A separated-flow model for collapsible-tube oscillations

1985 ◽  
Vol 157 ◽  
pp. 375-404 ◽  
Author(s):  
Claudio Cancelli ◽  
T. J. Pedley
Keyword(s):  
Equations Of Motion ◽  
Separated Flow ◽  
Propagation Speed ◽  
Adverse Pressure Gradient ◽  
Collapsible Tube ◽  
State Collapse ◽  
One Dimensional ◽  
Longitudinal Wall ◽  
Wave Propagation Speed ◽  
The One

A new model is presented to describe flow in segments of collapsible tube mounted between two rigid tubes and surrounded by a pressurized container. The new features of the model are the inclusion of (a) longitudinal wall tension and (b) energy loss in the separated flow downstream of the time-dependent constriction in a collapsing tube, in a manner which is consistent with the one-dimensional equations of motion. As well as accurately simulating steady-state collapse, the model predicts self-excited oscillations whose amplitude is large enough to be observable only if the flow in the collapsible tube becomes supercritical somewhere (fluid speed exceeding long-wave propagation speed). The dynamics of the oscillations is dominated by longitudinal movement of the point of flow separation, in response to the adverse pressure gradient associated with waves propagating backwards and forwards between the (moving) narrowest point of the constriction and the tube outlet.

Oscillating flames: multiple-scale analysis

2009 ◽  
Vol 465 (2107) ◽  
pp. 2089-2110 ◽  
Author(s):  
Luc Bauwens ◽  
C. Regis L. Bauwens ◽  
Ida Wierzba
Keyword(s):  
Approximate Solution ◽  
Reaction Front ◽  
Burning Velocity ◽  
Propagation Speed ◽  
Multiple Scale ◽  
Expansion Ratio ◽  
Scale Analysis ◽  
Dimensional Problem ◽  
One Dimensional ◽  
The One

A complete multiple-scale solution is constructed for the one-dimensional problem of an oscillating flame in a tube, ignited at a closed end, with the second end open. The flame front moves into the unburnt mixture at a constant burning velocity relative to the mixture ahead, and the heat release is constant. The solution is based upon the assumption that the propagation speed multiplied by the expansion ratio is small compared with the speed of sound. This approximate solution is compared with a numerical solution for the same physical model, assuming a propagation speed of arbitrary magnitude, and the results are close enough to confirm the validity of the approximate solution. Because ignition takes place at the closed end, the effect of thermal expansion is to push the column of fluid in the tube towards the open end. Acoustics set in motion by the impulsive start of the column of fluid play a crucial role in the oscillation. The analytical solution also captures the subsequent interaction between acoustics and the reaction front, the effect of which does not appear to be as significant as that of the impulsive start, however.

Integration of one-dimensional equations of motion

2020 ◽  
pp. 3-5
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Potential Energy ◽  
Equations Of Motion ◽  
Field Change ◽  
One Dimensional ◽  
System A ◽  
Small Correction ◽  
The Law ◽  
The One ◽  
The Given

If the potential energy is independent of time, the energy of the system remains constant during the motion of a closed system. A system with one degree of freedom allows for the determination of the law of motion in quadrature. In this chapter, the authors consider motion of the particles in the one-dimensional fields. They discuss also how the law and the period of a particle moving in the potential field change due to adding to the given field a small correction.

One-dimensional dislocations IV. Dynamics

1950 ◽  
Vol 201 (1065) ◽  
pp. 261-268 ◽  
Keyword(s):  
Wave Velocity ◽  
Equations Of Motion ◽  
Dislocation Model ◽  
Characteristic Wave ◽  
One Dimensional ◽  
Regular Sequences ◽  
All Solutions ◽  
Stable Equilibria ◽  
The One

Tho equations of motion of the one-dimensional dislocation model are studied, and all solutions representing disturbances propagated without change of form are obtained. These comprise: (i) dislocations, and regular sequences of the same, either of like or of alternating sign, travelling with velocity less than c , the characteristic wave velocity of the system; (ii) an iddislocations, and sequences of the spme, travelling with velocity greater than c; and (iii) waves of infinitesimal amplitude, belonging to two branches travelling respectively with velocities less than and greater than c . Only dislocations or sequences of dislocations of like sign, and waves of velocity less than c , correspond to stable equilibria. The dislocations exhibit ‘relativistic’ behaviour. The relevance of anti-dislocations to very fast slip in solids is considered, and rejected.

CRITICAL DYNAMICS OF THE XY-MODEL ON THE ONE-DIMENSIONAL SUPERLATTICE BY POSITION SPACE RENORMALIZATION GROUP

1996 ◽  
Vol 10 (22) ◽  
pp. 1077-1083 ◽  
Author(s):  
J.P. DE LIMA ◽  
L.L. GONÇALVES
Keyword(s):  
Renormalization Group ◽  
Equations Of Motion ◽  
Xy Model ◽  
Dynamic Scaling ◽  
Critical Dynamics ◽  
Renormalization Group Theory ◽  
Position Space ◽  
One Dimensional ◽  
Homogeneous Lattice ◽  
The One

The critical dynamics of the isotropic XY-model on the one-dimensional superlattice is considered in the framework of the position space renormalization group theory. The decimation transformation is introduced by considering the equations of motion of the operators associated to the excitations of the system, and it corresponds to an extension of the procedure introduced by Stinchcombe and dos Santos (J. Phys. A18, L597 (1985)) for the homogeneous lattice. The dispersion relation is obtained exactly and the static and dynamic scaling forms are explicitly determined. The dynamic critical exponent is also obtained and it is shown that it is identical to the one of the XY-model on the homogeneous chain.

