We analyze the effect of the mixing of the 1s and 2p x,y subbands on the ground state binding energy of the off-axis donors in cylindrical nanotubes by using the recently developed fractal dimension method. Curves of the D 0 ground state binding energies as a function of the donor distance from axis are presented and compared with those obtained previously without consideration of the effect of the subband mixing. Also, we analyze the density impurity states in nanotubes with randomly distributed donors.

In this research, a proportional integral derivative regulator, a first-order sliding-mode regulator, and a second-order sliding-mode regulator are compared, for the regulation of two different types of mathematical model. A first-order sliding-mode regulator is a method where a sign-mapping checks that the error decays to zero after a convergence time; it has the problem of chattering in the output. A second-order sliding-mode regulator is a smooth method to counteract the chattering effect where the integral of the sign-mapping is used. A second-order sliding-mode regulator is presented as a new class of algorithm where the trajectory is asymptotic and stable; it is shown to greatly improve the convergence time in comparison with other regulators considered. Simulation and experimental results are described in which an electric oven is considered as a stable linear mathematical model, and an inverted pendulum is considered as an asymmetrical unstable non-linear mathematical model.

In this paper, the cyclotron autoresonance acceleration of electrons in a stationary inhomogeneous magnetic field is studied. The trajectory and energy of electrons are found through a numerical solution of the relativistic Newton-Lorentz equation by a finite difference method. The electrons move along a TE 112 cylinder cavity in a steady-state magnetic field whose axis coincides with the cavity axis. The magnetic field profile is such that it keeps the phase difference between the electric microwave field and the electron velocity vector within the acceleration phase band. The microwaves amplitude of 6 kV=cm is used for numerical calculations. It is shown that an electron with an initial longitudinal energy of 8 keV can be accelerated up to 260 keV by 2.45 GHz microwaves at a distance of 17 cm.

The glow discharge is the basis of conventional techniques used to improve the tribological properties of materials, such as the generation of thin films using ionic beams and the sputtering process for the treatment of surfaces. This work focuses on the numerical study of the glow discharge in a system composed of a cylindrical quartz chamber containing argon gas, whose length and radius are 20 cm and 2.5 cm, respectively. Said chamber is limited by two copper electrodes whose potentials are 0 V (Anode) and -500 V(Cathode), respectively. In order to analyze this time-independent discharge, the generation of secondary electrons allowing the discharge to be self-sustained as well as the manifestation of fixed regions, among others, numerical modeling is carried out by using the Plasma Module of COMSOL Multiphysics software. The presented results in this paper can be useful to understand, design and build new technologies focused on the area of treatment of surfaces.

An autoresonance electron acceleration phenomenon in the combined steady-state inhomogeneous magnetic and microwave fields is analytically studied. Equations describing the evolution of the phase shift between the particle velocity and the microwave electric field, total energy, and longitudinal velocity of the electron are obtained. Linear and parabolic profiles of the magnetic field are examined. It is shown that the proper choice of the magnetic heterogeneity degree, the microwave electric field value, and initial electron velocity can retain the electron in the acceleration phase band. The results obtained in this work show a complete agreement with our previous autoresonance results obtained through simulations of the relativistic Newton-Lorentz equation.