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The space debris in Earth's orbit has increased drastically due to the failure of spacecraft, rocket bodies, and mission-related objects. These objects in orbit increase the space waste and challenge other flying objects such as spacecraft. A hypervelocity impact of space debris on spacecraft structures can have a range of effects (mechanical damage and functional failure), raising significant concerns about spacecraft safety. This paper reviews the different studies on the performance and development of the Whipple shield against the hypervelocity impact of space debris. The study focuses on the impact mechanism, dynamic Fragmentation of materials, strength models, Equation of state, characteristics, and model of the debris cloud. The strength models (Steinberg–Guinan and Johnson–Cook) and Mie–Gruneisen equation of state, primarily used for hypervelocity impact applications, are thoroughly covered in this study. The study also reported the various experimental and numerical techniques for high and hypervelocity impact. The study concluded that mesh-based, mesh-free, and hybrid finite element methods are reliable for analyzing Whipple shield targets to resist hypervelocity impact. The study also observed that the two-stage light gas gun technique investigates most experimental analyses of hypervelocity impact on the Whipple shield. Alongside reviewing the abovementioned aspects, this paper also underlines the future scope of study in this paradigm. The authors strongly believe that this study provides more insights into the fundamentals and perceptions of the Whipple shield to protect the spacecraft against the hypervelocity impact of space debris. [ABSTRACT FROM AUTHOR]

Numerous studies have introduced a variety of synchronization techniques that involve many structures. However, since the majority of synchronization methods influence or increase the system states from a stability perspective, these methods necessitate retuning the controller parameters, reconstructing a converter controller, or employing a different control construction. This paper proposes a novel, yet simple and straightforward, method for implementing a synchronization technique concept based on the conventional synchronization method known as the "dark lamp" process. Since the proposed method is based on logic functions, there is no additional state in the entire system of the model, which is the cornerstone of this paper. The proposed method is validated and studied in a time–domain simulation environment, specifically a PSCAD/EMTDC. The proposed new synchronization technique in this paper overcomes the discussed synchronization techniques in the literature by dispensing with the need either to use a phase-locked loop (PLL) or to retune the controller parameters and, furthermore, does not increase the system state equation. Meanwhile the proposed techniques in the literature increase the system state equation by at least two states, which affects the entire system performance and stability. The results of this paper show promising and important outcomes that will further the study of the synchronization technique. [ABSTRACT FROM AUTHOR]

In this paper, we compare and contrast the classical versus quantum dynamics of a cosmological model based on the literature (Modified) Berthelot equation of state for the description of the dark sector of the universe. At the classical background level we identify a Minkowski-like and a de Sitter-like equilibrium epochs, with the latter occurring only beyond a certain threshold for a parameter in the equation of state; at the classical perturbed level we find that this same parameter realizes a duality in the adiabatic speed of sound between the two equilibrium epochs. The quantum evolution of this model is studied in the context of quantum geometrodynamics by solving analytically the Wheeler–DeWitt equation in the Born–Oppenheimer approximation for the scalar field potentials about the two equilibrium epochs. We identify the phenomenon of quantum decoherence to arise at the same threshold which constitutes the bifurcation between the two equilibrium epochs at the classical level. We comment on the quantum modified power spectrum focusing on some consequences dealing with the formation of astrophysical structures within the Press–Schechter framework. Our paper is intended to scrutinize which classical features of a certain cosmological model are preserved at its quantum level, and under which assumptions. [ABSTRACT FROM AUTHOR]

In this paper, our focus is on exploring the relative controllability of systems governed by linear fractional differential equations incorporating state delay. We introduce a novel counterpart to the Cayley-Hamilton theorem. Leveraging a delayed perturbation of the Mittag-Leffler function, along with a determining function and an analog of the Cayley-Hamilton theorem, we establish an algebraic Kalman-type rank criterion for assessing the relative controllability of fractional differential equations with state delay. Moreover, we articulate necessary and sufficient conditions for relative controllability criteria concerning linear fractional time-delay systems, expressed in terms of a new α -Gramian matrix and define a control which transfer the system from any initial state to any final state within a given time. The theoretical findings are exemplified through the presentation of illustrative examples. [ABSTRACT FROM AUTHOR]

This paper studies the solution stability of convex optimization and discrete convex optimal control problems in Banach spaces, where the solution set may be empty. For both the optimization problem and the optimal control problem, formulas for the ε -subdifferential of the optimal value function are derived without qualification conditions. We first calculate the ε -subdifferential of the optimal value function to a parametric optimization problem with geometrical and functional constraints. We then use the obtained results to derive a formula for computing the ε -subdifferential of the optimal value function to a discrete convex optimal control problem with linear state equations, control constraints and initial, terminal conditions. [ABSTRACT FROM AUTHOR]

The process of the gravitational collapse might lead not only to a black hole but also to naked singularity formation. In this paper, we consider the generalized Vaidya spacetime with polytropic and generalized polytropic equations of state. We solve the Einstein and Einstein–Maxwell equations to obtain the explicit form of a mass function. We consider the limiting cases of solutions and find out, that generalized Vaidya spacetime might behave like Vaidya–de Sitter and Bonnor–Vaidya–de sitter solutions. Moreover, we explicitly show, that the part of solution, which depends on the polytropic index, is similar to cosmological fields surrounding both Vaidya and Bonnor–Vaidya black holes. The process of the gravitational collapse has been then considered. We have found out that the conditions of the naked singularity formation don't depend on the polytropic index. [ABSTRACT FROM AUTHOR]

