Parameters Of Equation Research Articles

Evaluation of Evaporation Fluxes for Pesticides and Low Volatile Hazardous Materials Based on Evaporation Kinetics of Net Liquids.

Evaporation is the phase transition process that plays a significant role in many spheres of life and science. Volatilization of hazardous materials, pesticides, petroleum spills, etc., impacts the environment and biosphere. Predicting evaporation fluxes under specific environmental conditions is challenging from theoretical and empirical points of view. A new practical method for estimating fluxes is proposed based on our experimental results and previously published data. It is demonstrated that some parameters in theoretical equations for near-equilibrium evaporation can be estimated from experiments, and these formulas can be exploited to predict steady-state evaporation fluxes in the air in a range of 8 orders of magnitude based on a single experiment carried out for nontoxic volatile compounds.

Mixing neural networks, continuation and symbolic computation to solve parametric systems of non linear equations

We consider a square non linear parametric equations system F(P,X) = 0 which is constituted of n non differential equations in the n unknowns {x1,…,xn} that are the components of X while P={p1,…,pm} is a set of m parameters that play a role in the definition of the equations F. We assume that P is restricted to lie in a bounded region and we are interested in developing a solver for obtaining all real solutions exactly (a notion that is defined in the paper) for any parameter values within the bounded region. The starting point of the proposed approach is that we assume that a numerical methods has allowed us to determine the real solutions (but not necessarily all of them) for a very limited number of fixed P called the initial solution set. Starting from this set we show that we can create multiple pairs (parameters, solution) and that these pairs may be structured into coherent learning sets that will be used to train multi-layer perceptrons (MLP). The training process is specific: although it still uses a decrease of a loss function its main objective is to maximize the success rate i.e. the number of occurrences, expressed in percentage of number of samples of the training set, for which the Newton scheme, initialized with the MLP prediction, converges toward the expected solution. We then show that for a sufficiently large number of MLPs we may obtain a 100% success rate for all learning sets. The solver is obtained by running a set of local solvers each of which is based on a specific MLP whose prediction may lead to an exact solution of the system. This solver is tested on verification sets i.e. set of samples constituted of parameter values (all different from the samples in the learning set) and all the solutions of the corresponding system. We show that these sets may be automatically generated and that they may also be used in a self-learning process for improving the performance of the solver established from the initial solution set.This approach is illustrated on two engineering problems in robotics and chemistry and it is shown that the solver provides all solutions for any instance of P with a high probability although we cannot guarantee it. The time required to design the final solver is large but the solving time is extremely low so that this approach should be used when the system has to be solved for a sufficient number of occurrences of the P. Furthermore we will show that the computation time required for establishing the solver may be drastically reduced by using a distributed implementation.

Stability of charged anisotropic thin shell gravastars admitting conformal motion in [formula omitted] gravity

This paper investigates the interesting features of gravastar configuration under charged anisotropic fluid distribution considering geometry-matter coupling theory. In the context of f(R,T) gravity, we derive exact solutions of the Einstein field equations using the linear form of the function f(R,T)=R+2γT, where R is the Ricci scalar and T is the trace of the energy–momentum tensor with conformal motion. We consider three different regions of gravastar, the interior region having a definite radius r, the intermediate layer of matter with the thickness ϵ, and the outer region with the radius r+ϵ. For the viability of our developed solution, we examine the metric potentials, energy density, and pressure components inside the thin shell for different values of theory parameter γ, and charge Q. Using the well-known matching conditions, we interpret the dynamical properties of gravastar such as surface charge density, surface pressure, proper length, equation of state parameter, entropy, and evolution of shell energy under the allowed range of parameters. Moreover, we analyze the presence of realistic matter inside the thin shell through energy conditions. The dynamical stability of the gravastar is checked through the equilibrium profile and speed of sound parameter, which shows the stable configuration of the gravastar in our theoretical studies.

