Parameters Of Equation Research Articles

Efficient approximation of global population dynamic models through statistical inference using local data

Biological growth curves are pivotal in predicting natural growth across disciplines, typically analyzed using nonlinear least squares or maximum likelihood methods. Bhowmick et al. (2014) introduced the interval-specific rate of parameters (ISRP) for growth equations, improving the estimation of relative growth rate (RGR) and model selection accuracy. Despite its effectiveness, computing these model-specific RGR estimates involves complex calculations and lacks explicit expressions for many nonlinear models. Also, for highly nonlinear models and non-monotonic data where the parameters are non-linearly related, the computation of interval estimates is almost impossible and may suffer from significant approximation errors. So, the need for a more efficient computation method for ISRP remains a significant challenge in growth studies. In this article, we propose a computational approach to obtain interval estimates of parameters based on the maximum likelihood estimation method. The likelihood function is maximized using the data on smaller intervals. Our study underscores the importance of an efficient ISRP computation technique, providing a more stable, unbiased, and normally distributed estimator. The most important advantage is that it can be implemented using existing optimizers in software packages efficiently, therefore, giving more accessibility to the practitioners. Both simulation studies and real data analysis have been carried out to validate the proposed estimation process. Additionally, its applicability to non-monotonic growth profiles and its robustness in handling highly non-linear growth equations highlight its versatility. We also developed a web application GpEM-R which is freely available for researchers and practitioners to analyze growth data.

Hyperelastic constitutive relations for porous materials with initial stress

Initial stress is widely observed in porous materials. However, its constitutive theory remains unknown due to the lack of a framework for modeling the interactions between initial stress and porosity. In this study, we construct the porous hyperelastic constitutive model with arbitrary initial stresses through the multiplicative decomposition approach. Based on the compression experiment of shale samples, the parameters in the constitutive equation are determined. Then, the explicit equations of in-plane elastic coefficients are proposed by linearizing the finite deformation formulation. The influences brought by the coexistence of initial stresses and porosity on these coefficients are revealed. Later, comparative analyses of the linearized equations between the present model, the initially-stressed models without pores, the Biot poroelasticity, and the porous hyperelastic model without initial stress are conducted to illustrate the performances of the two ingredients. As a specific example, we investigate the variation of pore sizes under external pressures and initial stresses since changes in pore sizes during deformation are crucial for understanding the accumulation and migration of shale oil and gas. The newly proposed model provides the first initially stressed porous hyperelasticity (ISPH), which is suitable for describing the finite deformation behavior of solid materials with large porosity and significant initial stress simultaneously.

Constraints on anisotropic properties of the universe in f(Q,T) gravity theory

Motivated by anomalies in cosmic microwave background observations, we investigate the implications of f(Q,T) gravity in Bianchi type-I spacetime, aiming to characterize the universe's spatially homogeneous and anisotropic properties. By using a linear combination of non-metricity Q and the energy-momentum tensor trace T, we parametrize the deceleration parameter and derive the Hubble solution, which we then impose in the Friedmann equations of f(Q,T) gravity. Bayesian analysis is employed to find the best-fit values of model parameters, with 1−σ and 2−σ contour plots illustrating the constraints from observational data, including H(z) data and the Pantheon+ sample. Our analysis reveals a transition from a decelerated to an accelerated expansion phase, with the present deceleration parameter indicating an accelerating universe. The energy density gradually decreases over time, approaching zero for the present and future, indicating continuous expansion. The anisotropic pressure, initially notably negative, transitions to slightly negative values, suggesting the presence of dark energy. The evolving equation of state parameter ω exhibits behavior akin to phantom energy, influenced by spacetime anisotropy. Violations of the null energy condition and the strong energy condition imply phantom-like behavior and accelerated expansion.

