On Chiral Model of Graphene

2012 ◽  
Vol 190 ◽  
pp. 59-62 ◽  
Author(s):  
Yu.P. Rybakov
Keyword(s):  
Approximate Solution ◽  
Carbon Atom ◽  
Order Parameter ◽  
Chiral Model ◽  
Graphene Surface ◽  
Wave Approximation ◽  
Long Wave ◽  
Valence Electrons ◽  
Long Wave Approximation ◽  
The Ideal

The hybridized sp-states of valence electrons in the carbon atom can be describedby SU(2) matrix considered as the order parameter. The chiral model of graphene based onthis order parameter is suggested in the long-wave approximation, the ideal graphene planebeing determined by the kink-like solution. Corrugation of the graphene surface is describedin the form of ripple and rings. The approximate solution corresponding to an infinite carbonnanotube is found.

scholarly journals Magnetic excitations of carbon nanotubes in chiral model of graphene

2018 ◽  
Vol 185 ◽  
pp. 11007 ◽  
Author(s):  
Yu.P. Rybakov
Keyword(s):  
Carbon Nanotube ◽  
Atomic Plane ◽  
New Order ◽  
Chiral Model ◽  
Winding Number ◽  
Long Wave ◽  
Hybridization Effect ◽  
Valence Electrons ◽  
Diamagnetic Behavior ◽  
Long Wave Approximation

Within the scope of the chiral model of graphene in 8-spinor realization, suggested earlier [1, 2], the combined spinor field Ψ is used as a new order parameter, which contains information on spin and quasispin excitations in graphene (8-spinor part) and also that on sp-hybridization effect of carbon valence electrons [SU(2)-matrix part]. This model admits two kinds of configurations describing, in the long-wave approximation, the graphene mono-atomic plane and the carbon nanotube respectively. The first one is given by the domain-wall (or kink-like) solution and the second one is described by the hedgehog ansatz with large topological charge (winding number n). We consider the infinite carbon nanotube in a static external magnetic field oriented along the tube and analyze the structure of the magnetic intensity on the outside. The diamagnetic behavior of the material is shown by the perturbation method which proves to be self-consistent for n ≫ 1.

Nonlinear dispersion hyperbolic models of continuous media

2007 ◽  
Vol 5 ◽  
pp. 273-278
Author(s):  
V.Yu Liapidevskii
Keyword(s):  
Boussinesq Equations ◽  
Nonlinear Dispersion ◽  
Order Of Accuracy ◽  
Flow Models ◽  
Wave Approximation ◽  
Long Wave ◽  
Primary Model ◽  
Nonequilibrium Flows ◽  
Internal Inertia ◽  
Long Wave Approximation

Nonequilibrium flows of an inhomogeneous liquid in channels and pipes are considered in the long-wave approximation. Nonlinear dispersion hyperbolic flow models are derived allowing taking into account the influence of internal inertia during the relative motion of phases upon the structure of nonlinear wave fronts. The asymptotic derivation of dispersion hyperbolic models is shown on the example of classical Boussinesq equations. It is shown that the hyperbolic approximation of the equations has the same order of accuracy as the primary model.

scholarly journals NUMERICAL MODELS OF HUGE TSUNAMIS OFF THE SANRIKU COAST

1976 ◽  
Vol 1 (15) ◽  
pp. 61
Author(s):  
Toshio Iwasaki
Keyword(s):  
Numerical Models ◽  
Source Model ◽  
Wave Source ◽  
Sanriku Coast ◽  
Wave Approximation ◽  
Long Wave ◽  
Small Wave ◽  
Wave Heights ◽  
Deep Region ◽  
Long Wave Approximation

Although numerical computations of the generation and propagation of tsunamis are successfully achieved in recent years, modeling of their wave sources is still a big problem. Three kinds of, wave source model, that is statistical, oceanographic and fault model, are studied in this paper. It is found that the first model gives reasonable wave heights as shown in the previous paper, the second one presents roughly one half of those for the first model and the last one produces too small wave heights. Based on the analysis of computed results, nature of undulations off from the shore boundary, directivity of wave propagation and the spindle shaped leading part are discussed. Comparing magnitude of various wave parameters for the leading wave along the minor axis of the wave source, it is shown that the long wave approximation modified by the slope effect illustrates the tsunamis in deep region of the sea and the slope effect is most dominant in shallow region.

Nonlinear dynamics of electrostatic Faraday instability in thin films

2018 ◽  
Vol 855 ◽  
Author(s):  
Dipin S. Pillai ◽  
R. Narayanan
Keyword(s):  
Thin Films ◽  
Standing Waves ◽  
Gas Holdup ◽  
Conducting Liquid ◽  
Mode Instability ◽  
Wave Approximation ◽  
Long Wave ◽  
Faraday Instability ◽  
Unstable Configuration ◽  
Long Wave Approximation

The nonlinear evolution of an interface between a perfect conducting liquid and a perfect dielectric gas subject to periodic electrostatic forcing is studied under the long-wave approximation. It is shown that inertial thin films become unstable to finite-wavelength Faraday modes at the onset, prior to the long-wave pillaring instability reported in the lubrication limit. It is further shown that the pillaring-mode instability is subcritical in nature, with the interface approaching either the top or the bottom wall, depending on the liquid–gas holdup. On the other hand, the Faraday modes exhibit subharmonic or harmonic oscillations that nonlinearly saturate to standing waves at low forcing amplitudes. Unlike the pillaring mode, wherein the interface approaches the wall, Faraday modes may exhibit saturated standing waves when the instability is subcritical. At higher forcing amplitudes, the interface may approach either wall, again depending on the liquid–gas holdup. It is also shown that a gravitationally unstable configuration of such thin films, under the long-wave approximation, cannot be stabilized by periodic electrostatic forcing, unlike mechanical Faraday forcing. In this case, it is observed that the interface exhibits oscillatory sliding behaviour, approaching the wall in an ‘earthworm-like’ motion.

Effect of gravity on the dynamics of non-isothermic ultra-thin two-layer films

2010 ◽  
Vol 661 ◽  
pp. 1-31 ◽  
Author(s):  
ALEXANDER NEPOMNYASHCHY ◽  
ILYA SIMANOVSKII
Keyword(s):  
Nonlinear Flow ◽  
Quiescent State ◽  
Horizontal Temperature Gradient ◽  
One Dimensional ◽  
Thermocapillary Flows ◽  
Wave Approximation ◽  
Long Wave ◽  
The Difference ◽  
Thermocapillary Forces ◽  
Long Wave Approximation

The effect of gravity on the dynamics of non-isothermic ultra-thin two-layer films is studied in this paper. The joint action of disjoining pressure and thermocapillary forces is taken into account. The problem is considered in a long-wave approximation. The linear stability of a quiescent state and thermocapillary flows is investigated. It has been found that the influence of the upper fluid density is significantly stronger than that of the difference of fluid densities. Nonlinear flow regimes are studied by means of numerical simulations. The gravity can lead to the formation of stripes or holes instead of droplets. The two-dimensional wavy patterns are replaced by one-dimensional waves with the fronts inclined or transverse to the direction of the horizontal temperature gradient.

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