This paper focuses on the topology optimization of a broadband acoustic transition section that connects two cylindrical waveguides with different radii. The primary objective is to design a transition section that maximizes the transmission of a planar acoustic wave while ensuring that the transmitted wave exhibits a planar shape. Helmholtz equation is used to model linear wave propagation in the device. We utilize the finite element method to solve the state equation on a structured mesh of square elements. Subsequently, a material distribution topology optimization problem is formulated to optimize the distribution of sound-hard material in the transition section. We employ two different gradient-based approaches to solve the optimization problem: namely, a deterministic approach using the method of moving asymptotes (MMA), and a stochastic approach utilizing both stochastic gradient (SG) and continuous stochastic gradient (CSG) methods. A comparative analysis is provided among these methodologies concerning the design feasibility and the transmission performance of the optimized designs, and the computational efficiency. The outcomes highlight the effectiveness of stochastic techniques in achieving enhanced broadband acoustic performance with reduced computational demands and improved design practicality. The insights from this investigation demonstrate the potential of stochastic approaches in acoustic applications, especially when broadband acoustic performance is desired. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate some exact cosmological models in F (R , T ¯) gravity theory. We have considered the arbitrary function F (R , T ¯) = R + λ T ¯ where λ is an arbitrary constant, R , T ¯ are respectively, the Ricci-scalar curvature and the torsion. We have solved the field equations in a flat FLRW spacetime manifold for Hubble parameter and using the MCMC analysis, we have estimated the best fit values of model parameters with 1 - σ , 2 - σ , 3 - σ regions, for two observational datasets like H(z) and Pantheon SNe Ia datasets. Using these best fit values of model parameters, we have done the result analysis and discussion of the model. We have found a transit phase decelerating-accelerating universe model with transition redshifts z t = 0. 4438 - 0.0790 + 0.1008 , 0. 3651 - 0.0904 + 0.1644 . The effective dark energy equation of state varies as - 1 ≤ ω de ≤ - 0.5176 and the present age of the universe is found as t 0 = 13. 8486 - 0.0640 + 0.1005 , 12. 0135 - 0.2743 + 0.6206 Gyrs, respectively for two datasets. [ABSTRACT FROM AUTHOR]

We study the effect of modifying the equation of state parameter () of dark energy on the results of the previous study [1] (hereafter Paper II), in which dark energy was assumed to be a cosmological constant. As a first step, solving the equation of motion, we found a relation between mass, , and the turn-around radius, . Then, we obtained a relationship between the velocity, , and radius, . The relation was fitted to data of the groups used in Paper II to obtain the Hubble parameter, and the mass, of the groups. We observe a significant reduction of the mass, , comparing Paper II results (for which ) and the case , while the Hubble constant increases going from to . [ABSTRACT FROM AUTHOR]

In this paper, we present some new static and spherically symmetric solutions of the Einstein equation in which the matter sector is accounted for by a free Dirac–Born–Infeld field. Our novel spacetimes can describe either a black hole, a wormhole, or a naked singularity depending on certain boundary conditions. By tracking the dynamical gravitational collapse, we enlighten the importance of the isotropy of the pressure for having an horizon as a result, as required by the Cosmic Censorship Conjecture. Our new spacetime solutions, the amount of exotic matter, its "complexity", and the equation of state along the tangential direction are analytical and written in closed forms. We identify a taming of the breaking of the null energy condition, customary for wormhole spacetimes in General Relativity, along both the radial and tangential direction. We assess the astrophysical applicability and perform a comparative analysis between our solutions and other literature ones, by identifying an ISO-like density profile of the matter field, which provides a flattening of the rotation curves, by discussing the motion of test particles, and the shadow properties. In our model, those effects are interpreted as a manifestation of a topological defect, and since they can observationally mimic the signatures of other spacetimes, a study of the perturbations is performed within the quasi-normal modes formalism. Having identified the Reissner–Nordström-like quasi-resonance, our paper is intended also to provide some insights on which combinations of background and perturbation properties should be observed, for claiming the nature of astrophysical compact objects. [ABSTRACT FROM AUTHOR]

In this paper, we first derive the existence and uniqueness theorems for solutions to a class of generalized mean-field delay stochastic differential equations and mean-field anticipated backward stochastic differential equations (MFABSDEs). Then we study the stochastic maximum principle for generalized mean-field delay control problem. Since the state equation is distribution-depending, we define the adjoint equation as a MFABSDE in which all the derivatives of the coefficients are in Lions' sense. We also provide a sufficient condition for the optimality of the control. [ABSTRACT FROM AUTHOR]

In order to improve the performance of sliding mode observer in detecting the state of induction motor, a state detection method based on particle swarm optimization (PSO)-backstepping (BS)-sliding mode observer (SMO) is proposed in this paper. In this method, the controller is constructed and the parameters of the control rate are optimized, so that the tracking accuracy and robustness of the new observer are improved relative to conventional observer, exponential observer, PI and PID. Firstly, the state equation of the induction motor under stator and rotor winding fault and stator current sensor fault is established. Secondly, the new sliding mode observer is designed using the backstepping method based on the new reaching law. Then, the new fitness function and PSO is used to optimize the parameters of the new sliding mode observer. Finally, the simulation comparison experiment of stator current state detection is carried out under the simulated fault condition of induction motor. The feasibility of the method is verified by comparing the state tracking situation and the state detection error. The comparative experimental results show that the method has less jitter, stronger robustness, and higher state tracking accuracy when detecting stator current states under different faults. [ABSTRACT FROM AUTHOR]

In this article, we consider the optimal control problem governed by the wave equation in a 2-dimensional domain Ω ϵ in which the state equation and the cost functional involves highly oscillating periodic coefficients A ϵ and B ϵ , respectively. This paper aims to examine the limiting behavior of optimal control and state and identify the limit optimal control problem, which involves the influences of the oscillating coefficients. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the following nonlinear Choquard equation with prescribed L 2 -norm constraint - Δ u = λ u + (| x | - 1 ∗ | u | 2) u in Ω , u = 0 on ∂ Ω , ∫ Ω | u | 2 d x = a 2 , where a > 0 , λ ∈ R appears as an unknown Lagrange multiplier and Ω ⊂ R 3 is an exterior domain with smooth boundary ∂ Ω ≠ ∅ such that R 3 \ Ω is bounded. By using the splitting lemma for the unconstrained problem in exterior domains, we prove the compactness of Palais–Smale sequences corresponding to the above problem at higher energy levels. Then combining the barycentric function and Brouwer degree theory, we establish the existence of positive normalized bound states for any a > 0 provided that R 3 \ Ω is contained in a small ball and explain that the restriction on domain Ω can be equivalently transferred to a. In addition, under the radial setting of domain Ω , we use genus theory to obtain the existence and multiplicity of radial normalized solutions for any a > 0 . Finally, we point out that the main results can be extended to a general mass subcritical Choquard equation. [ABSTRACT FROM AUTHOR]

