Field Coefficients Research Articles

Realizing the Calculation of a Fully Normalized Associated Legendre Function Based on an FPGA

A large number of fully normalized associated Legendre function (fnALF) calculations are required to compute Earth’s gravity field elements using ultra high-order gravity field coefficient models. In the surveying and mapping industry, researchers typically rely on CPU-based systems for these calculations, which leads to limitations in execution speed and power efficiency. Although modern CPUs improve instruction execution efficiency through instruction-level parallelism, the constraints of a shared memory architecture impose further limitations on the execution speed and power efficiency. This results in exponential increases in computation time as demand rises alongside high power consumption. In this article, we present a new computational implementation of an fnALF based on the ZYNQ platform. We design a task-parallel “pipeline” architecture which converts the original serial logic into a more efficient hardware implementation, and we utilize a redundant calculation layer to handle repetitive coefficient computations separately. The experimental results demonstrate that our system achieved accurate and rapid calculations. Under the only one geocentric residual latitude condition, we measured the computation times for spherical harmonic coefficient degrees of 360, 720, and 1080 to be 0.155922 s, 0.520950 s, and 1.401609 s, respectively. In the case of the multiple geocentric residual latitudes condition, our design generally yielded efficiency gains of over three times those of MATLAB R2020b implementation. Additionally, our calculated results were used to determine the geoid height in the field with an error of less than ±0.1m, confirming the reliability of our computations.

Study on heat transfer behavior of CFS-PSB composite walls

The cold-formed thin-walled steel (CFS)-paper straw board (PSB) composite walls takes as the research object. The thermal performance of the wall was analyzed by the building heat transfer theory and the finite element analysis software ANSYS, explored the influence of relevant parameters on heat transfer coefficient of composite wall and proposed supplementary correction coefficient for applying the type of composite walls. The heat flux density field, temperature distribution field, node temperature, and heat transfer coefficient of the walls were also obtained. The specific parameters analyzed using this model mainly included the insulation material, web height, thickness of the section steel, width of the flange, length of the hole, number of hole rows, and horizontal and longitudinal spacing of the holes. The findings show that an increase in the web height reduces the heat transfer coefficient of the composite wall, which is conducive to improving the thermal insulation performance of the walls. The CFS-PSB composite wall with a web opening can significantly improve the heat transfer performance of the wall, reduce heat loss, and control the local thermal bridging phenomenon. The hole length, specific gravity of the openings, and number of openings were the main parameters affecting the thermal insulation performance of the walls.

Low-degree gravity field coefficients based on inverse GNSS method: insights into hydrological and ice mass change studies

The relative displacements of stations from a global network of Global Navigation Satellite System (GNSS) sites provide information on global mass transport. In this study, we use 19 years of global GNSS station displacements from the 3rd International GNSS Service reprocessing campaign to estimate the coefficients of the spherical harmonics of the Earth’s gravity field up to degree and order 8 using the inverse GNSS method based on elastic loading theory. The results indicate that the C30 coefficient can be derived based on GNSS station displacements as an alternative to solutions provided by Satellite Laser Ranging (SLR) and Gravity Recovery and Climate Experiment (GRACE). GNSS may support GRACE solutions that face the problems of deriving C30, which has fundamental meaning in estimating ice mass changes in polar regions. The recovery of Antarctic ice sheet mass change from January 2007 to December 2020 based on coefficients replaced by GNSS estimates results in a linear trend of − 152 ± 4 Gt/year, in comparison to − 149 ± 2 Gt/year for the replacement based on SLR from GRACE Technical Note #14. The results indicate that the spatial and seasonal patterns of terrestrial water storage changes derived from GNSS are consistent with those estimated using GRACE/GRACE Follow-On and SLR at a few-millimeter level in the Amazon and Brahmaputra River basin regions.

Are the mycelium-based diffusers applicable?

The use of materials based on the mycelial growth on recycled materials is widely studied. The absorbent properties of such composites can be found in a number of articles. However, this one focuses on the possibility of using mycelium-based composites for the design of sound diffusers. Diffusion parameters were determined in the form of normalized and non-normalized diffusion coefficient in a free field according to ISO 17497-2. The measured results show that the use of mycelium for the construction of diffusers is promising. However, the results are not the best, which is due to the architectural design. . For further development, the optimization of the shape of the diffusers based on acoustic requirements is expected.

