Spherical Model Research Articles

Subsurface tidal gravity variation and gravimetric factor

SUMMARY Taking advantage of the simultaneous recording during 471 d between 2019 and 2021 by two superconducting gravimeters installed at the surface and 520 m under the surface at the Low Noise Underground Laboratory (LSBB) in Rustrel, France, we investigate whether a difference between the tidal gravity signals at the two locations can be detected. First, we model the periodical variations of the Earth’s gravity owing to the tidal influence from the Sun and Moon, at the Earth’s surface and at shallow depths. We provide analytical formulae for the Love numbers, gravimetric factor and gravity variation of simple spherical planetary models. We also numerically compute those parameters and function for a realistic spherical Earth model. We find that the fractional difference between the semi-diurnal tidal gravity variations at the surface and 520 m below is as small as 8.5 × 10$^{-5}$. We next evaluate the effect on the amplitude of the recorded gravity signal due to the calibration factors of the two superconducting gravimeters at LSBB. Finally, we compute the spectra of the difference between the gravity variations measured on and under the surface in the semi-diurnal band of the M$_2$ tidal wave. We find that the uncertainties associated to the calibration factors are larger than the theoretical or observational difference between the tidal gravity variations on the surface and at a 520-m depth.

An interval-valued spherical fuzzy CIMAS-WISP group decision-analytic model for blockchain platform selection in digital projects

Digital projects aspiring to reach target audiences are executed through decentralized and trustworthy blockchain platforms (BPs). Once the objectives and target audience of a digital project are defined, the selection of suitable BPs is undertaken. The primary objective of this research is to develop a decision support system that aids in the selection of BPs for transferring digital data and assets. Numerous quantitative parameters determine the performance of BPs, alongside qualitative parameters indicating their performance. In this study, the aim is to determine the performance of BPs based on both qualitative and quantitative parameters. Within this scope, a multi-criteria decision-making approach and interval-valued spherical fuzzy (IVSF) sets are adopted. IVSF sets are utilized to determine expert importance levels. The IVSF-criteria importance assessment (CIMAS) method is introduced for the weighting of criteria. IVSF-CIMAS enables the determination of reliability levels in calculating criterion weights. The IVSF-simple weighted sum product (WISP) method is formulated to obtain the performance ranking of BPs. Thus, in this research, the IVSF-CIMAS-WISP hybrid model is developed, and an algorithm for this novel decision-analytic model is presented. A case study is developed focusing on BP selection for a digital project to demonstrate the applicability of the proposed hybrid model. The robustness of IVSF-CIMAS-WISP is tested through extensive sensitivity analysis scenarios. According to the research results, the applicability of the IVSF-CIMAS-WISP hybrid method is supported and its robustness is confirmed. The research findings provide numerous insights for project managers and practitioners.

A New Sufficient & Necessary Condition for Testing Linear Separability Between Two Sets.

As a fundamental mathematical problem in the field of machine learning, the linear separability test still lacks a theoretically complete and computationally efficient method. This paper proposes and proves a sufficient and necessary condition for linear separability test based on a sphere model. The advantage of this test method is two-fold: (1) it provides not only a qualitative test of linear separability but also a quantitative analysis of the separability of linear separable instances; (2) it has low time cost and is more efficient than existing test methods. The proposed method is validated through a large number of experiments on benchmark datasets and artificial datasets, demonstrating both its correctness and efficiency.

Deciphering Radio Emissions from Accretion Disk Winds in Radio-quiet Active Galactic Nuclei

Unraveling the origins of radio emissions from radio-quiet active galactic nuclei (RQ AGNs) remains a pivotal challenge in astrophysics. One potential source of this radiation is the shock interaction between AGN disk winds and the interstellar medium (ISM). To understand this phenomenon, we construct a spherical, one-zone, and self-similar expansion model of shock structure between ultrafast outflows (UFOs) and the ISM. We then calculate the energy density distribution of nonthermal electrons by solving the transport equation, considering diffusive shock acceleration as the acceleration mechanism and synchrotron and inverse Compton cooling as the cooling mechanisms. Based on the derived energy distribution of nonthermal electrons, we model the radio synchrotron spectrum of the shocked ISM. For the 15 nearby RQ AGNs hosting UFOs, we investigate the shocked ISM parameters required to model their observed radio spectra based on X-ray observations and measured UFO velocities. Radio spectra of 11 out of 15 nearby RQ AGNs would be explained by the AGN disk wind model. This is a compelling indication that shock interactions between AGN disk winds and the ISM could indeed be the source of their radio emissions. The typical predicted source size and magnetic field strength are several 100 pc and 0.1 mG, respectively. We also discuss whether our prediction can be tested by future radio observations.