The critical state line (CSL) is important for characterizing soils' properties. However, particle breakage is inevitable for granular soils such as rockfill. Therefore, the impact of particle breakage on CSL has always been one of the main focuses. Unfortunately, it has not yet been adequately resolved how particle breakage influences CSL quantitatively. Large-scale drained triaxial shearing tests of rockfill materials under various initial gradations, initial void ratios and confining pressure have been conducted in this paper. It shows that particle breakage could result in decrements in both of the stress ratio and void ratio at the critical state. The equation for a critical state line with none breakage (NBCSL) was theoretically derived and demonstrated. The intercept and gradient of CSL and NBCSL are inextricably related because of particle breakage, which has been quantified as follows: the intercept of CSL is identical to NBCSL's, and the gradient of CSL is a breakage-related constant plus that of NBCSL. In other words, the CSL and NBCSL of rockfill materials has actually been described by a unified equation. Based on this, the translation and rotation of CSL induced by changing gradation and void ratio can be explained from the essence of particle breakage. [ABSTRACT FROM AUTHOR]

This paper explores the viability and stability of compact stellar objects characterized by anisotropic matter in the framework of f (Q , T) theory, where Q denotes non-metricity and T represents the trace of the energy-momentum tensor. We consider a specific model of this theory to obtain explicit expressions for the field equations governing the behavior of matter and geometry in this context. Furthermore, the Karmarkar condition is employed to assess the configuration of static spherically symmetric structures. The values of unknown constants in the metric potentials are determined through matching conditions of the interior and exterior spacetimes. Various physical quantities such as fluid parameters, energy constraints, equation of state parameters, mass, compactness and redshift are graphically analyzed to evaluate the viability of the considered compact stars. The Tolman–Oppenheimer–Volkoff equation is used to examine the equilibrium state of the stellar models. Moreover, the stability of the proposed compact stars is investigated through sound speed and adiabatic index methods. This study concludes that the proposed compact stars analyzed in this theoretical framework are viable and stable, as all the required conditions are satisfied. [ABSTRACT FROM AUTHOR]

Reservoir simulation is traditionally based on the assumption that water is an inert phase, while hydrocarbon components split into oil and gas phases. This approach is usually reasonable when modeling conventional hydrocarbon recovery, but specific applications may require accounting for mass exchange between the water and hydrocarbon phases. We here present the extension of our Graphics Processing Units (GPUs) compositional reservoir simulator (Esler et al. SPE J. 27(01), 597–612, 2021) to support gas-water equilibrium. Specifically, the Søreide and Whitson equation of state (EoS) (Søreide and Whitson Fluid Phase Equilib. 77, 217–240, 1992) was implemented to compute mutual solubilities of hydrocarbon/brine mixtures. The impact of salinity on phase equilibrium is accounted for, with salt being treated as an active tracer. The simulator uses a mass-variables formulation, meaning that little modifications to the construction of transport equations and Jacobian assembly was required; most of the required code changes are localized in the EoS module for the computation of component fugacities, and phase properties such as partial molar fractions and partial molar volumes. Treating salt as an active tracer instead of defining a further pseudo-component has an important advantage with the Søreide and Whitson EoS. If salinity changes as in water vaporization processes, our choice ensures that flash iterations can still be cast as a Gibbs Minimization problem with salinity being a constant parameter. On the contrary, salinity would change as flash iterations progress, jeopardizing the thermodynamic consistency of the phase equilibria. The overall reservoir simulation system of equations is still accurate to first order in time, at the cost of possibly slight volume imbalances at the end of converged timesteps. In this paper, we focused on CO 2 sequestration in saline aquifers, where solubility trapping is a key mechanism. The accuracy of our implementation with respect to conventional CPU ones is first demonstrated on a synthetic box model. We then select an open-access aquifer model (Gassnova 2016) to illustrate its applicability in an industrial setting. Finally, we show how being able to seamlessly run high resolution models allows for modeling of convective mixing. A key conclusion of this work is that the extreme performance of GPU-based reservoir simulation naturally transfers to new fields of study, which is critical when modeling saline aquifers whose extent is an order of magnitude larger than that of typical oil and gas fields. [ABSTRACT FROM AUTHOR]

The equation of state for an ideal gas is simple, which is P = n k B T . In the case of imperfect gases where mutual interactions among the constituents are important, pressure P can be expressed as the series expansion of density n with appropriate coefficients, known as virial coefficients B m . In this paper, we have obtained the first four virial coefficients for a model interaction potential Φ (r) using multidimensional Monte-Carlo integration and importance sampling methods. Next, we perform molecular dynamics simulations with the same Φ (r) for a many-particle system to obtain P as a function of T and n. We compare our numerical data with the virial equation of state. The plot of Mayer function f(r) as a function of radial distance r for Θ (r) for different inverse temperature β . [ABSTRACT FROM AUTHOR]

In this paper, we consider the scenario of a pure quark star which is completely composed of quarks in the pseudo-Wigner phase. The equation of state (EoS) of deconfined quark stars is studied in the framework of the two-flavor NJL model, and the self-consistent mean field approximation is employed by introducing a parameter α combining the original Lagrangian and the Fierz-transformed Lagrangian, L R = (1 − α) L + α L F , to measure the weights of different interaction channels. We assume deconfinement phase transition happens along with the chiral phase transition. Thus, due to the lack of description of confinement in the NJL model, the vacuum pressure is set to confine quarks at low densities, which is the pressure corresponding to the critical point of chiral phase transition. We find that the bag constant shifts from (130 MeV) 4 to (150 MeV) 4 as α grows. When α is around 0.9, the mass-radius relations of deconfined quark stars can meet the requirement of pulsar observations. In addition, the tidal deformability Λ is found to range in 253 – 482, which satisfies the astronomical constraint of Λ < 800 for 1.4-solar-mass neutron stars. [ABSTRACT FROM AUTHOR]

