Parameters Of Equation Research Articles

Cosmographic analysis of holographic nonzero torsion framework

In this paper, we use the cosmographic approach to discuss Friedmann space-time in the presence of torsion. For this, we explore equations of motion that explain creation in an isotropic and homogeneous cosmic backdrop with nonzero torsion. Here, we consider the energy density of holographic dark energy model [Formula: see text] where [Formula: see text] is a dimensionless parameter depending on redshift parameter [Formula: see text] is the reduced Planck mass and [Formula: see text] represents the holographic length scale. We examine this dark energy model with both constant and variable holographic length scales in terms of Hubble parameter to determine the best-fit scale. The interaction between dark sector components is taken to evaluate cosmographic parameters, like Hubble, equation of state, deceleration, jerk, snap, lerk and statefinder parameters. We consider four [Formula: see text] parametrizations, which are Chevallier–Polarski–Linder, Jassal–Bagla–Padmanabhan, Wetterich and Ma–Zhang for both cases. We obtain consistent results for specific choices of constant parameters in the underlying scenario.

Interleaved Modified SEPIC Converters with Soft Switching and High Power Factor for LED Lighting Appliance

A novel ac/dc LED driver with power factor correction and soft-switching functions is proposed. The circuit topology mainly consists of two modified single-ended primary inductance converters (SEPIC) with interleaved operation. The first half stage of SEPIC operates like a boost converter and the second half stage operates like a buck–boost converter. Each boost converter is designed to operate in discontinuous current mode (DCM) to function as a power factor corrector (PFC). The two buck–boost converters that share a commonly coupled inductor are designed to operate at near boundary conduction mode (BCM). Without using any active clamping circuit, auxiliary switch or snubber circuit, the active switches can achieve zero-voltage switching on, and all diodes achieve zero-current switching off. First, operation modes in steady state are analyzed, and the mathematical equations for design component parameters are derived. Finally, a prototype circuit of 180 W rated power was built and tested. Experimental results show satisfactory performance of the proposed circuit.

Numerical simulation of a partially ionized Oldroyd-B nanofluid flow driven by two homocentric rotating disks with motile microorganisms

Nanofluids are assumed to be an excellent source of enhanced heat transfer with advanced thermophysical characteristics. Nanofluids are the backbone of the heating and cooling in the industrial processes. This research delves into the dynamics of a partially ionized Oldroyd-B nanofluid flowing between stretchable rotating disks. The study investigates heat transfer mechanisms incorporating a modified Fourier law and convective heat conditions. The viscoelastic fluid model presented here allows for the examination of relaxation and retardation times. Furthermore, the heat and mass transport of the Oldroyd-B nanofluid is characterized using a Buongiorno model, which considers thermophoresis and Brownian diffusion effects. Additionally, the study explores the impact of gyrotactic microorganisms in nanofluids, potentially enhancing environmental management strategies. The governing equations transform into dimensionless forms using Von Karman similarity variables. Numerical investigation of the anticipated model is conducted using the bvp4c scheme in MATLAB. The variation of different parameters in the dimensionless equations is illustrated through graphs and in tabulated format. The results indicate that increasing thermophoresis and Lewis numbers lead to a decrease in fluid concentration. Moreover, the temperature of the fluid rises at the lower disk and declines at the upper disk relative to the Biot number. The proposed model is validated through comparison with closely related published work.

A Study on the Fracture Toughness Evaluation Considering Material Tensile Characteristic for Cryogenic Steel

Abstract ISO 12135, a representative standard for the evaluation of fracture toughness, was revised in 2021. In the previous standard published in 2016, only yield strength was reflected for material property in fracture toughness calculation. In the revised standard, however, yield to tensile strength ratio is additionally reflected in consideration of strain hardening effect of the material. The current fracture toughness calculation formula evaluates fracture toughness reasonably considering the tensile characteristic. However, in some cases of cryogenic steels, fracture toughness is evaluated very conservatively than the previous procedure in 2016. In the case of STS 304L, there is no ductile-brittle transition phenomenon and it has excellent ductility and strength in cryogenic temperature. However, due to the secondary hardening phenomenon, yield to tensile strength ratio is relatively low, and as a result, fracture toughness is evaluated very low. The target of this study is to resolve the undervaluation of fracture toughness of cryogenic steel in the revised ISO 12135. For this purpose, the elastic and the plastic parameters in crack tip opening displacement (CTOD) equation in ISO 12135 are examined. The crack tip profile is derived by a series of finite element analysis and crack tip opening displacement is calculated for the derivation of new parametric equations for cryogenic materials. The calculated crack tip opening displacement is validated by experimental results.