The Influence of CO2 Physical Properties on Casing and Its Prediction Method

In order to reveal the physical properties of CO2 under actual formation conditions, this paper establishes a mathematical model of the temperature field and pressure field in the wellbore under CO2 injection conditions, optimizes the state equation of CO2 physical-property parameters, calculates the change trend of CO2 density, viscosity, and compression factor along the wellbore, and obtains the influence law of CO2 corrosion on the casing and interface. The viscosity showed a downward trend along the well depth; the compression factor showed an upward trend. The surfaces of the three casings were smooth and flat without obvious defects, the cement structure was dense, and there was no obvious pore structure. After corrosion, with the increase of Cr content, the change of interfacial corrosion decreases. The morphology of the Q125 and 3Cr interface is loose after corrosion, while there is no obvious change in the 13Cr interface. With the prolongation of corrosion time, low wellbore internal pressure easily causes casing yield, and high wellbore internal pressure easily causes cement-sheath compression failure. The circumferential stress of the casing increases with the corrosion time extension, and the radial stress of the casing and cement sheath decreases first and then increases with the corrosion time. The compressive strength of the cement sheath does not exceed the compressive strength.

Dynamical system analysis of scalar field cosmology in coincident f(Q) gravity

In this article, we investigate scalar field cosmology in the coincident f(Q) gravity formalism. We calculate the motion equations of f(Q) gravity under the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a scalar field. We consider a non-linear f(Q) model, particularly f(Q) = − Q + α Q n , which is nothing but a polynomial correction to the Symmetric Teleparallel Equivalent to General Relativity (STEGR) case. Further, we assumed two well-known specific forms of the potential function, specifically the exponential from V(ϕ) = V 0 e −β ϕ and the power-law form V(ϕ) = V 0 ϕ −k . We employ some phase-space variables and transform the cosmological field equations into an autonomous system. We calculate the critical points of the corresponding autonomous systems and examine their stability behaviors. We discuss the physical significance corresponding to the exponential case for parameter values n = 2 and n = − 1 with β = 1, and n = − 1 with β=3 . Moreover, we discuss the same corresponding to the power-law case for the parameter value n = − 2 and k = 0.16. We also analyze the behavior of corresponding cosmological parameters such as scalar field and dark energy density, deceleration, and the effective equation of state parameter. Corresponding to the exponential case, we find that the results obtained for the parameter constraints in Case III is better among all three cases, and that represents the evolution of the Universe from a decelerated stiff era to an accelerated de-Sitter era via matter-dominated epoch. Further, in the power-law case, we find that all trajectories exhibit identical behavior, representing the evolution of the Universe from a decelerated stiff era to an accelerated de-Sitter era. Lastly, we conclude that the exponential case shows better evolution as compared to the power-law case.

Generalized ghost dark energy model in Brans–Dicke theory with logarithmic scalar field

We study generalized ghost dark energy model in Brans–Dicke theory within the framework of flat Friedmann–Lemaitre–Robertson–Walker Universe. We assume the well-motivated logarithmic form of Brans–Dicke scalar field in terms of the scale factor to find the observational parameters such as equation of state parameter [Formula: see text] and deceleration parameter q. It is observed that the equation of state parameter crosses the phantom divide line [Formula: see text] for a suitable range of model parameters. We observe that the deceleration parameter is time-dependent which shows the recent phase transition from decelerated to accelerated expansion of the Universe. Moreover, the model shows that the Universe will go through two future phase transitions, recent accelerated expansion to decelerated expansion and again decelerated expansion to accelerated expansion. We have also plotted the trajectories of the model in the [Formula: see text] plane for different values of parameters and explored the freezing and thawing regions. Further, we apply the sound squared speed method to check the stability of the model and found that the model is stable for suitable range of parameters.

