Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (19)

Search Parameters:
Keywords = polytropic gas equation

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
30 pages, 403 KiB  
Article
Asymptotic Stability of the Magnetohydrodynamic Flows with Temperature-Dependent Transport Coefficients
by Mingyu Zhang
Axioms 2025, 14(2), 100; https://doi.org/10.3390/axioms14020100 - 28 Jan 2025
Viewed by 637
Abstract
The objective of this paper is to analyze the asymptotic stability of global strong solutions to the boundary value problem of the compressible magnetohydrodynamic (MHD) equations for the ideal polytropic gas in which the viscosity λ and heat conductivity κ depend on temperature, [...] Read more.
The objective of this paper is to analyze the asymptotic stability of global strong solutions to the boundary value problem of the compressible magnetohydrodynamic (MHD) equations for the ideal polytropic gas in which the viscosity λ and heat conductivity κ depend on temperature, i.e., λ=θα and κ=θβ with α,β[0,+). Both the global-in-time existence and uniqueness of strong solutions are obtained under certain assumptions on the parameter α and initial data. Moreover, based on accurate uniform-in-time estimates, we show that the global large solutions decay exponentially in time to the equilibrium states. Compared with the existing results, the initial data could be large if α is small and the growth exponent β can be arbitrarily large. Full article
22 pages, 3621 KiB  
Article
A Three-Dimensional Model of a Spherically Symmetric, Compressible Micropolar Fluid Flow with a Real Gas Equation of State
by Angela Bašić-Šiško, Loredana Simčić and Ivan Dražić
Symmetry 2024, 16(10), 1330; https://doi.org/10.3390/sym16101330 - 9 Oct 2024
Cited by 1 | Viewed by 1394
Abstract
In this work, we analyze a spherically symmetric 3D flow of a micropolar, viscous, polytropic, and heat-conducting real gas. In particular, we take as a domain the subset of R3 bounded by two concentric spheres that present solid thermoinsulated walls. Also, here, [...] Read more.
In this work, we analyze a spherically symmetric 3D flow of a micropolar, viscous, polytropic, and heat-conducting real gas. In particular, we take as a domain the subset of R3 bounded by two concentric spheres that present solid thermoinsulated walls. Also, here, we consider the generalized equation of state for the pressure in the sense that the pressure depends, as a power function, on the mass density. The model is based on the conservation laws for mass, momentum, momentum moment, and energy, as well as the equation of state for a real gas, and it is derived first in the Eulerian and then in the Lagrangian description. Through the application of the Faedo–Galerkin method, a numerical solution to a corresponding problem is obtained, and numerical simulations are performed to demonstrate the behavior of the solutions under various parameters and initial conditions in order to validate the method. The results of the simulations are discussed in detail. Full article
(This article belongs to the Section Engineering and Materials)
Show Figures

Figure 1

12 pages, 681 KiB  
Communication
Radial Oscillations of Dark Matter Stars Admixed with Dark Energy
by Camila Sepúlveda and Grigoris Panotopoulos
Universe 2024, 10(1), 41; https://doi.org/10.3390/universe10010041 - 16 Jan 2024
Cited by 4 | Viewed by 1701
Abstract
We imagine spherically symmetric configurations made of both dark matter and dark energy in the halo of spiral galaxies. Adopting a polytropic equation of state for dark matter and the Extended Chaplygin gas equation of state for dark energy, we model the same [...] Read more.
We imagine spherically symmetric configurations made of both dark matter and dark energy in the halo of spiral galaxies. Adopting a polytropic equation of state for dark matter and the Extended Chaplygin gas equation of state for dark energy, we model the same object with three different dark matter–dark energy compositions. We compute the frequencies and the corresponding eigenfunctions of the ten lowest modes, integrating the equations for the radial perturbations by imposing the appropriate boundary conditions at the center and the surface of the object. Also, a comparison between the different models is made. Full article
(This article belongs to the Special Issue Cosmological Models of the Universe)
Show Figures