Reduced order model enhanced source iteration with synthetic acceleration for parametric radiative transfer equation

Applications such as uncertainty quantification, shape optimization, and optical tomography, require solving the radiative transfer equation (RTE) many times for various parameters. Efficient solvers for RTE are highly desired.Source Iteration with Synthetic Acceleration (SISA) is a popular and successful iterative solver for RTE. Synthetic Acceleration (SA) acts as a preconditioning step to accelerate the convergence of Source Iteration (SI). After each source iteration, classical SA strategies introduce a correction to the macroscopic particle density by solving a low order approximation to a kinetic correction equation. For example, Diffusion Synthetic Acceleration (DSA) uses the diffusion limit. However, these strategies may become less effective when the underlying low order approximations are not accurate enough. Furthermore, they do not exploit low rank structures concerning the parameters of parametric problems.To address these issues, we propose enhancing SISA with data-driven ROMs for the parametric problem and the corresponding kinetic correction equation. First, the ROM for the parametric problem can be utilized to obtain an improved initial guess. Second, the ROM for the kinetic correction equation can be utilized to design a low rank approximation to it. Unlike the diffusion limit, this ROM-based approximation builds on the kinetic description of the correction equation and leverages low rank structures concerning the parameters. We further introduce a novel SA strategy called ROMSAD. ROMSAD initially adopts our ROM-based approximation to exploit its greater efficiency in the early stage of SISA, and then automatically switches to DSA to leverage its robustness in the later stage. Additionally, we propose an approach to construct the ROM for the kinetic correction equation without directly solving it.Through a series of numerical tests, we compare the proposed methods with SI-DSA and DSA preconditioned Krylov solver. Particularly, for a multiscale parametric pin-cell problem, ROMSAD achieves approximately 10 times the acceleration compared to SI-DSA and 4 times acceleration compared to DSA preconditioned GMRES.

Collar plate effect on local joint flexibility of tubular K-joints under IPB moments: Parametric study and predictive equations

This study delves into the Local Joint Flexibility (LJF) of tubular K-joints reinforced with the collar plates under in-plane bending moments (IPBMs). 348 reinforced K-joints were simulated to analyze the impacts of the loading conditions (balanced and unbalanced moments), collar plate size (like the length and thickness) alongside the joints’ parameters (θ, γ, β, ξ) on the fLJF and its proportionality (ψ). The research outcomes demonstrate that factors such as η, λ, and β play a significant role in determining ψ, whereas the influence of ξ, and γ on ψ appears to be negligible. Also, in the reinforced joints, the fLJF is decreased by 77.4 % compared to the equivalent un-reinforced joint. While the role of the collar plate on the fLJF is remarkable, the matter had not been investigated on K-joints. Therefore, following the detailed parametric study, two novel equations are proposed to safety estimate the fLJF for such scenarios.

Investigation on Heterostructured SeO2–TiO2 Nanofluoroprobe for Highly Selective and Sensitive Detection of a Neonicotinoid Insecticide, Imidacloprid in Soil and Water Matrixes

