Stability of the solution of the differential equations of a one-dimensional viscous ideal gas

1988 ◽  
Vol 28 (4) ◽  
pp. 402-412
Author(s):  
A. Štikonas
Keyword(s):  
Differential Equations ◽  
Ideal Gas ◽  
One Dimensional ◽  
Stability Of The Solution

Similarity Solutions of Cylindrical Shock Waves in Magnetogasdynamics With Thermal Radiation

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Rajan Arora ◽  
Ankita Sharma
Keyword(s):  
Differential Equations ◽  
Unsteady Motion ◽  
Similarity Solutions ◽  
Ideal Gas ◽  
Time Dependent ◽  
Radiative Cooling ◽  
Azimuthal Magnetic Field ◽  
Cylindrical Shock Wave ◽  
One Dimensional ◽  
Lie Group Of Transformations

Using Lie group of transformations, here we consider the problem of finding similarity solutions to the system of partial differential equations (PDEs) governing one-dimensional unsteady motion of an ideal gas in the presence of radiative cooling and idealized azimuthal magnetic field. The similarity solutions are investigated behind a cylindrical shock wave which is produced as a result of a sudden explosion or driven out by an expanding piston. The shock is assumed to be strong and propagates into a medium which is at rest, with nonuniform density. The total energy of the wave is assumed to be time dependent obeying a power law. Indeed, with the use of the similarity solution, the problem is transformed into a system of ordinary differential equations (ODEs), which in general is nonlinear; in some cases, it is possible to solve these ODEs to determine some special exact solutions.

scholarly journals One-Dimensional Optimal System for 2D Rotating Ideal Gas

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1115 ◽  
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ideal Gas ◽  
Optimal System ◽  
Lie Point Symmetries ◽  
Rotating System ◽  
Partial Differential ◽  
One Dimensional ◽  
Rotating Systems ◽  
The One

We derive the one-dimensional optimal system for a system of three partial differential equations, which describe the two-dimensional rotating ideal gas with polytropic parameter γ > 2 . The Lie symmetries and the one-dimensional optimal system are determined for the nonrotating and rotating systems. We compare the results, and we find that when there is no Coriolis force, the system admits eight Lie point symmetries, while the rotating system admits seven Lie point symmetries. Consequently, the two systems are not algebraic equivalent as in the case of γ = 2 , which was found by previous studies. For the one-dimensional optimal system, we determine all the Lie invariants, while we demonstrate our results by reducing the system of partial differential equations into a system of first-order ordinary differential equations, which can be solved by quadratures.

Computerized Analysis of Dynamic Pressure Exchanger Scavenge Processes

1975 ◽  
Vol 189 (1) ◽  
pp. 149-158 ◽  
Author(s):  
P. H. Azoury ◽  
S. M. Hai
Keyword(s):  
Differential Equations ◽  
Specific Heat ◽  
High Performance ◽  
Gas Flow ◽  
Previous Analysis ◽  
Dynamic Pressure ◽  
Ideal Gas ◽  
Wave Processes ◽  
One Dimensional ◽  
Good Agreement

The present work supplements a previous analysis by Azoury of the basic wave processes in a d.p.e. (dynamic pressure exchanger) cell. A hybrid computerized method of integrating the differential equations of unsteady one-dimensional ideal gas flow is used to analyse the component scavenge processes of the d.p.e. in a looped arrangement. These processes are employed to investigate the effect of the relative nature of the interacting gases on d.p.e. performance. A criterion of high performance is proposed in terms of the overall strength of the interface between the gases and their relative specific heat ratios. The criterion gives good agreement with theory when tested with experimental results obtained on two d.p.e. test units.

scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

scholarly journals Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Raheel Kamal ◽  
Kamran ◽  
Gul Rahmat ◽  
Ali Ahmadian ◽  
Noreen Izza Arshad ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Inverse Laplace Transform ◽  
Contour Integral ◽  
Partial Differential ◽  
One Dimensional ◽  
The Laplace Transform

AbstractIn this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the Caputo–Fabrizio fractional derivative. In our numerical scheme the Laplace transform is used to avoid the time stepping procedure, and the local meshless method is used to produce sparse differentiation matrices and avoid the ill conditioning issues resulting in global meshless methods. Our numerical method comprises three steps. In the first step we transform the given equation to an equivalent time independent equation. Secondly the reduced equation is solved via a local meshless method. Finally, the solution of the original equation is obtained via the inverse Laplace transform by representing it as a contour integral in the complex left half plane. The contour integral is then approximated using the trapezoidal rule. The stability and convergence of the method are discussed. The efficiency, efficacy, and accuracy of the proposed method are assessed using four different problems. Numerical approximations of these problems are obtained and validated against exact solutions. The obtained results show that the proposed method can solve such types of problems efficiently.

Some differential equations for problems of wave scattering in a one-dimensional medium

Astrophysics ◽  
1999 ◽  
Vol 42 (3) ◽  
pp. 316-321 ◽  
Author(s):  
D. M. Sedrakian ◽  
A. Zh. Khachatrian
Keyword(s):  
Differential Equations ◽  
Wave Scattering ◽  
One Dimensional

The combined effect of lattice’s uniaxial strains and electron–phonon interaction’s screening on TBEC of the intersite bipolarons

2016 ◽  
Vol 30 (26) ◽  
pp. 1650186
Author(s):  
B. Yavidov ◽  
SH. Djumanov ◽  
T. Saparbaev ◽  
O. Ganiyev ◽  
S. Zholdassova ◽  
...  
Keyword(s):  
Ideal Gas ◽  
Einstein Condensation ◽  
Chain Model ◽  
One Dimensional ◽  
Electron Phonon Interaction ◽  
Model Lattice ◽  
Experimental Values ◽  
Bose Einstein ◽  
Derivatives Of ◽  
The Ideal

Having accepted a more generalized form for density-displacement type electron–phonon interaction (EPI) force we studied the simultaneous effect of uniaxial strains and EPI’s screening on the temperature of Bose–Einstein condensation [Formula: see text] of the ideal gas of intersite bipolarons. [Formula: see text] of the ideal gas of intersite bipolarons is calculated as a function of both strain and screening radius for a one-dimensional chain model of cuprates within the framework of Extended Holstein–Hubbard model. It is shown that the chain model lattice comprises the essential features of cuprates regarding of strain and screening effects on transition temperature [Formula: see text] of superconductivity. The obtained values of strain derivatives of [Formula: see text] [Formula: see text] are in qualitative agreement with the experimental values of [Formula: see text] [Formula: see text] of La[Formula: see text]Sr[Formula: see text]CuO4 under moderate screening regimes.

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