Torsion homology growth and cheap rebuilding of inner-amenable groups

We prove that virtually torsion-free, residually finite groups that are inner-amenable and non-amenable have the cheap 1-rebuilding property, a notion recently introduced by Abért, Bergeron, Frączyk and Gaboriau. As a consequence, the first \ell^{2} -Betti number with arbitrary field coefficients and log-torsion in degree 1 vanish for these groups. This extends results previously known for amenable groups to inner-amenable groups. We use a structure theorem of Tucker-Drob for inner-amenable groups showing the existence of a chain of q -normal subgroups.

Spatiotemporal coupling deep neural network for time-resolved flow field reconstruction around a circular cylinder

We propose a spatiotemporal coupling deep neural network approach for time-resolved reconstruction of the velocity field around a circular cylinder. The neural network leverages two distinct data types: (1) non-time-resolved velocity field around the cylinder, consisting of fixed frequency sampling and variable frequency sampling velocity field, and (2) the time-resolved surface pressure sequence around the cylinder. The deep neural network comprises two sub-networks: a convolutional autoencoder (CAE) for nonlinear mode extraction and a Transformer for sequence-to-sequence learning. We refer to this architecture as CTNet (CAE-Transformer Network). The encoder in the CAE maps non-time-resolved velocity field to a latent vector, enabling the extraction of nonlinear modal coefficients. An appropriate time window length for the surface pressure sequence is then selected to establish a Transformer sequence learning model, using the chosen sequence as input to predict the corresponding nonlinear modal coefficients. Once the Transformer is well trained, the time-resolved nonlinear modal coefficients of velocity field can be achieved. Along with the well-trained decoder in the CAE, the time-resolved velocity field can be reconstructed from the output of the Transformer. We verify the performance of CTNet by a simulated dataset at a representative Reynolds number of 3900. The results show a relative reconstruction error of just 6.3% for the time-resolved velocity field, demonstrating high reliability in the reconstruction. We further compare the reconstructed velocity field obtained with and without the utilization of variable frequency sampling velocity field. Notably, the inclusion of variable frequency sampling velocity field significantly improves the reconstruction quality.

Mixed convection flow and heat-mass transfer of cross liquid near a stagnation region with Dufour, Soret effects and chemical reaction

Heat-mass transfer in a liquid flow over a stretching surface at a stagnation regime is significant in optimal manufacturing and quality assurance depending on the rheological behavior of viscoelastic fluids in process machinery. Stretching sheet flow at a stagnation point is a standard procedure used in the metallurgical industries for manufacturing of different equipment and cooling systems. Due to its various applications in industrial operations, the current study aims to explore the heat-mass transfer of buoyancy-driven flow of cross liquid over a stretching sheet at a stagnation point. The heat and mass transfer under the framework of Dufour and Soret effects, radiant heat, and chemical reactions are assessed. Furthermore, the analysis also takes into account the linear and nonlinear convection-diffusion phenomena. The model findings are obtained by merging the Bvp4c in MATLAB using a local similarity technique up to the fourth truncation threshold. The findings illustrate that the action of magnetic field can be used to control the flow across the sheet. Temperature increases with thermal radiation, Biot number and Dufour number. The action of buoyancy ratio parameter result in improvement in fluid flow. With increasing trend of magnetic and Weissenberg number, the flow field and skin friction coefficient drops.

Force-Field based assisted control for upper-limb rehabilitation robots

Robot-assisted training with an assist-as-needed (AAN) control strategy has been used in clinical investigations to effectively enhance the subject’s active effort and promote the rehabilitation of individuals with upper-limb motor impairment. In this paper, a force field-based AAN control scheme is proposed for robot-assisted upper limb rehabilitation training and then implemented in a robot-assisted rehabilitation training system (RaRTS). A spatial varying assistance force field is constructed around the predetermined trajectory in this scheme, and then a varying force field coefficient based on the subject’s motor performance is adopted to deliver the AAN features with temporal freedom. The normal force field, tangential force field, and viscous force field are the three components of the constructed spatial varying assistance force field. Furthermore, the proposed scheme contains three training modes that are switched according to the subject’s trajectory tracking error. Finally, task-oriented continuous training experiments with different force field factors are conducted on able-bodied subjects to evaluate and validate the performance and feasibility of the proposed scheme. Preliminary experimental results and statistics analysis suggest that the subjects were able to keep much closer to the predetermined trajectory through an appropriate selection of force-field assistance factors. Furthermore, the robot would apply an assistance force as needed as the motor performance deteriorate, which could prevent the subject from losing confidence due to poor performance.