Dark matter reconstruction from stellar orbits in the Galactic centre

Context. Current constraints on distributed matter in the innermost Galactic centre (such as a cluster of faint stars and stellar remnants, dark matter, or a combination thereof) based on the orbital dynamics of the visible stars closest to the central black hole typically assume simple functional forms for the distributions. Aims. We aim to take a general model-agnostic approach in which the form of the distribution is not constrained by prior assumptions on the physical composition of the matter. This approach yields unbiased, entirely observation-driven fits for the matter distribution and places constraints on our ability to discriminate between different density profiles (and consequently between physical compositions) of the distributed matter. Methods. We constructed a spherical shell model with the flexibility to fit a wide variety of physically reasonable density profiles by modelling the distribution as a series of concentric mass shells. We tested this approach in an analysis of mock observations of the star S2. Results. For a sufficiently large and precise data set, we find that it is possible to discriminate among several physically motivated density profiles. However, for data coming from current and expected next generation observational instruments, the potential for profile distinction will remain limited by the precision of the instruments. Future observations will still be able to constrain the overall enclosed distributed mass within the apocentre of the probing orbit in an unbiased manner. We interpret this in the theoretical context of constraining the secular versus non-secular orbital dynamics. Conclusions. Our results show that while stellar data over multiple orbits of currently known stars will eventually yield model-agnostic constraints for the overall amount of distributed matter within the probe’s apocentre in the innermost Galactic centre, an unbiased model distinction made by determining the radial density profile of the distribution is, in principle, out of the measurement accuracy of the current and next-generation instruments. Constraints on dark matter models will therefore remain subject to model assumptions and will not be able to significantly downsize the zoo of candidate models.

Sedimentation of a spherical squirmer in a square tube under gravity

In this study, we used a three-dimensional lattice Boltzmann method to simulate the settling motion of a spherical squirmer in a square tube under the effect of gravity. A spherical squirmer model with chirality was chosen to simulate the motion of a real microswimmer in a three-dimensional space and to systematically analyze its kinematic properties. According to the results of this study, we identified seven different motion modes: diagonal plane large-amplitude oscillation, central stable sedimentation, bidirectional spiral motion, rebound motion, unidirectional spiral motion, corner stable motion, and near-wall attraction oscillation. It was shown that the formation of different motion modes is caused by the effects of squirmer-type factor and chirality. squirmer-type factor determines the stable motion position of the squirmer in the channel. Chirality makes the head direction of the squirmer more susceptible to change, thus changing the motion trajectory of the squirmer. In addition, it was found that the self-propelling strength determines the speed of squirmer’s motion, which affects the motion frequency of squirmer’s periodic oscillations.

Comparative study on calculation methods for compressive strength of low strength aggregate concrete

The compressive strength of concrete with low strength aggregate volume fractions of 10%, 20%, and 30% was calculated using both the graphical analysis method and mesomechanics method. In the calculation method based on graphical analysis, three-dimensional random spherical aggregate models of concrete with different volume contents of low strength aggregate were established and sliced. The results show that the graphical analysis method can effectively calculate the compressive strength of concrete with different volume contents of low strength aggregate. In the graphical analysis method, the relative errors of the calculated compressive strength of concrete with low strength aggregate volume fractions of 10%, 20%, and 30% were 4.84%, 4.84%, and 6.43%, respectively. Three-phase concrete models composed of mortar, aggregate, and interfacial transition zone were analyzed through the method of mesomechanics. The calculation results of the mesomechanics method show that the compressive strength of concrete was controlled by low strength aggregate, and the calculated compressive strength of concrete decreased with the increase in low strength aggregate volume content. In the mesomechanics method, the relative errors of the calculated compressive strength of concrete with low strength aggregate volume fractions of 10%, 20%, and 30% were 1.36%, 1.74%, and 3.7%, respectively. It can be found that the calculation results of the mesomechanics method are closer to the test values and have smaller relative errors, which indicate that the calculation method of mesomechanics theory is superior to the method of graphical analysis.

