THE COMPOSITION OF THE POSITIVE COLUMN OF A HELIUM GLOW DISCHARGE AT INTERMEDIATE PRESSURES

1979 ◽  
Vol 40 (C7) ◽  
pp. C7-127-C7-128
Author(s):  
F. Dothan ◽  
Yu. M. Kagan
Keyword(s):  
Glow Discharge ◽  
Differential Equations ◽  
Positive Column ◽  
Molecular Ions ◽  
Time Change ◽  
The Other ◽  
System Of Differential Equations ◽  
Plasma Parameters ◽  
Electron Collisions

The concentration of atomic and molecular ions and metastables is investigated for the positive column of a helium glow discharge. Recently (1,2) the system of differential equations for the helium afterglow describing the time change of these plasma parameters was written and solved. In the stationary positive column we can neglect some processes which are importent in the afterglow. On the other side we must take into account processes of excitation and ionization by electron collisions which can be neglected in the afterglow.

The effect of molecular ions on the plasma parameters in a medium pressure rare gas radio frequency discharge positive column

1992 ◽  
Vol 72 (7) ◽  
pp. 2632-2637 ◽  
Author(s):  
Jen‐Shih Chang ◽  
Y. Ichikawa ◽  
R. M. Hobson ◽  
S. Matsumura ◽  
S. Teii
Keyword(s):  
Radio Frequency ◽  
Positive Column ◽  
Molecular Ions ◽  
Rare Gas ◽  
Plasma Parameters ◽  
Medium Pressure ◽  
Radio Frequency Discharge

Snap-Through Phenomenon and Self-Contact of Spatial Elastica Subjected to Mid-Torque

2015 ◽  
Vol 07 (04) ◽  
pp. 1550057
Author(s):  
Boonchai Phungpaingam ◽  
Lawrence N. Virgin ◽  
Somchai Chucheepsakul
Keyword(s):  
Differential Equations ◽  
Shooting Method ◽  
Contact Point ◽  
Point Load ◽  
The Other ◽  
Arc Length ◽  
System Of Differential Equations ◽  
Kinematic Singularity ◽  
Euler Parameters ◽  
Equilibrium Configurations

This paper presents the snap-through phenomenon and effect of self-contact of the spatial elastica subjected to mid-length torque. One end of the elastica is clamped while the other end is placed in a sleeve joint. The total arc-length of the elastica can be varied by sliding the end through the sleeve joint. At a certain value of total arc-length, the sleeve joint is clamped and an external torque is applied at the mid-length of the elastica. The system of governing differential equations is derived from the equilibrium of an elastica segment and geometric relations of the inextensible elastica. The transformation matrix formulated in terms of Euler parameters is utilized to avoid the kinematic singularity. To display the behavior of the elastica, the system of differential equations needs to be integrated numerically from one end to the other end. The integration is performed so that the boundary conditions and some constraint conditions of the problem are satisfied, i.e., a shooting method is used. The effect of self-contact is taken into account by considering the contact force as a point load applying at contact point. From the results, the snap-through phenomenon, effect of self-contact and equilibrium configurations are highlighted herein.

scholarly journals MHV graviton scattering amplitudes and current algebra on the celestial sphere

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Shamik Banerjee ◽  
Sudip Ghosh ◽  
Partha Paul
Keyword(s):  
Scattering Amplitudes ◽  
Differential Equations ◽  
Current Algebra ◽  
Minimal Model ◽  
Symmetry Algebra ◽  
Local Symmetry ◽  
The Other ◽  
System Of Differential Equations ◽  
First Order ◽  
Celestial Sphere

