Wave growth characteristics

The threads at the LamRot are affected by cross-wind flow (Sect. 1.2, Fig. 22.2). Kitamura and Takahashi considered the influence of a cross-wind flow on the breakup characteristic with experiments and theoretically by means of stability analysis [32], Increasing gas-Weber number leads to larger critical nondimensional wave number k as well as wave growth rate Q (Fig. 22.3). 

In the breakup regime, spray characteristics include film angle, film velocity and thickness, breakup length, breakup rate, surface wave frequency, wavelength, growth rate, and penetration distance. These quantities, however, are extremely difficult to measure on account of the very small size and rapidly changing features of disintegrating Hquid jets or films. 

These complementary observational constraints indicate that another process participates to the transport of AM in solar-type stars, while MC and turbulence are successful in more massive stars. The two most likely candidates are the large-scale magnetic field which could be present in the radiative zone and the internal gravity waves (hereafter 1GW) which are generated by the external convective zone. As we just explained, the observations suggest that the efficiency of this process is finked to the growth of the convective enveiope. This is a characteristics of 1GW. 

In more detail, our approach can be briefly summarized as follows gas-phase reactions, surface structures, and gas-surface reactions are treated at an ab initio level, using either cluster or periodic (plane-wave) calculations for surface structures, when appropriate. The results of these calculations are used to calculate reaction rate constants within the transition state (TS) or Rice-Ramsperger-Kassel-Marcus (RRKM) theory for bimolecular gas-phase reactions or unimolecular and surface reactions, respectively. The structure and energy characteristics of various surface groups can also be extracted from the results of ab initio calculations. Based on these results, a chemical mechanism can be constructed for both gas-phase reactions and surface growth. The film growth process is modeled within the kinetic Monte Carlo (KMC) approach, which provides an effective separation of fast and slow processes on an atomistic scale. The results of Monte Carlo (MC) simulations can be used in kinetic modeling based on formal chemical kinetics. 

Clearly, a perturbation with a wave number n will decay, if the growth rate Xn is negative and for positive growth rates, the perturbations will grow. The qualitative dependence of the growth rate as a function of n is plotted in Fig. 47. It has a mo-notonically decreasing characteristic for n > 0, but exhibits a jump toward smaller... 

The classical linear stability theory for a planar interface was formulated in 1964 by Mullins and Sekerka. The theory predicts, under what growth conditions a binary alloy solidifying unidirectionally at constant velocity may become morphologically unstable. Its basic result is a dispersion relation for those perturbation wave lengths that are able to grow, rendering a planar interface unstable. Two approximations of the theory are of practical relevance for the present work. In the thermal steady state, which is approached at large ratios of thermal to solutal diffusivity, and for concentrations close to the onset of instability the characteristic equation of the problem... 

It appears that insofar as growth to stable detonation is concerned lead azide displays characteristics similar to those of heterogeneous secondary explosives. The delayed stress excursions evident in measured stress profiles were interpreted as reactions behind the shock front. Reactions produce pressure waves which travel through the explosive at a velocity at least equal to its velocity of sound and interact with the undecomposed explosive ahead of the reaction front, causing a nonuniform rate of growth. 

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