The kink pair theory is applied to model thermal activation of dislocation glide over the Peierls barrier below the athermal temperature Ta and to build a velocity law for this regime.
Such problems consist of an adatom (adsorbed atom) diffusion equation on terraces of different height; boundary conditions on terrace boundaries including the kinetic asymmetry in the adatom attachment and detachment; and the normal velocity law for the motion of such boundaries determined by a two-sided flux, together with the one-dimensional "surface" diffusion.
In any case, we can surely say that the difference in the wind velocity law does not appreciably affect the structure of the disk.
In the present study, we calculate numerically the structure of a protoplanetary disk exposed to stellar wind, as well as the radiation from a central star changing the strength of the wind, the velocity law of the wind (i.e., the radial dependence of the wind velocity), and the mass distribution of the disk.
The seismic features obtained are then changed into depth domain from the initial time domain, and this is done by a defined velocity law, in which the application of all data for seismic well calibration (synthetic seismogram) is the fundamental strategy for obtaining optimum result in the depth conversion (Chen and Oliver 2014; Gunning and Paterson 2001).
The results obtained by a number of numerical calculations can be summarized as the following three conclusions: (1) The temperature and the height of the disk surface are very insensitive to the adopted parameters describing the wind model (i.e., the wind strength and the velocity law of the wind) and the mass distribution model of the disk.
In this study, the mass distribution of the disk and the velocity law of the stellar wind are somewhat extended compared with those of Y07, and the dynamical balance equation is revised because the equation used in Y07 is incorrect (see Yun etal., 2010).
The aim of the present study is to investigate the thermal behavior of the protoplanetary disk exposed to stellar radiation and the stellar wind over a wide range of three principal parameters: the strength of the stellar wind, the parameters describing the mass distribution of the disk, and the velocity law of the stellar wind.
As a typical example, we adopt a velocity law of particles (with zero energy) which are influenced only by the gravity of the central star, that is, β(r) in Eq. (7) is put to be: (28)Note that, in the present wind model, the wind pressure Pw is reduced by a factor of β(r) compared with the case of the original constant velocity wind model with β(r) = 1.