Abstract The Cachazo-Strominger subleading soft graviton theorem for a positive helicity soft graviton is equivalent to the Ward identities for $$ \overline{\mathrm{SL}\left(2,\mathrm{\mathbb{C}}\right)} $$ SL 2 ℂ ¯ currents. This naturally gives rise to a $$ \overline{\mathrm{SL}\left(2,\mathrm{\mathbb{C}}\right)} $$ SL 2 ℂ ¯ current algebra living on the celestial sphere. The generators of the $$ \overline{\mathrm{SL}\left(2,\mathrm{\mathbb{C}}\right)} $$ SL 2 ℂ ¯ current algebra and the supertranslations, coming from a positive helicity leading soft graviton, form a closed algebra. We find that the OPE of two graviton primaries in the Celestial CFT, extracted from MHV amplitudes, is completely determined in terms of this algebra. To be more precise, 1) The subleading terms in the OPE are determined in terms of the leading OPE coefficient if we demand that both sides of the OPE transform in the same way under this local symmetry algebra. 2) Positive helicity gravitons have null states under this local algebra whose decoupling leads to differential equations for MHV amplitudes. An n point MHV amplitude satisfies two systems of (n − 2) linear first order PDEs corresponding to (n − 2) positive helicity gravitons. We have checked, using Hodges’ formula, that one system of differential equations is satisfied by any MHV amplitude, whereas the other system has been checked up to six graviton MHV amplitude. 3) One can determine the leading OPE coefficients from these differential equations.This points to the existence of an autonomous sector of the Celestial CFT which holographically computes the MHV graviton scattering amplitudes and is completely defined by this local symmetry algebra. The MHV-sector of the Celestial CFT is like a minimal model of 2-D CFT.

Critical Force in the Buckling of Drill Bits

1979 ◽  
Vol 46 (2) ◽  
pp. 461-462 ◽  
Author(s):  
L. E. Bobisud ◽  
C. O. Christenson
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Fourth Order ◽  
Critical Force ◽  
The Other ◽  
Maximum Force ◽  
System Of Differential Equations ◽  
Linearized Equations ◽  
Drill Bits

We consider a fourth-order nonlinear system of differential equations that describe the slope of a steadily rotating flexible rod, one end of which is clamped, and the other end of which is “hinged.” There is a force directed along the length of the rod. We graph against speed of rotation the maximum force that can be applied before buckling occurs, using linearized equations.

scholarly journals Investigation in the Effect of Applied Voltage and Working Pressure on Some Plasma Parameters in the Positive Column of Dc Glow Discharge

2019 ◽  
Vol 32 (2) ◽  
pp. 9
Author(s):  
Mustafa K. Jassim
Keyword(s):  
Glow Discharge ◽  
Cross Sections ◽  
Applied Voltage ◽  
Positive Column ◽  
Plasma Frequency ◽  
Debye Length ◽  
Experimental Results ◽  
Plasma Parameters ◽  
Working Pressure ◽  
Number Of Particles

     Comsol multiphysics software is established to make a simulation that is comparable with experimental device. by utilizing comsol, the positive column domain of direct-current glow discharge with argon is considered for both of different applied voltage and working gas pressure. The calculations are exhibited by using a precise collision cross sections and Townsend coefficients for the argon. The impacts of voltage and pressure on the Debye length, number of particles in Debye sphere and plasma frequency are calculated and graphically delineated. With this regard to the dependence of plasma parameters on the applied voltage and pressure, some of them are found to be compatible with the experimental results, while others are not. For example, the calculations of the COMSOL shows that the electron temperature is not always decreasing with the increase in the applied voltage, and the Debye length does not give a linearly decreasing relationship but rather an exponentially decreasing relationship. Also, the calculations do not reproduce and match the experimental results for the dependence electron density on working pressure at various potentials.

scholarly journals New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Osama Moaaz ◽  
Choonkil Park ◽  
Elmetwally M. Elabbasy ◽  
Waed Muhsin
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
The Other ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

scholarly journals Outflowing Envelopes From Stars at Arbitrary Optical Depths a New Approach to the Problem

1998 ◽  
Vol 11 (1) ◽  
pp. 381-381
Author(s):  
A.V. Dorodnitsyn
Keyword(s):  
Differential Equations ◽  
Massive Star ◽  
System Of Differential Equations ◽  
Continuous Transition ◽  
Satisfactory Description ◽  
Sonic Point ◽  
New Approach ◽  
Star Evolution ◽  
Matter Flux ◽  
Massive Star Evolution

We have considered a stationary outflowing envelope accelerated by the radiative force in arbitrary optical depth case. Introduced approximations provide satisfactory description of the behavior of the matter flux with partially separated radiation at arbitrary optical depths. The obtained systemof differential equations provides a continuous transition of the solution between optically thin and optically thick regions. We analytically derivedapproximate representation of the solution at the vicinity of the sonic point. Using this representation we numerically integrate the system of equations from the critical point to the infinity. Matching the boundary conditions we obtain solutions describing the problem system of differential equations. The theoretical approach advanced in this work could be useful for self-consistent simulations of massive star evolution with mass loss.

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