سال:1392 | دوره: | شماره: |تعداد مقالات:3

In this paper, the Lie algebraic method is applied to solve biological population models described by time-inhomogeneous birth-death processes. Notwithstanding no obvious symmetry, the solution is expressed by matrix exponentials through suitably generated low-dimensional Lie algebras. This methodology may offer useful insights for other biological and ecological applications.

A theoretical investigation concerning the propagation of compressive solitons in a plasma comprising electrons, positrons, and dust grains is presented by considering the dust grains of either positive charge or negative charge.Using reductive perturbation technique, a relevant Korteweg-deVries (KdV) equation is derived and then solved to obtain the expressions of amplitude and width of the solitons. The magnetic field is found to alter the dispersive property of the plasma, and hence, only the width of the solitons is reduced in the presence of higher magnetic field.Soliton amplitude is found to decrease/increase and the width to increase/decrease for the higher densities of negatively/positively charged dust grains. Moreover, the amplitude of such a soliton remains larger in the case of positively charged dust grains in comparison with the negatively charged dust grains. The effect of electron/positron drift velocities of the charged species is not pronounced on the properties of the compressive solitons. Under the limiting cases, our calculations reduce to the calculations by other investigators. This substantiates the generality of the present analysis.

Titanium nitride (TiN) films are prepared by direct current (DC) magnetron sputtering of a titanium (Ti) target in an argon (Ar)+nitrogen (N2) atmosphere on bare and pulsed DC plasma-nitrided high-speed steel (AISI M2) substrate. One set of coating is deposited using different N2 partial pressures keeping the working pressure fixed, and it leads to variable film thickness. Another set of coating of equal thickness is prepared at the same working pressure with variable substrate biasing voltage. The detailed structure of the coatings is analyzed by X-ray diffraction study. The texture coefficient (Tc) determined from X-ray diffraction studies at various deposition conditions gives information about crystallographic orientation. It is found that the same deposition condition leads to different orientation of TiN coatings on bare AISI M2 and plasma-nitrided AISI M2 substrate. The results are discussed in terms of energy minimization and substrate-induced preferred orientation.