4,961 research outputs found
Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods
We consider Dirichlet Laplacian in a thin curved three-dimensional rod. The
rod is finite. Its cross-section is constant and small, and rotates along the
reference curve in an arbitrary way. We find a two-parametric set of the
eigenvalues of such operator and construct their complete asymptotic
expansions. We show that this two-parametric set contains any prescribed number
of the first eigenvalues of the considered operator. We obtain the complete
asymptotic expansions for the eigenfunctions associated with these first
eigenvalues
Homogenization of the planar waveguide with frequently alternating boundary conditions
We consider Laplacian in a planar strip with Dirichlet boundary condition on
the upper boundary and with frequent alternation boundary condition on the
lower boundary. The alternation is introduced by the periodic partition of the
boundary into small segments on which Dirichlet and Neumann conditions are
imposed in turns. We show that under the certain condition the homogenized
operator is the Dirichlet Laplacian and prove the uniform resolvent
convergence. The spectrum of the perturbed operator consists of its essential
part only and has a band structure. We construct the leading terms of the
asymptotic expansions for the first band functions. We also construct the
complete asymptotic expansion for the bottom of the spectrum
Spectral and localization properties of the Dirichlet wave guide with two concentric Neumann discs
Bound states of the Hamiltonian describing a quantum particle living on three
dimensional straight strip of width are investigated. We impose the Neumann
boundary condition on the two concentric windows of the radii and
located on the opposite walls and the Dirichlet boundary condition on the
remaining part of the boundary of the strip. We prove that such a system
exhibits discrete eigenvalues below the essential spectrum for any .
When and tend to the infinity, the asymptotic of the eigenvalue is
derived. A comparative analysis with the one-window case reveals that due to
the additional possibility of the regulating energy spectrum the anticrossing
structure builds up as a function of the inner radius with its sharpness
increasing for the larger outer radius. Mathematical and physical
interpretation of the obtained results is presented; namely, it is derived that
the anticrossings are accompanied by the drastic changes of the wave function
localization. Parallels are drawn to the other structures exhibiting similar
phenomena; in particular, it is proved that, contrary to the two-dimensional
geometry, at the critical Neumann radii true bound states exist.Comment: 25 pages, 7 figure
Propagation of axions in a strongly magnetized medium
The polarization operator of an axion in a degenerate gas of electrons
occupying the ground-state Landau level in a superstrong magnetic field G is investigated in a model with a
tree-level axion-electron coupling. It is shown that a dynamic axion mass,
which can fall within the allowed range of values , is generated under the conditions of strongly
magnetized neutron stars. As a result, the dispersion relation for axions is
appreciably different from that in a vacuum.Comment: RevTex, no figures, 13 pages, Revised version of the paper published
in J. Exp. Theor. Phys. {\bf 88}, 1 (1999
A Hardy inequality in twisted waveguides
We show that twisting of an infinite straight three-dimensional tube with
non-circular cross-section gives rise to a Hardy-type inequality for the
associated Dirichlet Laplacian. As an application we prove certain stability of
the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes.
Namely, it is known that any local bending, no matter how small, generates
eigenvalues below the essential spectrum of the Laplacian in the tubes with
arbitrary cross-sections rotated along a reference curve in an appropriate way.
In the present paper we show that for any other rotation some critical strength
of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page
1RXS J180834.7+101041 is a new cataclysmic variable with non-uniform disc
Results of photometric and spectroscopic investigations of the recently
discovered disc cataclysmic variable star 1RXS J180834.7+101041 are presented.
Emission spectra of the system show broad double peaked hydrogen and helium
emission lines. Doppler maps for the hydrogen lines demonstrate strongly
non-uniform emissivity distribution in the disc, similar to that found in IP
Peg. It means that the system is a new cataclysmic variable with a spiral
density wave in the disc. Masses of the components (M_WD = 0.8 +/- 0.22 M_sun
and M_RD = 0.14 +/- 0.02 M_sun), and the orbit inclination (i = 78 +/- 1.5 deg)
were estimated using the various well-known relations for cataclysmic
variables.Comment: 4 pages, 3 figures, conference "European White Dwarf Workshop, 2010",
Tuebingen, German
Multi-filament structures in relativistic self-focusing
A simple model is derived to prove the multi-filament structure of
relativistic self-focusing with ultra-intense lasers. Exact analytical
solutions describing the transverse structure of waveguide channels with
electron cavitation, for which both the relativistic and ponderomotive
nonlinearities are taken into account, are presented.Comment: 21 pages, 12 figures, submitted to Physical Review
Profession loss crisis at an old age: Specific features, factors, and mechanisms of coping
This article discusses the specific characteristics of profession loss crisis at an old age. Profession loss crisis is the last normative crisis of personal professional development that is caused by the completion of one's professional biography after reaching a certain age. The research employs a psychobiographic method and a critical events method. These methods are based on the use of a formalized biographical questionnaire worked out by Norakidze V.G. and reconstructed by Zeer E.F. The authors have identified and provided a detailed description of the main factors that cause profession loss crisis: Random events, adverse circumstances while implementing professional plans, etc. The article outlines the main strategies for coping with this crisis: Changing jobs, re-training, the assistance of colleagues and administration, etc. The authors suggest technologies to minimize the effects of these factors and overcome profession loss crisis effectively. © 2019 by the authors
CPT and Lorentz violation effects in hydrogen-like atoms
Within the framework of Lorentz-violating extended electrodynamics, the Dirac
equation for a bound electron in an external electromagnetic field is
considered assuming the interaction with a CPT-odd axial vector background
. The quasi-relativistic Hamiltonian is obtained using a -series
expansion. Relativistic Dirac eigenstates in a spherically-symmetric potential
are found accurate up to the second order in . -induced CPT-odd
corrections to the electromagnetic dipole moment operators of a bound electron
are calculated that contribute to the anapole moment of the atomic orbital and
may cause a specific asymmetry of the angular distribution of the radiation of
a hydrogen atom.Comment: 13 pages, 1 figure; (5.14) is corrected to conform to the
normalization convention for Laguerre polynomials adopted at present; minor
grammatical change
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