scholarly journals Brillouin backscattering instability in inhomogeneous collisional plasma

2001 ◽  
Vol 19 (2) ◽  
pp. 223-229 ◽  
Author(s):  
BASSAM SHALABI ◽  
AHMED AL-KHATEEB
Keyword(s):  
Growth Rate ◽  
Convective Instability ◽  
Linear Density ◽  
Amplification Factor ◽  
Collisional Plasma ◽  
Square Root ◽  
Threshold Intensity ◽  
Times Square ◽  
Coupling Equations ◽  
Scale Length

Brillouin backscattering instability is investigated in inhomogeneous collisional plasma. The slow-coupling equations for the instability in a medium with linear density ramp are obtained. For large inhomogeneity scale length, the homogeneous growth rate is found to be modified by a factor of[1/square root(2) times square root(ω02/ (ω02 + νe2) + ω0/square root(ω02 + νe2))]For the convective instability, the amplification factor is found to be[Λ = (|γB0|2/2β)(ω02/ω02 + νe2)]The presence of collisions leads to a reduction in both the growth rate and the amplification factor, where the threshold intensity for the instability to occur increases.

Parametric instabifity of transverse and Langmuir waves in a plasma

1975 ◽  
Vol 13 (2) ◽  
pp. 317-326 ◽  
Author(s):  
Kai Fong Lee
Keyword(s):  
Growth Rate ◽  
Electromagnetic Field ◽  
Kinetic Model ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Threshold Intensity ◽  
Langmuir Waves ◽  
Scale Perturbation ◽  
The Subject ◽  
Parametric Instabilities

The parametric excitation of transverse and Langmuir waves by an externally-driven electromagnetic field of frequency (ω0 > 2ωp) in a warm and collisional plasma is studied, using the fluid equations. By an application of the multiple- time-scale perturbation method, the threshold intensity and the growth rate above threshold are obtained. The results are compared with those of Goldman (1969) and Prasad (1968), both of whom worked with a kinetic model.The theory of parametric instabilities in plasmas has been the subject of numerous investigations in recent years. Broadly speaking, the instabilities can be grouped into two categories: those for which the excited waves are purely electrostatic (see e.g. DuBois & Goldman 1965, 1967; Silin 1965; Lee & Su 1966; Jackson 1967; Nishikawa 1968; Kaw & Dawson 1969; Tzoar 1969; Sanmartin 1970; McBride 1970; Perkins & Flick 1971; Fejer & Leer 1972a, b; Bezzerides & Weinstock 1972; DuBois & Goldman 1972), and those for which one of the excited waves is electromagnetic (see e.g. Goldman & Dubois 1965; Montgomery & Alexeff 1966; Chen & Lewak 1970; Bodner & Eddleman 1972; Fejer & Leer 1972b; Lee & Kaw 1972; Forslund et al. 1972).

scholarly journals Model of oscillatory instability in vertically-homogeneous atmosphere

2009 ◽  
Vol 15 ◽  
pp. 57-63
Author(s):  
P. B. Rutkevich ◽  
P P. Rutkevych
Keyword(s):  
Growth Rate ◽  
Coriolis Force ◽  
Convective Instability ◽  
Linear Phase ◽  
Oscillatory Behaviour ◽  
Nonlinear Simulation ◽  
Analytical Analysis ◽  
Rfbr Grant ◽  
Amplitude Growth ◽  
Abstract Existence

Abstract. Existence and repeatability of tornadoes could be straightforwardly explained if there existed instability, responsible for their formation. However, it is well known that convection is the only instability in initially stable air, and the usual convective instability is not applicable for these phenomena. In the present paper we describe an instability in the atmosphere, which can be responsible for intense vortices. This instability appears in a fluid with Coriolis force and dissipation and has oscillatory behaviour, where the amplitude growth is accompanied by oscillations with frequency comparable to the growth rate of the instability. In the paper, both analytical analysis of the linear phase of the instability and nonlinear simulation of the developed stage of the air motion are addressed. This work was supported by the RFBR grant no. 09-05-00374-a.

