Parameters Of Equation Research Articles

High‐precision numerical simulation method for thermal–mechanical coupling in rubbers

AbstractImproving the precision of numerical simulations in thermal–mechanical coupling for amorphous polymer materials is crucial for their effective utilization. To enhance the precision of rubber numerical simulations, this study proposed a method considering the temperature and strain rate to establish tensile testing conditions based on the principle of time–temperature equivalence. Additionally, to obtain more precise parameters for hyperelastic constitutive equations, stress relaxation experiments were conducted to determine a set of stress values under complete rubber stress relaxation, which were used to fit the hyperelastic components of the hyper‐viscoelastic algorithm. A finite element model of rubber rebound was established, and a hyperelastic model based on loss factor and a hyperelastic model based on Prony series (hyper‐viscoelastic) were used to calculate the temperature changes caused by rubber rebound coefficient and energy dissipation during the rebound process at 110, 120, and 130°C. We compared the calculation results of these two algorithms with experimental data to verify their accuracy. The research results show that the average error of the rebound coefficient of the hyperelastic algorithm at three temperatures is 3.63%, and the average error of the rebound coefficient of the hyper‐viscoelastic algorithm at these three temperatures is 0.93%. The comparison with the rebound test results shows that the hyper‐viscoelastic method is more accurate and better captures the viscoelastic hysteresis of rubber, but the model calculation time is longer. In addition, at the moment of rebound sample impact, the maximum temperature rise amplitude of the hyperelastic algorithm sample impact position is 2.60, 1.75, and 0.91°C, which are 110, 120, and 130°C, respectively; The maximum heating amplitudes of the hyper‐viscoelastic algorithm are 2.05, 1.35, and 0.61°C. The hyper‐viscoelastic algorithm is closer to the actual test results.Highlights Applied the principle of time–temperature equivalence. Determination of material parameters using the hyper‐viscoelastic algorithm. Calculated the temperature change during the rubber rebound process.

Symmetric teleparallel gravity with variable deceleration parameter

In this paper, our investigation focuses on the cosmic history in modified [Formula: see text] gravity, a different theory that describes the gravitational force using a non-metricity scalar. The equations of the theory are solved by assuming a parametric form for the deceleration parameter. The parameters of the model are estimated by using the Cosmic Chronometer dataset. A number of parameters, like the deceleration parameter, whose signature changes with redshift and shows typical behavior in late-time cosmology, are subject of our analysis. We also show the evolution of other parameters, such as the equation of state parameter and energy density. The parametrization approach used here in [Formula: see text] modified gravity provides a better description of the late-time cosmic evolution without dark energy.

Catchment response to climatic variability: implications for root zone storage and streamflow predictions

Abstract. This paper investigates the influence of multi-decadal climatic variability on the temporal evolution of root zone storage capacities (Sr,max) and its implications for streamflow predictions in the Meuse basin. Through a comprehensive analysis of 286 catchments across Europe and the US that are hydro-climatically comparable to the Meuse basin, we construct inter-decadal distributions of past deviations in evaporative ratios (IE) from expected values based on catchment aridity (IA). These distributions of ΔIE were then used to estimate inter-decadal changes in Sr,max and to quantify the associated consequences for streamflow predictions in the Meuse basin. Our findings reveal that, while catchments do not strictly adhere to their specific parametric Budyko curves over time, the deviations in IE are generally very minor, with an average ΔIE=0.01 and an interquartile range (IQR) of −0.01 to 0.03. Consequently, these minor deviations lead to limited inter-decadal changes in Sr,max, mostly ranging between −10 and +21 mm (−5 % to +10 %). When these changes (ΔSr,max) are accounted for in hydrological models, the impact on streamflow predictions in the Meuse basin is found to be marginal, with the most significant shifts in monthly evaporation and streamflow not exceeding 4 % and 12 %, respectively. Our study underscores the utility of parametric Budyko-style equations for first-order estimates of future Sr,max in hydrological models, even in the face of climate change and variability. This research contributes to a more nuanced understanding of hydrological responses to changing climatic conditions and offers valuable insights for future climate impact studies in hydrology.

