Analytical Equations Research Articles

The First Estimation of the Ambipolar Diffusivity Coefficient from Multi-scale Observations of the Class 0/I Protostar, HOPS-370

Protostars are born in magnetized environments. As a consequence, the formation of protostellar disks can be suppressed by the magnetic field, efficiently removing the angular momentum of the infalling material. Nonideal MHD effects are proposed as one way to allow protostellar disks to form. Thus, it is important to understand their contributions to observations of protostellar systems. We derive an analytical equation to estimate the ambipolar diffusivity coefficient at the edge of the protostellar disk in the Class 0/I protostar, HOPS-370, for the first time, under the assumption that the disk radius is set by ambipolar diffusion. Using previous results of the protostellar mass, disk mass, disk radius, density and temperature profiles, and magnetic field strength, we estimate the ambipolar diffusivity coefficient to be 1.7−1.4+1.5×1019cm2s−1 . We quantify the contribution of ambipolar diffusion by estimating its dimensionless Elsässer number to be ∼1.7−1.0+1.0 , indicating its dynamical importance in this region. We compare our results to those of the chemical calculations of the ambipolar diffusivity coefficient using the Non-Ideal Magnetohydrodynamics Coefficients and Ionization Library, which are consistent with our results. In addition, we compare our derived ambipolar diffusivity coefficient to the diffusivity coefficients for ohmic dissipation and the Hall effect, and find ambipolar diffusion is dominant in our density regime. These results demonstrate a new methodology to understand nonideal MHD effects in observations of protostellar disks. More detailed modeling of the magnetic field, envelope, and microphysics, along with a larger sample of protostellar systems, is needed to further understand the contributions of nonideal MHD.

Influence factors and research on higher vocational students' reluctance to advance to higher education based on random forest and structural equation modelling

This study aims to explore the key factors influencing Chinese higher vocational students' reluctance to pursue higher education. By combining two analytical methods, Random Forest and Structural Equation Modeling, the study targeted students enrolled in Guangdong Finance and Trade Vocational College, designed a questionnaire containing various aspects such as study habits, self-perception, and internship experience, and collected 107 samples for analysis. The study found that students' personal intention to pursue higher education was the most critical factor influencing whether they chose to continue their studies, followed by the evaluation of their own learning ability and economic considerations. In addition, family cultural resources and learning environment also influence students' attitudes towards further education to a certain extent. The study also reveals the effects of the positive interaction between personal factors and family cultural resources support, and the negative interaction between personal factors and economic factors on the intention to pursue higher education. Based on these findings, the article presents recommendations for the school, family, and social levels to promote higher education students' willingness to pursue higher education and educational equity.

A note on complex combined boundary value problem for the nonhomogeneous tri-analytic equation

In this paper, a combination of boundary value problems for the nonhomogeneous analytic equations have been studied. The aim of this paper is to find a solution for the Schwarz-(Dirichlet-Neumann) problem and obtain its solvability conditions.

Numerical and artificial neural network analysis of tunnel liner design parameters – a comparative study

ABSTRACT This paper proposes the development of an analytical-based Artificial Neural Network (ANN) model for predicting the concrete segmental lining parameters and comparing it with the finite element method, Rocscience tool. To achieve this aim, the dataset was prepared for twelve different loading conditions using the analytical equations by Muir Wood and Curtis. Using this dataset, an ANN model was developed for predicting the segmental lining parameters, viz. displacement, bending moment, axial and shear force. Furthermore, the Rocscience tool was used to analyse the aforementioned design parameters, and the results of these two methods were compared and summarised. It is found that the developed ANN model shows reasonable results of liner design parameters with the Rocscience program. The efficiency of both techniques was evaluated using the statistical measures viz. Mean Absolute Error, Root Mean Square Error, and Coefficient of Efficiency. It is observed that the ANN model is best fitted for the prediction of liner shear and axial force, while it could not find the optimised solution for liner displacement and bending moment. The finding of this study showed that the developed ANN model can be applied to predict the tunnel liner design parameters instead of the alternative complicated and time-consuming techniques.

