Analogy between soap film and gas dynamics. II. Experiments on one-dimensional motion of shock waves in soap films

2003 ◽  
Vol 34 (2) ◽  
pp. 173-180 ◽  
Author(s):  
C. Y. Wen ◽  
S. K. Chang-Jian ◽  
M. C. Chuang
Keyword(s):  
Shock Waves ◽  
Gas Dynamics ◽  
Soap Film ◽  
Soap Films ◽  
One Dimensional

scholarly journals A Björling representation for Jacobi fields on minimal surfaces and soap film instabilities

2020 ◽  
Vol 476 (2238) ◽  
pp. 20190903
Author(s):  
Gareth P. Alexander ◽  
Thomas Machon
Keyword(s):  
Minimal Surfaces ◽  
General Framework ◽  
Soap Film ◽  
Jacobi Field ◽  
Soap Films ◽  
Jacobi Fields ◽  
One Dimensional ◽  
Stable Domain ◽  
Transverse Gradient ◽  
Geometric Nature

We develop a general framework for the description of instabilities on soap films using the Björling representation of minimal surfaces. The construction is naturally geometric and the instability has the interpretation as being specified by its amplitude and transverse gradient along any curve lying in the minimal surface. When the amplitude vanishes, the curve forms part of the boundary to a critically stable domain, while when the gradient vanishes the Jacobi field is maximal along the curve. In the latter case, we show that the Jacobi field is maximally localized if its amplitude is taken to be the lowest eigenfunction of a one-dimensional Schrödinger operator. We present examples for the helicoid, catenoid, circular helicoids and planar Enneper minimal surfaces, and emphasize that the geometric nature of the Björling representation allows direct connection with instabilities observed in soap films.

Gasdynamic-Like Equations for Oblique Shock Waves and Nozzle Flows in Soap Films

2004 ◽  
Vol 20 (1) ◽  
pp. 69-76 ◽  
Author(s):  
C.-Y. Wen ◽  
J.-Y. Lai
Keyword(s):  
Shock Waves ◽  
Compressible Flows ◽  
Specific Property ◽  
Oblique Shock ◽  
Soap Films ◽  
Governing Equations ◽  
One Dimensional ◽  
Velocity Relation ◽  
Short Time ◽  
Nozzle Flows

ABSTRACTThe governing equations for oblique shock waves and nozzle flows in soap films are formulated based on their very specific property equations. The θ-β-M relation for oblique shock waves and the width-velocity relation for quasi-one-dimensional nozzle flows are presented. The results are similar to those of compressible gases. On short time scales, the analogy of soap films to two-dimensional (2-D) compressible gases with a specific heat ratio of γ = 1.0 that is shown by Wen and Lai [1], Wen, et al. [2] and Chomaz [3] is again demonstrated. The present results supplement the theory of compressible flows in soap films.

scholarly journals On the evolution of shock-waves in mathematical models of the aorta

1981 ◽  
Vol 22 (3) ◽  
pp. 257-269 ◽  
Author(s):  
L. K. Forbes
Keyword(s):  
Shock Wave ◽  
Blood Flow ◽  
Shock Waves ◽  
Gas Dynamics ◽  
Pulse Propagation ◽  
One Dimensional ◽  
Flow Models ◽  
Wave Development ◽  
Blood Flow Models ◽  
The One

AbstractThe one-dimensional, non-linear theory of pulse propagation in large arteries is examined in the light of the analogy which exists with gas dynamics. Numerical evidence for the existence of shock-waves in current one-dimensional blood-flow models is presented. Some methods of suppressing shock-wave development in these models are indicated.

scholarly journals Quantitative Experimental and Theoretical Investigations on the Interaction of Shock Waves with Magnetic Fields

1969 ◽  
Vol 24 (10) ◽  
pp. 1449-1457
Author(s):  
H. Klingenberg ◽  
F. Sardei ◽  
W. Zimmermann
Keyword(s):  
Magnetic Fields ◽  
Shock Waves ◽  
Physical Model ◽  
Spectroscopic Method ◽  
Experimental Results ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Theoretical Investigations ◽  
Theoretical Predictions ◽  
Interaction Of Shock Waves

Abstract In continuation of the work on interaction between shock waves and magnetic fields 1,2 the experiments reported here measured the atomic and electron densities in the interaction region by means of an interferometric and a spectroscopic method. The transient atomic density was also calculated using a one-dimensional theory based on the work of Johnson3 , but modified to give an improved physical model. The experimental results were compared with the theoretical predictions.

Propagation of one-dimensional planar and nonplanar shock waves in nonideal radiating gas

2021 ◽  
Vol 33 (4) ◽  
pp. 046106
Author(s):  
Mayank Singh ◽  
Rajan Arora
Keyword(s):  
Shock Waves ◽  
One Dimensional
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