Search Results (17)

Centrifugal compressors are critical assets in the oil and gas, petrochemical, and power generation industries, where unplanned downtime results in severe economic and safety consequences. Despite the application of digital twin technology for predictive maintenance, existing approaches struggle to combine accurate degradation modeling with formal assurance evidence that regulators and operators demand before trusting machine learning-augmented systems. This paper proposes a hybrid digital twin framework whose architecture is structured around a formal safety case template, addressing both the accuracy and the trustworthiness challenges simultaneously. The methodology couples a first-principles thermodynamic model with a neural-network residual learner, and the complete system is organized through a design-stage safety case constructed in Goal Structuring Notation. The design stage identifies the requirements for operational deployment. Validation through a simulation study on a one-year synthetic operational dataset shows that the hybrid model reduces root-mean-square prediction error by over 50% for both pressure ratio and polytropic efficiency compared to the physics-only baseline. The anomaly detection module, presented here as a proof of concept, achieves 92% recall in identifying injected faults, and a composite health index tracks the progression of fouling, erosion, and seal wear over the simulated service life. This study is purely theoretical, with no experimental measurements conducted. It demonstrates the structural viability and coherence of the proposed framework within a controlled environment, providing a solid theoretical and computational foundation for future physical validation efforts. These findings provide preliminary evidence that embedding a structured safety argument into the design of a hybrid digital twin is technically feasible and beneficial for building the confidence needed to deploy such systems in safety-critical industrial environments. Full article

The paper investigates the structural properties of self-gravitating fluid spheres composed of a dilute, homogeneous, and ultracold Bose gas, assuming repulsive, short-range interactions. For the first time, the Lee–Huang–Yang (LHY) correction is incorporated to the standard polytropic equation-of-state with index $n=1$, which extends beyond the Hartree mean-field approximation by accounting for quantum fluctuations. The findings indicate that this correction significantly affects the mass–radius relationships and other properties of condensate dark stars, such as the compactness factor and tidal Love numbers. Notably, the impact of the LHY correction is more pronounced for equations of state that support higher maximum stellar masses. Full article

This paper presents a numerical model of the discharge cycle of a subsea open-cycle hydro-pneumatic energy storage system intended for offshore long-duration energy storage. During discharge at high pressure ratios, air expansion can lead to significant cooling, penalising system performance. The modelled system comprises a subsea pipeline which stores compressed air coupled to a pair of reciprocating liquid pistons that expand the air to drive a hydraulic motor. The study focuses on the transient thermal behaviour of the system during air expansion at high pressure ratios, starting from an initial pressure of 200 bar in the subsea air receiver pipeline down to a target pre-charge pressure of 80 bar. A parametric study investigates the influence of the output hydraulic power and the convective heat transfer coefficients, assessing the ability of the system to approach ideal isothermal expansion. The results indicate that for the high pressure ratios considered and using currently available heat transfer coefficient correlations, significant cooling occurs within the subsea liquid piston pipeline. For a baseline output hydraulic power of 500 kW, a polytropic index of 1.23 and a work ratio just below 64% were obtained. However, the results also show that by reducing the output hydraulic power and integrating internal heat transfer mechanisms, this cooling can be substantially mitigated, resulting in quasi-isothermal conditions with work ratios higher than 86%. Full article

We present a Physics-Informed Neural Network (PINN) approach to solving the Lane–Emden equation, a model used to describe polytropic stars’ behavior in astrophysics. The equation is reformulated as a two-dimensional problem; we treat both the radial coordinate and polytropic index as inputs for the neural network. In order to improve stability and accuracy, we introduced coordinate embedding via Random Fourier Features, residual blocks, and gating mechanisms. Experiments show that our neural networks outperform other traditional numerical methods, including Monte Carlo simulations and standard fully connected PINNs. We achieve accurate predictions for both trained and extrapolated polytropic indices. The code used to implement our method is publicly available providing researchers with the resources to replicate and extend our work. Full article

The inlet operating conditions of centrifugal compressors in natural gas storage reservoirs, as well as the natural gas composition, continuously vary over time, significantly impacting compressor performance. To analyze the influence of these factors on centrifugal compressors, a method for converting the performance curves of centrifugal compressors under actual operating conditions has been established. This performance conversion process is implemented through a custom-developed program, which incorporates the polytropic index and exhaust temperature calculations. Verification results show that the conversion error of this method is within 2%. Based on the proposed performance prediction method for non-similar operating conditions, the effects of varying inlet temperatures, pressures, and natural gas compositions on compressor performance are investigated. It is observed that an increase in inlet temperature results in a decrease in compressor power and pressure ratio; an increase in inlet pressure leads to higher power consumption, while the pressure ratio varies with the flow rate at the operating point; and as the average molar mass of natural gas decreases, both the pressure ratio and power exhibit a certain degree of reduction. Full article