Figure 1

15 pages, 759 KiB  
Communication
On Exotic Objects Made of Dark Energy and Dark Matter: Mass-to-Radius Profiles and Tidal Love Numbers
by Camila Sepúlveda and Grigoris Panotopoulos
Galaxies 2023, 11(5), 101; https://doi.org/10.3390/galaxies11050101 - 22 Sep 2023
Cited by 3 | Viewed by 1893
Abstract
We investigate some properties of exotic spherical configurations made of dark matter and dark energy. For the former, we adopt a polytropic equation-of-state, while for the latter, we adopt the extended Chaplygin gas equation-of-state. Solving the Tolman–Oppenheimer–Volkoff equations, within the two-fluid formalism, we [...] Read more.
We investigate some properties of exotic spherical configurations made of dark matter and dark energy. For the former, we adopt a polytropic equation-of-state, while for the latter, we adopt the extended Chaplygin gas equation-of-state. Solving the Tolman–Oppenheimer–Volkoff equations, within the two-fluid formalism, we compute the factor of compactness, the mass-to-radius relationships, as well as the tidal Love numbers and dimensionless deformabilities. A comparison between single-fluid objects and two-fluid configurations is made as well. Full article
Show Figures

Figure 1

20 pages, 1002 KiB  
Article
Study of Time-Fractional Nonlinear Model Governing Unsteady Flow of Polytropic Gas
by Brajesh K. Singh, Haci Mehmet Baskonus, Neetu Singh, Mukesh Gupta and D. G. Prakasha
Axioms 2023, 12(3), 285; https://doi.org/10.3390/axioms12030285 - 8 Mar 2023
Viewed by 1514
Abstract
The present study is concerned with studying the dynamical behavior of two space-dimensional nonlinear time-fractional models governing the unsteady-flow of polytropic-gas (in brief, pGas) that occurred in cosmology and astronomy. For this purpose, two efficient hybrid methods so-called optimal homotopy analysis J-transform [...] Read more.
The present study is concerned with studying the dynamical behavior of two space-dimensional nonlinear time-fractional models governing the unsteady-flow of polytropic-gas (in brief, pGas) that occurred in cosmology and astronomy. For this purpose, two efficient hybrid methods so-called optimal homotopy analysis J-transform method (OHAJTM) and J-variational iteration transform method (J-VITM) have been adopted. The OHAJTM is the hybrid method, where optimal-homotopy analysis method (OHAM) is utilized after implementing the properties of J-transform (JT), and in J-VITM is the J-transform-based variational iteration method. Banach’s fixed point approach is adopted to analyze the convergence of these methods. It is demonstrated that J-VITM is T-stable, and the evaluated dynamics of pGas are described in terms of Mittag–Leffler functions. The proposed evaluation confirms that the implemented methods perform better for the referred model equation of pGas. In addition, for a given iteration, the proposed behavior via OHAJTM performs better in producing more accurate behavior in comparison to J-VITM and the methods introduced recently. Full article
(This article belongs to the Special Issue Mathematical Models and Simulations)
Show Figures

Figure 1

19 pages, 6571 KiB  
Article
A Study of a Bistable Reciprocating Piston Pump Driven by Shape Memory Alloys and Recuperative Springs
by Mihail Kostov, Todor Todorov, Rosen Mitrev, Konstantin Kamberov and Rumen Nikolov
Actuators 2023, 12(2), 90; https://doi.org/10.3390/act12020090 - 17 Feb 2023
Cited by 8 | Viewed by 2552
Abstract
This paper presents and examines a new design concept for a bistable reciprocating piston pump. The bistable pump mechanism belongs to the bistable mechanisms, which have two stable positions at the end of the suction and discharge strokes. The transition between the stable [...] Read more.
This paper presents and examines a new design concept for a bistable reciprocating piston pump. The bistable pump mechanism belongs to the bistable mechanisms, which have two stable positions at the end of the suction and discharge strokes. The transition between the stable positions is achieved by using triggering force at each beginning of suction and discharge and subsequent movement using a recuperative spring. In this mechanism, the triggering forces are created by two Shape Memory Alloy (SMA) wires. Geometric and force expressions for the pump suction and discharge strokes are derived. Additional equations are obtained for the balance of moments for the two stable equilibrium positions and the unstable position in the middle of the stroke. Numerical studies have been conducted for the suction and discharge strokes, considering the force exerted by the gas on the piston, which is modelled by an indicator diagram assuming a polytropic process. It was found that the load on the mechanism has significant non-uniformity. The diagrams illustrating the distribution of total moments showed that the cold SMA wire shifted the point of instability. The numerical example shows how to choose the right spring stiffness to obtain energy recovery. In this way, the triggering SMA forces act only at the beginning of the two strokes and, after that, the recuperative forces substitute the action of the SMA forces. The theoretical relationships and methods presented here are suitable for synthesizing new pumps or analyzing similar mechanisms. Full article
(This article belongs to the Special Issue Innovative Actuators Based on Shape Memory Alloys)
Show Figures