Theoretical insights and implications of bouncing cosmology in f(R,T2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\mathcal {R},\ extrm{T}^2)$$\\end{document} theory

In this paper, we explore cosmological bouncing solutions to investigate the cosmic evolution in the framework of energy-momentum squared gravity. We consider flat Friedmann–Robertson–Walker spacetime with a perfect matter distribution. We assume two different functional forms of f(R,T2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\mathcal {R},T^2)$$\\end{document} gravity model to examine the impact of this modified framework in the evolution of the universe. Furthermore, we consider a specific scale factor to investigate different cosmological parameters, analyzing the evolutionary behavior of the universe in this gravity. We also perform stability analysis using the perturbation technique. Our findings indicate that the null energy condition violates at the bounce point and equation of state parameter exhibits characteristics of a quintessence era or phantom regimes. These aspects highlight the complex interplay between energy conditions and stability in bouncing cosmological model. We conclude that the f(R,T2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\mathcal {R},T^2)$$\\end{document} theory successfully provides viable alternatives to the standard cosmological scenarios, offering insights into the early universe and the nature of gravity.

Probing barrow entropy models with future event horizon as IR cutoff

We develop formulations for barrow holographic dark energy (BHDE) in both non-interacting and interacting scenarios within a cosmological framework, applying the conventional holographic principle. Model parameter constraints are determined through the Markov Chain Monte Carlo (MCMC) method, utilizing different datasets. The investigation excavates into the models' kinematic behavior, exploring the transition from deceleration to acceleration and tracking the evolution of the equation of state parameters. Further, these models can pretend the evolution of dark energy and matter in the Universe. Additionally, a thermodynamic analysis employing future event horizons is conducted, confirming the validation of the generalized second law of thermodynamics. The resultant of the BHDE models strongly suggests that the Universe is presently experiencing an accelerated phase attributed to dark energy.

Dynamical system analysis for scalar field potential in teleparallel gravity

AbstractIn this paper, we have presented a power law cosmological model and its dynamical system analysis in $$f(T,\phi )$$ f ( T , ϕ ) gravity, where T is the torsion scalar and $$\phi $$ ϕ is the canonical scalar field. The two well-motivated forms of the non-minimal coupling function $$F(\phi )$$ F ( ϕ ) , the exponential form and the power law form, with exponential scalar field potential, are investigated. The dynamical system analysis is performed by establishing the dimensionless dynamical variables, and the critical points were obtained. The evolution of standard density parameters is analysed for each case. The behaviour of the equation of state (EoS) and deceleration parameter agree with the result of recent cosmological observations. The model parameters are constrained using the existence and the stability conditions of the critical points describing different epochs of the evolution of the Universe.

NEC violation in [formula omitted] gravity in the context of a non-canonical theory via modified Raychaudhuri equation

In this work, we develop the Raychaudhuri equation in f(R̄,T̄) gravity in the setting of a non-canonical theory, namely K-essence theory. We solve the modified Raychaudhuri equation for the additive form of f(R̄,T̄), which is f1(R̄)+f2(T̄). For this solution, we employ two different scale factors to give two types of f(R̄,T̄) solutions. The ongoing debate between Fisher et al. and Harko et al. in 2020 regarding the additive form of f(R̄,T̄) may provide a resolution within the modified f(R̄,T̄) gravity theory. By conducting a viability test and analyzing energy conditions, we have determined that in the first scenario, the null energy condition (NEC) is violated between two regions where the NEC is satisfied. Additionally, we have observed that this violation of the NEC exhibits a symmetric property during the phase transition. These observations indicate that bouncing events may occur as a result of the symmetrical violation of the NEC during the expansion of the universe. Moreover, this model indicates that resonant-type quantum tunneling may take place during the period when the NEC is violated. The findings of NEC violation through the power law of scale factor may have empirical relevance in contemporary observations. In the second scenario, our model indicates that the strong energy condition is violated, but the NEC and weak energy conditions are satisfied. The effective energy density decreases and is positive, while the effective pressure and equation of state parameters are negative. This suggests that the universe is expanding with acceleration and is dominated by dark energy.

