SOME EXACT SOLUTIONS OF THE LORENTZ INVARIANT PROBLEM OF THE MOTION OF TWO ELECTRIC FLUIDS

1955 ◽  
Vol 33 (12) ◽  
pp. 819-823 ◽  
Author(s):  
J. J. Gibbons
Keyword(s):  
Steady State ◽  
Exact Solutions ◽  
Cylindrical Symmetry ◽  
Axially Symmetric ◽  
Two Fluids ◽  
Body Forces ◽  
Steady State Solutions

Methods of generating exact steady-state solutions for the flow of superimposed positive and negative fluids are developed for the cases of linear and cylindrical motion. The two fluids are assumed to be subject only to body forces arising from the total E and B fields. It is shown that the only axially symmetric solutions are of cylindrical symmetry, i.e. rotating spheres or rings of charge cannot satisfy the equations where the two fluids overlap.

Exact Solutions for Unsteady Magnetohydrodynamic Oscillatory Flow of a Maxwell Fluid in a Porous Medium

2013 ◽  
Vol 68 (10-11) ◽  
pp. 635-645 ◽  
Author(s):  
Ilyas Khan ◽  
Farhad Ali ◽  
Sharidan Shafie ◽  
Keyword(s):  
Steady State ◽  
Exact Solutions ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Transform Method ◽  
Transient Solutions ◽  
The Laplace Transform ◽  
Porous Half Space ◽  
The Given ◽  
Steady State Solutions

In this paper, exact solutions of velocity and stresses are obtained for the magnetohydrodynamic (MHD) flow of a Maxwell fluid in a porous half space by the Laplace transform method. The flows are caused by the cosine and sine oscillations of a plate. The derived steady and transient solutions satisfy the involved differential equations and the given conditions. Graphs for steady-state and transient velocities are plotted and discussed. It is found that for a large value of the time t, the transient solutions disappear, and the motion is described by the corresponding steady-state solutions.

scholarly journals Steady state solutions for a lubrication multi-fluid flow

2011 ◽  
Vol 22 (6) ◽  
pp. 581-612 ◽  
Author(s):  
LAURENT CHUPIN ◽  
BÉRÉNICE GREC
Keyword(s):  
Steady State ◽  
Shear Velocity ◽  
Stationary Flow ◽  
Stationary Solutions ◽  
Original Method ◽  
Physical Parameters ◽  
Square Root ◽  
Two Fluids ◽  
Superposed Fluids ◽  
Steady State Solutions

We describe possible solutions for a stationary flow of two superposed fluids between two close surfaces in relative motion. Physically, this study is within the lubrication framework, in which it is of interest to predict the relative positions of the lubricant and the air in the device. Mathematically, we observe that this problem corresponds to finding the interface between the two fluids, and we prove that this interface can be viewed as a square root of a polynomial of degree at most 6. We solve this equation using an original method. First, we check that our results are consistent with previous work. Next, we use this solution to answer some physically relevant questions related to the lubrication setting. For instance, we obtain theoretical and numerical results, which can predict the occurrence of a full film with respect to physical parameters (fluxes, shear velocity, viscosities). In particular, we present a figure giving the number of stationary solutions depending on the physical parameters. Moreover, we give some indications for a better understanding of the multi-fluid case.

scholarly journals Global Circulation in an Axially Symmetric Shallow-Water Model, Forced by Off-Equatorial Differential Heating

2010 ◽  
Vol 67 (4) ◽  
pp. 1275-1286 ◽  
Author(s):  
Ori Adam ◽  
Nathan Paldor
Keyword(s):  
Steady State ◽  
Shallow Water ◽  
Hadley Circulation ◽  
Present Theory ◽  
Water Model ◽  
Tropical Region ◽  
Axially Symmetric ◽  
Shallow Water Model ◽  
Differential Heating ◽  
Steady State Solutions

Abstract An axially symmetric inviscid shallow-water model (SWM) on the rotating Earth forced by off-equatorial steady differential heating is employed to characterize the main features of the upper branch of an ideal Hadley circulation. The steady-state solutions are derived and analyzed and their relevance to asymptotic temporal evolution of the circulation is established by comparing them to numerically derived time-dependent solutions at long times. The main novel feature of the steady-state solutions of the present theory is the existence of a tropical region, associated with the rising branch of the Hadley circulation, which extends to about half the combined width of the Hadley cells in the two hemispheres and is dominated by strong vertical advection of momentum. The solutions in this tropical region are characterized by three conditions: (i) the meridional temperature gradient is very weak but drastically increases outside of the region, (ii) moderate easterlies exist only inside this region and they peak off the equator, and (iii) angular momentum is not conserved there. The momentum fluxes of the new solutions at the tropics differ qualitatively from those of existing nearly inviscid theories and the new flux estimates are in better agreement with both observations and axially symmetric simulations. As in previous nearly inviscid theories, the steady solutions of the new theory are determined by a thermal Rossby number and by the latitude of maximal heating.

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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