3D large-scale forward modeling of gravitational fields using triangular spherical prisms with polynomial densities in depth

To take the sphericity of the Earth into account, tesseroids are often utilized as grid elements in large-scale gravitational forward modeling. However, such elements in a latitude–longitude mesh suffer from degenerating into poorly shaped triangles near poles. Moreover, tesseroids have limited flexibility in describing laterally variable density distributions with irregular boundaries and also face difficulties in achieving completely equivalent division over a spherical surface that may be desired in a gravity inversion. We develop a new method based on triangular spherical prisms (TSPs) for 3D gravitational modeling in spherical coordinates. A TSP is defined by two spherical surfaces of triangular shape, with one of which being the radial projection of the other. Due to the spherical triangular shapes of the upper and lower surfaces, TSPs enjoy more advantages over tesseroids in describing mass density with different lateral resolutions. In addition, such an element also allows subdivisions with nearly equal weights in spherical coordinates. To calculate the gravitational effects of a TSP, we assume the density in each element to be polynomial along radial direction so as to accommodate a complex density environment. Then, we solve the Newton’s volume integral using a mixed Gaussian quadrature method, in which the surface integral over the spherical triangle is calculated using a triangle-based Gaussian quadrature rule via a radial projection that transforms the spherical triangles into linear ones. A 2D adaptive discretization strategy and an extension technique are also combined to improve the accuracy at observation points near the mass sources. The numerical experiments based on spherical shell models show that the proposed method achieves good accuracy from near surface to a satellite height in the case of TSPs with various dimensions and density variations. In comparison with the classical tesseroid-based method, the proposed algorithm enjoys better accuracy and much higher flexibility for density models with laterally irregular shapes. It shows that to achieve the same accuracy, the number of elements required by the proposed method is much less than that of the tesseroid-based method, which substantially speeds up the calculation by more than 2 orders. The application to the tessellated LITHO1.0 model further demonstrates its capability and practicability in realistic situations. The new method offers an attractive tool for gravity forward and inverse problems where the irregular grids are involved.

Analytical investigation of vesicle dynamics via the modified Riemann-Liouville fractional derivative: Mittag-Leffler function solution and comparative analysis with Caputo's derivative.

The solution of fractional differential equations is a significant focus of current research, given their prevalence in various fields of application. This paper introduces an innovative exploration of vesicle dynamics using Jumarie's modified Riemann-Liouville fractional derivative within a five-dimensional fractional rigid sphere model. The study reveals an exact solution through the Mittag-Leffler function, providing a deep understanding of intricate vesicle dynamics, including alternative motions, such as tank-treading with over-damped and under-damped vesicle oscillations, respectively, TT-OD and TT-UD. A comparative analysis with Caputo's derivative emphasizes the effectiveness of these fractional derivatives, contributing not only to theoretical insights but also practical implications in applied mathematics and biophysical systems. The findings advance our understanding of complex vesicle behaviors, particularly in mimicking real cell-like behaviors, and pave the way for further research and applications in the field.

Multibubble sonoluminescence in supercooled water.

Cavitation in supercooled water has been induced by the short ultrasound pulses of an ultrasonic horn driven at 20kHz. The cavitation during the ultrasonic pulses and occasionally the crystallization events thereafter have been imaged by a high-speed camera. The probability of ice crystallization in dependence on the pulse duration and temperature showed a high chance for the water to remain liquid if sufficiently short bursts of moderate acoustic power were applied. This regime has been used for the assessment of sonoluminescence (SL) from the generated cavitation bubbles in the supercooled liquid state. To this end, light emitting events were summed up over a number of ultrasonic pulses by an image intensifier. SL appeared mostly directly under the tip of the ultrasonic horn and sometimes also a few millimeters below the tip. The intensity of SL events showed a slight rise for a decrease in temperature, i.e., for an increase in supercooling. This behavior is in accord with the SL dependence on temperature above the freezing point and might be attributed to a further lowering of vapor pressure. An increase in the bubble collapse peak temperature for increased supercooling is calculated on the basis of spherical bubble model calculations, which supports the findings. The simulations predict further that the peak temperature will fall off again beyond a certain supercooling level.

3D Computational Modeling of Defective Early Endosome Distribution in Human iPSC-Based Cardiomyopathy Models.