The paper studies different observational features in the case of a specific cubic gravity theory, based on third order contractions of the Riemann tensor. Considering viable cosmic chronometers data, baryon acoustic oscillations, and supernovae, we analyze the viability of such a theoretical model, obtaining specific constraints for different parameters in the current scenario. It is shown that the present extension of the Λ CDM cosmological model is compatible with recent data sets. The results indicate that the dark energy equation of state is exhibiting a phantom regime in the near past in the case of the best fitted values, a behavior which is in agreement with various phenomenological studies. [ABSTRACT FROM AUTHOR]

This paper focuses on the empirical modeling for viscosities of a hydrofluoroolefin refrigerant, R1234ze(Z), which is considered an environmentally friendly alternative to hydrofluorocarbons. The refrigerant has favorable thermophysical properties and a low global warming potential. A new fundamental equation of state (EoS) for R1234ze(Z) was developed in 2019, which aligns with the recent trends of developing accurate fundamental equations of state. However, previously published experimental viscosity data were reported using an old equation of state of the fluid. In this paper, the revised experimental viscosity data based on the latest EoS has been reported for R1234ze(Z). Additionally, the viscosity model of this fluid is presented using the extended corresponding states (ECS) and modified fluid-specific residual entropy scaling (RES) techniques. By using the adjustable parameters, the ECS and the modified fluid-specific RES transport equations can represent the experimental data within reported uncertainties. The average absolute deviations (AAD) for viscosity were found to be 1.40% and 1.65% using the ECS and the RES method, respectively. This study also highlights the importance of using the most accurate EoS when reporting experimental data, especially when formulating transport property models based on these techniques. [ABSTRACT FROM AUTHOR]

The nature of equation of state for the matter in the neutron star plays an important role in determining its maximal mass. In addition, it must comply with the condition of causality. Noting that the central density of a maximally massive neutron star is well above the nuclear saturation density, a deconfined quark core in the central region is motivated in this paper. We analyze this scenario by employing the MIT bag model to represent the core region and one of the unified equations of state for the region outside the core. Such a combination is found to solve the problem of causality violation. In each case of the combined equations of state, the radial profile of ρ r 2 displays a peak and the dominant contribution to the total mass of the star comes from the region around the peak value of ρ r 2 , whereas the contribution is small from the regions near the center and the surface. This peak occurs in the region of hadronic matter for the combinations considered in this paper. Importantly, we find that the position of the peak in ρ r 2 is well-correlated with the maximal mass—the highest value of 1.98 M ⊙ obtains for the case with the peak occurring farthest from the center. This gravitational threshold being obtained for a non-rotating neutron star, we expect the threshold to lie well above 2 M ⊙ for a rapidly rotating neutron star, that may explain the existence of massive pulsars from recent astronomical observations. [ABSTRACT FROM AUTHOR]

In this paper, the emergent universe model (EU) is explored (as per Mukherjee e t a l. ) in a flat scenario with equation of state (E o S) p = B ρ − A ρ 1 2 (where A and B are constants). Here, the temperature function is evaluated in terms of the EoS parameters and redshift under the conditions of balanced particle creation and annihilation. To examine the thermodynamic evolution and find a viable EU model, constraints on its EoS parameters are determined. First, constraints on A s , and B (where A s = A ρ e u 0 1 2 and ρ e u 0 is the present energy density) are obtained from the acceptable transition redshift limit z t r and decoupling temperature limit T d as A s ≈ (0.84 − 1.07) and B ≈ (0.38 − 0.42) for the general EU model. Finally, stricter constraints on z t r are drawn from recent T (z) − z and observed Hubble data (OHD). These z t r and T d values are then utilized to obtain acceptable limits on A s , and B . On average, the acceptable limits on z t r , A s , and B are 0.79 ± 0.03 (in the 1 σ error limit), ≈ (1.11 − 1.15) and ≈ (0.41 − 0.43) , respectively, for the general EU model. In the B = 1 3 model, obtained value z t r = 0.71 ± 0.01 (at the 1 σ level). The present values of the EoS parameters are determined, and the viability of the models is examined with plots of the deceleration parameter (q ), equation of state (ω ) and squared adiabatic sound speed ( c s 2 ) with redshift (z ). The distance modulus (μ ) of this EU model is compared with the HIIG and Union2.1 data. The models with B (= − 1 3 , 0) , are not suitable at all according to the present analysis, whereas, the B = 1 3 model is quite similar to the observations. [ABSTRACT FROM AUTHOR]

In this paper, we study the construction of black string thin-shell wormhole models with generalized Chaplygin gas under the effect of minimally coupled modified gravity with quadratic correction in the Ricci scalar using the "cut and paste" method. We use junction conditions in geometrical representation for matching between two space-times across the hypersurface Σ , recently computed by Rosa (Phys Rev D 103:104069, 2021). In this scenario, we assumed the matter sector is demonstrated by isotropic perfect fluid distribution. We determine the distinct components of Lanczos equations in the context of a considered quadratic model by employing generalized Chaplygin gas. We investigate static stable solutions utilizing radial perturbation in the perspective of the considered gravity. The positive value of the second-order derivative of potential around the throat radius might be interpreted as the stability criterion. For the widest feasible range of model parameters, the impact of mass and equation of state parameter is also investigated via the constructed equations. We also examine the stable and unstable static black string thin-shell wormhole solutions and illustrate them graphically. [ABSTRACT FROM AUTHOR]