Establishment of a 241Am gamma calibration field based on international standards and its conversion coefficients.

A 241Am gamma (γ)-ray calibration field that meets the requirements for a γ-ray reference field as specified in the ISO 4037 standard series was established in the Facility of Radiation Standards of the Japan Atomic Energy Agency. The reference air kerma rates were measured using a reference ionization chamber calibrated by the N-80 quality X-ray calibration field of the national metrology standard in Japan and with a correction to account for differences in photon energy due to the calibration field. Conversion coefficients for the 241Am γ-ray calibration field, including those not listed in the ISO 4037 standard series, were calculated based on the measured γ-ray fluence rate spectra.

Orbit design for a future geodetic satellite and gravity field recovery

Spherical geodetic satellites tracked by satellite laser ranging (SLR) stations provide indispensable scientific products that cannot be replaced by other sources. For studying the time-variable gravity field, two low-degree coefficients C20 and C30 derived from GRACE and GRACE Follow-On missions are replaced by the values derived from SLR tracking of geodetic satellites, such as LAGEOS-1/2, LARES-1/2, Starlette, Stella, and Ajisai. The subset of these satellites is used to derive the geocenter motion which is fundamental in the realization of the origin of the terrestrial reference frames. LAGEOS satellites provide the most accurate standard gravitational product GM of the Earth. In this study, we use the Kaula theorem of gravitational perturbations to find the best possible satellite height, inclination, and eccentricity for a future geodetic satellite to maximize orbit sensitivity in terms of the recovery of low-degree gravity field coefficients, geocenter, and GM. We also derive the common station-satellite visibility-coverability coefficient as a function of the inclination angle and satellite height. We found that the best inclination for a future geodetic satellite is 35°–45° or 135°–145° with a height of about 1500–1700 km to support future GRACE/MAGIC missions with C20 and C30. For a better geocenter recovery and derivation of the standard gravitational product, the preferable height is 2300–3500 km. Unfortunately, none of the existing geodetic satellites has the optimum height and inclination angle for deriving GM, geocenter, and C20 because there are no spherical geodetic satellites at the heights between 1500 (Ajisai and LARES-1) and 5800 km (LAGEOS-1/2, LARES-2).

Investigation of thermal radiation and joule heating effects on variable viscosity Casson nanofluid flow over a stretching sheet in Darcy–Forchheimer porous medium

Nanofluids possess unique thermal and rheological properties that offer significant advantages in enhancing heat transfer efficiency in various applications, such as heat exchangers, cooling systems, and microdevices. In this study, we investigate the combined effects of thermal radiation, Joule heating, variable viscosity, and a two-phase model on the flow behavior and heat transfer characteristics of a magnetohydrodynamic Casson nanofluid flowing over a stretching sheet in Darcy-Forchheimer porous media. The governing partial differential equations are converted into a system of first-order ordinary differential equations numerically solved using the bvp5c package in MATLAB. Consequently, the result indicates that the velocity profile increases with thermal radiation, variable viscosity, and viscous dissipation, decreasing with the magnetic field, permeability index, and Forchheimer coefficient. Also, the temperature profile shows an increase with the permeability index, viscous dissipation, and thermal radiation, but a decrease with the Forchheimer Coefficient, variable viscosity, and magnetic field. Additionally, the concentration profile exhibits an increase with the Forchheimer coefficient and permeability index, and variable viscosity while it decreases with viscous dissipation, magnetic field, and thermal radiation. Analyzing the skin friction coefficient reveals an increase with magnetic field and thermal radiation and a decrease with permeability index and Forchheimer coefficient as well as variable viscosity. Moreover, the local heat transfer rate demonstrates an increase with the variable viscosity, and magnetic field as well as the Forchheimer coefficient and permeability index. At the same time, it decreases with the viscous dissipation. Furthermore, the local mass transfer rate displays an increase with the magnetic field and thermal radiation and viscous dissipation, while it decreases with the variable viscosity as well as permeability index, viscous dissipation, and Forchheimer coefficient. Finally, the current findings are compared with that of the existing literature and a sound agreement was established.

Compressibility effects on Rayleigh-Taylor instability in magnetized strongly coupled dusty plasma

The compressibility effects have been studied on the internal wave modes and Rayleigh-Taylor (R-T) instability in a magnetized strongly coupled dusty plasma (SCDP). A dusty fluid model is constructed considering the effects of weakly coupled electrons/ions and strongly coupled dust grains under the influence of the gravitational field. The effects of the magnetic field and viscoelastic coefficients have been incorporated under the generalized hydrodynamic (GH) fluid description in a quasineutral dusty plasma. The dispersion relation of R-T instability is derived analytically and discussed in the strongly coupled limit. The compressibility effects have appeared in the internal wave modes, significantly modifying the R-T instability criterion and growth rates. The Coulomb coupling parameter and dust magnetosonic speed suppress the growth rate of the R-T instability in a compressible SCDP.