Heterostructured SeO2–TiO2 nanoparticles were used as a highly sensitive and selective fluoroprobe for the detection and determination of neonicotinoid insecticide imidacloprid. The sonication-assisted co-precipitation technique was used to create nanoparticles, which were then characterized using UV–Vis, SEM–EDS, HRTEM, XRD, and TGA. These analyses revealed that the nanoparticles had globular morphology, a crystallite size of 14 nm, a bandgap of 2.45 eV, and stability at high temperatures. Fluorescence emission at 548 nm wavelength exhibits high sensitivity and selectivity for imidacloprid over other pesticides with complete fluorescent quenching at 2 × 10–4 M concentration of imidacloprid. Stern–Volmer equation and thermodynamic parameters applied to the experimental data over a temperature range of 20–50 °C provide the Ksv value in the range of 1.56 × 105 to 2.69 × 105 M−1 and indicate strong interactions, dynamic, spontaneous, and endothermic quenching process. Furthermore, the excellent salient features and notably the unaffected performance even in the presence of various anions, fertilizer, and binary mixture of pesticides often sprayed on plants, will pave the way for the development of rapid, affordable, selective fluoroprobe for onsite monitoring of imidacloprid. The reliability for determination is also examined for spiked soil samples to develop a hybrid SeO2–TiO2 nanoparticles fluoroprobe as a simple alternative to existing techniques for the detection of imidacloprid.Graphical

Generalized ghost pilgrim dark energy model in Non-Riemannian geometry

In this paper, we analyze cosmic evolution and current expansion using the generalized ghost pilgrim dark energy model for the flat Friedmann-Robertson-Walker universe in f(Q) gravity, where Q represents the non-metricity. For this objective, we examine interacting forms of dark energy model and reconstruct f(Q) gravity in terms of red-shift parameter. We establish various standard cosmological parameters including the equation of state parameter, the squared speed of sound, ωD−ωD′ and r − s-planes to examine the impact of this dark energy model. The analysis reveals that all the reconstructed models exhibit an increasing or decreasing trend in the pilgrim dark energy parameter. The equation of state parameter depicts the phantom era, while the squared speed of sound reveals a stable generalized ghost pilgrim dark energy model for the entire cosmic evolutionary paradigm. Finally, we study the cosmography of the ωD−ωD′ and r − s planes that correspond to the freezing region and Chaplygin gas model, respectively. We conclude that all the outcomes are consistent with the pilgrim dark energy phenomenon.

On more insightful dimensionless numbers for computational viscoelastic rheology

Abrupt contraction flows involving viscoelastic fluids represent a longstanding computational challenge within the field of non-Newtonian fluid mechanics. Despite the apparent simplicity of the geometry, these flows have given rise to intricate discussions in the study of viscoelastic phenomena. This study aims to re-examine the numerical solutions for flows through abrupt contractions, offering a fresh interpretation through the lens of reformulated dimensionless numbers. These numbers are designed to consider the characteristic shear rate of the problem, providing a more comprehensive understanding of the underlying dynamics.When investigating models with intermediate levels of complexity, such as the Giesekus and Phan-Thien-Tanner constitutive equations, the usual comparison with the corresponding Oldroyd-B model becomes inadequate because it tends to rely on the nominal relaxation time (λ) and the nominal total viscosity (η) instead of their effective counterparts when defining the Reynolds number (Re), the Weissenberg number (Wi) and the ratio of solvent to total viscosities (β) (β plays a role only in rheological models involving a solvent contribution). If these dimensionless numbers are tailored to account for the characteristic shear rate specific to the problem under investigation, the choice of the corresponding Oldroyd-B flow, at the adequate values of Re, Wi, and β allows for significantly better quantification of the correct effects of nonlinear viscoelasticity of the original model.We show the conventional approach tends to overemphasize the role of the nonlinear parameter in nonlinear constitutive equations, like the Giesekus and PTT models, when examining standard abrupt contraction flow outputs such as the Couette correction and vortex size. This overestimation occurs because the conventional method does not allow the Reynolds and Weissenberg numbers (and possibly β) to carry the portion of the nonlinear effect that can potentially be captured by the linear Oldroyd-B model through the use of characteristic shear rate-based values. We believe the present approach provides a better perspective of the role played by the nonlinear parameter and its extension to more general flows is also discussed.

