional otoscopic imaging. The developed OCT otoscope can readily fit into the hearing clinic workflow and provide new relevant information for diagnosing and managing TM and ME disease.

Effects of different decaffeination methods on caffeine contents, physicochemical, and sensory properties of coffee

Abstract 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.

DiffSim: a user-friendly tool for precise magmatic timescale determination and error propagation via major element diffusion chronometry in magmatic phases

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.

Comparing heart PET scans: an adjustment of Kolmogorov-Smirnov test under spatial autocorrelation

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.

Omni-directional orientation analysis of a triplet-stator spherical piezoelectric motor system

ABSTRACT 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.

The Transpolar Drift current: an ocean-ice-wind complex in rotating, spherical coordinates

Starting from the governing equations for a viscous, incompressible fluid, written in a rotating, spherical coordinate system that is valid at the North Pole, the thin-shell approximation is invoked. No further approximations are needed in the derivation of the system of asymptotic equations used here. Suitable stress conditions on the upper and lower surfaces of the ice are described, leading to the construction of a solution for the Transpolar Drift current. This involves the specification of a suitable geostrophic flow, combined with an Ekman component. Then, via the stress conditions across the ice at the surface, a solution for the motion of the ice, and for the associated wind blowing over it, are obtained. In addition, the model adopted here provides a prediction for the reduction in ice thickness along the Transpolar Drift current as it passes through the Fram Strait. The formulation that we present allows considerable freedom in the choices of the various elements of the flow; the model chosen for the physical properties of the ice is particularly significant. All these aspects are discussed critically, and it is shown that many avenues for future investigation have been opened.