Vortex expansion of the monatomic gas

2014 ◽  
Vol 10 ◽  
pp. 110-113
Author(s):  
R.F. Shayakhmetova
Keyword(s):  
Gas Dynamics ◽  
Invariant Solution ◽  
Three Dimensional ◽  
Equations Of Gas Dynamics ◽  
The One ◽  
Monatomic Gas

We consider the one invariant solution on a three-dimensional subalgebra admitted by the equations of gas dynamics for a monatomic gas. It sets the expansion of gas into a vacuum. The motion of the particles occurs over hyperbole lying on an elliptical cone.

scholarly journals New Exact Solutions with a Linear Velocity Field for the Gas Dynamics Equations for Two Types of State Equations

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 123
Author(s):  
Renata Nikonorova ◽  
Dilara Siraeva ◽  
Yulia Yulmukhametova
Keyword(s):  
Velocity Field ◽  
Exact Solutions ◽  
Gas Dynamics ◽  
Three Dimensional ◽  
State Equation ◽  
Linear Velocity ◽  
State Equations ◽  
Gas Dynamics Equations ◽  
Linear Velocity Field ◽  
Monatomic Gas

In this paper, exact solutions with a linear velocity field are sought for the gas dynamics equations in the case of the special state equation and the state equation of a monatomic gas. These state equations extend the transformation group admitted by the system to 12 and 14 parameters, respectively. Invariant submodels of rank one are constructed from two three-dimensional subalgebras of the corresponding Lie algebras, and exact solutions with a linear velocity field with inhomogeneous deformation are obtained. On the one hand of the special state equation, the submodel describes an isochoric vortex motion of particles, isobaric along each world line and restricted by a moving plane. The motions of particles occur along parabolas and along rays in parallel planes. The spherical volume of particles turns into an ellipsoid at finite moments of time, and as time tends to infinity, the particles end up on an infinite strip of finite width. On the other hand of the state equation of a monatomic gas, the submodel describes vortex compaction to the origin and the subsequent expansion of gas particles in half-spaces. The motion of any allocated volume of gas retains a spherical shape. It is shown that for any positive moment of time, it is possible to choose the radius of a spherical volume such that the characteristic conoid beginning from its center never reaches particles outside this volume. As a result of the generalization of the solutions with a linear velocity field, exact solutions of a wider class are obtained without conditions of invariance of density and pressure with respect to the selected three-dimensional subalgebras.

A Very Efficient Class of HOC Schemes for the One-Dimensional Euler Equations of Gas Dynamics

2015 ◽  
Vol 813-814 ◽  
pp. 643-651 ◽  
Author(s):  
Bidyut B. Gogoi
Keyword(s):  
Shock Tube ◽  
Euler Equations ◽  
Gas Dynamics ◽  
Laval Nozzle ◽  
Numerical Solutions ◽  
Weighted Average ◽  
One Dimensional ◽  
Equations Of Gas Dynamics ◽  
De Laval Nozzle ◽  
The One

This manuscript introduces a class of higher order compact schemes for the solution of one dimensional (1-D) Euler equations of gas dynamics. These schemes are fourth order accurate in space and second or lower order accurate in time, depending on a weighted average parameter μ. The robustness and efficiency of our proposed schemes have been validated by applying them to three different shock-tube problems of gas dynamics, including the famous SOD shock-tube problem. Later on, the 1-D convergent-divergent nozzle problem (De laval nozzle problem) is also considered and numerical simulations are performed. In all the cases, our computed numerical solutions are found to be in excellent match with the exact solutions or available results in the existing literature. Overall the schemes are found to be efficient and accurate.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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