Intracellular cargo delivery via distinct transport routes relies on vesicle carriers. A key trafficking route distributes cargo taken up by clathrin-mediated endocytosis (CME) via early endosomes. The highly dynamic nature of the endosome network presents a challenge for its quantitative analysis, and theoretical modelling approaches can assist in elucidating the organization of the endosome trafficking system. Here, we introduce a new computational modelling approach for assessment of endosome distributions. We employed a model of induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) with inherited mutations causing dilated cardiomyopathy (DCM). In this model, vesicle distribution is defective due to impaired CME-dependent signaling, resulting in plasma membrane-localized early endosomes. We recapitulated this in iPSC-CMs carrying two different mutations, TPM1-L185F and TnT-R141W (MUT), using 3D confocal imaging as well as super-resolution STED microscopy. We computed scaled distance distributions of EEA1-positive vesicles based on a spherical approximation of the cell. Employing this approach, 3D spherical modelling identified a bi-modal segregation of early endosome populations in MUT iPSC-CMs, compared to WT controls. Moreover, spherical modelling confirmed reversion of the bi-modal vesicle localization in RhoA II-treated MUT iPSC-CMs. This reflects restored, homogeneous distribution of early endosomes within MUT iPSC-CMs following rescue of CME-dependent signaling via RhoA II-dependent RhoA activation. Overall, our approach enables assessment of early endosome distribution in cell-based disease models. This new method may provide further insight into the dynamics of endosome networks in different physiological scenarios.

Asymptotic profiles of mean zonal flows generated by thermal convection of Boussinesq fluid in a rapidly rotating thin spherical shell

The asymptotic behavior of the profiles of mean zonal flows generated by thermal convection of a Boussinesq fluid in a rapidly rotating thin spherical shell was studied by extending the integration time of the numerical experiments of a previous study under similar conditions. Calculations were performed for the whole globe, as well as for a one-eighth sector region, with various values of the hyper-diffusion parameters. For sufficiently weak hyper-diffusion, a prograde zonal jet and alternating narrow zonal jets appeared at the equator and in the middle and high latitudes, respectively, as reported in the previous study. However, further integrations showed that the middle and high latitude flows are asymptotically accelerated eastward, jet peaks merge, and the banded zonal flow structure eventually disappears. Thus, the rotating thin spherical shell convection model of a Boussinesq fluid used in the previous studies seems inadequate to explain the surface banded structures of Jovian planetary atmospheres without modification of the standard setups. To maintain the alternating jet structure in the middle and high latitudes over the long-term, some sort of scale-independent dissipation process should be specified that prevents the evolution of zonal flows toward the long-term asymptotic state.

Free Energy Fluctuations of the Bipartite Spherical SK Model at Critical Temperature

Free Energy Fluctuations of the Bipartite Spherical SK Model at Critical Temperature

Kinetic theory of weakly ionized plasma and electrolyte mixtures including Onsager matrix and frequency dispersion effects

AbstractWe summarize the method of hydrodynamic approximation for weakly ionized plasmas developed with Klimontovich in 1962 and give a generalization to many—component systems using Onsagers matrix theory and including dispersion effects. We develop the conductivity theory of complex plasma and electrolyte mixtures based on the model of charged hard spheres with given non‐additive contact distances, including frequency‐dependent electric fields. These generalizations are made with the aim to allow applications to complex natural systems as atmospheric plasmas and seawater. Finally, we give as an example a numerical calculation of the single ion conductivities of a six‐component seawater model.

Solution Dynamics of Covalent Open-[60]Fullerene Dimers.

The translational diffusivity of covalent open-[60]fullerene dimers in an organic solvent was found to be well describable by a prolate ellipsoid model while a monomeric open-[60]fullerene behaves like a sphere model. The water association dynamics were examined for two open-[60]fullerene dimers, showing a higher water affinity for the sp3-linked dimer relative to sp2-linked dimer owing to an effective orbital-orbital overlap identified by π(fullerene)→σ*(H2O) interactions as suggested by theoretical calculations.

Structural evolution and electronic properties of the La-doped germanium clusters

The geometric structure, relative stability, and electronic properties of LaGe n − (n = 3–14) are systematically studied by density functional theory, and the results are compared with the experimental literature data. It is found that the structures of 10A-I, 11A-I, and 14A-I are clearly two-parted and have the potential to design molecular chains. Combined with the average binding energy and second-order differential energy analysis, it is speculated that LaGe 9 − is a magic number cluster. The density of states and natural population analysis indicate that electrons consistently transfer from the La atom to Ge atoms. Doped La atom increases the interaction with Ge atoms and improve the stability of pure germanium clusters. Interestingly, LaGe 9 − has a high transfer charge number, and its high stability can be further explained by the spherical jellium model. The investigation into LaGe 9 − magic number clusters offer valuable insights for the exploration of novel materials with superior stability and performance.