Factors influencing macular atrophy growth rates in neovascular age-related macular degeneration treated with ranibizumab or aflibercept according to an observe-and-plan regimen

2018 ◽  
Vol 103 (7) ◽  
pp. 900-905 ◽  
Author(s):  
Irmela Mantel ◽  
Marta Zola ◽  
Sophie De Massougnes ◽  
Ali Dirani ◽  
Ciara Bergin
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Pigment Epithelium ◽  
Age Related Macular Degeneration ◽  
Square Root ◽  
Factors Associated ◽  
Macular Atrophy ◽  
Age Related ◽  
Lower Baseline ◽  
Fellow Eyes

Background/aimsTo investigate the factors associated with macular atrophy (MA) growth rates in neovascular age-related macular degeneration treated with either ranibizumab or aflibercept.MethodsWe obtained data from two identical prospective studies using ranibizumab or aflibercept under observe-and-plan variable dosing regimens. We analysed eyes that presented MA within 2 years. After applying square root transformations to MA sizes, we calculated MA growth rate from baseline to the year 2 endpoint and used univariate and multivariate analyses to detect ocular and treatment factors associated with the MA growth rate.ResultsIncluded were 109 eyes from 101 patients (mean age 80.6 years). The mean square-root-transformed MA growth rate was 0.54±0.34 mm/year. The univariate analyses revealed that MA growth rates were significantly associated with lower baseline visual acuities (p=0.001) and thicker subretinal tissue complexes (p=0.006) and near-significantly associated with the presence of pigment epithelium detachment (p=0.057) and choroidal neovascularisation subtypes (p=0.069). Our multivariate analysis confirmed the significance of lower baseline visual acuities (p=0.008) and pigment epithelium detachments higher than 200 µm (p=0.035). Furthermore, MA growth rates in neovascular eyes significantly correlated with MA growth rates in non-neovascular fellow eyes (n=61; p=0.003).ConclusionMA growth rates were associated with ocular factors in the study eyes and the fellow eyes but not with the drug or the number of injections within this variable dosing regimen.

Lateral Diffusion of Platinum Through Pt2Si in Pt/Si Couples

1982 ◽  
Vol 18 ◽  
Author(s):  
L. R. Zheng ◽  
L. S. Hung ◽  
J. W. Mayer
Keyword(s):  
Activation Energy ◽  
Growth Rate ◽  
Electron Microprobe ◽  
Lateral Diffusion ◽  
Square Root ◽  
Diffusion Couples ◽  
X Ray ◽  
Temperature Range ◽  
Scanning Electron

Lateral diffusion couples formed by depositing platinum islands on silicon layers on Al2O3 were used in conjunction with scanning electron microprobe measurements to investigate the growth of platinum silicides in the temperature range 400–700 °C. The phase Pt2Si grows over a length of 4–30 μm with a rate proportional to the square root of time and an activation energy of approximately 1.3 eV. With samples containing 7 at.% Rh in the platinum, the growth rate of Pt2Si is reduced and the activation energy is increased to about 2.0 eV. In these Pt–7at.% Rh samples, electron-induced X-ray measurements indicate that rhodium remains in the original deposited region while both platinum and silicon diffuse in the formed Pt2Si region.

Dynamics of kink instability in a non-uniform magnetoplasma

1987 ◽  
Vol 38 (2) ◽  
pp. 309-316 ◽  
Author(s):  
R. Bharuthram ◽  
P. K. Shukla
Keyword(s):  
Growth Rate ◽  
Dispersion Relation ◽  
Stationary Solution ◽  
Mode Coupling ◽  
Magnetized Plasma ◽  
Linear Regime ◽  
Electron Current ◽  
Coupling Equations ◽  
Kink Instability ◽  
Nonlinear Fluid

Accounting for an external electron current gradient, a set of nonlinear fluid equations governing the dynamics of kink instability in an inhomogeneous magnetized plasma has been derived. In the linear regime, the dispersion relation is analysed and the variation of the growth rate is graphically shown. In the nonlinear regime, it is shown that a quasi-stationary solution of the mode coupling equations can be represented as a dipolar vortex. Conditions under which the latter arises are given.