Exploring Universe acceleration through observational constraints via Hubble parameter reconstruction

In this article, we introduce an innovative parametric representation of the Hubble parameter, providing a model-independent means to explore the dynamics of an accelerating cosmos. The model's parameters are rigorously constrained through a Markov Chain Monte Carlo (MCMC) approach, leveraging a comprehensive dataset consisting of 31 data points from cosmic chronometers (CC), 1701 updated observations of Pantheon supernovae type Ia (SNeIa), and 6 data points from baryonic acoustic oscillations (BAO). Our analysis delves into the behavior of various cosmological parameters within the model, including the transition from a decelerating phase to an accelerating one, as well as the density parameters and the equation of state (EoS) parameter. The outcomes of our investigation reveal that the equation of state parameter aligns with characteristics reminiscent of the phantom model, supporting the prevailing understanding of our universe's current state of acceleration. This research contributes valuable insights into the ongoing cosmic expansion and underscores the utility of our novel parametric approach.

Positional embeddings for solving PDEs with evolutional deep neural networks

This work extends the paradigm of evolutional deep neural networks (EDNNs) to solving parametric time-dependent partial differential equations (PDEs) on domains with geometric structure. By introducing positional embeddings based on eigenfunctions of the Laplace-Beltrami operator, geometric properties are encoded intrinsically and Dirichlet, Neumann and periodic boundary conditions of the PDE solution are enforced directly through the neural network architecture. The proposed embeddings lead to improved error convergence for static PDEs and extend EDNNs towards computational domains of realistic complexity.Several steps are taken to improve performance of EDNNs: Solving the EDNN update equation with a Krylov solver avoids the explicit assembly of Jacobians and enables scaling to larger neural networks. Computational efficiency is further improved by an ad-hoc active sampling scheme that uses the PDE dynamics to effectively sample collocation points. A modified linearly implicit Rosenbrock method is proposed to alleviate the time step requirements of stiff PDEs. Lastly, a completely training-free approach, which automatically enforces initial conditions and only requires time integration, is compared against EDNNs that are trained on the initial conditions. We report results for the Korteweg-de Vries equation, a nonlinear heat equation and (nonlinear) advection-diffusion problems on domains with and without holes and various boundary conditions, to demonstrate the effectiveness of the method. The numerical results highlight EDNNs as a promising surrogate model for parametrized PDEs with slow decaying Kolmogorov n-width.

Research on calculation model for ultimate bearing capacity of tensile type anchor cables and the shape of internal fracture surface in anchorage segment

AbstractThe generalized model and parameter equation for the internal fracture surface of tensile type anchor cable anchorage section are constructed, and the calculation model of ultimate bearing capacity is derived based on the principle of limit equilibrium. The shape of the internal fracture surface in the anchorage section and the expression of its parameter equation are experimentally studied, and the variation law of the parameter equation and fracture range with the diameter of the anchor cable and confining pressure is analyzed. The parameter equation is substituted into the calculation model to realize the calculation and verification of the model. Through theoretical derivation, a calculation model of ultimate bearing capacity of anchor cable is obtained, which comprehensively considers the average shear strength of anchorage section, the shape of fracture surface, fracture range and confining pressure. The tests show that according to the magnitude of the confining pressure on the anchorage section, the internal fracture surface takes on two shapes: cylindrical and trumpet‐shaped, the parameter equation of trumpet‐shaped fracture surface obeys logarithmic distribution approximately. The coefficient a decreases with the increase of confining pressure but increases with the increase of anchor cable diameter, the constant b increases with the increase of confining pressure but decreases with the increase of anchor cable diameter. The ranges of horizontal and vertical fracture decrease with the increase of confining pressure, and increase with the increase of anchor cable diameter. The deviations between the theoretical calculation and the experimental results are less than 6.5%.