Cognitive Model Based on The Dl Random Forest Method for Profi t Forecasting and Fuzzy Algorithm for Assessing Company Sustainability in Conditions of Uncertainty

The article is devoted to the problem of supporting management decision-making on choosing a strategic partner whose activities would be effective and sustainable. During the study, based on the results of the work of enterprises in the domestic confectionery industry, a dataset was generated, which was subsequently used for the deep learning model DL-model "Random Forest" in order to calculate the predicted values of the net profi t of enterprises in the industry. Assessing companies for the purpose of selecting a strategic partner, using models such as: deep learning model "Random Forest" (DL Random Forest), VaR, Z-Altman, Hurwitz matrix, Fuzzy algorithm in modern conditions has great practical significance. The relevance of the study lies in the fact that in conditions of increasing market uncertainty, approaches to ensuring the sustainable development of an organization based on AI systems are increasingly being used. The scientific novelty lies in the fact that the study used a set of models that made it possible to assess the actual sustainability of companies and, based on the calculated forecast values of net profi t, as well as business efficiency indicators ROE and ROS, to make a decision on the choice of potential business partners. During the study the following were developed: a VaR model, which made it possible to obtain an assessment of fi nancial risk, a Z-Altman model for assessing the risk of bankruptcy of an enterprise. In addition, based on the calculated parameters of the regression equation, a Hurwitz matrix was formed, which made it possible to draw a conclusion about the sustainability of each enterprise as a system. The use of the Fuzzy algorithm made it possible to obtain a decision on choosing a partner enterprise.

Critical buckling load analysis of Euler-Bernoulli beam on two-parameter foundations using Galerkin method

The critical buckling load determination of Euler-Bernoulli beams on two-parameter elastic foundations (EBBo2PFs) is important to avert buckling failures. The governing equation for buckling of thin beam on two-parameter elastic foundation is a homogeneous ordinary differential equation (HODE) of fourth order and constant parameters when the beam is prismatic and homogeneous. The HODE has been solved in this work by Galerkin method for simply supported, clamped and clamped-simply supported ends. One-parameter algebraic shape function formulation was used to reduce the problem to an algebraic eigenvalue problem, which is solved to find the critical buckling load for each studied case. The critical buckling load for EBBo2PF for simply supported boundary conditions was found to be closely identical to the exact solutions. The solutions for clamped-clamped edges and clamped-simple supports were found to be accurate. The merit of the Galerkin method is the simplicity and the accuracy even when one-parameter shape function has been used.

Prediction of rotational bending fatigue life of bearing steel based on damage mechanics

Based on the theory of continuous damage mechanics, this paper proposes a fatigue damage evolution model and numerical calculation method considering the influence of vacuum chemical heat treatment process, and studies the rotational bending fatigue damage analysis and life prediction method of M50NiL bearing steel. Firstly, the constitutive model, fatigue damage evolution equation and material parameter calibration method in the theoretical model are given. Secondly, based on the ABAQUS platform, the damage mechanics-finite element numerical calculation method of fatigue damage analysis considering the influence of hardened layer is realized by writing the UMAT subroutine; then, the rotational bending fatigue test of M50NiL bearing steel treated by vacuum chemical heat treatment of quenching and tempering, carburizing and carbonitriding is carried out, and the influence of heat treatment process on fatigue performance is analyzed; finally, based on the proposed fatigue damage model and numerical calculation method, the rotational bending fatigue life of M50NiL bearing steel is predicted, and the results are compared with the experimental results to verify the correctness of the proposed method.