Tailoring the statistics of light emitted from two interacting quantum emitters

The interaction between quantum emitters leads to the formation of superradiant and subradiant states with possible applications in quantum technologies. To improve the characterization of light emission from these systems, we present here a systematic theoretical analysis of the intensity correlation from two strongly interacting quantum emitters at cryogenic temperatures as a function of the frequency and intensity of the excitation laser. This analysis effectively accounts for the effect of vibrational modes of the emitters and of phonons of the environment through the combined Debye-Waller/Franck-Condon factor. First, we analyze the color-blind intensity correlation and show that it can be tailored from strong antibunching to strong bunching by tuning the laser from the two-photon resonance to the transition frequency of the superradiant state. We also find a particularly complex behavior of the intensity correlation when the laser frequency is tuned to that of the transition of the subradiant state, giving raise to the possibility of emitting bunched and antibunched light depending on the laser intensity and the detuning between the two emitters. The numerical results are supported by analytical equations that can be used for the experimental characterization of the interacting emitters. Additionally, by selecting photons of particular frequencies, we analyze the rich landscape of frequency-resolved intensity correlations, which also depend on the laser detuning and intensity. The analysis of the frequency-resolved correlations provides further information about the different relaxation processes underlying the photon emission, unveiling one-photon and two-photon emission processes that cannot be resolved neither in the emission spectrum nor in the color-blind intensity correlation. These results show that two interacting emitters are a versatile and practical source of quantum light and highlight the usefulness of the intensity correlation to unveil complex dynamics in this system. Published by the American Physical Society 2024

Large-scale self-normalizing neural networks

Self-normalizing neural networks (SNN) regulate the activation and gradient flows through activation functions with the self-normalization property. As SNNs do not rely on norms computed from minibatches, they are more friendly to data parallelism, kernel fusion, and emerging architectures such as ReRAM-based accelerators. However, existing SNNs have mainly demonstrated their effectiveness on toy datasets and fall short in accuracy when dealing with large-scale tasks like ImageNet. They lack the strong normalization, regularization, and expression power required for wider, deeper models and larger-scale tasks. To enhance the normalization strength, this paper introduces a comprehensive and practical definition of the self-normalization property in terms of the stability and attractiveness of the statistical fixed points. It is comprehensive as it jointly considers all the fixed points used by existing studies: the first and second moment of forward activation and the expected Frobenius norm of backward gradient. The practicality comes from the analytical equations provided by our paper to assess the stability and attractiveness of each fixed point, which are derived from theoretical analysis of the forward and backward signals. The proposed definition is applied to a meta activation function inspired by prior research, leading to a stronger self-normalizing activation function named “bi-scaled exponential linear unit with backward standardized” (bSELU-BSTD). We provide both theoretical and empirical evidence to show that it is superior to existing studies. To enhance the regularization and expression power, we further propose scaled-Mixup and channel-wise scale & shift. With these three techniques, our approach achieves 75.23% top-1 accuracy on the ImageNet with Conv MobileNet V1, surpassing the performance of existing self-normalizing activation functions. To the best of our knowledge, this is the first SNN that achieves comparable accuracy to batch normalization on ImageNet.

Equivalent network modeling of eddy-current transfer functions

The use of eddy-current techniques as a measurement method for material characterization instead of simple fault detection requires transformation of the electrical response signals to quantifiable physical parameters that correlate with material properties. Apart from calibration-curve methods, exact approaches that correctly represent all interactions between excitation field and response field are computationally intensive and not well suited to real-time application. In this work, an equivalent circuit network model is constructed and its analytical equation for the voltage transfer function is derived. This model is then implemented in a soft sensor system. Finally, measurement results from various materials with different electromagnetic properties are presented.