A Prediction Model of Two-Sided Unbalance in the Multi-Stage Assembled Rotor of an Aero Engine

In rotating machinery with a multi-stage assembled rotor, such as is found in aero engines, any unbalance present will undergo unknown changes at each stage when rotating the assembly phases of the rotor. Repeated disassembly and adjustments are often required to meet the rotor’s residual unbalance specifications. Therefore, developing a prediction model of this two-sided unbalance for a multi-stage assembled rotor is crucial for improving the first-time assembly pass rate and assembly efficiency. In this paper, we propose a prediction model of the two-sided unbalance seen in the multi-stage assembled rotor of an aero engine. Firstly, a method was proposed to unify the mass feature parameters of each stage’s rotor into a geometric measurement coordinate system, achieving the synchronous transmission of geometric and mass feature parameters during the assembly process of the multi-stage rotor. Building upon this, a linear parameter equation of the actual rotation axis of the multi-stage rotor was established. Based on this axis, the mass eccentricity errors of the rotor were calculated at each stage, further enabling the accurate prediction of two-sided unbalance and its action phase in a multi-stage rotor. The experimental results indicate that the maximum prediction errors of the two-sided unbalance and its action phase for a four-stage rotor are 9.6% and 2.5%, respectively, when using this model, which is a reduction of 53.0% and 38.1% compared to the existing model.

Reconsidering bulk viscosity in Brans–Dicke theory

In this paper, we reconsider the concept of bulk viscosity in Brans–Dicke theory to study accelerated expansion of the universe in a flat Friedmann–Robertson–Walker metric. In recent works on bulk viscosity in Brans–Dicke theory, the power-law form of Brans–Dicke scalar field has been taken to explain recent phase transition of the universe, however, power-law form confronts constant deceleration parameter problem. Therefore, we consider recently proposed well-motivated logarithmic form of Brans–Dicke scalar field to discuss bulk viscous model in Brans–Dicke theory. We obtain the values of deceleration parameter and equation of state parameter for the model, and plot their graphs against the redshift parameter z. The plots show that the model is able to explain the recent phase transition of the universe and equation of state parameter shows the behavior of dark energy. Further, we apply two important analysis, namely, [Formula: see text] analysis and thermodynamic analysis to examine our model. The [Formula: see text] analysis shows that our model belong to thawing region and shows similarities with quintessence model. All the trajectories start from the point [Formula: see text] with different negative values of w having quintessence behavior. The thermodynamic analysis shows that the model satisfies generalized second law of thermodynamics.

Bulk viscous cosmological model in [formula omitted] modified gravity

This article explores the impact of bulk viscosity on understanding the universe’s accelerated expansion within the context of modified f(T,T) gravity, which is an extension of the f(T) gravitational theory, allowing a broad coupling between the energy–momentum scalar T and the torsion scalar T. We consider two f(T,T) functions, specifically f(T,T)=αT+βT and f(T,T)=α−T+βT, where α and β are arbitrary constants, along with the fluid part incorporating the coefficient of bulk viscosity ζ=ζ0>0. We calculate the analytical solutions of the corresponding field equations for a flat FLRW environment, and then we constrain the free parameters of the obtained solution using CC, Pantheon+, and the CC+Pantheon+ samples. We perform the Bayesian statistical analysis to estimate the posterior probability utilizing the likelihood function and the MCMC random sampling technique. Further, to assess the effectiveness of our MCMC analysis, we estimate the corresponding AIC and BIC values, and we find that there is strong evidence supporting the assumed viscous modified gravity models for all three data sets. Also, we find that the linear model precisely mimics the ΛCDM model. We also investigate the evolutionary behavior of some prominent cosmological parameters. We observe that the effective equation of state parameter for both models predict the accelerating behavior of the cosmic expansion phase. In addition, from the statefinder test, we find that the parameters of the considered MOG models favor the quintessence-type behavior. Further, we observe that the behavior of Om(z) curves corresponding to both models represent a consistent negative slope across the entire domain. We infer that our cosmological setting utilizing f(T,T) gravity models with the viscous matter fluid embodies quintessence-like behavior and can successfully describe the late-time scenario.

