Assuming that the equations of the two curves in ((K h, omega)) plane are (omega_{1}=omega_{1} (Kh,beta)) and (omega_{2}=omega _{2} (Kh,beta)), the integrated error between the phase velocities was then calculated on a specified interval as (C beta)=int_{0}^{eta}|c_{1}(Kh,beta -c_{2}(Kh,beta -c_{2}d(Kh,betahere (c_{1}(Kh,beta)) and (c_{2}(Kh,beta)) are the numerical phase velocities.
It is shown that the superthermality of electrons (via (kappa)), the charged dust impurity and the external magnetic field shift the MI domains around the (omega -theta) plane, where (omega) is the wave frequency and (theta) stands for modulational obliqueness.
We numerically investigate different stable and unstable regions in the (omega -theta) plane as shown in Fig. 2. We find that the charged dust impurity (represented by the parameter (mu) with (0
From panels (a, b) it is clear that as (mu) increases, i.e., as the number of charged dust grains decreases, a part of the instability region (with (theta omega -theta) plane increases.
While deformation twinning is resulted from 1/6<11̄1̄> homogeneous shear in consecutive {211} planes, omega transformation can be attributed to the 1/12<11̄1̄>, 1/3<11̄1̄> and 1/12<11̄1̄> inhomogeneous shear in consecutive {211} planes.
Figures 10 and 11 show the zero level sets of (mathcal {G}) and (mathcal{H}) in the ((nu,omega)) plane for two different points on the dispersion curve of Fig. 9.
The general solution of a second-order ode depends on two independent constants (C_1) and (C_2), it generates a two-parameter family of plane curves (omega (x,y,C_1,C_2)=0).
In this paper, an algorithmic method is presented such that phase characteristics on the jω omega axis in the s plane are preserved on the unit circle in the z plane.
The HG appeared as a protrusion on the supratemporal plane, with an omega, hook, or mushroom shape.
The omega and phi scans revealed good out-of-plane and in-plane alignments.
This follows by the embedding in the plane (see [6, 7], and [8]) W^{1, 2}_{0} (Omega) hookrightarrowexp_{2}( Omega) and by the duality relation (see [9]) bigl((exp_{2}) (Omega) bigr)'=L log L ^{frac{1}{2}} (Omega).