Explicit solutions for the ground displacement of a sliding model simulating both the frictional and rotational effects under idealized acceleration pulses

AbstractFor the first time, the present work derives explicit equations predicting the downward ground displacement of a sliding model simulating both the frictional and rotational effects under idealized acceleration pulses, in the form of simple formulas. Explicit equations allow not only accurate predictions in all cases, but also analysis of the solutions and derivation of expressions for limit cases. Half and full cycles of (i) rectangular, (ii) triangular, (iii) trapezoidal, and (iv) sinusoidal pulses and slopes both under static stability and instability are considered. For this purpose, for pulse cases (i)–(iii) recently proposed implicit analytical solutions are used, while for case (iv), first the analytical equations predicting the sliding displacement and velocity of a sinusoidal pulse in terms of time are obtained and then the time duration of motion is estimated, by using the Bhaskara approximation of the sine and cosine functions. Then, from these, solutions for the particular limit cases corresponding to the “conventional” sliding‐block model (Case A) and the post‐failure run‐off movement without any applied pulse (Case B) are derived. The results for Case A provide a useful tabulation of sliding‐block solutions, some of which are not reported in the literature. The results for Case B provide novel predictions of the time duration of motion in the case of post‐failure movement. The general solutions are analyzed graphically and the deviation from the solutions of Cases A and B is illustrated. Finally, the explicit solutions are compared to solutions of actual accelerograms.

High Frequency Response of Volatile Memristors

AbstractIn this theoretical study, the high‐frequency response of the electrothermal NbO2‐Mott threshold switch is focused, a real‐world electronic device, which has been proved to be relevant in several applications and is classified as a volatile memristor. Memristors of this kind, have been shown to exhibit distinctive non‐linear behaviors crucial for cutting‐edge neuromorphic circuits. In accordance with well‐established models for these devices, their resistances depend on their body temperatures, which evolve over time following Newton's Law of Cooling. Here, it is demonstrated that HP's NbO2‐Mott memristor can manifest up to three distinct steady‐state oscillatory behaviors under a suitable high‐frequency periodic voltage input, showcasing increased versatility despite its volatile nature. Additionally, when subjected to a high‐frequency periodic voltage signal, the device body temperature oscillates with a negligible peak‐to‐peak amplitude. Since the temperature remains almost constant over an input cycle, the devices under study behave as linear resistors during each input cycle. Based on these insights, this paper presents analytical equations characterizing the response of the NbO2‐Mott memristor to high‐frequency voltage inputs, demarcating regions in the state space where distinct initial conditions lead to various asymptotic oscillatory behaviors. Importantly, the mathematical methods introduced in this manuscript are applicable to any volatile electrothermal resistive switch. Additionally, this work presents analytical equations that accurately reproduce the temperature time‐waveform of the studied device during both its transient and steady‐state phases when subjected to a zero‐mean sinusoidal voltage input oscillating in the high‐frequency limit. This analytical approach not only increases the comprehension of volatile electrothermal memristors but also provides a theoretical framework to harness the enhanced dynamical capabilities of real‐world volatile memristors in practical applications.

Design, kinematics and dynamic analysis of a novel double – scissors link deployable mechanism for space antenna truss

A novel truss deployable mechanism composed of scissors links is proposed in this paper. First, the geometry analysis of the general single modular unit of truss deployable antenna and the construction of the planar double scissors link mechanism module is conducted. The entire antenna is prepared by connecting the single module in a circular configuration. Using the Gruebler's method, the mobility of the double scissors link truss deployable module is proved equals to 1. Furthermore, based on the Newtonian approach, kinematic characteristics of the double scissors link truss deployable mechanism are examined. The velocities and accelerations of the antenna components obtained analytically are validated through simulations in MATLAB, SolidWorks and ADAMS. In addition to this, the forces, torques and bearing stresses involved in various struts and joints are calculated to ensure that the operation is within the yield limits. The dynamic characteristics of the antenna i.e., acceptable natural frequency is calculated by developing a 10 DoF vibration model. The analytical equations are solved using MATLAB, and the results are validated through simulations in ANSYS Workbench. The novel antenna assembly gives the natural frequency response of 0.0652 Hz with a 1.6 % error. The proposed double scissors link truss deployable mechanism shows storage ratio of 1 and 10.2 along vertical and radial directions respectively. The dynamic response and storage ratio of novel assembly is validated with results in literature. The research lays the foundation for the kinematics and dynamics analysis of other space deployable mechanisms.

