Homogeneous Sphere Research Articles

Analytical Approach of three-dimensional Flawed Multilayered Structure for EC Inspection

This article is devoted to the development of two current source models for the analysis of 3D electromagnetic phenomena in a conductive part of spherical geometry based on the second-order magnetic vector potential method for eddy current nondestructive testing (ECNDT). The first model, for a homogeneous single-layer sphere, allows the analytical calculation of all electromagnetic quantities in the charge. The second allows to treat in addition to the three-dimensional aspect of the problem, the heterogeneity of the charge (with several layers of different conductivities). An investigations using a multifrequency system have shown better results in detection of small cracks. The observations take about the calculation of normalized impedance based on dissipate energy and Joule losses in conductive material.

Some Numerical Results of the Albedo Problem in Spherical Geometry with Linearly Anisotropic Scattering

We examine the effect of linear anisotropic scattering on the solution of spherical geometry transport problems. We consider the albedo problem of a solid homogeneous sphere with linearly anisotropic scattering and write two matrix equations to solve the albedo problem with the H N and SVD methods in pseudo slab geometry. These methods are based on Case method of singular eigenfunctions. The numerical results of both methods are in agreement with each other.

Scattering of a spinning dielectric sphere to polarized plane waves

The exact expression of the wave vector inside a spinning homogeneous dielectric sphere illuminated by polarized plane waves is derived utilizing the “instantaneous rest-frame” hypothesis and Minkowski’s theory. On this basis, the analytical expressions of the electromagnetic field in the rotation sphere system are attained. The asymmetry of the system is discussed, in which the cause is emphasized. The influence of the polarization states and rotation angular velocity on the scattering are analyzed, including the optical rotation effect and photonic hook (PH). The results of this manuscript have extensive application prospects in optical tweezers, particle manipulation, and antenna design.

On the Interpretation of Cosmic Acceleration

In relativity, the Newtonian concepts of velocity and acceleration are observer-dependent quantities that vary with the chosen frame of reference. It is well established that in the comoving frame, cosmic expansion is currently accelerating; however, in the rest frame, this expansion is actually decelerating. In this paper, we explore the implications of this distinction. The traditional measure of cosmic acceleration, denoted by q, is derived from the comoving frame and describes the acceleration of the scale factor a for a 3D space-like homogeneous sphere. We introduce a new parameter qE representing the acceleration experienced between observers within the light cone. By comparing qE to the traditional q using observational data from Type Ia supernovae (SN) and the radial clustering of galaxies and quasars (BAO)—including the latest results from DESI2024—our analysis demonstrates that qE aligns more closely with these data. The core argument of the paper is that Λ—regardless of its origin—creates an event horizon that divides the manifold into two causally disconnected regions analogous to conditions inside a black hole’s interior, thereby allowing for a rest-frame perspective qE in which cosmic expansion appears to be decelerating and the horizon acts like a friction term. Such a horizon suggests that the universe cannot maintain homogeneity outside. The observed cosmological constant Λ can then be interpreted not as a driver of new dark energy or a modification of gravity but as a boundary term exerting an attractive force, akin to a rubber band, resisting further expansion and preventing event horizon crossings. This interpretation calls for a reconsideration of current cosmological models and the assumptions underlying them.

Preparation of spherical NiO-8YSZ composite powder through spray drying

Homogeneous sphere NiO-8YSZ composite powder with a narrow size distribution is significant for the fabrication of high-quality solid oxide fuel cell (SOFC) anodes. In this study, spray drying was used to prepare evenly distributed and spherical NiO-8YSZ composite particles used for the fabrication of SOFC anodes. The result showed that the particles prepared with a solid content of 65 wt %, atomizing pressure of 60 kPa, drying temperature of 180 °C, and sintering at 1200 °C for 2 h exhibited the best holistic quality with high sphericity (90 % over 0.84), narrow size distribution (D10 = 27.78 μm, D90 = 45.49 μm), high collection rate (70 %), and low content of unstable phases. The influence of these main parameters on the quality of the prepared particles was investigated and discussed as well. It was found that the solid content and the atomizing pressure demonstrated opposite effects on the particle size, with the former showing a positive correlation and the latter showing a negative correlation. The drying temperature decided the agglomeration degree of the prepared powder, which was involved in the presence of grape-like particles. In addition, the collection rate appeared to be positively correlated with the solid content and the atomizing pressure. The atmospheric plasma sprayed coating fabricated using the sprayed-dried powder prepared with the optimal parameters demonstrated significantly improved micromorphology and structure when compared with the coating fabricated using the mechanical mixed composite powder, which proved the prominent advantage of the powder produced through this spray drying method. All these progresses were considered good instructions for the studies on powder granulation and its applications in manufacturing high-quality coating materials.