scholarly journals The One-dimensional Coulomb-force Problem in Classical Radiation Reaction Theories

1977 ◽  
Vol 32 (7) ◽  
pp. 685-691
Author(s):  
W. Heudorfer ◽  
M. Sorg
Keyword(s):  
Coulomb Potential ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Radiation Reaction ◽  
Coulomb Force ◽  
Stationary States ◽  
One Dimensional ◽  
The One ◽  
Force Problem ◽  
Classical Radiation

Abstract Numerical solutions of the recently proposed equations of motion for the classically radiating electron are obtained for the case where the particle moves in a one-dimensional Coulomb potential (both attractive and repulsive). The solutions are discussed and found to be meaningful also in that case, where the well-known Lorentz-Dirac equation fails (attractive Coulomb force). Discrete, stationary states are found in a non-singular version of the Coulomb potential. During the transition between those stationary states the particle looses energy by emission of radiation, which results in a smaller amplitude of the stationary oscillations.

An Application of Mixture Theory to Particulate Sedimentation

1980 ◽  
Vol 47 (2) ◽  
pp. 261-265 ◽  
Author(s):  
C. D. Hill ◽  
A. Bedford ◽  
D. S. Drumheller
Keyword(s):  
Particle Concentration ◽  
Equations Of Motion ◽  
Mixture Theory ◽  
Solid Particles ◽  
Two Phase ◽  
Small Perturbations ◽  
One Dimensional ◽  
Blood Sedimentation ◽  
The One ◽  
Extended Variational Principle

Equations for two-phase flow are used to analyze the one-dimensional sedimentation of solid particles in a stationary container of liquid. A derivation of the equations of motion is presented which is based upon Hamilton’s extended variational principle. The resulting equations contain diffusivity terms, which are linear in the gradient of the particle concentration. It is shown that the solution of the equations for steady sedimentation is stable under small perturbations. Finally, finite-difference solutions of the equations are compared to the data of Whelan, Huang, and Copley for blood sedimentation.

Green's function approach to the Ising model

1969 ◽  
Vol 47 (7) ◽  
pp. 769-777 ◽  
Author(s):  
K. C. Lee ◽  
Robert Barrie
Keyword(s):  
Ising Model ◽  
Green’S Function ◽  
Green's Function ◽  
Body Problem ◽  
Equations Of Motion ◽  
Function Technique ◽  
Many Body ◽  
One Dimensional ◽  
Spinless Fermion ◽  
The One

It is shown that the spin [Formula: see text] Ising model can be formulated as a spinless fermion many-body problem and that the Green's function technique can be applied to it. The hierarchy of Green's function equations of motion terminates at the (q + 1)-particle Green's function, where q is the coordination number. This finite number of equations yields Fisher's transformation of correlations. The technique discussed in this paper can be used to obtain exact results for the one-dimensional Ising model.

Turbulence measurements in an ‘equilibrium’ axisymmetric wall jet

1975 ◽  
Vol 71 (2) ◽  
pp. 317-338 ◽  
Author(s):  
B. R. Ramaprian
Keyword(s):  
Pressure Gradient ◽  
Time Scale ◽  
Adverse Pressure Gradient ◽  
Turbulent Energy ◽  
Wall Jet ◽  
Self Similarity ◽  
Mean Velocity ◽  
One Dimensional ◽  
The One ◽  
Rate Of Dissipation

This paper reports measurements of turbulent quantities in an axisymmetric wall jet subjected to an adverse pressure gradient in a conical diffuser, in such a way that a suitably defined pressure-gradient parameter is everywhere small. Self-similarity is observed in the mean velocity profile, as well as the profiles of many turbulent quantities at sufficiently large distances from the injection slot. Autocorrelation measurements indicate that, in the region of turbulent production, the time scale of ν fluctuations is very much smaller than the time scale ofufluctuations. Based on the data on these time scales, a possible model is proposed for the Reynolds stress. One-dimensional energy spectra are obtained for theu, vandwcomponents at several points in the wall jet. It is found that self-similarity is exhibited by the one-dimensional wavenumber spectrum of$\overline{q^2}(=\overline{u^2}+\overline{v^2}+\overline{w^2})$, if the half-width of the wall jet and the local mean velocity are used for forming the non-dimensional wavenumber. Both the autocorrelation curves and the spectra indicate the existence of periodicity in the flow. The rate of dissipation of turbulent energy is estimated from the$\overline{q^2}$spectra, using a slightly modified version of a previously suggested method.

scholarly journals Violent Relaxation and Mixing in 1-D Gravitational Systems

1987 ◽  
Vol 127 ◽  
pp. 523-524
Author(s):  
Marc Luwel
Keyword(s):  
Surface Density ◽  
Gravitational Force ◽  
Equations Of Motion ◽  
Dimensional System ◽  
Double Precision ◽  
One Dimensional ◽  
Gravitational Systems ◽  
Gravitational Model ◽  
The One

The one dimensional gravitational model consists of N mass sheets with surface density mi, parallel to the (y, z)–plane and constrained to move along the x-axis under influence of their mutual gravitational force Fij = −2πGmimj sgn(xi – xj). in order to study the evolution of this one–dimensional system, the N Newtonian equations of motion are integrated numerically, using an “exact” double precision algorithm.

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