New analytical thermodynamic models developed for pure H2, CH4, CO2 and H2 containing mixtures based on molecular simulations

Pressure-volume-temperature-composition (PVTX) properties of gas mixtures are important to model and predict flow and compression performance in a range of industrial processes. It is time consuming and sometimes impractical to obtain these properties from experiments. Here, molecular dynamics (MD) simulations were conducted to compute the thermodynamic volumetric properties of pure H2, CH4, CO2, and binary mixtures of H2/CH4 and H2/CO2 at temperatures of 310.9–470 K, pressures up to 172 MPa. MD simulation results were used to develop five analytical equations explicit in pressure as a function of density or volume, temperature, and composition, for the pure gases and mixtures. Our simulated results matched very well with the predictions from the established GERG-2008 equation and data published by NIST. The simplified equations of state (EOS) developed in this work will be more computationally efficient than other EOS for mixed systems. This can be significant in reservoir simulations.

Analytical spatiotemporal distribution equations of viscous slurry grouting pressure during the grouting process in rock fissures

To give a simpler theoretical solving approach for modeling the grouting process of viscous slurry in porous/broken rocks, this work derives two theoretical spatiotemporal distribution equations of viscous slurry penetration in rock fissures based on the Darcy seepage model (DM) and the Bingham fluid model (BM) through a hypothetical micro-element model. Through a two-dimensional (2D) conceptual grouting hole model with porous media, the applicability of the two proposed theoretical spatiotemporal distribution equations of viscous slurry pressure is validated by comparing the analytical results with the numerical results obtained from the two-phase flow simulation. The results indicate that the analysis results obtained from two proposed theoretical spatiotemporal distribution equations are well consistent with the simulation results at different times and under different grouting velocities. That means the time-consuming numerical simulation of the porous/broken rocks grouting process can be replaced by two proposed theoretical spatiotemporal distribution equations, which will greatly reduce the difficulty of real-time evaluation of the grouting effects in engineering practice and shorten the assessment time.

Estimation of mixed-gas selectivity of membranes using the linear friction-based model

The development of analytical models for predicting the transport properties of membranes in the separation of multicomponent mixtures is highly relevant because (1) measurements of permeability and sorption of gas mixtures in membrane materials are laborious and time-consuming, and (2) estimation of transport properties based on pure gas measurements is desirable, however, rather unreliable and can lead to serious errors. In this paper, within the framework of the well-known frictional-coefficient formalism, we present nonlinear equations for the fluxes of gas mixture components through the membrane, which take into account the diffusional coupling of the fluxes compared to independent gas transport. As a result, an analytical equation for the mixed-gas selectivity was obtained. This equation has an implicit form, which is not quite convenient for practical application, since it has to be solved numerically. A simple explicit expression for mixed gas selectivity was derived using the so-called linear transport model, which is a linearized version of the original nonlinear flux equations. It is important to emphasize that a comparison of the linear model with the formally more rigorous nonlinear model showed only minor quantitative differences. The input parameters for the model are the single gas transport parameters. Testing the linear model using experimental data for the separation of hydrocarbons (n-butane/methane, n-butane/i-butane, propylene/propane) revealed an acceptable fit. A comparison of the model with recent experimental data on the separation of CO2-containing mixtures using microporous polymers is also presented. It is found that the calculated CO2/N2 mixed gas selectivity is in good agreement with the experimental data, while only a semi-quantitative agreement is observed for the CO2/CH4 separation. Besides, it is shown that the model developed for binary gas separation can be extended to ternary gas mixtures.