We model compact objects of known stellar mass and radius made of isotropic matter within Einstein’s gravity. The interior solution describing hydrostatic equilibrium we are using throughout the manuscript corresponds to the Tolman IV exact analytic solution obtained a long time ago. The three free parameters of the solutions are determined by imposing the matching conditions for objects of known stellar mass and radius. Finally, using well established criteria, it is shown that, contrary to the Kohler Chao solution, the Tolman IV solution is compatible with all requirements for well-behaved and realistic solutions, except for the relativistic adiabatic index that diverges at the surface of stars. The divergence of the index Γ may be resolved, including a thin crust assuming a polytropic equation of state, which is precisely the case seen in studies of neutron stars. To the best of our knowledge, we model here for the first time the recently discovered massive pulsar PSR J0740+6620 and the strangely light HESS compact object via the Tolman IV solution. The present work may be of interest to model builders as well as a useful reference for future research. Full article

We investigate the Chandrasekhar mass limit of white dwarfs in various models of $f\left(R\right)$ gravity. Two equations of state for stellar matter are used: the simple relativistic polytropic equation with polytropic index $n=3$ and the realistic Chandrasekhar equation of state. For calculations, it is convenient to use the equivalent scalar–tensor theory in the Einstein frame and then to return to the Jordan frame picture. For white dwarfs, we can neglect terms containing relativistic effects from General Relativity and we consider the reduced system of equations. Its solution for any model of $f\left(R\right)=R+\beta R^m$ ($m\ge 2$, $\beta >0$) gravity leads to the conclusion that the stellar mass decreases in comparison with standard General Relativity. For realistic equations of state, we find that there is a value of the central density for which the mass of a white dwarf peaks. Therefore, in frames of modified gravity, there is a lower limit on the radius of stable white dwarfs, and this minimal radius is greater than in General Relativity. We also investigate the behavior of the Chandrasekhar mass limit in $f\left(R\right)$ gravity. Full article

This study aims to optimize and assess the quality of the sorting process into homogeneous size classes of dried and chopped medicinal plants, by obtaining multivariate regression functions of polytropic and polynomial forms. Assessment of sorting quality was carried out by calculating the average coefficient of separation. The influence of several important factors (material feed rate on the sieve, sieve dimensions, sieve inclination angle, sieve oscillation frequencies) on the sorting process was followed. Research was carried out on dried nettle herb (Urtica dioica) using a plant sorter with plane sieves, which allowed for modifying some constructive and functional parameters, making it possible to obtain optimal values. The results showed that the dry nettle herb chopped in bulk at 4 mm, with a moisture of 11.45%, was optimally sorted (index of average separation coefficient, 0.922) if the following parameters were met: drive mechanism speed n = 1000 rpm; sieve inclination angle α = 12.08°; material-specific flow q = 4 kg/dm·h; recommended sieve length L = 1.4 m. It was observed that at high rates, the average coefficient of separation decreased with the decrease in the sieve drive mechanism speed, and when the inclination angle of the sieve decreased, the average coefficient of separation increased. The maximum average deviation of the average separation coefficient was 5.5% for the polytropic function. The new advanced processing technologies of medicinal plants involve the short-term production of quality-finished products, thus supporting the processors of medicinal plants and the consumers of phytotherapeutic products with beneficial effects for health. Full article

To investigate the static characteristics of aerostatic journal bearings with porous bushing, the flow model—in which the compressibility of lubricating gas is considered—is established based on the Reynolds lubrication equation, Darcy equation for porous material, and continuity equation. With the finite difference method, difference schemes for non-uniform grids, relaxation method, and virtual node method, the numerical method for the governing equations of compressible flow in porous journal bearings is proposed. The effects of nominal clearance of bearings and compressibility of gas on the static characteristics are analyzed. Under the same minimum film thickness and the same gas compressibility, as the nominal clearance widens, the load capacity, mass flow rate, and power consumption increase. Under the same minimum film thickness and the same nominal clearance, with the increase in gas polytropic index, the load capacity strengthens, while the mass flow rate and power consumption decline. This study could provide a reference for the design of porous journal bearings. Full article

A Newtonian-like theory inspired by the Brans–Dicke gravitational Lagrangian has been recently proposed by us. For static configurations, the gravitational coupling acquires an intrinsic spatial dependence within the matter distribution. Therefore, the interior of astrophysical configurations may provide a testable environment for this approach as long as no screening mechanism is evoked. In this work, we focus on the stellar hydrostatic equilibrium structure in such a varying Newtonian gravitational coupling G scenario. A modified Lane–Emden equation is presented and its solutions for various values of the polytropic index are discussed. The role played by the theory parameter $\omega$, the analogue of the Brans–Dicke parameter, in the physical properties of stars is discussed. Full article

