445 research outputs found
Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models
Motion of a classical particle in 3-dimensional Lobachevsky and Riemann
spaces is studied in the presence of an external magnetic field which is
analogous to a constant uniform magnetic field in Euclidean space. In both
cases three integrals of motions are constructed and equations of motion are
solved exactly in the special cylindrical coordinates on the base of the method
of separation of variables. In Lobachevsky space there exist trajectories of
two types, finite and infinite in radial variable, in Riemann space all motions
are finite and periodical. The invariance of the uniform magnetic field in
tensor description and gauge invariance of corresponding 4-potential
description is demonstrated explicitly. The role of the symmetry is clarified
in classification of all possible solutions, based on the geometric symmetry
group, SO(3,1) and SO(4) respectively
Motion Caused by Magnetic Field in Lobachevsky Space
We study motion of a relativistic particle in the 3-dimensional Lobachevsky
space in the presence of an external magnetic field which is analogous to a
constant uniform magnetic field in the Euclidean space. Three integrals of
motion are found and equations of motion are solved exactly in the special
cylindrical coordinates. Motion on surface of the cylinder of constant radius
is considered in detail.Comment: 4 page
On elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation
The Conte-Musette method has been modified for the search of only elliptic
solutions to systems of differential equations. A key idea of this a priory
restriction is to simplify calculations by means of the use of a few Laurent
series solutions instead of one and the use of the residue theorem. The
application of our approach to the quintic complex one-dimensional
Ginzburg-Landau equation (CGLE5) allows to find elliptic solutions in the wave
form. We also find restrictions on coefficients, which are necessary conditions
for the existence of elliptic solutions for the CGLE5. Using the investigation
of the CGLE5 as an example, we demonstrate that to find elliptic solutions the
analysis of a system of differential equations is more preferable than the
analysis of the equivalent single differential equation.Comment: LaTeX, 21 page
Using a Laguerre-Gaussian beam to trap and cool the rotational motion of a mirror
We show theoretically that it is possible to trap and cool the rotational
motion of a macroscopic mirror made of a perfectly reflecting spiral phase
element using orbital angular momentum transfer from a Laguerre-Gaussian
optical field. This technique offers a promising route to the placement of the
rotor in its quantum mechanical ground state in the presence of thermal noise.
It also opens up the possibility of simultaneously cooling a vibrational mode
of the same mirror. Lastly, the proposed design may serve as a sensitive
torsional balance in the quantum regime.Comment: New cavity design, reworked title; to appear in Phys. Rev. Let
The Nikolaevskiy equation with dispersion
The Nikolaevskiy equation was originally proposed as a model for seismic
waves and is also a model for a wide variety of systems incorporating a
neutral, Goldstone mode, including electroconvection and reaction-diffusion
systems. It is known to exhibit chaotic dynamics at the onset of pattern
formation, at least when the dispersive terms in the equation are suppressed,
as is commonly the practice in previous analyses. In this paper, the effects of
reinstating the dispersive terms are examined. It is shown that such terms can
stabilise some of the spatially periodic traveling waves; this allows us to
study the loss of stability and transition to chaos of the waves. The secondary
stability diagram (Busse balloon) for the traveling waves can be remarkably
complicated.Comment: 24 pages; accepted for publication in Phys. Rev.
Staeckel systems generating coupled KdV hierarchies and their finite-gap and rational solutions
We show how to generate coupled KdV hierarchies from Staeckel separable
systems of Benenti type. We further show that solutions of these Staeckel
systems generate a large class of finite-gap and rational solutions of cKdV
hierarchies. Most of these solutions are new.Comment: 15 page
The formation of oxide layers on a titanium surface by irradiation with femtosecond laser pulses
By subjecting technical grade titanium to irradiation with femtosecond laser pulses with highenergy density, we create a microporous nanocrystalline oxide layer with a thickness of ∼50 μm on its surface. The structure and phase composition of the modified surface layers are studied using X-ray diffraction and high-resolution scanning and transmission electron microscopie
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