Vignetting Compensation Method for CMOS Camera Based on LED Spatial Array

To solve the problem of pixel light intensity information distortion caused by camera vignetting in optical devices such as CMOS or CCD cameras, existing studies mainly focus on small spatial light fields and point light sources and adopt an integrating sphere and function model for vignetting correction, but it is not suitable for large LED optical composite display devices. Under this background, this paper innovatively proposes a camera vigneting compensation method based on an LED spatial array, independently develops a two-dimensional translation device driven by a high-precision guide rail, uses spatial array technology to obtain the brightness distribution of the corrected display screen to quantify its camera vigneting distortion characteristics, and adopts systematic mathematical operations and iterative compensation strategies. Industry standard tests show that the brightness uniformity of the display has been improved by 5.06%. The above research results have been applied to mass production and industrialization.

Investigating students’ insight after attending a planetarium presentation about the apparent motion of the Sun and stars

We present two studies to investigate the extent to which attending a planetarium presentation increases secondary school students’ understanding of the apparent motion of the Sun and stars. In the first study, we used the Apparent Motion of Sun and Stars (AMoSS) test in a pretest/post-test/retention test setting to measure learning gains and improved insight of 404 students (16- to 17-year-olds) after attending a classical planetarium presentation at the Brussels Planetarium. The AMoSS test is a questionnaire on the daily and yearly apparent motion and the observer’s position. It consists of six multiple-choice questions about the Sun and six similar multiple-choice questions about the stars. We asked the students to explain their choices. The learning gains are rather small and the scores improve more on the Sun questions than on the star questions. This difference is largest for questions about the yearly apparent motion. We found that this is due to the fact that many students copy their knowledge about the Sun to the stars. Based on the results of this survey, we developed a new planetarium presentation with particular attention to the use of the celestial sphere model. We also developed a learning module that prepares students at school for this planetarium presentation. In a second study, we measured the learning gains after attending this new planetarium presentation among 339 students, also 16- to 17-year-olds. Some school groups had worked through the preparatory learning module at school and others had not. We find that the learning gains on the star questions are significantly higher than in the first study, due to better scores on the yearly apparent motion questions. In this regard, it is notable that we do not see significant differences between those students who prepared the presentation at school and those who did not. In the second study, the number of students who answer all questions correctly after attending the planetarium presentation or working through the learning module increases, but only significantly for those students who worked through the learning module at school. Published by the American Physical Society 2024

Formation of Three-Dimensional Thinking as one of the Significant Professional Qualities of an Architect

The article touches upon the problems of the professional formation of an architect, the development of his three-dimensional thinking in the process of studying the disciplines of the artistic cycle. The architect's vision must meet the strict requirements imposed by the specifics of visual activity, the laws of figurative literacy and the tasks of a particular stage of work, correlate with the ultimate ideals and purpose of creative activity. In the study of light as a means of artistic expression, an important role must be given to the psychology of the perception of light in nature and in the image. Only having a developed three-dimensional thinking a student can convincingly and accurately convey the character of a three-dimensional shape, its plasticity and movement.The recognition of three-dimensional forms, including natural objects based on three-dimensional vision of images, through an accurate assessment of light and shadow gradations, adequate transfer of color phenomena of reality to the possibilities of the visual sphere and skillful modeling of forms depicted by light and shadow, becomes an emphasis in the training of an architect. The position of color in the image of shapes in space is no less significant.Pedagogical techniques for the formation of three-dimensional thinking of students and the development of their graphic skills in drawing three-dimensional objects, including architectural ones, are based on scientific discoveries of scientists, scientists and artists since the Renaissance.The integrity of perception, attention to detail, the study of space, understanding of form, possession of means of shaping and the image of a three-dimensional object in a two-dimensional format are becoming universal criteria that allow us to talk about the high-quality training of future architects.

The reliability analysis and experiment verification of pressure spherical model for deep sea submersible based on data BP and machine learning technology

Spherical pressure-resistant shells, as a universal structural component of deep-sea submersibles, provide a safe and normal operating environment for personnel and internal equipment. In the paper it presented and optimized the BP neural network model based on a genetic algorithm (GA) accordingly, and the method and accuracy are validated through by a beam model. Simultaneously focusing on steel spherical shells, the study proposed a dataset that captures the influence of the primary dimension of the shell (radius-to-thickness ratio, R/t) on the critical pressure response. The genetic algorithm is employed to optimize the back propagation (BP) neural network model for predicting critical pressure. The structural reliability is adopted as a design criterion to determinate and optimize the geometric parameters and critical pressure of the spherical shell structure. Finally, an ultra-high-strength steel spherical model is designed, constructed and meanwhile collapse pressure tests are accomplished to verify the accuracy of the presented improved BP neural network model based on the computational reliability method. The results reveal that the machine learning optimization design method proposed in this paper can effectively enhance the accuracy of critical pressure predictions and the precision of reliability assessments for deep-sea spherical shells.