Beam shape coefficients of the hollow vortex Gaussian beam and near-field scattering

The beam shape coefficients (BSCs) of the electromagnetic field of hollow vortex Gaussian beams (HVGBs) are formulated, based on the spherical wave expansion of the scalar function. The cylindrical wave spectrum decomposition is employed to expand the scalar function in the spherical coordinates. Numerical results on the beam field reproduced from the BSCs confirm that the BSC evaluation is efficient and reliable. The scattering in the near-field zone is calculated and discussed, revealing the dependence of the straight and curved photonic jets on the topological charge of the HVGB. The paper may be useful for studying the interaction between the HVGB and a spherical particle.

CFD Calculation of Natural Convection Heat Transmission in a Three-Dimensional Pool with Hemispherical Lower Head

The integrity of a pressure vessel (PRV) is affected by the decay heat of the molten pool in the lower head, so it is very important to study the natural convection heat transmission in the lower head. Scholars from all over the world have carried out a lot of experimental studies and calculations to determine the convection mechanism and heat transmission characteristics of the molten pool. Most of them were based on the empirical formula of convective heat transmission on the wall of a hemispherical molten pool based on two-dimensional slice experiments and simulation calculations. In this study, FLUENT 2021R1 software was used to simulate the three-dimensional convective heat transmission process of the hemispherical molten pool, and the temperature, velocity and wall heat transmission coefficients of the flow field were analyzed. The results were in good agreement with experimental data from UCLA (University of California, Los Angeles). Through research on the heat transmission of the lower head, the results showed that in the region where the wall angle was θ between approximately 72 and 90 degrees, heat transmission coefficients had larger fluctuations, and a more reasonable empirical relation was proposed. Comparing between the simulation results of CFD and the two-dimensional empirical formula, it was found that the latter one was smaller under the same θ angle condition. Finally, the convection phenomena of different external temperatures were simulated, and the main factors affecting the flow field by temperature were analyzed.

Magnetothermopower of Nodal-Line Semimetals

The search for materials with large thermopower is of great practical interest. Dirac and Weyl semimetals have recently proven to exhibit superior thermoelectric properties, particularly when subjected to a quantizing magnetic field. Here, we consider whether a similar enhancement arises in nodal-line semimetals, for which the conduction and valence band meet at a line or ring in momentum space. We compute the Seebeck and Nernst coefficients for arbitrary temperature and magnetic field and we find a wealth of different scaling regimes. Most strikingly, when a sufficiently strong magnetic field is applied along the direction of a straight nodal line or in the plane of a nodal ring, the large degeneracy of states leads to a large linear-in-B thermopower that is temperature independent even at low temperatures. Our results suggest that nodal-line semimetals may offer significant opportunity for efficient low-temperature thermoelectrics. Published by the American Physical Society 2024

Deciphering a Million-Plus RSA Integer with Ultralow Local Field Coefficient h and Coupling Coefficient J of the Ising Model by D-Wave 2000Q

Deciphering a Million-Plus RSA Integer with Ultralow Local Field Coefficient h and Coupling Coefficient J of the Ising Model by D-Wave 2000Q