A Versatile Electrochemical Sensor Polyaniline−Polypyrrole Co-Polymer for the Ultra-Sensitive Quercetin Detection

Quercetin has been shown to enhance inflammation, blood pressure, and blood sugar control. It may also have brain-protective, anti-allergy, and anticancer effects. In this work, a chemical oxidative polymerization approach is employed to synthesis of PANI-PPy copolymer for electrochemical biosensing of quercetin molecule. Unique, sustainable, low-cost, and simple to use, a synthesis of PANI-pPY copolymer has been achieved. The prepared PANI-PPy copolymer characterized with different technique like XRD, FT-IR, Raman, XPS, FESEM with EDAX and HR-TEM for identifying crystalline nature, functional group band gap, chemical composition, and morphology respectively. The surface morphology of the synthesized copolymers were in homogenous sphere like architecture. Synthesized copolymer is modified on glassy carbon electrode (GCE) to senses the biomolecule (Quercetin) by electrochemical method. PANI-PPy copolymer will greatly enhance the electrocatalytic oxidation of Quercetin (QR). The detection limit and quantification limit have been worked out to be 11.2 and 37.34 µM µA-1, respectively at neutral pH. All of the findings suggest that the PANI-PPy modified GCE is more sensitive to the oxidation of Quercetin. Eventually, the synthesized PANI-PPy hybrid may be used in catalysis research in addition to analytical laboratories due to its advantageous properties of enhanced catalytic activity and electrochemical sensitivity.

Effects of Aluminum/Carbon and Morphology on Optical Characteristics and Radiative Forcing of Alumina Clusters Emitted by Solid Rockets in the Stratosphere

Alumina (Al2O3) particles, the primary combustion products of solid rockets, can accumulate in the stratosphere, changing the global radiative balance. These Al2O3 particles were usually treated as homogeneous spheres. However, they contain impurities and may form clusters during the combustion process. Models representing Al-containing and C-containing Al2O3 clusters were developed, denoted as Al2O3 shell model (ASM) and Al2O3 core model (ACM), respectively. The superposition T-matrix method (STMM) was applied to examine their optical characteristics. Subsequently, a method to obtain the top-of-atmosphere flux was proposed by integrating the models with the moderate resolution atmospheric transmission code (MODTRAN). With the addition of Al/C, the absorption cross-section enhances by several orders of magnitude at 0.55 μm and increases slightly at 10 μm. The equivalent sphere models will weaken their scattering ability. A 4Tg mass burden of Al2O3 produces radiative forcing of −0.439 Wm−2. However, the addition of Al and C reduces the forcing by up to 15% and 12%, respectively. In summary, the optical characteristics and radiative forcing of Al2O3 clusters are sensitive to Al/C and morphology models. While our findings are impacted by various uncertainties, they contribute valuable insights into the radiative forcing of Al2O3 particles, potential climatic changes by space activities.

Vibration eigenfrequencies of an elastic sphere with large radius

An estimation is given for the free vibration eigenfrequencies (normal modes) of a homogeneous solid sphere with a large radius, with application to Earth's free vibrations. The free vibration eigenfrequencies of a fluid sphere are also derived as a particular case. Various corrections arising from static and dynamic gravitation, rotation, and inhomegeneities are estimated, and a tentative notion of an earthquake temperature is introduced.

Computational modeling of Chlamydomonas reinhardtii cellular radiation properties with synergistic consideration of complex structures and compositions.