In this paper, we study the viability and stability of anisotropic compact stars in the context of f (Q) theory, where Q is non-metricity scalar. We use Finch–Skea solutions to investigate the physical properties of compact stars. To determine the values of unknown constants, we match internal spacetime with the exterior region at the boundary surface. Furthermore, we study the various physical quantities, including effective matter variables, energy conditions and equation of state parameters inside the considered compact stars. The equilibrium and stability states of the proposed compact stars are examined through the Tolman–Oppenheimer–Volkoff equation, causality condition, Herrera cracking approach and adiabatic index, respectively. It is found that viable and stable compact stars exist in f (Q) theory as all the necessary conditions are satisfied. [ABSTRACT FROM AUTHOR]

Several thermodynamic models have been proposed in literature to estimate the amount of asphaltene precipitation (AAP); however, they usually need several many inputs, and the characterization of the samples is often not accurate enough. This paper compares the performance of four data-driven methods, including Extreme Gradient Boosting (XGBoost), Multi-Layer Perceptron (MLP), Least Squares – Support Vector Machine coupled with a Particle Swarm Optimization (LSSVM-PSO), and Multilinear Regression (MLR), to predict the AAP as a function of oil composition, API, SARA fractions, solvent molar mass, dilution ratio, pressure, and temperature. The dataset includes 1703 samples, 20% of which is used for testing. An innovative nested K-fold cross-validation is also proposed to tune the hyperparameters of the data-driven methods. The contributions of this work include a comparison of the performance of different data-driven methods to estimate the AAP and introducing a novel cross-validation technique. Data-driven results are compared with those of the Perturbed Chain – Statistical Associating Fluid Theory Equation of State. The results reveal the superiority of the data-driven methods over the thermodynamic model, except for the MLR. Meanwhile, XGBoost showed the best performance among other data-driven methods. Coefficients of determination of 99.57%, 98.96%, 98.17%, 85.23%, and 90.40% were achieved by the XGBoost, LSSVM-PSO, MLP, MLR, and the thermodynamic model, respectively. Finally, it is shown that the proposed nested K-fold cross-validation positively affected the generalization of the data-driven methods. The findings of this study can help engineers select reliable methods to estimate the AAP and improve their generalization using the nested K-fold cross-validation. [ABSTRACT FROM AUTHOR]

This paper reviews the 40-year evolution and application of the magnetic suspension balance (MSB) and discusses some challenging issues of the technique. An MSB, as defined herein, is a magnetic suspension coupling (MSC) connected to an analytical balance. With an MSC, an object can be weighed in a different environment than the balance itself, making it possible for contactless weighing. Over the past 40 years, the MSB has been commonly used in research areas requiring accurate object weighings, notably gas density measurements by MSB-based densimeters and gas adsorption measurements by MSB-based sorption analyzers. More than 15 MSB-based densimeters have been built to date; these are generally called two-sinker densimeter and single-sinker densimeter. They have produced highly accurate density data of many pure fluids and fluid mixtures. These data serve as the basis for the development of reference equations of state, which play an essential role in various industrial and scientific areas. Moreover, such systems are central to the metrology program of many countries. The MSB technique is also very successful in adsorption science: more than 85 MSB-based sorption analyzers have been set up in over 20 countries. The number of new MSB-based sorption analyzers, and peer-reviewed publications resulting from them, are both increasing exponentially since 2004. They have produced highly reliable gas adsorption data at high pressures for many applications, mainly in the energy and environmental sectors. Although further development of innovative instruments based on the MSB is threatened by the proprietary nature of MSB technology, the development will continue, e.g., toward cryogenic measurements and a more compact design. [ABSTRACT FROM AUTHOR]

Recently, the authors of the current paper established in Chen et al. (Calc Var Partial Differ Equ 59:1–38, 2020) the existence of a ground-state solution to the following bi-harmonic equation with the constant potential or Rabinowitz potential: 0.1 (- Δ) 2 u + V (x) u = f (u) in R 4 , when the nonlinearity has the special form f (t) = t (exp (t 2) - 1) and V (x) ≥ c > 0 is a constant or the Rabinowitz potential. One of the crucial elements used in Chen et al. (Calc Var Partial Differ Equ 59:1–38, 2020) is the Fourier rearrangement argument. However, this argument is not applicable if f(t) is not an odd function. Thus, it still remains open whether the Eq. (0.1) with the general critical exponential nonlinearity f(u) admits a ground-state solution even when V(x) is a positive constant. The first purpose of this paper is to develop a Fourier rearrangement-free approach to solve the above problem. More precisely, we will prove that there is a threshold γ ∗ such that for any γ ∈ (0 , γ ∗) , the Eq. (0.1) with the constant potential V (x) = γ > 0 admits a ground-state solution, while does not admit any ground-state solution for any γ ∈ (γ ∗ , + ∞) . The second purpose of this paper is to establish the existence of a ground-state solution to the Eq. (0.1) with any degenerate Rabinowitz potential V vanishing on some bounded open set. Among other techniques, the proof also relies on a critical Adams inequality involving the degenerate potential which is of its own interest. [ABSTRACT FROM AUTHOR]

Inflationary spacetimes have been argued to be past geodesically incomplete in many situations. However, whether the geodesic incompleteness implies the existence of an initial spacetime curvature singularity or whether the spacetime may be extended (potentially into another phase of the universe) is generally unknown. Both questions have important physical implications. In this paper, we take a closer look at the geometrical structure of inflationary spacetimes and investigate these very questions. We first classify which past inflationary histories have a scalar curvature singularity and which might be extendible and/or non-singular in homogeneous and isotropic cosmology with flat spatial sections. Then, we derive rigorous extendibility criteria of various regularity classes for quasi-de Sitter spacetimes that evolve from infinite proper time in the past. Finally, we show that beyond homogeneity and isotropy, special continuous extensions respecting the Einstein field equations with a perfect fluid must have the equation of state of a de Sitter universe asymptotically. An interpretation of our results is that past-eternal inflationary scenarios are most likely physically singular, except in situations with very special initial conditions. [ABSTRACT FROM AUTHOR]