Figure 1

21 pages, 3936 KiB  
Article
Application of a Machine Learning Algorithm for Evaluation of Stiff Fractional Modeling of Polytropic Gas Spheres and Electric Circuits
by Fawaz Khaled Alarfaj, Naveed Ahmad Khan, Muhammad Sulaiman and Abdullah M. Alomair
Symmetry 2022, 14(12), 2482; https://doi.org/10.3390/sym14122482 - 23 Nov 2022
Cited by 16 | Viewed by 2638
Abstract
Fractional polytropic gas sphere problems and electrical engineering models typically simulated with interconnected circuits have numerous applications in physical, astrophysical phenomena, and thermionic currents. Generally, most of these models are singular-nonlinear, symmetric, and include time delay, which has increased attention to them among [...] Read more.
Fractional polytropic gas sphere problems and electrical engineering models typically simulated with interconnected circuits have numerous applications in physical, astrophysical phenomena, and thermionic currents. Generally, most of these models are singular-nonlinear, symmetric, and include time delay, which has increased attention to them among researchers. In this work, we explored deep neural networks (DNNs) with an optimization algorithm to calculate the approximate solutions for nonlinear fractional differential equations (NFDEs). The target data-driven design of the DNN-LM algorithm was further implemented on the fractional models to study the rigorous impact and symmetry of different parameters on RL, RC circuits, and polytropic gas spheres. The targeted data generated from the analytical and numerical approaches in the literature for different cases were utilized by the deep neural networks to predict the numerical solutions by minimizing the differences in mean square error using the Levenberg–Marquardt algorithm. The numerical solutions obtained by the designed technique were contrasted with the multi-step reproducing kernel Hilbert space method (MS-RKM), Laplace transformation method (LTM), and Padé approximations. The results demonstrate the accuracy of the design technique as the DNN-LM algorithm overlaps with the actual results with minimum percentage absolute errors that lie between 108 and 1012. The extensive graphical and statistical analysis of the designed technique showed that the DNN-LM algorithm is dependable and facilitates the examination of higher-order nonlinear complex problems due to the flexibility of the DNN architecture and the effectiveness of the optimization procedure. Full article
(This article belongs to the Special Issue Trends in Fractional Modelling in Science and Innovative Technologies)
Show Figures

Figure 1

96 pages, 971 KiB  
Article
K-Essence Lagrangians of Polytropic and Logotropic Unified Dark Matter and Dark Energy Models
by Pierre-Henri Chavanis
Astronomy 2022, 1(3), 126-221; https://doi.org/10.3390/astronomy1030011 - 28 Sep 2022
Cited by 10 | Viewed by 3217
Abstract
We determine the k-essence Lagrangian of a relativistic barotropic fluid. The equation of state of the fluid can be specified in different manners depending on whether the pressure is expressed in terms of the energy density (model I), the rest-mass density (model II), [...] Read more.
We determine the k-essence Lagrangian of a relativistic barotropic fluid. The equation of state of the fluid can be specified in different manners depending on whether the pressure is expressed in terms of the energy density (model I), the rest-mass density (model II), or the pseudo rest-mass density for a complex scalar field in the Thomas-Fermi approximation (model III). In the nonrelativistic limit, these three formulations coincide. In the relativistic regime, they lead to different models that we study exhaustively. We provide general results valid for an arbitrary equation of state and show how the different models are connected to each other. For illustration, we specifically consider polytropic and logotropic dark fluids that have been proposed as unified dark matter and dark energy models. We recover the Born-Infeld action of the Chaplygin gas in models I and III and obtain the explicit expression of the reduced action of the logotropic dark fluid in models II and III. We also derive the two-fluid representation of the Chaplygin and logotropic models. Our general formalism can be applied to many other situations such as Bose-Einstein condensates with a |φ|4 (or more general) self-interaction, dark matter superfluids, and mixed models. Full article
13 pages, 1094 KiB  
Article
A Reliable Way to Deal with Fractional-Order Equations That Describe the Unsteady Flow of a Polytropic Gas
by M. Mossa Al-Sawalha, Ravi P. Agarwal, Rasool Shah, Osama Y. Ababneh and Wajaree Weera
Mathematics 2022, 10(13), 2293; https://doi.org/10.3390/math10132293 - 30 Jun 2022
Cited by 18 | Viewed by 2209
Abstract
In this paper, fractional-order system gas dynamics equations are solved analytically using an appealing novel method known as the Laplace residual power series technique, which is based on the coupling of the residual power series approach with the Laplace transform operator to develop [...] Read more.
In this paper, fractional-order system gas dynamics equations are solved analytically using an appealing novel method known as the Laplace residual power series technique, which is based on the coupling of the residual power series approach with the Laplace transform operator to develop analytical and approximate solutions in quick convergent series types by utilizing the idea of the limit with less effort and time than the residual power series method. The given model is tested and simulated to confirm the proposed technique’s simplicity, performance, and viability. The results show that the above-mentioned technique is simple, reliable, and appropriate for investigating nonlinear engineering and physical problems. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications II)
Show Figures