The radiation characteristics of microalgae are of great significance for the design of photobioreactors and ocean optical remote sensing. Yet the complex structure of microalgae makes it difficult to theoretically predict its radiation characteristics based on traditional Mie theory. In this work, taking Chlamydomonas reinhardtii as an example, a multi-component cell model with a complex structure is proposed, which considers the organelles and shape of microalgae, and the volume change during the production of Chlamydomonas reinhardtii lipids. The theoretical calculation is carried out using the discrete dipole approximation method, and an improved transmission method is used for experimental measurement. The experimental data are compared and analyzed with the multi-component complex structure model, the homogeneous sphere model and the coated sphere model. The results show that the calculation accuracy of the multi-component complex structure model is higher, the error of the scattering cross-section is reduced by more than 8.6% compared with the homogeneous sphere model and coated sphere model, and the absorption cross-section and the scattering phase function are in good agreement with the experimental results. With the increase of lipids, the absorption cross-section and the scattering phase function vary slightly. However, the scattering cross-section has an observed change with increasing wavelength. In addition, the theoretical calculation error can be reduced when the influence of the culture medium is taken into account.

Scattering of partially coherent electromagnetic beams by a sphere.

We examine the scattering of a partially coherent, partially polarized electromagnetic beam by a homogeneous sphere (Mie scattering). The degree of polarization and the Stokes parameters in the far zone are found to be strongly dependent on the state of coherence and polarization of the incident beam. In particular, we demonstrate the emergence of polarization singularities and show that partial spatial coherence gives rise to significant depolarization effects. In addition we explore the symmetry properties of the scattered field.

Unraveling the dust activity of naked-eye comet C/2022 E3 (ZTF)

A morphological and photometric analysis of the naked-eye long-period comet C/2022 E3 (ZTF) before perihelion is presented in this study. The observation images taken by the Zwicky Transient Facility survey telescope from July 2022 to October 2022 show a gradually brightening dust coma and a tail with a clear structure. The morphology of the dust coma reveals nonsteady-state emission with an ejection velocity lower than 14 m s−1 for particles larger than 100 µm. According to the syndyne-synchrone analysis, dust particles larger than about 10 µm contribute significantly to the observed tail. The model simulations of the 10 October 2022 image suggest that the radii of large particles lingering near the nucleus range from 0.1 to 1 mm. Assuming that the nucleus of comet E3 is a homogeneous sphere with an albedo of 0.1, the photometry analysis sets the lower and upper limits of the nucleus radius to be 0.81 ± 0.07 km and 2.79 ± 0.01 km, respectively. The dust production rates increased continuously from 241 ± 3 kg s−1 in July to 476 ± 9 kg s−1 in October. The dependence of the ejection velocity v⊥ perpendicular to the orbital plane of comet E3 on the particle size a can be simplified as v⊥ ∝ a−1/2, which indicates that the dust emission is likely driven by gas. The water-production rate is inferred as ~368 ± 72 kg s−1 in October 2022, which is sustained by an equilibrium-sublimating area of 8.2 × 106 m2 at least. The comparative analysis of the characteristics of comet E3 with those of comets belonging to different types shows that the activity profile of long-period comet E3 surprisingly aligns more closely with those of short-period comets within a heliocentric distance range of about [1.7, 3.4] AU, where the images of comet E3 that we used in this study were taken.

2D boundary-condition-free nonlinear inversion technique applied to optical shear vibration induced microelastography

Optical microelastography (OME) has emerged as a new technique for quantifying cellular mechanical properties. However, accurately reconstructing viscoelastic properties at the microscale level from noisy 2D displacement fields remains a challenge. This study introduces a 2D boundary-condition-free nonlinear inversion (2D-NoBC-NLI) approach, addressing challenges of interpreting noisy data and deducing full-field 3D displacements from 2D measurements. OME requires vibrating the cell and mapping the shear modulus based on wave-induced displacements within the cell. The shear modulus distribution is recovered via a coupled adjoint field NLI reconstruction to allow 2D-NoBC-NLI. Validation was conducted through numerical simulations at 36 kHz on a homogeneous sphere of 75 μm diameter and an assigned viscoelastic modulus, G*, of 800 + i150 Pa. The same reconstruction approach was also applied to experimental data obtained from polyacrylamide (PAAm) microbeads of the same diameter. Results demonstrated relative differences from true simulated values of 0.7% and 45% for storage and loss moduli, respectively, with a coefficient of variation under 1% for homogeneous regions. When applying this method to PAAm microbeads, viscoelastic reconstructions showed the potential of OME under experimental conditions. These findings highlight the accuracy of 2D-No BC-NLI reconstruction in OME for precise microscale characterization and mapping of the viscoelastic cell structure.