Phase transition investigation of ferroelectric and dielectric properties of (NH 2 CH 2 COOH)3 H2SO4 crystal using green function method and two sublattice PLCM model Hamiltonian

The Greens function technique and extended two sublattice pseudospin lattice coupled-mode (PLCM) model Hamiltonian have been applied to study the phase transition mechanism in (NH2CH2COOH)3H2SO4 compound. The two sublattice PLCM model Hamiltonian is modified by considering anharmonic phonon interactions, extra spin-lattice interactions, and an external applied electric field term. By using the double-time thermal-dependent Green function technique, the theoretical equations for the total shift, total width, normal mode frequency, transition temperature, relative permittivity, dielectric tangent loss, acoustic attenuation and spontaneous polarization are derived. By fitting the distinct model parameters in the theoretical equations, we calculated the temperature dependence of normal mode frequency, relative permittivity, tangent loss, acoustic attenuation and spontaneous polarization. The numerically obtained results are hold well and correlated with experimental data.

A study on solid-shell finite element formulations applied to nonlinear thermoelastic analysis of thin-walled structures

The solid-shell elements have shown great advantages in three-dimensional (3D) finite element (FE) simulation of thin-walled structures. To overcome the numerical lockings for 3D element with a large span-thickness ratio, the assumed natural strain (ANS) method combined by either the hybrid stress (HS) or enhanced assumed strain (EAS) formulations are commonly used. In this work, two types of finite element formulations of the solid-shell elements are developed for nonlinear thermoelastic analysis of thin-walled structures, which are termed as the “ANS+HS” and “ANS+EAS” formulations. Accordingly, two eight-node solid-shell elements (CSSH8 and CSSE8) are developed based on the “ANS+HS” and “ANS+EAS” formulations, respectively. The Green–Lagrange displacement–strain relation is applied to involve the geometrical nonlinearities, and both the thermal expansion and temperature-dependent material properties are considered. Nonlinear thermoelastic equilibrium equations are constructed in the framework of the two types of finite element formulations using the Hellinger–Reissner and conventional variational principles, respectively. The proposed method can easily realize three different coupling analyses for thermal–mechanical loads by modifying the parameters of nonlinear thermoelastic equilibrium equations. Numerical examples demonstrate that the proposed method using CSSH8 and CSSE8 elements traces the nonlinear thermoelastic response of the isogrid stiffened panel as accurately as the shell, solid-shell, and solid elements of ABAQUS. Furthermore, the path-following capability of the proposed method using the CSSH8 with “ANS+HS” formulation is slightly superior to that using the CSSE8 with “ANS+EAS” formulation, but both better than ABAQUS.

Comprehending symmetry in epidemiology: A review of analytical methods and insights from models of COVID-19, Ebola, Dengue, and Monkeypox.

The challenge of developing comprehensive mathematical models for guiding public health initiatives in disease control is varied. Creating complex models is essential to understanding the mechanics of the spread of infectious diseases. We reviewed papers that synthesized various mathematical models and analytical methods applied in epidemiological studies with a focus on infectious diseases such as Severe Acute Respiratory Syndrome Coronavirus-2, Ebola, Dengue, and Monkeypox. We address past shortcomings, including difficulties in simulating population growth, treatment efficacy and data collection dependability. We recently came up with highly specific and cost-effective diagnostic techniques for early virus detection. This research includes stability analysis, geographical modeling, fractional calculus, new techniques, and validated solvers such as validating solver for parametric ordinary differential equation. The study examines the consequences of different models, equilibrium points, and stability through a thorough qualitative analysis, highlighting the reliability of fractional order derivatives in representing the dynamics of infectious diseases. Unlike standard integer-order approaches, fractional calculus captures the memory and hereditary aspects of disease processes, resulting in a more complex and realistic representation of disease dynamics. This study underlines the impact of public health measures and the critical importance of spatial modeling in detecting transmission zones and informing targeted interventions. The results highlight the need for ongoing financing for research, especially beyond the coronavirus, and address the difficulties in converting analytically complicated findings into practical public health recommendations. Overall, this review emphasizes that further research and innovation in these areas are crucial for addressing ongoing and future public health challenges.

