scholarly journals Statistical equilibrium of bubble oscillations in dilute bubbly flows

2008 ◽  
Vol 20 (4) ◽  
pp. 040902 ◽  
Author(s):  
Tim Colonius ◽  
Rob Hagmeijer ◽  
Keita Ando ◽  
Christopher E. Brennen
Keyword(s):  
Statistical Equilibrium ◽  
Bubbly Flows ◽  
Bubble Oscillations

A Two Time Scales Turbulence Model of Turbulent Bubbly Flows

2013 ◽  
Vol 40 (3) ◽  
pp. 185-203
Author(s):  
Dhahri Maher ◽  
Bellakhel Ghazi ◽  
Chahed Jamel
Keyword(s):  
Time Scales ◽  
Turbulence Model ◽  
Bubbly Flows

Assessment of turbulence models for bubbly flows: Toward a five-equation turbulence model

2020 ◽  
Vol 220 ◽  
pp. 115425
Author(s):  
Ghazi Bellakhal ◽  
Fathia Chaibina ◽  
Jamel Chahed
Keyword(s):  
Turbulence Model ◽  
Turbulence Models ◽  
Bubbly Flows

Collective oscillations in bubble clouds

2011 ◽  
Vol 680 ◽  
pp. 114-149 ◽  
Author(s):  
ZORANA ZERAVCIC ◽  
DETLEF LOHSE ◽  
WIM VAN SAARLOOS
Keyword(s):  
Frequency Response ◽  
Acoustic Field ◽  
Low Frequency ◽  
Acoustic Energy ◽  
Viscous Damping ◽  
Edge States ◽  
Bubble Cloud ◽  
Collective Oscillations ◽  
The Individual ◽  
Bubble Oscillations

In this paper the collective oscillations of a bubble cloud in an acoustic field are theoretically analysed with concepts and techniques of condensed matter physics. More specifically, we will calculate the eigenmodes and their excitabilities, eigenfrequencies, densities of states, responses, absorption and participation ratios to better understand the collective dynamics of coupled bubbles and address the question of possible localization of acoustic energy in the bubble cloud. The radial oscillations of the individual bubbles in the acoustic field are described by coupled linearized Rayleigh–Plesset equations. We explore the effects of viscous damping, distance between bubbles, polydispersity, geometric disorder, size of the bubbles and size of the cloud. For large enough clusters, the collective response is often very different from that of a typical mode, as the frequency response of each mode is sufficiently wide that many modes are excited when the cloud is driven by ultrasound. The reason is the strong effect of viscosity on the collective mode response, which is surprising, as viscous damping effects are small for single-bubble oscillations in water. Localization of acoustic energy is only found in the case of substantial bubble size polydispersity or geometric disorder. The lack of localization for a weak disorder is traced back to the long-range 1/r interaction potential between the individual bubbles. The results of the present paper are connected to recent experimental observations of collective bubble oscillations in a two-dimensional bubble cloud, where pronounced edge states and a pronounced low-frequency response had been observed, both consistent with the present theoretical findings. Finally, an outlook to future possible experiments is given.

COPING WITH UNCERTAINTY IN n-PERSON GAMES

2000 ◽  
Vol 08 (05) ◽  
pp. 503-523 ◽  
Author(s):  
SILVIU GUIASU
Keyword(s):  
Characteristic Function ◽  
Security Council ◽  
Shapley Value ◽  
Statistical Equilibrium ◽  
Individual Rationality ◽  
Von Neumann ◽  
Minimum Deviation ◽  
The Shapley Value ◽  
Un Security Council ◽  
Person Game

A solution of n-person games is proposed, based on the minimum deviation from statistical equilibrium subject to the constraints imposed by the group rationality and individual rationality. The new solution is compared with the Shapley value and von Neumann-Morgenstern's core of the game in the context of the 15-person game of passing and defeating resolutions in the UN Security Council involving five permanent members and ten nonpermanent members. A coalition classification, based on the minimum ramification cost induced by the characteristic function of the game, is also presented.

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