Theoretical and experimental study on the radiative properties of Parachlorella kessleri: considering the effect of internal microstructure.

A microalgal cell model with multiple organelles considering both the irregular overall shape and internal microstructure was proposed. The radiative properties of Parachlorella kessleri during the normal phase, starch-rich phase, and lipid-rich phase were calculated by the discrete dipole approximation method in the visible wavelengths. The accuracy of the model is verified with experimental measurements. The results showed that the theoretical calculation of the established microalgal cell model is more accurate than those of the equal volume spheres, such as the homogeneous sphere and the coated sphere, with the errors of the scattering cross-section reduced by more than 10.7%. The calculated scattering phase function of the multi-component model is basically in good agreement with the experimental results. Compared to the normal growth phase, the lipid enrichment during the lipid-rich phase leads to a sharp increase in the scattering cross-section by three to four times, while the absorption cross-section remains stable. Remarkably, in the starch-rich phase, the abundant production of starch results in a reduction of two to three times in the absorption cross-section compared to the normal growth phase, while the scattering cross-section varies little. The results can provide basic data and theoretical support for the design and optimization of photobioreactors.

High-Performance Lithium-Ion Batteries with High Stability Derived from Titanium-Oxide- and Sulfur-Loaded Carbon Spherogels.

This study presents a novel approach to developing high-performance lithium-ion battery electrodes by loading titania-carbon hybrid spherogels with sulfur. The resulting hybrid materials combine high charge storage capacity, electrical conductivity, and core-shell morphology, enabling the development of next-generation battery electrodes. We obtained homogeneous carbon spheres caging crystalline titania particles and sulfur using a template-assisted sol-gel route and carefully treated the titania-loaded carbon spherogels with hydrogen sulfide. The carbon shells maintain their microporous hollow sphere morphology, allowing for efficient sulfur deposition while protecting the titania crystals. By adjusting the sulfur impregnation of the carbon sphere and varying the titania loading, we achieved excellent lithium storage properties by successfully cycling encapsulated sulfur in the sphere while benefiting from the lithiation of titania particles. Without adding a conductive component, the optimized material provided after 150 cycles at a specific current of 250 mA g-1 a specific capacity of 825 mAh g-1 with a Coulombic efficiency of 98%.

A localized approximation approach for the calculation of beam shape coefficients of acoustic and ultrasonic Bessel beams

The description of acoustical waves can be achieved using an expansion over basic functions with weighting coefficients which may be called beam shape coefficients (BSCs). There is a strong analogy between the scalar formalism of acoustical waves and the vectorial electromagnetic formalism, known as generalized Lorenz–Mie theory (GLMT), describing the interaction between a homogeneous sphere and an arbitrary illuminating beam. In particular, BSCs have been introduced as well in GLMT and the mathematical arsenal to evaluate them, developed since several decades, can be used mutatis mutandis to evaluate BSCs in acoustics. In particular, the present paper introduces a method named localized approximation to the evaluation of the acoustical BSCs, similar to the localized approximation used to evaluate electromagnetic BSCs, in the case of Bessel beams. Such a formalism akin to the electromagnetic GLMT may be viewed as an acoustical GLMT and should allow a renewal of the calculation of various properties of acoustical wave scattering, in particular to the design of acoustical tweezers similar to optical tweezers.