Effects of the Characterization Methods of Heptane Plus Components (C7+) on the Phase Behavior of Volatile Fluids

For reservoir fluids with strong volatile tendencies, such as gas condensate and volatile oil, the determination of the characteristic parameters of the equation of state has a great influence on the fluid phase behavior and subsequent reservoir engineering, production engineering, and surface facilities design calculations. However, the process of characterizing reservoir fluid lacks a unified and standardized procedure, and the methods are largely empirical and rather complicated. In this paper, three main stages are defined for the characterization of the equation of state parameters for these volatile reservoir fluids, including (1) determining the C7+ distribution, (2) calculating the equation of state parameters for the C7+ single-carbon component, and (3) lump components. The typical calculation methods in each step and their effects on the fluid phase behavior calculations are quantitatively analyzed and compared. Finally, the workflow and the suitable characterization methods for gas condensate and volatile oil phase behavior calculations are selected. The results show that C7+ distribution and C7+ single carbon component properties have a greater influence on the phase behavior prediction of condensate gas and volatile oil, while the lumping of C7+ single carbon component has relatively little influence.

Prediction of pure and mixture thermodynamic properties and phase equilibria using an optimized equation of state – part 1: Parameter estimation

This study presents a novel three-parameter equation of state (EOS) wherein attraction parameter polynomial coefficients are optimized to enhance predictive capabilities. The performance of the proposed EOS is systematically compared with established models including Peng-Robinson, Patel-Teja, and Twu-Coon-Cunningham equations. Through comprehensive evaluation, it is demonstrated that the proposed EOS exhibits superior accuracy in vapor pressure and latent enthalpy predictions, while maintaining comparable precision in liquid density estimations. Notably, the fugacity expression of the proposed EOS closely resembles that of a two-parameter equation, resulting in significantly reduced computational overhead. Additionally, a comprehensive table of equation of state parameters for all four equations is available in an online repository, facilitating easy implementation and comparison. Furthermore, a reliable generalized polynomial correlation is provided for the proposed EOS parameters against the true compressibility factor and acentric factor, leveraging data accessibility and enhancing its applicability and versatility. These findings underscore the potential of the optimized attraction parameter polynomial coefficients approach in advancing the accuracy and efficiency of EOS modeling, thereby offering promising avenues for diverse applications in thermodynamics and process engineering.

Rutin and Physalis peruviana Extract: Population Pharmacokinetics in New Zealand Rabbits

Background/Objectives: An extract of calyces from Physalis peruviana with hypoglycemic activity is being considered as a potential herbal medicine. Preclinical pharmacokinetics (PK) studies of the extract in rats, focusing on plasma concentrations of its main compound, rutin, and its metabolites, revealed PK interactions in the extract matrix that improved the absorption of rutin metabolites compared to the pure compound, among other PK effects. This research aimed to study the PK of rutin alone and in the extract and assess potential PK interactions in the extract matrix on the flavonoid and its metabolites in rabbits, a nonrodent species; Methods: Animals received pure rutin or extract orally and intravenously. The PK analysis used noncompartmental and population pharmacokinetics (popPK) methods, and simple allometry was applied to predict human PK parameters; Results: The rutin concentration–time profile fit a two-compartment model with first-order elimination, while its metabolites fit a double first-order absorption model. The extract matrix led to increased absorption, distribution, and elimination of rutin as well as increased bioavailability of its metabolites in rabbits; Conclusions: The popPK model defined the equations for PK parameters describing these findings, and the increased volume of distribution and clearance of rutin was maintained in human predictions. These results will support the development of a new herbal medicine.

Exploring cosmological evolution and constraints in [formula omitted] teleparallel gravity

This study explores the extension of teleparallel gravity within the framework of general relativity, introducing an algebraic function f(T) dependent on the torsion scalar T. Motivated by the teleparallel formulation, we investigate cosmological implications, employing the simplest parametrization of the dark energy equation of state. Our chosen f(T) function, f(T)=α(−T)n, undergoes stringent constraints using recent observational data (H(z), SNeIa, BAO, and CMB). The model aligns well with cosmic dynamics, exhibiting quintessence behavior. The evolution of the deceleration parameter, the behavior of dark energy components, and the Om(z) diagnostic further reveal intriguing cosmological phenomena, emphasizing the model’s compatibility with quintessence scenarios.