Short-voltage pulse generation for induction heating load detection on a multi-output inverter with shared power devices

Purpose The purpose of this paper is to develop a load detection method for domestic induction cooktops. The solution aims to minimize its impact in the converter power transmission while enabling the estimation of the equivalent electrical parameters of the load. This method is suitable for a multi-output resonant inverter topology with shared power devices. Design/methodology/approach The considered multi-output converter presents power devices that are shared between several loads. Thus, applying load detection methods in the literature requires a halt in the power transfer to ensuring safe operation. The proposed method uses a complementary short-voltage pulse to excite the induction heating (IH) coil without stopping the power transfer to the remaining IH loads. With the current through the coil and the analytical equations, the equivalent inductance and resistance of the load is estimated. The precision of the method has been evaluated by simulation, and experimental results are provided. Findings The measurement of the current through the induction coil as a response to a short-time single-pulse voltage variation provides enough information to estimate the load equivalent parameters, allowing to differentiate between no-load, non-suitable IH load and suitable IH load situations. Originality/value The proposed method provides a solution for load detection without requiring additional circuitry. It aims for low power transmission to the load and ensures zero-voltage switching and reduced peak current even in no-load cases. Moreover, the proposed solution is extensible to less complex converters, as the half bridge.

Origin of bent ridge-kink based on disclination relaxation

In this study, we have developed a geometric model for bent kinks by introducing sequences of ortho-connected kink bands into ridge-kinks to provide insights into the possible reasons why kinks are bent and the resulting geometry when they are bent. We first formulated the Frank angles and coordinates of the disclinations formed in the bent kinks, which enable our discussion on the influence of the introduction of ortho-kinks on the Gibbs energy by utilizing Romanov’s disclination model. It turns out that the introduction of ortho-kinks can relax the elastic strain energy and thus reduce the Gibbs energy of the system under compression states with lower external stresses. On the other hand, the introduction of ortho-kinks increases the Gibbs energy at higher compression stresses, implying sharp ridge-kinks are preferred under such conditions. This trend resembles the experimental observations reported by previous studies that the shapes of newly formed kinks tend to transition from pre-kinks with bent shapes to ridge-kinks with sharp shapes as the compression test progresses. The smoothly bent kink with smoothly distributed misorientation, formed by increasing the number of introduced ortho-kinks, can further reduce the Gibbs energy at lower applied stresses. Subsequently, based on the Rank-1 condition for the connection of kink bands, we further analyzed the geometry of such smoothly bent kinks and derived the analytical equations for the constraints on the orientation distribution. Finally, we conducted EBSD measurements on bent kinks observed in directionally solidified (DS) LPSO-Mg alloys and confirmed that the derived equations for the orientation distribution are in good agreement with the experimental results.

Technical Feasibility of Extraction of Freshwater from Produced Water with Combined Forward Osmosis and Nanofiltration.

This study assesses the technical feasibility of a forward-osmosis-based system for concentrating produced water and extracting freshwater. Forward osmosis was combined with nanofiltration, the latter system used to restore the initial osmotic pressure of the diluted draw solutions while concurrently obtaining the final freshwater product. Three draw solutions, namely, MgCl2, NaCl, and C3H5NaO2, were initially tested against a synthetic water mimicking a pretreated produced water effluent having an osmotic pressure equal to 16.3 bar. MgCl2 was thus selected for high-recovery experiments. Different combinations of draw solution osmotic pressure (30, 40, 60, 80, and 120) and draw-to-feed initial volume ratios (1, 1.6, and 2.2) were tested at the laboratory scale, achieving recovery rates between roughly 35% and 70% and water fluxes between 4 and 8 L m-2h-1. One-dimensional, system-wide simulations deploying the analytical FO water flux equation were utilized to validate the experiments, investigate co-current and counter-current configurations, and understand the system potential. The diluted draw solutions were then transferred to nanofiltration to regenerate their original osmotic pressure. There, the highest observed rejection was 96.6% with an average flux of 21 L m-2h-1, when running the system to achieve 100% relative recovery.

