Multiple existence of steady state solutions of acoustic streaming in a long two‐dimensional rectangular box

2003 ◽  
Vol 114 (4) ◽  
pp. 2329-2329
Author(s):  
Takeru Yano
Keyword(s):  
Steady State ◽  
Acoustic Streaming ◽  
Two Dimensional ◽  
Steady State Solutions

scholarly journals The viscous froth model: steady states and the high-velocity limit

2009 ◽  
Vol 465 (2108) ◽  
pp. 2391-2405 ◽  
Author(s):  
S. J. Cox ◽  
D. Weaire ◽  
G. Mishuris
Keyword(s):  
Steady State ◽  
High Velocity ◽  
Steady States ◽  
Two Dimensional ◽  
Isolated Points ◽  
Physical Effects ◽  
Straight Lines ◽  
Steady State Solutions ◽  
Finite Extent

The steady-state solutions of the viscous froth model for foam dynamics are analysed and shown to be of finite extent or to asymptote to straight lines. In the high-velocity limit, the solutions consist of straight lines with isolated points of infinite curvature. This analysis is helpful in the interpretation of observations of anomalous features of mobile two-dimensional foams in channels. Further physical effects need to be adduced in order to fully account for these.

Detonation in supersonic radial outflow

2014 ◽  
Vol 760 ◽  
pp. 313-341 ◽  
Author(s):  
Aslan R. Kasimov ◽  
Svyatoslav V. Korneev
Keyword(s):  
Steady State ◽  
Supersonic Flow ◽  
Radial Flow ◽  
Gaseous Detonation ◽  
Two Dimensional ◽  
Structure And Dynamics ◽  
Cellular Detonations ◽  
The Stability ◽  
Radial Outflow ◽  
Steady State Solutions

AbstractWe report on the structure and dynamics of gaseous detonation stabilized in a supersonic flow emanating radially from a central source. The steady-state solutions are computed and their range of existence is investigated. Two-dimensional simulations are carried out in order to explore the stability of the steady-state solutions. It is found that both collapsing and expanding two-dimensional cellular detonations exist. The latter can be stabilized by putting several rigid obstacles in the flow downstream of the steady-state sonic locus. The problem of initiation of standing detonation stabilized in the radial flow is also investigated numerically.

scholarly journals Stability and instability results for the 2D [alpha]-Euler equations

2017 ◽  
Author(s):  
◽  
Shibi Kapisthalam Vasudevan
Keyword(s):  
Steady State ◽  
Euler Equations ◽  
Nonlinear Term ◽  
Zero Mode ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Fourier Decomposition ◽  
Inviscid Incompressible Fluid ◽  
Stability And Instability ◽  
Steady State Solutions

We study stability and instability of time independent solutions of the two dimensional a-Euler equations and Euler equations; the a-Euler equations are obtained by replacing the nonlinear term (u [times] [del.])u in the classical Euler equations of inviscid incompressible fluid by the term (v [times] [del.])u, where v is the regularized velocity satisfying (1 -[alpha]2[delta])v [equals] u, and [alpha] [greater than] 0. In the first part of the thesis, for the a-model, we develop analogues of the classical Arnol'd type stability criteria based on the energy-Casimir method for several settings including multi connected domains, periodic channels, and others. In the second part of the thesis, we study stability of a particular steady state, the unidirectional solution of the a-Euler equation on the two dimensional torus, having only one non zero mode in its Fourier decomposition. Using continued fractions, we give a proof of instability of the steady state under fairly general conditions. In the third part of the thesis we study various properties of a family of elliptic operators introduced by Zhiwu Lin in his work on instability of steady state solutions of the two dimensional Euler equations. This involves Birman-Schwinger type operators associated with the linearization of the Euler equations about the steady state and certain perturbation determinants.

Time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of a line current

1968 ◽  
Vol 2 (1) ◽  
pp. 51-57 ◽  
Author(s):  
R. C. Hewson-Browne ◽  
D. N. Burghes
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Time History ◽  
Time Dependent ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Line Current ◽  
History Of ◽  
Steady State Solutions ◽  
The Magnetic Field

This paper concerns the time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of a line current. The two-dimensional problem is formulated and solved with two particular classes of solutions being given; namely, the steady-state solutions and the time-history of the interaction with a cloud of flux.

Explicit steady state solutions for a particularM(x)/M/1 queueing system

1977 ◽  
Vol 24 (4) ◽  
pp. 651-659 ◽  
Author(s):  
George L. Jensen ◽  
Albert S. Paulson ◽  
Pasquale Sullo
Keyword(s):  
Steady State ◽  
Queueing System ◽  
Steady State Solutions

Nonlinear Vibrations of Viscoelastic Plane Truss Under Harmonic Excitation

2014 ◽  
Vol 14 (04) ◽  
pp. 1450009 ◽  
Author(s):  
Andrew Yee Tak Leung ◽  
Hong Xiang Yang ◽  
Ping Zhu
Keyword(s):  
Steady State ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Homotopy Continuation ◽  
Response Curves ◽  
System A ◽  
Structural Responses ◽  
Voigt Model ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

This paper is concerned with the steady state bifurcations of a harmonically excited two-member plane truss system. A two-degree-of-freedom Duffing system having nonlinear fractional derivatives is derived to govern the dynamic behaviors of the truss system. Viscoelastic properties are described by the fractional Kelvin–Voigt model based on the Caputo definition. The combined method of harmonic balance and polynomial homotopy continuation is adopted to obtain steady state solutions analytically. A parametric study is conducted with the help of amplitude-response curves. Despite its seeming simplicity, the mechanical system exhibits a wide variety of structural responses. The primary and sub-harmonic resonances and chaos are found in specific regions of system parameters. The dynamic snap-through phenomena are observed when the forcing amplitude exceeds some critical values. Moreover, it has been shown that, suppression of undesirable responses can be achieved via changing of viscosity of the system.

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