Study of gravastar admitting Tolman IV spacetime in Rastall theory

In this paper, we present a novel solution representing the gravastar (or gravitational vacuum star) model within the framework of non-conservative Rastall gravity. As a viable alternative to black holes, the geometry of a gravastar comprises three distinct regions: the inner sector, the intermediate layer, and the exterior domain. Utilizing the temporal component of Tolman IV spacetime, we derive the singularity-free radial metric potentials for both the inner and intermediate regions. Further, by aligning the thin shell with the external Schwarzschild line element, we establish boundary conditions in order to determine unknown constants that appear due to the chosen ansatz and performing some integrations. Subsequently, we investigate various properties for the gravastar’s shell, including the equation of state parameter, proper length, energy, entropy and gravitational redshift for four different values of the Rastall parameter. It is concluded that the gravastar structure exists and provides a feasible substitute of black holes in the framework of Rastall theory.

The continuous memory: A neural network with ordinary differential equations for continuous-time series analysis

Continuous-time series analysis has garnered significant research interest due to its extensive applications; however, it remains a challenging endeavor. In recent years, deep learning methods have achieved remarkable success in tasks such as time series classification and forecasting. Nevertheless, the inherent continuity of time series data has not been fully addressed, presenting a persistent obstacle to performance. Recent studies have highlighted a natural similarity between differential equations and continuous-time series, as both inherently encapsulate the concept of continuity. However, several critical issues with differential equations hinder their direct applicability to time series analysis. These issues include the elusive nature of analytical solutions, the indirect observability of the effects of differential equation parameters, and the dependence of numerical solutions on initial conditions. In this context, we propose the integration of differential equations into neural networks to serve as the continuous memory of the model. This integration imparts a continuous nature to the model, resulting in the development of an efficient deep learning architecture known as Long Short Deep Memory (LSDM). Furthermore, we analyze the characteristics of differential equations when employed as the memory component in neural networks, which leads to the proposal of a novel pre-training approach that incorporates an innate memory mechanism into these networks. Additionally, we utilize LSDM to construct a stacked architecture for processing very long time series data. The proposed model can naturally accommodate arbitrary time gaps between observations, thereby enhancing its effectiveness and suitability for continuous time series analysis tasks. Extensive experiments conducted on various real-world datasets demonstrate that the proposed model outperforms existing methods, providing a new solution to the challenges associated with continuous time series analysis.

Stability and viability of charged anisotropic pulsar SAX J1748.9-2021 in extended symmetric teleparallel gravity

This manuscript aims to study the viability and stability of a pulsar SAX J1748.9-2021, containing a charged anisotropic matter configuration within the framework of f(Q,T) theory (Q and T are the non-metricity scalar and energy–momentum tensor, respectively). We employ a non-singular solution and a specific model of this gravitational theory and use junction conditions to determine the unknown constants in the metric coefficients. We explore different geometric and physical properties using astrophysical observations from the pulsar SAX J1748.9-2021, which is found in X-ray binary systems within globular clusters. This framework establishes relationships between various physical quantities, including fluid parameters, anisotropy, mass–radius relation, redshift, the Zeldovich condition, energy conditions, causality conditions, adiabatic index, Tolman–Oppenheimer–Volkoff equation, equation of state parameter and compactness. Our findings affirm the feasibility and stability of the proposed charged pulsar within this theoretical framework.