AC Loss Modeling of a CORC Cable via an Analytical Equation and Finite Elements

AC Loss Modeling of a CORC Cable via an Analytical Equation and Finite Elements

Testing analytical methods to derive the cosmic-ray ionisation rate in cold regions via synthetic observations

Context. Cosmic rays (CRs) heavily impact the chemistry and physics of cold and dense star-forming regions. However, the characterisation of their ionisation rate continues to pose a challenge from the observational point of view. Aims. In the past, a few analytical formulas have been proposed to infer the cosmic-ray ionisation rate, ζ2, from molecular line observations. These have been derived from the chemical kinetics of the involved species, but they have not yet been validated using synthetic data processed with a standard observative pipeline. In this work, we aim to bridge this gap. Methods. We performed a radiative transfer on a set of three-dimensional magneto-hydrodynamical simulations of prestellar cores, exploring different initial ζ2, evolutionary stages, types of radiative transfer (for instance assuming local-thermodynamic-equilibrium conditions), and telescope responses. We then computed the column densities of the involved tracers to determine ζ2, employing a recently proposed method based on the detection of H2D+. We compared this approach with a previous method, based on more common tracers. Both approaches are commonly used. Results. Our results confirm that the equation based on the detection of H2D+ accurately retrieves the actual ζ2 within a factor of two to three in the physical conditions explored in our tests. Since we have also explored a non-local thermodynamic equilibrium (non-LTE) radiative transfer, this work indirectly offers insights into the excitation temperatures of common transitions at moderate volume densities (n ≈ 105 cm−3). We also performed a few tests using a previous methodology that is independent of H2D+, which overestimates the actual ζ2 by at least two orders of magnitude. We considered a new derivation of this method, however, we found that it still leads to high over-estimations. Conclusions. The method based on H2D+ is further validated in this work and demonstrates a reliable method for estimating ζ2 in cold and dense gas. On the contrary, the former analytical equation, as already pointed out by its authors, has no global domain of application. Thus, we find that it ought to be employed with caution.

The effect of superstructure properties on the re-centering capability of Friction Pendulum (PS) isolator

The re-centering capability after the seismic excitation is one of the fundamental properties of a seismic isolation system. This study examines the effects of superstructure properties on the re-centering capability of the Friction Pendulum (FP) isolator. To this end, a comprehensive parametric study is conducted using a two-degree-of-freedom (2DOF) model that accounts for the nonlinear behavior of the superstructure and isolator. This study evaluates the re-centering capability of the FP isolator by calculating the ratio of residual displacement (dres) to the maximum displacement (dmax). The effect of superstructure properties, including strength reduction ratio R, fundamental vibration period Ts, post-yield stiffness ratio αs, superstructure damping ratio ξs, and the ratio of superstructure mass to total mass of the system γm on the dres/dmax ratios is thoroughly analyzed. The findings suggest that while estimating the residual displacement of isolation systems, it is important to consider the impact of superstructure parameters. An analytical equation is proposed to predict dres/dmax ratio based on effective superstructure and isolator parameters.

DEFORMATION OF END CROSSBEAMS OF STEEL BRIDGES RELATED TO SUSTAINABILITY OF BRIDGE JOINTS

Both AASHTO and Eurocode stipulate that the deflection of end crossbeams of bridges must be limited to 5 mm under the influence of frequent traffic loads. After a thorough literature review and survey of data from manufacturers of bridge joints, it must be concluded that the background of this requirement is not really based on facts. Durability of bridge joints certainly does not appear to be the basis. Another valid reason can be the comfort of road user, which is effectively disturbed by driving over bumps and thresholds. Although the road user expects light shocks at the end of a bridge, the acceleration inside the vehicle must be limited. Therefore, the state of a wheel driving over a threshold has been studied, by applying analytical equations taken from literature and extended. These allow a fairly accurate simulation of the state. Force required to cross the threshold produces an acceleration of wheel, which is transmitted to vehicle's sprung chassis. In the latter one finds the acceleration to which persons are subjected. Several values of comfort can be considered. It turns out that 5 mm limit is very conservative, and one could easily allow up to double the end cross beam’s deflection.