scholarly journals A qualitative study of a nanotube model using an iterative Taylor method

2017 ◽  
Vol 28 (03) ◽  
pp. 1750036 ◽  
Author(s):  
M. Gadella ◽  
L. P. Lara ◽  
J. Negro
Keyword(s):  
Magnetic Field ◽  
Energy Eigenvalue ◽  
Equation Of Motion ◽  
Minimal Energy ◽  
Approximate Methods ◽  
Symmetry Properties ◽  
Exactly Solvable ◽  
Taylor Method ◽  
Physical Reasons ◽  
Weyl Equation

Physical properties of graphene nanotubes may strongly depend on external fields. In a recent paper V. Jakubský, S. Kuru, J. Negro, J. Phys. A: Math. Theor. 47, 115307 (2014), the authors have studied a model of carbon nanotubes under the presence of an external magnetic field, chosen for some symmetry properties. The model admits an exact solution, provided that the value of a parameter, here denoted as [Formula: see text], be equal to zero. This parameter is the eigenvalue of the component of the momentum in the direction of the nanotube axis. However, it seems that this parameter cannot be discarded for physical reasons. The choice of nontrivial values for this parameter produces an equation of motion for electrons in the nanotube (a Dirac–Weyl equation), which cannot be exactly solvable. Then, we proposed some iterative approximate methods to solve this equation and obtaining its eigenvalues. Some tests have shown that an iterative Taylor method is more efficient than some others we have used. For [Formula: see text], we have found that, excluding the minimal energy eigenvalue, the lowest energy values obtained for [Formula: see text] split into two different ones and, therefore, producing gaps in the energy spectrum.

Motion of a charged particle in superposed Heliotron and biconical cusp fields

1969 ◽  
Vol 3 (2) ◽  
pp. 255-267 ◽  
Author(s):  
M. P. Srivastava ◽  
P. K. Bhat
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Magnetic Moment ◽  
Particle Trajectory ◽  
Three Dimensional ◽  
Equation Of Motion ◽  
Neutral Point ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Hybrid Type

We have studied the behaviour of a charged particle in an axially symmetric magnetic field having a neutral point, so as to find a possibility of confining a charged particle in a thermonuclear device. In order to study the motion we have reduced a three-dimensional motion to a two-dimensional one by introducing a fictitious potential. Following Schmidt we have classified the motion, as an ‘off-axis motion’ and ‘encircling motion’ depending on the behaviour of this potential. We see that the particle performs a hybrid type of motion in the negative z-axis, i.e. at some instant it is in ‘off-axis motion’ while at another instant it is in ‘encircling motion’. We have also solved the equation of motion numerically and the graphs of the particle trajectory verify our analysis. We find that in most of the cases the particle is contained. The magnetic moment is found to be moderately adiabatic.

Small oscillations of systems with several degrees of freedom

2020 ◽  
pp. 29-40
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Magnetic Field ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Free Oscillations ◽  
Small Oscillations ◽  
Symmetry Properties ◽  
Gyroscopic Forces ◽  
Simple Molecules ◽  
Simple Systems ◽  
Three Degrees Of Freedom

This chapter addresses the free and forced oscillations of simple systems (with two or three degrees of freedom), the free oscillations of systems with the degenerate frequencies, and the eigen-oscillations of the electromechanical systems. This chapter also studies the oscillations of more complex systems using orthogonality of eigenoscillations and the symmetry properties of the system, the free oscillations of an anisotropic charged oscillator moving in a uniform constant magnetic field, and the perturbation theory adapted for the small oscillations. Finally, the chapter addresses oscillations of systems in which gyroscopic forces act and the eigen-oscillations of the simple molecules.

Approximate Analytic Method of Piping Systems With Elasto-Plastic Damper

2002 ◽  
Author(s):  
Shigeru Aoki ◽  
Takeshi Watanabe
Keyword(s):  
Simple Procedure ◽  
Continuous System ◽  
Approximate Solutions ◽  
Continuous Model ◽  
Equation Of Motion ◽  
Forced Response ◽  
Mode Shapes ◽  
Piping System ◽  
Restoring Force ◽  
Approximate Methods

An elasto-plastic damper is one of the vibration absorbers in which energy is absorbed by elasto-plastic deformation of the hysteretic type damper. It is used for the piping system. The piping system is continuous system. Since it is difficult to find the analytical solution of the equation of motion for the system with elasto-plastic damper, the equation of motion is treated by various approximate methods in which the system is usually considered as a single- or a multiple-degree-of-freedom system, but not as a continuous system. In order to analyze the response of a nonlinear continuous system, however, it is necessary to consider the system as a continuous system. In this paper, the nonlinear steady-state response of the piping system with elasto-plastic damper is undertaken by approximate solutions, which are easily obtained by a simple procedure and are more practical than the exact solutions. As a continuous model of the piping system, a beam simply supported or clamped at one end, with elasto-plastic damper at the other end is used. The restoring force is modeled as hysteresis loop characteristics in order to consider the energy loss in the damper. In the analysis, the restoring force is expanded into the Fourier series, and only fundamental terms are considered. The resonance curves and mode shapes of the beam are obtained from the approximate solution. And effect of elasto-plastic damper on the forced response of continuous system is examined.

scholarly journals Thermal properties of a two-dimensional Duffin–Kemmer–Petiau oscillator under an external magnetic field in the presence of a minimal length

2020 ◽  
Vol 35 (33) ◽  
pp. 2050278
Author(s):  
H. Aounallah ◽  
B. C. Lütfüoğlu ◽  
J. Kříž
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Energy Eigenvalue ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Summation Formula ◽  
Minimal Length ◽  
Two Dimensional ◽  
Relativistic Limit ◽  
Ordinary Quantum

Generalized uncertainty principle puts forward the existence of the shortest distances and/or maximum momentum at the Planck scale for consideration. In this article, we investigate the solutions of a two-dimensional Duffin–Kemmer–Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) scale. First, we obtain the eigensolutions in ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of an ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions in the non-relativistic limit. We show that in the ordinary quantum mechanic limit, where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler–Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale.

scholarly journals 8. Ionized gas in a magnetic field

1958 ◽  
Vol 6 ◽  
pp. 71-80 ◽  
Author(s):  
A. Schlüter
Keyword(s):  
Magnetic Field ◽  
Conservation Laws ◽  
Hydrodynamic Equation ◽  
Practical Importance ◽  
Equation Of Motion ◽  
Negligible Effect ◽  
Fluid Models ◽  
Mechanical Interaction ◽  
Ionized Gas ◽  
Pressure Diffusion

The ionized gas is described as a mixture of several fluids; each obeying a quasi-hydrodynamic equation of motion with additional terms describing the mechanical interaction. Particularly, two- and three-fluid models are considered. The nature of the approximations (‘quasi-neutrality’, ‘creeping diffusion’) is discussed. Conservation-laws are formulated for the case of negligible effect of mutual encounters and of pressure diffusion. These models lead to a generalization of Ohm's law; it is shown that the additional terms are of practical importance if one has three components, of which one may be neutral.

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