Figure 1

24 pages, 1684 KiB  
Article
Invariant Finite-Difference Schemes for Plane One-Dimensional MHD Flows That Preserve Conservation Laws
by Vladimir Dorodnitsyn and Evgeniy Kaptsov
Mathematics 2022, 10(8), 1250; https://doi.org/10.3390/math10081250 - 11 Apr 2022
Cited by 3 | Viewed by 1902
Abstract
Invariant finite-difference schemes are considered for one-dimensional magnetohydrodynamics (MHD) equations in mass Lagrangian coordinates for the cases of finite and infinite conductivity. The construction of these schemes makes use of results of the group classification of MHD equations previously obtained by the authors. [...] Read more.
Invariant finite-difference schemes are considered for one-dimensional magnetohydrodynamics (MHD) equations in mass Lagrangian coordinates for the cases of finite and infinite conductivity. The construction of these schemes makes use of results of the group classification of MHD equations previously obtained by the authors. On the basis of the classical Samarskiy–Popov scheme, new schemes are constructed for the case of finite conductivity. These schemes admit all symmetries of the original differential model and have difference analogues of all of its local differential conservation laws. New, previously unknown, conservation laws are found using symmetries and direct calculations. In the case of infinite conductivity, conservative invariant schemes are constructed as well. For isentropic flows of a polytropic gas the proposed schemes possess the conservation law of energy and preserve entropy on two time layers. This is achieved by means of specially selected approximations for the equation of state of a polytropic gas. In addition, invariant difference schemes with additional conservation laws are proposed. A new scheme for the case of finite conductivity is tested numerically for various boundary conditions, which shows accurate preservation of difference conservation laws. Full article
Show Figures

Figure 1

15 pages, 2715 KiB  
Article
Theoretical and Numerical Investigations on Static Characteristics of Aerostatic Porous Journal Bearings
by Yandong Gu, Jinwu Cheng, Chaojie Xie, Longyu Li and Changgeng Zheng
Machines 2022, 10(3), 171; https://doi.org/10.3390/machines10030171 - 24 Feb 2022
Cited by 19 | Viewed by 3137
Abstract
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, [...] Read more.
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
(This article belongs to the Special Issue Optimization and Flow Characteristics in Advanced Fluid Machinery)
Show Figures

Figure 1

17 pages, 1272 KiB  
Article
Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel
by Meshari Alesemi, Naveed Iqbal and Thongchai Botmart
Mathematics 2022, 10(4), 615; https://doi.org/10.3390/math10040615 - 17 Feb 2022
Cited by 35 | Viewed by 2887
Abstract
This article presents a homotopy perturbation transform method and a variational iterative transform method for analyzing the fractional-order non-linear system of the unsteady flow of a polytropic gas. In this method, the Yang transform is combined with the homotopy perturbation transformation method and [...] Read more.
This article presents a homotopy perturbation transform method and a variational iterative transform method for analyzing the fractional-order non-linear system of the unsteady flow of a polytropic gas. In this method, the Yang transform is combined with the homotopy perturbation transformation method and the variational iterative transformation method in the sense of Caputo–Fabrizio. A numerical simulation was carried out to verify that the suggested methodologies are accurate and reliable, and the results are revealed using graphs and tables. Comparing the analytical and actual solutions demonstrates that the proposed approaches are effective and efficient in investigating complicated non-linear models. Furthermore, the proposed methodologies control and manipulate the achieved numerical solutions in a very useful way, and this provides us with a simple process to adjust and control the convergence regions of the series solution. Full article
Show Figures