Semi-analytical layerwise solutions for FG MEE complex shell structures

This paper presents a unique analytical layerwise solution for functionally graded magneto-electric-elastic shell with complex geometry. The middle surface of the shell is modeled by a parametric equation and the Lamé parameter and radii of curvature is modeled by Differential Geometry. The mechanical displacements, electrical and magnetic potentials are written in term of a simple cosine layerwise based on a unified formulation. The highly coupled differential equations are discretized by the Chebyshev-Gauss-Lobatto grid points and solved numerically via the Differential Quadrature Method (DQM). Lagrange interpolation polynomials are employed as the basis functions. The highly coupled differential equations are solved for shells subjected to different loads and boundary conditions. Since extremely few results on this topic is available in the literature, benchmarks complex shell problems and their solutions are introduced in this paper for the very first time.

Inflationary model in Brans–Dicke theory

In this paper, we present a model of inflation in the original form of Brans–Dicke (BD) theory without any modification and without adding any dark energy candidate. We consider a log function of the scale factor in the BD scalar field to discuss the inflationary era of the universe. We obtain the expressions for the deceleration parameter and the equation of state parameter, and plot their graphs against the cosmic scale factor. We observe that the universe starts with decelerated expansion and experiences an early time phase transition from a decelerated phase to an accelerated phase. After a very short period, the accelerated expansion ends in a decelerated expansion, showing the inflationary era of the cosmic evolution. To analyze the model on thermodynamic ground, we consider generalized second law of thermodynamics and observe that the law is satisfied within the model. Further, we study the stability of the model using the squared sound speed method. We plot the squared sound speed against cosmic time t and discuss the effects of the parameters on the stability of the model. We observe that for suitable values of the model parameters our model is stable.

Constraining the parameters of generalized and viscous modified Chaplygin gas and black hole accretion in Einstein-Aether gravity

In this paper, we investigate the phenomenon of the accelerated cosmic expansion in the late universe and the mass accretion process for a four-dimensional Einstein-Aether black hole. Starting with the basics of Einstein-Aether gravity theory, we first consider the field equations and two well-known models of Chaplygin gas, i.e., the generalized cosmic Chaplygin gas model and viscous modified Chaplygin gas model. We then obtain the energy density and Hubble parameter equations for these models in terms of various dimensionless density parameters and some unknown parameters. After finding the required parameters, we proceed with the mass accretion process. For both models, we obtain the equation of mass in terms of the redshift function and graphically represent the change in the mass of the black hole with a redshift. At the same time, we perform a graphical comparison between these models and the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model of the universe. Finally, we conclude that the mass of a four-dimensional black hole will increase along the evolution of the universe within the framework of Einstein-Aether gravity.

Impact of Fenton aging on the incipient motion of microplastic particles in open-channel flow

Upon entering the environment, Microplastics (MPs) experience aging processes that modify their properties and integrity. Previous methods for predicting the incipient motion of MPs have been validated using pristine plastics, which do not account for the effects of aging. This can lead to uncertainties in both quantification and characterization. This study investigates the effect of aging on the incipient motion of MPs with different bed roughness (smooth and rough beds) and MP properties (e.g., grain sizes and densities) in an open-channel flow. Five types of MPs were subjected to four different degrees of aging using the Fenton reagent, and their incipient velocities were tested on beds with two distinct roughness. The results suggest that the incipient velocity of MPs increases linearly with aging. However, this increase is not uniform across different particles and bed roughness. Upon comparing various commonly employed sediment incipient velocity equations, experimental results are in agreement with Ruijin Zhang's equation as the most precise. The parameters in Ruijin Zhang's equation are modified to enhance its applicability for predicting the incipient velocity of aged MPs. This study provides novel insights into the incipient motion of aged MPs in an open-channel flow, highlighting the intricate interaction between aged MP characteristics and bed roughness.

Adaptive Ant Colony Optimization Algorithm Based on Real-Time Logistics Features for Instant Delivery.