A hidden square-root boundary between growth rate and biomass yield

2009 ◽  
Vol 102 (1) ◽  
pp. 73-80 ◽  
Author(s):  
Wilson W. Wong ◽  
Linh M. Tran ◽  
James C. Liao
Keyword(s):  
Growth Rate ◽  
Biomass Yield ◽  
Square Root

Dependence of Cu/Sn and Cu/60Sn40Pb Solder Joint Strength on Diffusion Controlled Growth of Cu3Sn and Cu6Sn5

1984 ◽  
Vol 40 ◽  
Author(s):  
D. S. Dunn ◽  
T. F. Marinis ◽  
W. M. Sherry ◽  
C. J. Williams
Keyword(s):  
Growth Rate ◽  
Intermetallic Compounds ◽  
Isothermal Aging ◽  
Joint Strength ◽  
Tensile Tests ◽  
Square Root ◽  
Butt Joints ◽  
Substrate Orientation ◽  
Diffusion Controlled ◽  
Temperature Aging

AbstractThe growth of intermetallic compounds and the strength of Cu/ Sn and Cu/ 60Sn40Pb butt joints were studied as a function of isothermal aging. The effects of single-crystal (100), (110), and (111) oriented copper on the growth rates of Cu3Sn and Cu6Sn5 intermetallic compounds are characterized and the influence of elevated temperature aging on the tensile strength of butt joints analyzed. Substrate orientation appears to influence the growth rate. Metallographic measurements showed that the intermetallic compounds grew at a rate proportional to the square root of time. Tensile tests of aged butt joints revealed a more complex time dependence.

scholarly journals Secondary instability of the stably stratified Ekman layer

2013 ◽  
Vol 728 ◽  
pp. 29-57 ◽  
Author(s):  
Nadia Mkhinini ◽  
Thomas Dubos ◽  
Philippe Drobinski
Keyword(s):  
Growth Rate ◽  
Prandtl Number ◽  
Convective Instability ◽  
Richardson Number ◽  
Finite Amplitude ◽  
Secondary Instability ◽  
Base Flow ◽  
Unstable Wave ◽  
Minor Role ◽  
Ekman Flow

AbstractThe Ekman flow, an exact solution of the Boussinesq equations with rotation, is a prototype flow for both atmospheric and oceanic boundary layers. The effect of stratification on the finite-amplitude longitudinal rolls developing in the Ekman flow and their three-dimensional stability is studied by means of linearized and nonlinear numerical simulations. Similarities and differences with respect to billows developing in the Kelvin–Helmholtz (KH) unidirectional stratified shear flow are discussed. Prandtl number effects are investigated as well as the role played by the buoyant-convective instability. For low Prandtl number, the amplitude of the saturated rolls vanishes at the critical bulk Richardson number, while at high Prandtl number, finite-amplitude rolls are found. The Prandtl number also affects how the growth rate of the secondary instability evolves as the Richardson number is increased. For low Prandtl number, the growth rate decreases as the Richardson number increases while it remains significant for large Prandtl number over the range of stratification studied. This behaviour is likely a result of the differing amplitudes of the roll vortices. Furthermore, the most unstable wave vector is much lower than for the secondary instability of KH billows. Examination of the energetics of the secondary instability shows that buoyant-convective instability is present locally at high Reynolds and Prandtl numbers but plays an overall minor role despite the presence in the base flow of statically unstable regions characterized by a high Richardson number.

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