A variational problem in one-dimensional unsteady gas dynamics

1985 ◽  
Vol 19 (4) ◽  
pp. 667-671
Author(s):  
A. I. Rylov
Keyword(s):  
Variational Problem ◽  
Gas Dynamics ◽  
One Dimensional

A Theory for the High-Speed Flow of Gas-Solids Mixtures under Conditions of Equilibrium and Constant Fractional Lag

1969 ◽  
Vol 184 (3) ◽  
pp. 59-66 ◽  
Author(s):  
B. N. Cole ◽  
H. M. Bowers ◽  
F. R. Mobbs
Keyword(s):  
Mach Number ◽  
Speed Of Sound ◽  
Gas Dynamics ◽  
High Speed ◽  
Solid Particles ◽  
High Speed Flow ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Speed Flow ◽  
Constant Area

A theory is presented for the high-speed, one-dimensional flow of a gas-solids mixture, assuming constant fractional lags of temperature and velocity between the solid particles and the gas. A mixture speed of sound is is derived and used as the basis of a mixture Mach number. Expressions are deduced which are parallel to many well-known relationships in orthodox one-dimensional gas dynamics. The investigation covers frictionless flow in a variable area duct and flow with friction in a constant area duct. The effect of solids volume is also taken into account.

ASYMPTOTICAL ANALYSIS OF ONE DIMENSIONAL GAS DYNAMICS EQUATIONS

2001 ◽  
Vol 6 (1) ◽  
pp. 117-128 ◽  
Author(s):  
A. Krylovas ◽  
R. Čiegis
Keyword(s):  
Gas Dynamics ◽  
Numerical Experiments ◽  
Method Of Averaging ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Resonance Case ◽  
Gas Dynamics Equations ◽  
Weakly Nonlinear ◽  
One Dimensional ◽  
Asymptotical Analysis

A method of averaging is developed for constructing a uniformly valid asymptotic solution for weakly nonlinear one dimensional gas dynamics systems. Using this method we give the averaged system, which disintegrates into independent equations for the non‐resonance systems. Conditions of the resonance for periodic and almost periodic solutions are presented. In the resonance case the averaged system is solved numerically. Some results of numerical experiments are given.

scholarly journals ON A LATTICE GENERALISATION OF THE LOGARITHM AND A DEFORMATION OF THE DEDEKIND ETA FUNCTION

2020 ◽  
Vol 102 (1) ◽  
pp. 118-125
Author(s):  
LAURENT BÉTERMIN
Keyword(s):  
Variational Problem ◽  
Theta Function ◽  
Dedekind Eta Function ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Natural Logarithm ◽  
Two Parameters

We consider a deformation $E_{L,\unicode[STIX]{x1D6EC}}^{(m)}(it)$ of the Dedekind eta function depending on two $d$-dimensional simple lattices $(L,\unicode[STIX]{x1D6EC})$ and two parameters $(m,t)\in (0,\infty )$, initially proposed by Terry Gannon. We show that the minimisers of the lattice theta function are the maximisers of $E_{L,\unicode[STIX]{x1D6EC}}^{(m)}(it)$ in the space of lattices with fixed density. The proof is based on the study of a lattice generalisation of the logarithm, called the lattice logarithm, also defined by Terry Gannon. We also prove that the natural logarithm is characterised by a variational problem over a class of one-dimensional lattice logarithms.

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