Ant colony optimization (ACO) algorithm is widely used in the instant delivery order scheduling because of its distributed computing capability. However, the order delivery efficiency decreases when different logistics statuses are faced. In order to improve the performance of ACO, an adaptive ACO algorithm based on real-time logistics features (AACO-RTLFs) is proposed. First, features are extracted from the event dimension, spatial dimension, and time dimension of the instant delivery to describe the real-time logistics status. Five key factors are further selected from the above three features to assist in problem modeling and ACO designing. Second, an adaptive instant delivery model is built considering the customer's acceptable delivery time. The acceptable time is calculated by emergency order mark and weather conditions in the event dimension feature. Third, an adaptive ACO algorithm is proposed to obtain the instant delivery order schedules. The parameters of the probability equation in ACO are adjusted according to the extracted key factors. Finally, the Gurobi solver in Python is used to perform numerical experiments on the classical datasets to verify the effectiveness of the instant delivery model. The proposed AACO-RTLF algorithm shows its advantages in instant delivery order scheduling when compared to the other state-of-the-art algorithms.

Establishment of unified parametric equation and performance analysis of screw motor stator and rotor linetype

Aiming at the screw motor stator and rotor linetype parameter equations are not uniform and the linetype characteristics have not been completely studied, resulting in the linetype design and selection method is not perfect and poor interchangeability and so on. In this paper, the unified parameter of linetype equation of the screw motor stator and rotor and the thermo-mechanical coupling model and the shell-bushing cohesive zone model of the 5/6 screw motor under the three linetypes of equidistant hypocycloid, equidistant epicycloid and hypocycloid and epicycloid are established. The relationship between the three linetypes of stator and rotor and the lagging heat generation of the bushing, drilling fluid pressure, downhole temperature and shell-bushing bonding performance is studied. The results show that the stator temperature rise of the equidistant epicycloid method is 22%–30% lower than that of the other two types of stator. The stator with equidistant epicycloid is less affected by drilling fluid pressure and is more conducive to forming conjugate sealing cavity in deep wells. The downhole temperature has a certain influence on the stator linetype, which needs to be considered in the design. The CSMAXSCRT value of the bonding interface of the screw motor using the equidistant epicycloid method is 6.1%–10.1% higher than that of the screw motor using the other two linetypes, which is prone to bonding failure. When the interference is small, the equidistant hypocycloid method and the hypocycloid and epicycloid method can be used, and the equidistant hypocycloid method is recommended when the interference is large. The research in this paper provides a theoretical basis for the design and selection of screw motor linetypes, and has important engineering practical significance for realizing product interchangeability.

Generalized ghost pilgrim dark energy model in f(ℚ,) theory

This study investigates the reconstruction technique for the generalized ghost pilgrim dark energy model within the framework of f(Q,T) gravity ( Q represents the non-metricity and T denotes the trace of the energy-momentum tensor). For this purpose, we implement a correspondence scheme for the configuration of dust fluid within a flat Friedmann-Robertson-Walker universe. We examine the cosmic behavior of the reconstructed model by studying cosmological diagnostic parameters in conjunction with phase planes. The analysis reveals that within certain ranges of free parameters, the equation of state parameter characterizes a phantom regime. The trajectories on the ωDE−ωDE′ plane indicate a freezing region, while the phase plane of r − s corresponds to the Chaplygin gas model. The squared sound speed parameter provides stable model for the evolutionary paradigm of the Universe. It is worth noting that our results closely align with the recent observational data.