Assessing and mapping cropland abandonment risk in China

AbstractCropland abandonment (CA) in China worsens the human‐land conflict and endangers national food sustainability. Scientifically assessing cropland abandonment risk (CAR) can provide valuable information for early warning and prevention of CA. Despite the extensive literature on the identification, determinants, and consequences of CA, the research on CAR still needs to be improved, especially on a grid scale. Therefore, this study constructed an evaluation indicators system regarding farming conditions, socio‐economic, and patch characteristics and used optimal parametric geographical detector and structural equation modeling to assess the CAR in China from 2010 to 2020. The results show China's CAR decreased from west to east. Very high and high CAR areas were in plateaus and mountains in western China. Medium CAR areas were mainly in central and southeastern China. Very low and low CAR areas were mainly in the Sichuan Basin and eastern plains. In 2010, the high and medium CARs accounted for a larger share of the area, 24.814% and 24.759%, respectively. The area share of very low, low, and very high CAR was 19.294%, 19.501%, and 11.633%, respectively. By 2020, both low and very high CARs increased, while the opposite was true for other grades of CAR. Very high CAR increased most evidently in the Loess Plateau. Although high CAR decreased, 43,327 km2 of medium CAR was converted to high CAR. CAR's centers of gravity in China were located at the junction of the Loess Plateau and the Huang‐Huai‐Hai Plain and have shifted to the northwest by 5445.34 m. The findings will assist stakeholders in developing targeted cropland protection strategies to prevent CA and efficiently allocate resources for agricultural production.

Differentiating the Yield of Chemical Reactions Using Parameters in First-Order Kinetic Equations to Identify Elementary Steps That Control the Reactivity from Complicated Reaction Path Networks.

The yield of a chemical reaction is obtained by solving its rate equation. This study introduces an approach for differentiating yields by utilizing the parameters of the rate equation, which is expressed as a first-order linear differential equation. The yield derivative for a specific pair of reactants and products is derived by mathematically expressing the rate constant matrix contraction method, which is a simple kinetic analysis method. The parameters of the rate equation are the Gibbs energies of the intermediates and transition states in the reaction path network used to formulate the rate equation. Thus, our approach for differentiating the yield allows a numerical evaluation of the contribution of energy variation to the yield for each intermediate and transition state in the reaction path network. In other words, a comparison of these values automatically extracts the factors affecting the yield from a complicated reaction path network consisting of numerous reaction paths and intermediates. This study verifies the behavior of the proposed approach through numerical experiments on the reaction path networks of a model system and the Rh-catalyzed hydroformylation reaction. Moreover, the possibility of using this approach for designing ligands in organometallic catalysts is discussed.

Speed of sound and scalar spectral index: Reconstructing inflation and reheating in a non-canonical theory

In this article we analyze the reconstruction of inflation in the framework of a non-canonical theory. In this sense, we study the viability of reconstructing the background variables assuming a non-linear kinetic term given by K(X,ϕ)=X+g(ϕ)X2, with X the standard kinetic term associated to the scalar field ϕ and g(ϕ) an arbitrary coupling function. In order to achieve this reconstruction in the context of inflation, we assume the slow-roll approximation together with the parametrization of the scalar spectral index ns and the speed of sound cs as a function of the number of e−folds N. By assuming the simplest parametrizations for ns−1=−2/N and cs∝N−β with β a constant, we find the reconstruction of the effective potential V(ϕ) and the coupling function g(ϕ) in terms of the scalar field. Besides, we study the reheating epoch by considering a constant equation of state parameter, where we determine the temperature and number of e−folds during the reheating epoch in terms of the reconstructed variables and the observational parameters. In this way, the parameter-space related to the reconstructed inflationary model are constrained during the epochs of inflation and reheating by assuming the current astronomical data from Planck and BICEP/Keck results.