This paper describes the thermodynamic properties of zirconium in a high-pressure region. The available experimental data on isothermal and shock compression of this metal are summarized in the form of a simple model that specifies a pressure function of the specific volume and specific internal energy. The results of calculations of the thermodynamic characteristics of the body-centered cubic crystalline phase and zirconium melt are presented in comparison with the available experimental data in the studied range of thermodynamic parameters. The resulting equation of state can be used in the numerical modeling of adiabatic processes at high energy concentrations. [ABSTRACT FROM AUTHOR]

This paper presents a new method for determining the parameters of the Jones–Wilkins–Lee (JWL) equation of state of explosives on the basis of experimental data. The experimentally obtained values of pressures and mass velocities on the expansion–deceleration adiabat of explosion products are used as reference points. The parameter values of the JWL equation of state are determined using an iterative algorithm. [ABSTRACT FROM AUTHOR]

Phase field modeling finds utility in various areas. In optimization theory in particular, the distributed control and Neumann boundary control of phase field models have been investigated thoroughly. Dirichlet boundary control in parabolic equations is commonly addressed using the very weak formulation or an approximation by Robin boundary conditions. In this paper, the Dirichlet boundary control for a phase field model with a non-singular potential is investigated using the Dirichlet lift technique. The corresponding weak formulation is analyzed. Energy estimates and problem-specific embedding results are provided, leading to the existence and uniqueness of the solution for the state equation. These results together show that the control to state mapping is well defined and bounded. Based on the preceding findings, the optimization problem is shown to have a solution. [ABSTRACT FROM AUTHOR]

This is an important and natural question as the spacetime shear, inhomogeneity and tidal effects are all intertwined via the Einstein field equations. Though many solutions with these properties exist in the literature, in this paper we identify, via a geometrical analysis, the important physical reason behind these solutions. We show that such scenarios are possible for limited classes of equations of state that are solutions to a highly nonlinear and fourth order differential equation. To show this, we use a covariant semitetrad spacetime decomposition and present a novel geometrical classification of shear-free locally rotationally symmetric perfect fluid self-gravitating systems, in terms of the covariantly defined fluid acceleration and the fluid expansion. Noteworthily, we deduce the governing differential equation that gives the possible limited equations of state of matter. [ABSTRACT FROM AUTHOR]

Recent observations have shown that our universe is currently undergoing a period of accelerating expansion. In view of the astrophysical data we find that the equation of state of the dark energy lies in a narrow range around w = −1. In this paper we discuss the possibility of treating a spinor field as dark energy to realize the equation of state parameter w < −1 or w > −1. We derive the main equations which govern the evolution of the universe and then discuss the evolution and attractor property of this model, and show a late time de Sitter attractor. Finally we rewrite them with the observable quantities. [ABSTRACT FROM AUTHOR]

In the present paper, a new equation for the dynamic viscosity of propane is presented, which is suitable for the application in mixture models. The dilute-gas contribution was adopted from Vogel and Herrmann (J Phys Chem Ref Data 45:043103, 2016). The residual part is an empirical approach designed following the example of thermodynamic Helmholtz equations of state. With this functional form, an approach is proposed, which will allow to combine pure-fluid equations in the manner of high precision Helmholtz equations of state in a multifluid mixture model in the future. The parameters of the equation are adjusted to experimental data, so that the data are mostly reproduced within their experimental uncertainty. The present equation is valid in a temperature range from 90 K to 525 K with a maximum pressure of 145 MPa. [ABSTRACT FROM AUTHOR]

The rapid development of industrial technology and the increasing computational power have provided the possibility to improve the accuracy of multiphase flow field simulation studies. In addition, the chaotic nature of boiling phenomena increases the difficulty of experimental studies, and there is an urgent need to improve the computational methods to meet the needs of industrial applications. This paper presents a comprehensive review of the published literatures on the study of pool boiling using computational methods in the last two decades, including macroscopic-scale computational methods based on continuous medium theory, mesoscopic-scale methods based on lattice Boltzmann method (LBM), and nanoscale molecular dynamics. The advantages and disadvantages of different approaches to study bubble dynamics, including nucleation mechanisms, bubble growth, bubble detachment, and nucleation sites density, are evaluated based on different modeling features and phase change mechanisms. After considering micro-layer evaporation, wall convection, and transient conduction in the macroscopic scale model, the shape diffraction of isolated bubbles and departure diameters obtained by the macroscopic approach agree well with experimental data, and the Rensselaer Polytechnic Institute model achieves promising results for the simulation of low concentration nanofluids as well. The coupling of Shan–Chen model (S–C model) and Peng–Robinson (P–R) equation of state and considering the thermal lattice Boltzmann approach can effectively solve the phase separation problem, and the simulation results can match the theoretical analysis with the highest accuracy. In addition to the above results, a complete boiling heat transfer curve was successfully simulated for the first time using the LBM method. Molecular dynamics provides an in-depth mechanistic explanation of nucleation of nanobubbles in microstructures and on different wettability surfaces in terms of free energy and pressure fluctuations. Although different methods have achieved different degrees of success in pool boiling simulations, problems of boundary capture and heat and mass transfer near macroscopic methods, mesh accuracy in mesoscopic methods, treatment of density ratios and error terms, and accuracy of gas–liquid interfaces in molecular dynamics methods still limit the development of numerical computation. Therefore, this review also presents the challenges and future directions of simulation methods for modeling at different scales from the authors' perspective. Multi-scale coupling methods will be highlighted as an important goal to accommodate the development of advanced pool boiling simulations. [ABSTRACT FROM AUTHOR]