Modeling and analyzing stability of hybrid stars within [formula omitted] gravity

This study uses the Krori–Barua type metric to represent hybrid stars within the f(Q) theory of gravity. We postulate that the hybrid star also contains strange quark matter in addition to regular baryonic matter. To investigate the physical viability of the hybrid star model, we present the graphical behavior of the energy density, radial pressure, and tangential pressure, equation of state parameters, anisotropy, and stability analysis, respectively, by choosing the compact star EXO 1785-248 with a mass of 1.3−0.2+0.2M⊙ and radius 8.849−0.4+0.4 km with five different values of the coupling constants as a=2, a=4, a=6, a=8, and a=10. The maximum allowed masses and corresponding radii have been calculated using the M−R curve for three different coupling parameter ’a’ values which match the observational data of three distinct compact stars, namely LMC X-4, SMC X-1, and 4U 1538-52. So, the f(Q) theory of gravity can provide results that are plausible for describing the macroscopical characteristics of hybrid star candidates.

Enhanced syngas production through dry reforming of methane with Ni/CeZrO2 catalyst: Kinetic parameter investigation and CO2-rich feed simulation

Natuna's natural gas reserve, which contains 70 %–v CO2 and 30 %–v CH4, opens a prospective method for producing syngas through the dry reforming of methane (DRM). This study used the equation and determination of kinetic parameters in a fixed-bed reactor to develop the operating conditions for the DRM process. The catalyst used was 10 %Ni/CeZrO2 and followed the Langmuir-Hinshelwood mechanism, with CH4 dissociation (activation of C–H bonds) on the Ni catalyst as the rate-determining step. According to the results, the simulation and experimental data have error values of ≤ 5 % and RMSE < 0.046. This indicates that the equation and kinetic parameters used in the simulation are valid for reactor modeling. Steady-state modeling was then conducted using a 1D quasihomogeneous model. The feed composition of CO2:CH4 = 70:30 (Natuna gas field composition) has optimized results with temperature 700 °C, CH4 conversion at 92 %, CO2 conversion at 28 %, and H2/CO ratio 1.42, and carbon formation at 7.1 mgC/gcat. This study also found that a higher CO2:CH4 feed ratio could reduce carbon formation during DRM.

Theoretical probes of Higgs boson-axion nonperturbative couplings

In this work we investigate the phenomenological implications of several nontrivial Higgs-boson- axion couplings, which cover most of the possible nonperturbative scenarios. Specifically we consider the combination of having higher-order nonrenormalizable Higgs-boson-axion couplings originating from a weakly coupled effective theory combined with nonperturbative couplings of the form ∼εΛc2|H|2cos(ϕfa). Since we consider the misalignment axion, the nonperturbative couplings can be expanded in the form of a perturbation expansion in powers of ϕ/fa, thus after the electroweak symmetry breaking, the effective potential of the axion is drastically affected by these terms. We investigate the phenomenological implications of these terms for various values of the mass scale Λc, and some scenarios are theoretically disfavored, while other scenarios with nonperturbative Higgs-boson-axion couplings of the form ∼εΛc2|H|2cos(ϕfa) with Λc∼10−10×ma and ma∼10−10 eV, lead to a characteristic pattern in the stochastic gravitational wave background via the deformation of the background equation of state parameter occurring at frequencies probed by the Einstein Telescope. We also consider loop effects from the Higgs sector caused by the term ∼εΛc2|H|2cos(ϕfa) if we close the Higgs in one loop. Published by the American Physical Society 2024