Quintessential f(G) gravity with statistically fitting of H(z)

Inspired by high-energy physics and by considering standard gravity theory as the low-energy limit of quantum theory, the modification of general relativity as [Formula: see text] has been proposed. This paper is dedicated to investigating the cosmological model of modified Gauss–Bonnet gravity in four dimensions. General field equations for the four-dimensional Friedmann– Robertson–Walker metric are given in detail. Also, it is well known that Hubble parameter [Formula: see text] measurements are helpful for the inference of cosmological model parameters. We try to explain the MCMC statistical approach used to calculate Hubble’s parameter. The resulting form of [Formula: see text] was limited using Cosmic Chronometric data, Standard Candles SN Ia from Pantheon, and Baryon Acoustic Oscillations to obtain the best match values by using the regression equation. Finally, to examine the late-time dynamics of our Universe, the behavior of physical and kinematic variables like the deceleration parameter [Formula: see text], State-finder parameters [Formula: see text], diagnostic parameter ([Formula: see text]), equation of state parameter as well as the behavior of energy conditions versus redshift with the parameter values are presented.

An Innovative Approach in Inspecting a Damped Mathieu Cubic–Quintic Duffing Oscillator

Abstract Purpose The objective of the present study is to analyze a damped Mathieu–cubic quintic Duffing oscillator as a parametric nonlinear oscillatory dynamical system. This equation has multiple applications in diverse fields, including optics, quantum physics, and general relativity. There are multiple concerns related to periodic motion and the analysis of boundary-value problems with elliptic symmetries. The current effort aims to determine the frequency amplitude of parametric nonlinear issues. Method The non-perturbative approach (NPA) is employed to transform the nonlinear ordinary differential equation (ODE) into a linear equation. The derivation of the approximate solutions is achieved without relying on typical perturbation approaches, separate from the series expansion. Hence, the objective of this study is to depart from traditional perturbation methods and acquire approximated solutions for minor amplitude parametric components without imposing any limitations. Furthermore, the technique is extended to ascertain optimal solutions for the nonlinear large amplitude of fluctuation. Results The current approach allows for rapid estimation of the frequency-amplitude relationship in order to attain successive approximations of the solutions for parametric nonlinear fluctuations. A validation is obtained for the derived parametric equation, demonstrating a high level of agreement with the original equation. An analysis of stability behavior is conducted in multiple scenarios. In addition, the Floquet theory is used to examine the transition curves. Conclusion The current technique is characterized by its clear principles, making it practical, user-friendly, and capable of achieving exceptionally high numerical precision. The current approach is highly beneficial for addressing nonlinear parametric problems due to its ability to minimize algebraic complexity during implementation.

Asymptotic expansion method with respect to a small parameter for fractional differential equations with Riemann–Liouville derivate

In this paper, we proposed an asymptotic approach with respect to a small parameter for fractional differential equations, with the small parameter linked to the fractional order derivative. This approach allows the splitting of the field variable and consequently the Riemann–Liouville Integral as the sum of two contributions. One describes the unperturbed state and the other describes the behavior of the model in the perturbed state due to the presence of the fractional derivative. This approach allows mapping time-fractional differential equations into a system of two coupled partial differential equations with integer order. By solving these partial differential equations we are able to obtain solutions of the assigned fractional differential equations. To obtain solutions we determine the approximate Lie symmetries through which the system of two coupled partial differential equations is reduced to a system of two coupled ordinary differential equations. As an application, we consider the time fractional diffusion–reaction equation with a linear source term; we test the proposed procedure by comparing the profiles of the obtained approximate solutions with solutions found in the fractional context for values of the fractional parameter tending to the integer value.

Effect of annealing on the corrosion-fatigue strength and hot salt corrosion resistance of fine-grained titanium near-α alloy Ti-5Al-2V obtained using Rotary Swaging