Tolman VII solution (Tolman in Phys Rev 55(4):364, 1939) is an exact analytic solution to the Einstein field equations describing the space-time of a static spherically symmetric distribution of matter. The solution has been shown to be capable of describing the interior of compact objects like neutron stars. Generalized (Raghoonundun and Hobill in Phys Rev D 92(12):124005, 2015) and modified (Jiang and Yagi in Phys Rev D 99(12):124029, 2019) versions of the solution are also available in the literature, which have been subsequently developed to accommodate a wide range of neutron star EOS. The stability of the modified Tolman VII solution has recently been analyzed (Posada et al in Phys Rev D 103(10):104067, 2021), which provides a critical value of the adiabatic index above which the stellar configuration becomes unstable against radial oscillations. In this paper, making use of the generalized version of the Tolman VII solution, we prescribe an upper bound on the compactness (M/R) beyond which the star becomes unstable against radial oscillations (Chandrasekhar in Phys Rev Lett 12(4):114, 1964). Our study brings to attention the role of model parameters in the generalized Tolman VII solution. The analysis also provides new insight into the role of inhomogeneity of the matter distribution vis-a-vis equation of state (EOS) on the compactness of a relativistic star. [ABSTRACT FROM AUTHOR]

Models of neutron stars are considered in the case of a uniform density distribution. An algebraic equation, valid for any equation of state, is obtained. This equation allows one to find the approximate mass of a star of a given density without resorting to the integration of differential equations. The solutions presented in the paper for various equations of state, including more realistic ones, differ from the exact solutions obtained by the numerical integration of differential equations by at most 20%. [ABSTRACT FROM AUTHOR]

In this paper, we exhibit analytical solutions for the evolution of the mass of an astrophysical object accreting cosmic fluid according to the Bondi–Hoyle–Lyttleton mechanism. The key assumption of this model is that the adiabatic speed of sound within the accreted fluid directly affects the rate of change of the mass of the accreting object. We consider different literature equations of state, as the (Modified) Berthelot, Logotropic, generalized polytropic of index n, and quadratic models. We assume the fluid to evolve either according to General Relativity or to the Randall-Sundrum type 1 gravity model far away from the astrophysical object in an asymptotically Friedman universe. We claim that this accretion mechanism is unlikely to affect the mass-radius relationship of the photon sphere beyond the Schwarzschild one at the present time, and that the critical point of accretion in the (Modified) Berthelot fluid flow is hidden by the event horizon. Our work belongs to the broader research line investigating the interplay of small-scale and large-scale Physics in the modeling of gravitational phenomena. [ABSTRACT FROM AUTHOR]

In this paper, we adopt minimal gravitational decoupling scheme to extend a non-static spherically symmetric isotropic composition to anisotropic interior in f (R , T , R ab T ab) theory. A geometric deformation is applied only on g rr metric component through which the modified field equations are separated into two sets, each of them correspond to their parent (seed and newly added) source. An isotropic model suggested by the Friedmann–Lemaitre–Robertson–Walker metric is adopted to reduce the unknowns in the first set. We then obtain an isotropic solution by making use of a linear equation of state and a particular form of the scale factor. A density-like constraint is chosen to solve the other sector containing the deformation function and multiple components of an additional matter source. Further, the graphical interpretation of the developed model is carried out to analyze how a decoupling parameter and modified gravity influence the evolutionary phases of the universe. It is concluded that only the radiation-dominated era meets stability criteria everywhere in this matter-geometry coupled theory. [ABSTRACT FROM AUTHOR]

This paper introduces a three-stable locally active memristor whose internal state equation is composed of sign functions related to internal state and voltage. The memristor has three asymptotically stable equilibrium points and a locally active region. The non-volatility and local activity of the memristor are verified by the POP (power-off plot) and the DC V - I plot, respectively. Furthermore, the proposed memristor has a petal-like continuous DC V - I curve, and thus it also is a new type of 4-lobe Chua corsage memristor. Biasing the memristor at its locally active region and connecting it in series with an inductor, a second-order oscillator is developed in this paper. The required inductance and the oscillation frequency are determined by analyzing the admittance function Y(iw,V) of memristor's small-signal equivalent circuit. Based on Hopf bifurcation theory and the pole-zero diagram of the composite admittance function Y c (s , Q) , the dynamics of the resultant oscillator circuit are analyzed in detail. In addition, a third-order chaotic oscillation circuit is obtained by adding a capacitor to the second-order oscillation circuit. Its dynamical characteristics are analyzed through Lyapunov exponent spectrum, bifurcation diagram and dynamic diagram. Finally, simulation results based on Multisim are given to verify the correctness of the numerical simulation. [ABSTRACT FROM AUTHOR]

For a vibrating system where the pendulum and vibrators are coupled together, the relevant dynamic model and the corresponding synchronization problem are rarely studied, due to its complex dynamic coupling relationships. In this paper, a vibrator–pendulum coupling system is proposed to study its synchronization principle; here, the pendulum is driven by the synchronous motion of the two vibrators directly. By exploiting the system motion differential equations and their vibration responses, the synchronization criterion of the two vibrators is deduced via the average method. After that, the stability criterion for the synchronous states is presented according to the convergence and divergence characteristics of the perturbed differential equation in the balanced state. Based on the theoretical results, the synchronous stable states and motion characteristics of the system under different parameter conditions are discussed by numerical qualitative analyses, and the reasonable parameters matching principles in designing the real vibrating machine are provided. A series of numerical simulations and experiments are further given to examine the validity of the theoretical methods and the obtained results. The dynamic model and research results presented in this paper can be applied to design a new kind of vibrating jaw crusher; in this case, the pendulum is served as the moving jaw and can work with its swing motion trajectory under the premise of the stable zero-phase difference between the two vibrators. [ABSTRACT FROM AUTHOR]