Numerical simulation of wave propagation through a spherical particle within the framework of generalised Lorenz-Mie theory

Holography has been widely used for measuring and visualising transients in multiphase flows. Earlier, one of the drawbacks of this approach was the need to register on various photosensitive elements and its subsequent transfer to digital format and restoration. With the development of digital technologies, direct registration of interference patterns (holographic images) into a CCD matrix became possible. However, even in digital holography there are a number of problems that need to be solved. These problems pertain to recovery algorithms, efficient data processing and resolution, among others. Currently, the numerical implementation of the restoration and processing of holographic images can be done within the framework of classical diffraction theory or with the help of generalised Lorenz-Mie theory. The first implies an indirect solution of Maxwell's equations, i.e., application of the Huygens-Fresnel principle. The second approach involves a direct solution of Maxwell's equations for the holographic problem. In the framework of this work, a numerical simulation of holographic imaging of fields from spherical particles based on the generalised Lorenz-Mie theory is proposed. Within the framework of this work, a numerical implementation of modelling of holographic images of a homogeneous sphere based on the generalised Lorenz-Mie theory is presented. The implementation code in the python programming language is presented. The results of the study demonstrate the possibility of effective use of digital holography for visualisation and analysis of spherical objects.

Polarized radiative transfer: Monte Carlo code Ventspils RTMC. Testing of it and RADMC3D

We have created Monte Carlo code Ventspils RTMC for polarized radiative transfer modelling in an isotropic, optically inactive medium of arbitrary configuration and morphology, and made it public. Its main advantages are simplicity of structure and usage, which can be a benefit for simple physical problems, together with use of sound and fully defined basic equations describing the scattering process. We compared the numeric results of Ventspils RTMC with those of RADMC3D created by Dullemond et al., as well as with the direct solution of Fredholm integral equations for source functions. A model of homogeneous sphere with Rayleigh scattering and concentric star inside it was used for comparison. The conclusion is that all three codes give essentially the same results if the radial optical thickness of the sphere does not exceed 5. If the optical thickness is between 5 and 10 then the statistical noise increases, and some small but systematic trends of differences appear between the results of three codes; however, the three codes are compatible. For optical thickness exceeding 10, the current version of Ventspils RTMC is too slow. There is a theoretical uncertainty about the adequacy of diffusion approximation of polarized radiative transfer used in RADMC3D for optical thickness exceeding 15. While RADMC3D is a very complex code usable for broad scope of applications, our Ventspils RTMC is a much simpler code usable for continuum transfer in case of modest optical thickness.

Resolving an inverse problem through a momentum flow within the framework of electromagnetic scattering.

Although there have been many approaches to inverse problem in the classic theory of potential scattering, they are implicitly confined to the analysis of the scattered electric field, and thus the magnetic counterpart of the scattered wave is ignored, which limits the further application of those approaches to some extent. Here, we propose a new, to the best of our knowledge, technique for an inverse problem within the framework of electromagnetic scattering. This technique aims at reconstructing the correlation function of the scattering potential of a random medium through measuring the electromagnetic momentum flow of the scattered field in the far zone. As illustrative examples, we use the technique to determine the correlation functions of the scattering potentials of homogeneous, isotropic, and Gaussian-correlated spheres. Our new inversion approach works both microscopically and macroscopically.

Multifunctional hollow silica carriers with spiny structure for enhanced foliar adhesion and triple-responsive pesticide delivery

Intelligent responsive pesticide formulations hold great promise for enhancing foliage retention and effective utilization. Herein, hollow silica (S-HS) nanocarriers with spiny structure were constructed for pesticide delivery. The S-HS nanocarriers presented homogeneous spiny spheres with an average size of 220 nm. This spiny structure can achieve effective retention on foliage by the “hanger-hat” topology effect. For constructing the responsive layer, the S-HS nanocarriers were further functionalized with surface vinyl groups. After loading imidacloprid (IMI), the temperature sensitive poly N-isopropylacrylamide (pNIPAm) and tannic acid–Fe complexes (TA-Fe) were introduced to encapsulate pesticides (IMI@S-HS-pNT). The TA-Fe complex layer served as a wall material and photothermal agent. The S-HS-pNT carriers achieved a loading capacity for IMI (26.6 %), high photothermal conversion effect (η = 36.1 %), and good biocompatibility. Except for excellent photostability and foliar adhesion property, the IMI@S-HS-pNT exhibited pH, temperature and near infrared (NIR) responsive release behavior. Moreover, the S-HS nanocarriers could be effectively transported to various parts of tobacco plants under the root immerse or foliar spray. The IMI@S-HS-pNT showed the high control efficacy against Plutella xylostella. Overall, this work provides insight into improving the efficiency of utilization and prolonging pesticide retention on plant leaves.

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

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