The Phenomenon of Steady-State String Motion

2000 ◽  
Vol 68 (4) ◽  
pp. 568-574 ◽  
Author(s):  
R. Miroshnik
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Analytical Solutions ◽  
Textile Industry ◽  
Constant Velocity ◽  
High Speed ◽  
Nonlinear Differential Equations ◽  
Viscous Medium ◽  
General Boundary Conditions ◽  
Theoretical Results

The paper examines the phenomenon of steady-state motion for a string traveling with constant velocity along an invariant curve under gravity in a viscous medium. This technically important phenomenon has been known in the literature for about 120 years and may be applied in high-speed turbines, the textile industry, etc. The conditions for the phenomenon’s existence are found. Concepts of two critical string velocities as well as sub, super, and hypercritical domains are introduced. The analytical solutions for the nonlinear differential equations and arbitrary constants for the general boundary conditions are found. The theoretical results are very close to the experimental ones.

scholarly journals Cooling of a plate with general boundary conditions

2000 ◽  
Vol 23 (7) ◽  
pp. 477-485
Author(s):  
F. D. Zaman ◽  
R. Al-Khairy
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Constant Velocity ◽  
Mixed Boundary ◽  
Infinite Plate ◽  
Mixed Boundary Conditions ◽  
General Boundary Conditions ◽  
Steady State Temperature ◽  
Special Cases ◽  
Hopf Method

We consider steady state temperature distribution in a homogeneous rectangular infinite plate the lower part of which is cooled by a fluid flowing at a constant velocity while the upper part satisfies the general mixed boundary conditions. The Wiener-Hopf method has been used to obtain the solution in the infinite series form and some special cases have been discussed.

Paper 1: Computer Solution of Surge Problems

1965 ◽  
Vol 180 (5) ◽  
pp. 62-82
Author(s):  
Victor L. Streeter
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
High Speed ◽  
Transient Flow ◽  
Nonlinear Differential Equations ◽  
Pressure Fluctuations ◽  
Transient Pressure ◽  
Pump Failure ◽  
Flow Equations ◽  
Flow Impedance

Methods for handling the transient flow equations are developed for application of the high-speed digital computer. For incompressible flow cases ordinary nonlinear differential equations occur which are solved simultaneously by established sub-routines on the computer, such as the Runge-Kutta method. For the partial differential equations of compressible water hammer with nonlinear terms such as friction, the method of characteristics and of specified time intervals are employed for those problems in which the flow changes from one steady-state to another steady-state. For steady-oscillatory flow, impedance methods have been adapted to the computer with harmonic analysis of the exciting disturbance. Experimental evidence is presented to confirm the accuracy of the procedures for single and series pipes, for pump failures, and for reciprocating pumps. Additionally the design problem of optimum operation of a valve to minimize transient pressure fluctuations has been introduced and applied to single and series pipes, including a pump failure situation.

A numerical investigation of magnetic reconnection

1996 ◽  
Vol 55 (3) ◽  
pp. 431-448 ◽  
Author(s):  
Craig Anderson ◽  
Ferdinand Jamitzky
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Magnetic Reconnection ◽  
Current Sheet ◽  
High Speed ◽  
Plasma Jets ◽  
Mhd Equations ◽  
Initial Condition ◽  
Reconnection Rate ◽  
Final Steady State

A time-dependent two-dimensional MHD simulation program is used to investigate the magnetic reconnection process with a spatially uniform diffusivity. Various initial conditions are considered and are allowed to evolve until a final steady state is produced. The boundary conditions are carefully handled in order that they be as strict as possible. In the first series of simulations the initial condition is taken to be an analytical solution of the ideal MHD equations given by Biskamp. Dirichlet (fixed) boundary conditions are used, with a small amount of flexibility allowed on the boundary for the stream function in order to prevent any unphysical currents forming. The final steady- state contains a current sheet whose width and length are found to vary as and respectively, and the reconnection rate is found to be independent of the value of Rm, indicative of fast reconnection. Additionally, as Rm, is increased, a region of reversed current and a high-speed jet of plasma are observed to develop along the MHD shock separating the inflow and outflow regions. The second series of simulations uses a slightly different initial condition that allows a faster outflow of plasma from the simulation region. The current sheet width of the final steady state is again found to vary as , and the reconnection rate is again independent of Rm. However, no reversed currents or plasma jetting along the shock are observed, indicating that the plasma jets of previous simulations are due to restrictive outflow conditions, which force the high-speed plasma emerging from the end of the current sheet to divert along the MHD shock. Lastly, the analytical model of Petschek is utilized to provide an initial condition. For this case, however, it is not possible to keep the boundary conditions as strict as before, since both the stream and flux functions have to be allowed to vary slightly in order to deal with the discontinuities of the Petschek model. Although steady-state solutions can be obtained, they are found, owing to the laxness of the boundary conditions, not to exhibit the well-defined structure or small current sheets of the previous results.

Polydyne Cam Mechanisms for Typehead Positioning

1972 ◽  
Vol 94 (1) ◽  
pp. 250-254 ◽  
Author(s):  
K. Kanzaki ◽  
K. Itao
Keyword(s):  
Boundary Conditions ◽  
High Speed ◽  
Design Method ◽  
Polynomial Equations ◽  
Cam Design ◽  
Wide Range ◽  
Theoretical Results

This paper describes a cam design method for typehead positioning in high-speed teleprinters. By this method, residual vibrations are extinguished at plural adjacent rise times and reduced over a comparatively wide range of rise times. The polynomial equations for the cam followers are determined upon consideration of the boundary conditions and the characteristics of the residual vibrations. The theoretical results are verified by the experiments.

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