As is well known, average-cost optimality inequalities imply the existence of stationary optimal policies for Markov decision processes with average costs per unit time, and these inequalities hold under broad natural conditions. This paper provides sufficient conditions for the validity of the average-cost optimality equation for an infinite state problem with weakly continuous transition probabilities and with possibly unbounded one-step costs and noncompact action sets. These conditions also imply the convergence of sequences of discounted relative value functions to average-cost relative value functions and the continuity of average-cost relative value functions. As shown in this paper, the classic periodic-review setup-cost inventory control problem with backorders and convex holding/backlog costs satisfies these conditions. Therefore, the optimality inequality holds in the form of an equality with a continuous average-cost relative value function for this problem. In addition, the K-convexity of discounted relative value functions and their convergence to average-cost relative value functions, when the discount factor increases to 1, imply the K-convexity of average-cost relative value functions. This implies that average-cost optimal (s, S) policies for the inventory control problem can be derived from the average-cost optimality equation. [ABSTRACT FROM AUTHOR]

This paper derives necessary optimality conditions for a certain class of optimal control problems without linearity or convexity assumptions. The optimal control problem has a general objective function of integral type and a finite number of isoperimetric type constraints. For proving the main result derived in this paper, the Lagrange function and the control Hamiltonian are introduced and an adjoint differential equation is stated. In addition, we formulate some examples where the derived necessary optimality conditions are applied. [ABSTRACT FROM AUTHOR]

This paper presents new wide-ranging correlations for the viscosity and thermal conductivity of 1-hexene based on critically evaluated experimental data. The viscosity correlation is valid from the triple point to 580 K and up to 245 MPa pressure, while the thermal conductivity is valid from the triple point to 620 K and 200 MPa pressure. Both correlations are designed to be used with a recently published equation of state that extends from the triple point to 535 K, at pressures up to 245 MPa. The estimated uncertainty (at a 95 % confidence level) for the viscosity is 2 % for the low-density gas (pressures below 0.5 MPa), and 4.8 % over the rest of the range of application. For thermal conductivity, the expanded uncertainty is estimated to be 3 % for the low-density gas and 4 % over the rest of the range. [ABSTRACT FROM AUTHOR]

Hard thermal loops describe how soft gauge fields are screened and damped in hot plasmas. As such they are used to calculate transport coefficients, Sphaleron rates, equations of state, and particle production. However, most calculations are done using one-loop hard thermal loop self-energies. And two-loop contributions can be large. To that end this paper provides vector two-loop self-energies for generic models: any scalar, fermion, or vector representation; and all possible renormalizable terms. Several examples are given to showcase the results. Two-loop results for higher-point functions are also given. [ABSTRACT FROM AUTHOR]

Gas injection can increase oil recovery because the gas–oil interfacial tension is less than the water–oil interfacial tension (IFT) and tends to zero in the miscibility state. However, little information has been provided on the gas–oil movement and penetration mechanisms in the fracture system at the porosity scale. The IFT of oil and gas in the porous medium changes and can control oil recovery. In this study, the IFT and the minimum miscibility pressure (MMP) are calculated using the cubic Peng-Robinson equation of state that has been modified using the mean pore radius and capillary pressure. The calculated IFT and MMP change with the pore radius and capillary pressure. To investigate the effect of a porous medium on the IFT during the injection of CH4, CO2, and N2 in the presence of n-alkanes and for validation, measured experimental values in references have been used. According to the results of this paper, changes in IFT vary in terms of pressure in the presence of different gases and, the proposed model has good accuracy for measuring the IFT and the MMP during the injection of hydrocarbon gases and CO2. In addition, as the average radius of the pores gets smaller, the interfacial tension tends to lower values. This effect is different with increasing the mean size of interstice in two different intervals. In the first interval, i.e. the Rp from 10 to 5000 nm, the IFT changes from 3 to 10.78 mN/m and in the second interval, i.e. the Rp from 5000 nm to infinity, the IFT changes from 10.78 to 10.85 mN/m. In other words, increasing the diameter of the porous medium to a certain threshold (i.e. 5000 nm) increases the IFT. As a rule, changes in IFT affected by exposure to a porous medium affect the values of the MMP. In general, IFT decreases in very fine porous media, causing miscibility at lower pressures. [ABSTRACT FROM AUTHOR]

In this study, a wheeled mobile manipulator was modeled while considering the case of wheel-ground slippage. Considering the whole system, the number of states in the dynamic system equation was reduced by the kinematic solution, which facilitates the control of the system. For the system state equation, the improved sliding mode control method was applied, a flush continuous control term and a super-twisting algorithm were used to achieve the improved sliding mode control, and the gain of the super-twisting algorithm was adaptively controlled. The modeling error in the subsystem and the uncertain slippage were approximated by a neural network. The middle layer weights of the neural network were updated by the adaptive control law, and the stability of the system was demonstrated by a quadratic Lyapunov function. The simulation results show the superiority of the control method proposed in this paper by comparing them with results for the traditional sliding-mode control method and the improved sliding-mode control method. [ABSTRACT FROM AUTHOR]

The mass of compact objects in General Relativity (GR), which as is well known, is obtained via the Tolman–Oppenheimer–Volkov (TOV) equations, is a well defined quantity. However, in alternative gravity, this is not in general the case. In the particular case of f(T) gravity, where T is the scalar torsion, some authors consider that this is still an open question, since it is not guaranteed that the same equation used in TOV GR holds. In this paper we consider such an important issue and compare different ways to calculate the mass of compact objects in f(T) gravity. In particular, we argue that one of them, the asymptotic mass, may be the most appropriate way to calculate mass in this theory. We adopt realistic equations of state in all the models presented in this article. [ABSTRACT FROM AUTHOR]

In this paper, modeling for a current mode controlled (CMC) flyback LED driver with a stabilizing ramp is performed in a step-by-step procedure. Discrete time state equations for the system are derived and linearized with respect to a steady-state operating point. At this operating point, the switching control law, the condition that determines the duty ratio, is also linearized. In the next step, a closed-loop system model is derived by combining the two models of the flyback driver and the switching control law. The root locus analysis in the z-plane is used to investigate the characteristics of the combined linearized system and obtain design guidelines for feedback loops. The feasibility of the proposed design is confirmed through the experimental results for the CMC flyback LED driver. [ABSTRACT FROM AUTHOR]