Numerical model of Phobos’ motion incorporating the effects of free rotation

Context. High-precision ephemerides are not only useful in supporting space missions, but also in investigating the physical nature of celestial bodies. This paper reports an update to the orbit and rotation model of the Martian moon Phobos. In contrast to earlier numerical models, this paper details a dynamical model that fully considers the rotation of Phobos. Here, Phobos’ rotation is first described by Euler’s rotational equations and integrated simultaneously with the orbital motion equations. We discuss this dynamical model, along with the differences with respect to the model now in use. Aims. This work is aimed at updating the physical model embedded in the ephemerides of Martian moons, considering improvements offered by exploiting high-precision observations expected from future missions (e.g., Japanese Martian Moons exploration, MMX), which fully supports future studies of the Martian moons. Methods. The rotational motion of Phobos can be expressed by Euler’s rotational equations and integrated in parallel with the equations of the orbital motion of Phobos around Mars. In order to investigate the differences between the two models, we first reproduced and simulated the dynamical model that is now used in the ephemerides, but based on our own parameters. We then fit the model to the newest Phobos ephemeris published by Institut de Mécanique Céleste et de Calcul des Éphémérides (IMCCE). Based on our derived variational equations, the influence of the gravity field, the Love number, k2, and the rotation behavior were studied by fitting the full model to the simulated simple model. Our revised dynamic model for Phobos was constructed as a general method that can be extended with appropriate corrections (mainly rotation) to systems other than Phobos, such as the Saturn and Jupiter systems. Results. We present the variational equation for Phobos’ rotation employing the symbolic Maple computation software. The adjustment test simulations confirm the latitude libration of Phobos, suggesting gravity field coefficients obtained using a shape model and homogeneous density hypothesis should be re-examined in the future in the context of dynamics. Furthermore, the simulations with different k2 values indicate that it is difficult to determine k2 efficiently using the current data.

Performance assessment of corroded stiffened steel plates considering non-Gaussian spatial correlated corrosion random field

This paper investigates the effect of corrosion randomness on the compression performance of stiffened steel plates. An anisotropic non-Gaussian random filed model is proposed to characterize the corrosion depth of the corroded steel plate surface. The specimens of corroded steel plate were obtained utilizing the artificial climate environment method. Corrosion characteristics were measured through 3D-scanning and reverse modeling. Statistical methods are utilized to analyze corrosion depth, including probability distribution and correlation coefficient. Two models are proposed for steel plate placing flatly and inclinedly, respectively. It is found that for both models corrosion depth follows truncated GEV distribution, and the correlation coefficient follows a bidirectional exponential function. To investigate the effect of non-Gaussian and correlation characteristics on bearing capacity, the proposed model is used for generating anisotropic non-Gaussian corrosion random fields for stiffened steel plates. Generated samples were used for finite element analysis. It is found the ignorance of non-Gaussian or correlation of the corrosion depth field will underestimate the deterioration of bearing capacity of stiffened steel plates. Finally, a parametric study on the correlation coefficients of the corrosion field indicates that correlation length will affect the residual bearing capacity of corroded steel plate. The proposed random field for corrosion depth of steel plate could be used for potential application on the safety assessment of corroded steel structures.

Irreducible representations of the Poincaré group with reflections and two-fold Wigner degeneracy

Not all complete set of spinors can be used as expansion coefficients of a quantum field. In fact, Steven Weinberg established the uniqueness of Dirac spinors for this purpose provided: (a) one paid due attention to the multiplicative phases for each of the spinors, and (b) one paired these to creation and annihilation operators in a specific manner. This is implicit in his implementation of the rotational symmetry for the spin half quantum field. Among the numerous complete set of spinors that are available to a physicist, Elko occupies a unique status that allows it to enter as expansion coefficients of a quantum field without violating Weinberg’s no go theorem. How this paradigm changing claim arises is the primary subject of this communication. Weinberg’s no go theorem is evaded by exploiting a uniquely special feature of Elko that allows us to introduce a doubling of the particle-antiparticle degrees of freedom from four to eight. Weinberg had dismissed this degeneracy on the ground that, “no examples are known of particles that furnish unconventional representations of inversions.” Here we will find that this degeneracy, once envisioned by Eugene Wigner, in fact gives rise to a quantum field that has all the theoretical properties required of dark matter.

Photostimulated Nernst effect in two-dimensional compositional semiconductor superlattices under the influence of confined phonons

The photostimulated Nernst effect in compositional semiconductor superlattices under the influence of a confined acoustic phonon is studied by using the quantum kinetic equation. The case of the confined electron-confined acoustic phonon scattering process is examined in detail. The obtained analytical results reveal that the Nernst coefficient (NC) depends on the external field such as magnetic field B, the frequency Ω, and the amplitude E 0 of the electromagnetic wave in a complicated way but also like a function of the temperature of the system and the period of the superlattice. It also depends on the quantum number m-describing the confined acoustic phonon. The theoretical results are depicted and discussed for GaAs/AlxGa 1 − xAs compositional semiconductors superlattices. The results indicate that the Shubnikov-De hass oscillations have appeared. The confined phonons make the magnitude of the Nernst coefficient higher and more obvious than the case of a bulk phonon. In addition, the magneto-photon resonance condition is also proved. Besides, the Nernst coefficient decreases significantly as the temperature increases. The oscillations Nernst coefficient in a magnetic field are consistent with the previous experimental.