Design and Testing of the Double-Symmetric Eccentric Exciter for Fruit Tree Vibration Harvest

The amplitude of excitation force from exciters used in fruit tree vibration harvesting remains constant at a given frequency, leading to poor fruit detachment ratio and tree damage. A solution has been proposed through the development of a Double-Symmetric Eccentric Exciter (DSEE). This new exciter allows for the adjustment of excitation force amplitude while maintaining a constant frequency by varying the phase angle of the DSEE. To validate the effectiveness of the DSEE, vibration tests were conducted on fruit trees using different parameter exciting forces. Acceleration sensors were employed to measure the vibration accelerations of the tree branches. The experimental results revealed that when a fixed frequency excitation force with a constant phase angle was applied to the trunk, the vibration acceleration of branches exhibited inconsistent variations due to differences in the vibration differential equation parameters of each branch. Furthermore, it was observed that increasing the phase angle of the DSEE at a fixed frequency led to larger vibration accelerations in every branch. This signifies that adjusting the phase angle of the DSEE can effectively increase the amplitude of the exciting force. Consequently, the ability to control both the amplitude and frequency of the excitation force independently can mitigate issues such as low fruit harvest rates and minimize damage to fruit trees.

Fabrication of electrical devices on conformal surfaces based on array nozzle and five-axis motion mechanism

It has been known that conformal printing with a single nozzle has low efficiency. This study proposes a novel non-expandable curved surface printing method that could realize high-efficiency printing with array nozzles. First, based on the non-uniform rational B-splines curved surface reconstruction method, the parameter equation of the stereolithography format curved surface model is obtained. An equidistant parallel curve filling method is proposed based on the parameter equation. According to the filling accuracy, a spatial equidistant curve network model is established by fitting the surface. Using each node on the curve network as the filling pixel increases the filling rate of the non-expandable surface and improves the printing accuracy. Compared with that of the traditional equidistant filling, the droplet filling rate could be increased by 13.05 % in this study. Finally, based on the self-developed five-axis curved surface inkjet printing system and normal vector printing method, samples of concave, convex, and multi-material conformal surfaces are sequentially printed. Our research finding lays the foundation for high-efficiency integrated molding of electronic devices with complex conformal surfaces.

Simultaneously probing the sound speed and equation of state of the early Universe with pulsar timing arrays

Recently, several major pulsar timing array (PTA) collaborations have assembled strong evidence for the existence of a gravitational-wave background at frequencies around the nanohertz regime. Assuming that the PTA signal is attributed to scalar-induced gravitational waves, we jointly employ the PTA data from the NANOGrav 15-year data set, PPTA DR3, and EPTA DR2 to probe the conditions of the early Universe. Specifically, we explore the equation of state parameter (w), the reheating temperature (T rh), and the sound speed (cs ), finding w = 0.59+0.36 -0.40 (median + 90% credible interval), and T rh ≲ 0.2 GeV at the 95% credible interval for a lognormal power spectrum of the curvature perturbation. Furthermore, we compute Bayes factors to compare different models against the power-law spectrum model, effectively excluding the pressure-less fluid domination model. Our study underscores the significance of scalar-induced gravitational waves as a powerful tool to explore the nature of the early Universe.

Thermodynamical analysis with extended phase transition of AdS hairy black hole in gravitational decoupling theory

This article explores various thermodynamical aspects and the extended phase space of the AdS hairy black hole within the context of gravitational decoupling. This study focused on thermodynamic properties such as geometrical mass, Hawking temperature, entropy, specific heat, Gibbs free energy (both locally and globally) and P-V criticality at the horizon radius. The thermodynamic stability of the AdS hairy black hole has been established based on its positive heat capacity. The analysis of Gibbs free energy is utilized to investigate the behavior of the first-order phase transition. Thermodynamic pressure, denoted by P, is related to the cosmological constant by the formula P=−Λ8π . In addition, a numerical investigation has been carried out to examine the equation of the state parameter and its critical values.

Digital Twinning of Cardiac Electrophysiology Models From the Surface ECG: A Geodesic Backpropagation Approach.