The corrosion-fatigue strength in 3 % aqueous NaCl solution and the resistance against hot salt corrosion (HSC) of the fine-grained near-α alloy Ti-5Al-2V (Russian analogue of Grade 9 titanium alloy with increased aluminium content) have been studied. The properties of the Ti-5Al-2V alloy in the coarse-grained state, in the fine-grained state after cold Rotary Swaging (RS), in the partly recrystallized state and in the fully recrystallized state have been investigated. The mechanical properties of the alloy were characterised using compression tests and microhardness measurements. The effects of RS, the annealing temperature, the time on the characteristics of corrosion destruction of the surface and the composition of the products of the HSC were studied. RS was shown to increase the depth of the intergranular corrosion defects, whereas recrystallization annealing promoted an increase in the corrosion resistance of the Ti-5Al-2V titanium alloy. The parameters of the Basquin equation for the corrosion-fatigue curves for the near-α Ti-5Al-2V alloy in the coarse-grained state, in the severely strained state and after recrystallization annealing were determined for the first time. An effect of non-monotonous dependencies of the slopes of the corrosion-fatigue curves for the strained near-α Ti-5Al-2V alloy on the recrystallization annealing temperature has been observed.

Assessment of α and γ parameters in landslide volume estimation equations based on geological variability

Assessment of α and γ parameters in landslide volume estimation equations based on geological variability

Length-Weight relationship and condition factor of Lutjanus peru and L. guttatus from the Gulf of California Mexico.

Fulton’s condition factor (k) and the length-weight relationship (LWR) are the most important biological tools with respect to basic aspects of fish population dynamics; they are applicable to strategic plans for the conservation and management of fisheries. A total of 478 snappers Lutjanus peru and L. guttatus were analyzed in Santa Rosalía, Baja California Sur, in the Gulf of California. The total length of Lutjanus peru ranged from 21 to 55 cm, and weight ranged from 215 to 1,920 g, whereas total length of L. guttatus ranged from 21 to 59 cm, and weight ranged from 290 to 1,675 g. The LWR and condition factor were estimated for the two species and intraspecific factors were analyzed (sex, season, maturity stage) using Bayesian hierarchical models with random effects. The parameters of the LWR equation were similar for the two snapper species (α≈0.026 and β ≈ 2.8); they both presented negative allometric growth (p(β<3)>85%). The L. peru growth rate was greater in the warm season (p(βwarm>βcold)≈97%), whereas this difference was not as evident in L. guttatus (p(βwarm<βcold)≈72%). The condition factor k was greater than 1 for all categories in the two species (p(μk)=100%), which suggests that they keep a good body condition. This indicates that L. peru and L. guttatus in Santa Rosalía experience environmental conditions that benefit their body condition, as a function of year-round food availability. This information is useful for future conservation studies and for monitoring snapper captures, as most L. peru individuals caught were sexually immature.

Distribution of the acoustobrightness temperature satisfies heat equation

Passive acoustic thermometry (PAT), a method proposed for medical applications, involves direct measurement of the acoustobrightness temperature which is the intensity of the thermal acoustic radiation expressed in degrees. The hypothesis has been proposed that the acoustobrightness temperature measured on the surface of the object under study obeys the 2D heat equation whose parameters coincide or are uniquely connected with the parameters of the 3D heat equation governing the deep temperature of the object. Since in PAT a noise signal is measured, the achievement of an acceptable error level (0.5–1 K) requires a considerable integration time (about a minute). The proposed hypothesis will enable linking together the data obtained by acoustothermometric sensors separated in space, at different points in time. This, in turn, will lower the dimensionality of the problem of temperature distribution reconstruction and enable reducing the integration time without loss of accuracy. The proposed hypothesis has been confirmed experimentally and with the aid of computer simulation for the case where local hyperthermia of soft tissues of the human organism is modeled.

A stochastic approximation for the finite-size Kuramoto–Sakaguchi model

We perform a stochastic model reduction of the Kuramoto–Sakaguchi model for finitely many coupled phase oscillators with phase frustration. Whereas in the thermodynamic limit coupled oscillators exhibit stationary states and a constant order parameter, finite-size networks exhibit persistent temporal fluctuations of the order parameter. These fluctuations are caused by the interaction of the synchronised oscillators with the non-entrained oscillators. We present numerical results suggesting that the collective effect of the non-entrained oscillators on the synchronised cluster can be approximated by a Gaussian process. This allows for an effective closed evolution equation for the synchronised oscillators driven by a Gaussian process which we approximate by a two-dimensional Ornstein–Uhlenbeck process. Our reduction reproduces the stochastic fluctuations of the order parameter and leads to a simple stochastic differential equation for the order parameter.