The Bernoulli integral describes the energy conservation of a fluid along specific streamlines. The integral is the sum of individual terms that contain the plasma density, speed, temperature, and magnetic field. Typical solar wind analyses use the fluctuations of the Bernoulli integral as a criterion to identify different plasma streamlines from single spacecraft observations. However, the accurate calculation of the Bernoulli integral requires accurately determining the plasma polytropic index from the analysis of density and temperature observations. To avoid this complexity, we can simplify the calculations by keeping only the dominant terms of the integral. Here, we analyze proton plasma and magnetic field observations obtained by the Wind spacecraft at 1 au, during 1995. We calculate the Bernoulli integral terms and quantify their significance by comparing them with each other. We discuss potential simplifications of the calculations in the context of determining solar wind proton thermodynamics using single spacecraft observations. Full article

We examine the relationships between temperature tensor elements and their connection to the polytropic equation, which describes the relationship between the plasma scalar temperature and density. We investigate the possibility to determine the plasma polytropic index by fitting the fluctuations of temperature either perpendicular or parallel to the magnetic field. Such an application is particularly useful when the full temperature tensor is not available from the observations. We use solar wind proton observations at ~1 au to calculate the correlations between the temperature tensor elements and the scalar temperature. Our analysis also derives the polytropic equation in selected streamlines of solar wind plasma proton observations that exhibit temperature anisotropies related to stream-interaction regions. We compare the polytropic indices derived by fitting fluctuations of the scalar, perpendicular, and parallel temperatures, respectively. We show that the use of the parallel or perpendicular temperature, instead of the scalar temperature, still accurately derives the true, average polytropic index value, but only for a certain level of temperature anisotropy variability within the analyzed streamlines. The use of the perpendicular temperature leads to more accurate calculations, because its correlation with the scalar temperature is less affected by the anisotropy fluctuations. Full article

Through the introduction of multifrequency ultrasound technology, remarkable results have been achieved in tissue ablation and other aspects. By using the nonlinear dynamic equation of spherical bubble, the effects of the combination mode of multifrequency ultrasound, the peak negative pressure and its duration, the phase angle difference, and the polytropic index on the transient cavitation threshold in four different media of water, blood, brain, and liver are simulated and analyzed. The simulation results show that under the same frequency difference and initial bubble radius, the transient cavitation threshold of the high-frequency, triple-frequency combination is higher than that of the low-frequency, triple-frequency combination. When the lowest frequency of triple frequencies is the same, the larger the frequency difference, the higher the transient cavitation threshold. When the initial bubble radius is small, the frequency difference has little effect on the transient cavitation threshold of the triple-frequency combination. With the increase of initial bubble radius, the influence of frequency difference on the transient cavitation threshold of the higher frequency combination of triple frequency is more obvious than that of the lower frequency combination of triple frequency. When the duration of peak negative pressure or peak negative pressure of the multifrequency combined ultrasound is longer than that of the single-frequency ultrasound, the transient cavitation threshold of the multifrequency combined ultrasound is lower than that of the single-frequency ultrasound; on the contrary, the transient cavitation threshold of the multifrequency combined ultrasound is higher than that of the single-frequency ultrasound. When the phase angle difference of multifrequency excitation is zero, the corresponding transient cavitation threshold is the lowest, while the change of the polytropic index has almost no effect on the transient cavitation threshold for the multifrequency combination. The research results can provide a reference for multifrequency ultrasound to reduce the transient cavitation threshold, which is of great significance for the practical application of cavitation. Full article

This paper improves our understanding of the interplay of the proton plasma turbulent heating sources of the expanding solar wind in the heliosphere. Evidence is shown of the connections between the polytropic index, the rate of the heat absorbed by the solar wind, and the rate of change of the turbulent energy, which heats the solar wind in the inner and outer heliosphere. In particular, we: (i) show the theoretical connection of the rate of a heat source, such as the turbulent energy, with the polytropic index and the thermodynamic process; (ii) calculate the effect of the pick-up protons in the total proton temperature and the relationship connecting the rate of heating with the polytropic index; (iii) derive the radial profiles of the solar wind heating in the outer and inner heliosphere; and (iv) use the radial profile of the turbulent energy in the solar wind proton plasma in the heliosphere, in order to show its connection with the radial profiles of the polytropic index and the heating of the solar wind. Full article

The polytropic index of space plasmas is typically determined from the relationship between the measured plasma density and temperature. In this study, we quantify the errors in the determination of the polytropic index, due to uncertainty in the analyzed measurements. We model the plasma density and temperature measurements for a certain polytropic index, and then, we apply the standard analysis to derive the polytropic index. We explore the accuracy of the derived polytropic index for a range of uncertainties in the modeled density and temperature and repeat for various polytropic indices. Our analysis shows that the uncertainties in the plasma density introduce a systematic error in the determination of the polytropic index which can lead to artificial isothermal relations, while the uncertainties in the plasma temperature increase the statistical error of the calculated polytropic index value. We analyze Wind spacecraft observations of the solar wind protons and we derive the polytropic index in selected intervals over 2002. The derived polytropic index is affected by the plasma measurement uncertainties, in a similar way as predicted by our model. Finally, we suggest a new data-analysis approach, based on a physical constraint, that reduces the amount of erroneous derivations. Full article