The eikonal equation has become an indispensable tool for modeling cardiac electrical activation accurately and efficiently. In principle, by matching clinically recorded and eikonal-based electrocardiograms (ECGs), it is possible to build patient-specific models of cardiac electrophysiology in a purely non-invasive manner. Nonetheless, the fitting procedure remains a challenging task. The present study introduces a novel method, Geodesic-BP, to solve the inverse eikonal problem. Geodesic-BP is well-suited for GPU-accelerated machine learning frameworks, allowing us to optimize the parameters of the eikonal equation to reproduce a given ECG. We show that Geodesic-BP can reconstruct a simulated cardiac activation with high accuracy in a synthetic test case, even in the presence of modeling inaccuracies. Furthermore, we apply our algorithm to a publicly available dataset of a biventricular rabbit model, with promising results. Given the future shift towards personalized medicine, Geodesic-BP has the potential to help in future functionalizations of cardiac models meeting clinical time constraints while maintaining the physiological accuracy of state-of-the-art cardiac models.

Influence of shear deformation on the formation of dynamic structure in protic ionic liquids. Representation of the temperature dependence of viscosity within the framework of Angell’s fragility concept

The rheological properties of a liquid containing two types of basic centers and hydroxyl groups (BGE-Im), as well as protic ionic liquids (ILs) derived from it, were studied in a wide range of shear rates (γ̇) (10−6–103 s−1) at various temperatures from 10 to 50 °C. Viscosity (η) of the BGE-Im does not depend on the scanning direction of shear stress (σ), i.e. this compound behaves like a Newtonian fluid over the entire range of σ. The dependence log η (1/T) of BGE-Im in Arrhenius coordinates is linear. Protonation of basic centers of BGE-Im leads to a strong increase in the viscosity of ILs obtained on its basis, and the temperature dependence of the viscosity of these ILs is described by the Vogel–Fulcher–Tammann (VFT) equation. It has been established that in the region of low shear rates, the viscosity of the ILs increases with decreasing shear rate, which leads to the appearance of a yield stress (σY). This indicates the formation of a fluctuation rheopectic structure in the ILs. In this sense, ILs are heterogeneous systems and their behavior is similar to that of highly concentrated suspensions and emulsions. For the first time, a quantitative comparison between the parameters of the VFT equation, the fragility (according to Angell’s model) of ILs, the relative coordination number of ILs molecules and the rheological yield stress characterizing the shear-induced fluctuation rheopectic structure of ILs has been made and the relationship between these characteristics has been shown.

Parametric learning of time-advancement operators for unstable flame evolution

This study investigates the application of machine learning, specifically Fourier neural operator (FNO) and convolutional neural network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our focus is on extending existing operator learning methods to handle additional inputs representing PDE parameters. The goal is to create a unified learning approach that accurately predicts short-term solutions and provides robust long-term statistics under diverse parameter conditions, facilitating computational cost savings and accelerating development in engineering simulations. We develop and compare parametric learning methods based on FNO and CNN, evaluating their effectiveness in learning parametric-dependent solution time-advancement operators for one-dimensional PDEs and realistic flame front evolution data obtained from direct numerical simulations of the Navier–Stokes equations.

A nonlinear hyperbolic optimized grey model for market clearing price prediction: Analysis and case study

Market Clearing Price (MCP) of an energy market is an operating equilibrium attained, when consumer demand and supply bid curves intersect with each other. Early anticipation of MCP provides an upper hand to any generating company to exercise the market power in its own favour. MCP prediction technologies are evolved in recent years and emphasis is given on developing a robust mechanism for anticipating dynamic conditions. This work presents an application of a nonlinear whitening term enabled grey model for prediction of the MCP. Detailed mathematical analysis and development of the model is presented. The proposed model is named as Nonlinear Hyperbolic Optimized Grey Model (NHOGM). For optimizing the whitening equation parameters, Linear Population Size Reduction (LPSR) Success History Based Parameter Adaption Differential Evolution (L-SHADE) algorithm has been applied. Results reveal that proposed nonlinear hyperbolic grey model yields satisfactory results as compared with the state of art grey methods and other well-known optimization based methods.