REMaQE: Reverse Engineering Math Equations from Executables

Cybersecurity attacks on embedded devices for industrial control systems and cyber-physical systems may cause catastrophic physical damage as well as economic loss. This could be achieved by infecting device binaries with malware that modifies the physical characteristics of the system operation. Mitigating such attacks benefits from reverse engineering tools that recover sufficient semantic knowledge in terms of mathematical equations of the implemented algorithm. Conventional reverse engineering tools can decompile binaries to low-level code, but offer little semantic insight. This paper proposes the REMaQE automated framework for reverse engineering of math equations from binary executables. Improving over state-of-the-art, REMaQE handles equation parameters accessed via registers, the stack, global memory, or pointers, and can reverse engineer equations from object-oriented implementations such as C++ classes. Using REMaQE, we discovered a bug in the Linux kernel thermal monitoring tool “tmon”. To evaluate REMaQE, we generate a dataset of 25,096 binaries with math equations implemented in C and Simulink. REMaQE successfully recovers a semantically matching equation for all 25,096 binaries. REMaQE executes in 0.48 seconds on average and in up to 2 seconds for complex equations. Real-time execution enables integration in an interactive math-oriented reverse engineering workflow.

Phaseless inverse scattering with a parametrized spatial spectral volume integral equation for finite scatterers in the soft x-ray regime

Soft x-ray wafer-metrology experiments are characterized by low signal-to-noise ratios and lack phase information, which both cause difficulties with the accurate three-dimensional profiling of small geometrical features of structures on a wafer. To this end, we extend an existing phase-based inverse-scattering method to demonstrate a sub-nanometer and noise-robust reconstruction of the targets by synthetic soft x-ray scatterometry experiments. The targets are modeled as three-dimensional finite dielectric scatterers embedded in a planarly layered medium, where a scatterer’s geometry and spatial permittivity distribution are described by a uniform polygonal cross section along its height. Each cross section is continuously parametrized by its vertices and homogeneous permittivity. The combination of this parametrization of the scatterers and the employed Gabor frames ensures that the underlying linear system of the spatial spectral Maxwell solver is continuously differentiable with respect to the parameters for phaseless inverse-scattering problems. In synthetic demonstrations, we demonstrate the accurate and noise-robust reconstruction of the parameters without any regularization term. Most of the vertex parameters are retrieved with an error of less than λ/13 with λ=13.5nm, when the ideal sensor model with shot noise detects at least five photons per sensor pixel. This corresponds to a signal-to-noise ratio of 3.5 dB. These vertex parameters are retrieved with an accuracy of λ/90 when the signal-to-noise ratio is increased to 10 dB, or approximately 100 photons per pixel. The material parameters are retrieved with errors ranging from 0.05% to 5% for signal-to-noise ratios between 10 dB and 3.5 dB.

Prediction of rotational bending fatigue life of bearing steel based on damage mechanics

Based on the theory of continuous damage mechanics, this paper proposes a fatigue damage evolution model and numerical calculation method considering the influence of vacuum chemical heat treatment process, and studies the rotational bending fatigue damage analysis and life prediction method of M50NiL bearing steel. Firstly, the constitutive model, fatigue damage evolution equation and material parameter calibration method in the theoretical model are given. Secondly, based on the ABAQUS platform, the damage mechanics-finite element numerical calculation method of fatigue damage analysis considering the influence of hardened layer is realized by writing the UMAT subroutine; then, the rotational bending fatigue test of M50NiL bearing steel treated by vacuum chemical heat treatment of quenching and tempering, carburizing and carbonitriding is carried out, and the influence of heat treatment process on fatigue performance is analyzed; finally, based on the proposed fatigue damage model and numerical calculation method, the rotational bending fatigue life of M50NiL bearing steel is predicted, and the results are compared with the experimental results to verify the correctness of the proposed method.

Stability analysis of a linear system coupling wave and heat equations with different time scales

In this paper we consider a system coupling a wave equation with a heat equation through its boundary conditions. The existence of a small parameter in the heat equation, as a factor multiplying the time derivative, implies the existence of different time scales between the constituents of the system. This suggests the idea of applying a singular perturbation method to study stability properties. In fact, we prove that this method works for the system under study. Using this strategy, we get the stability of the system and a Tikhonov theorem, which allows us to approximate the solution of the coupled system using some appropriate uncoupled subsystems.