Comparative investigation of heat extraction performance in 3D self-affine rough single fractures using CO2,N2O and H2O as heat transfer fluid

The type and thermophysical properties of heat transfer fluids significantly impact the heat extraction rate of Enhanced Geothermal Systems (EGS). Studies based on field-scale stochastic discrete fracture network geometric models have certain limitations and uncertainties. To compare the heat extraction performance of heat transfer fluids H2O, CO2, and N2O in a core-scale (φ50 × 100 mm) rough single fracture in hot dry rock, we first constructed the fracture geometry with rock surface roughness characteristics using a fractal self-affine function, with a joint roughness coefficient (JRC) of 12.38. Then, at temperatures ranging from 37 to 300°C and a pressure of 30 MPa, we established a thermo-hydraulic (TH) coupling model based on the thermophysical parameter equations of the three heat transfer fluids. Finally, we conducted a comparative study of the changes in the outlet mean temperature and heat extraction rate after flowing through the fracture, as well as the temperature distribution on the fracture surface, under conditions of constant inlet flow velocity with varying inlet temperature and constant inlet temperature with varying inlet flow velocity. The results indicate that (1) with the increase in inlet flow velocity and temperature, the outlet mean temperature and heat extraction rate of CO2 and N2O at the fracture outlet are essentially the same and lower than those of H2O. (2) When the inlet flow velocity increases from 0.005 m/s to 0.025 m/s, the thermal convection effect from the rock matrix to the fluid in the fracture predominates, and flow velocity is the main factor affecting the heat transfer process between the fluid and the rock matrix. When the inlet temperature increases from 37°C to 57°C, the thermal conduction effect from the rock matrix to the fluid in the fracture predominates, and temperature is the main factor affecting the heat transfer process between the fluid and the rock matrix.(3)When maintaining constant inlet temperature, increasing inlet flow velocity from 0.005 m/s to 0.025 m/s results in CO2 experiencing a maximum heat extraction rate increase of 118.85 W. In contrast, N2O experiences 117.05 W, and H2O experiences 266.4 W.(4) When the inlet flow rate is constant, the maximum increase in heat extraction rate for CO2 is 15.34 W as the inlet temperature increases from 37 °C to 57 °C; for N2O, it is 13.9 W; and for H2O, it is 45.45 W.

A unique approach to address avoided crossings in the charge stabilization curve for LUMO identification.

In quantum chemistry, Lowest Unoccupied Molecular Orbital (LUMO) is important for studying various chemical processes, including photochemical reactions, electron attached states, and electron excites states. Recently, an effective method has been introduced that involves the use of the Parametric Equation of Motion (PEM) in conjunction with the nuclear charge stabilization method for precise identification of true LUMO. However, the inclusion of extra diffuse functions in the basis set, which is necessary for describing electron-attached and electron-excited states, can cause issues due to the presence of the same symmetry states, leading to avoided crossing. Identifying the true LUMO among these avoided crossings is challenging due to the mixing of states and the exchange of their orbital character. This article introduces a modification of the PEM to identify the true LUMO by preventing the stabilization of specific states involved in avoided crossings. The present method is highly effective and requires minimal computational cost.

Constraining parameters for the accelerating universe in [formula omitted] gravity

In the paper, we present an accelerating cosmological model in f(R,Lm) gravity with the parameter constrained through the cosmological data sets. At the beginning, we have employed a functional form of f(R,Lm)=R2+αR2+Lmβ, where α and β are model parameters. This model is well motivated from the Starobinsky model in f(R) gravity and the power law form of f(Lm). The Hubble parameter has been derived with some algebraic manipulation and constrained by Hubble data and Pantheon+ data. With the constraint parameters, present value of deceleration parameter has been obtained to as q0≈−0.63 with the transition at zt≈0.7. It shows the early deceleration and late time acceleration behaviour. The present value of other geometric parameters such as the jerk and snap parameter are obtained to be j0≈0.78 and s0≈0.1 respectively. The state finder diagnostic test gives the quintessence behaviour at present and converging to ΛCDM at late times. Moreover the Om(z) diagnostics gives negative slope which shows that the model favours the state finder diagnostic result. Also the current age of Universe has been obtained as, t0=13.64Gyrs. The equation of state parameter also shows the quintessence behaviour. Based on the present analysis, it indicates that the f(R,Lm) gravitational theory may be another alternative to study the dark energy models.