Figure 1

19 pages, 1389 KiB  
Article
Porous Medium Equation in Graphene Oxide Membrane: Nonlinear Dependence of Permeability on Pressure Gradient Explained
by Lukáš Mrazík and Pavel Kříž
Membranes 2021, 11(9), 665; https://doi.org/10.3390/membranes11090665 - 29 Aug 2021
Cited by 4 | Viewed by 2442
Abstract
Membrane performance in gas separation is quantified by its selectivity, determined as a ratio of measured gas permeabilities of given gases at fixed pressure difference. In this manuscript a nonlinear dependence of gas permeability on pressure difference observed in the measurements of gas [...] Read more.
Membrane performance in gas separation is quantified by its selectivity, determined as a ratio of measured gas permeabilities of given gases at fixed pressure difference. In this manuscript a nonlinear dependence of gas permeability on pressure difference observed in the measurements of gas permeability of graphene oxide membrane on a manometric integral permeameter is reported. We show that after reasoned assumptions and simplifications in the mathematical description of the experiment, only static properties of any proposed governing equation can be studied, in order to analyze the permeation rate for different pressure differences. Porous Medium Equation is proposed as a suitable governing equation for the gas permeation, as it manages to predict a nonlinear behavior which is consistent with the measured data. A coefficient responsible for the nonlinearity, the polytropic exponent, is determined to be gas-specific—implications on selectivity are discussed, alongside possible hints to a deeper physical interpretation of its actual value. Full article
Show Figures

Figure 1

15 pages, 966 KiB  
Article
A Comparative Analysis of Fractional-Order Gas Dynamics Equations via Analytical Techniques
by Shuang-Shuang Zhou, Nehad Ali Shah, Ioannis Dassios, S. Saleem and Kamsing Nonlaopon
Mathematics 2021, 9(15), 1735; https://doi.org/10.3390/math9151735 - 22 Jul 2021
Cited by 2 | Viewed by 2334
Abstract
This article introduces two well-known computational techniques for solving the time-fractional system of nonlinear equations of unsteady flow of a polytropic gas. The methods suggested are the modified forms of the variational iteration method and the homotopy perturbation method by the Elzaki transformation. [...] Read more.
This article introduces two well-known computational techniques for solving the time-fractional system of nonlinear equations of unsteady flow of a polytropic gas. The methods suggested are the modified forms of the variational iteration method and the homotopy perturbation method by the Elzaki transformation. Furthermore, an illustrative scheme is introduced to verify the accuracy of the available techniques. A graphical representation of the exact and derived results is presented to show the reliability of the suggested approaches. It is also shown that the findings of the current methodology are in close harmony with the exact solutions. The comparative solution analysis via graphs also represents the higher reliability and accuracy of the current techniques. Full article
Show Figures

Figure 1

16 pages, 1027 KiB  
Article
Modeling Acoustic Cavitation Using a Pressure-Based Algorithm for Polytropic Fluids
by Fabian Denner, Fabien Evrard and Berend van Wachem
Fluids 2020, 5(2), 69; https://doi.org/10.3390/fluids5020069 - 13 May 2020
Cited by 19 | Viewed by 3942
Abstract
A fully coupled pressure-based algorithm and finite-volume framework for the simulation of the acoustic cavitation of bubbles in polytropic gas-liquid systems is proposed. The algorithm is based on a conservative finite-volume discretization with collocated variable arrangement, in which the discretized governing equations are [...] Read more.
A fully coupled pressure-based algorithm and finite-volume framework for the simulation of the acoustic cavitation of bubbles in polytropic gas-liquid systems is proposed. The algorithm is based on a conservative finite-volume discretization with collocated variable arrangement, in which the discretized governing equations are solved in a single linear system of equations for pressure and velocity. Density is described by the polytropic Noble-Abel stiffened-gas model and the interface between the interacting bulk phases is captured by a state-of-the-art algebraic Volume-of-Fluid (VOF) method. The new numerical algorithm is validated using representative test-cases of the interaction of acoustic waves with the gas-liquid interface as well as pressure-driven bubble dynamics in infinite and confined domains, showing excellent agreement of the results obtained with the proposed algorithm compared to linear acoustic theory, the Gilmore model and high-fidelity experiments. Full article
(This article belongs to the Special Issue Modelling of Reactive and Non-reactive Multiphase Flows)
Show Figures

Figure 1

Back to TopTop