On Hoyle-Narlikar-Wheeler mechanism of vibration energy powered magneto-dipole emission of neutron stars

We revisit the well-known Hoyle-Narlikar-Wheeler proposition that neutron star emerging in the magnetic-flux-conserving process of core-collapse supernova can convert the stored energy of Alfven vibrations into power of magneto-dipole radiation. We show that the necessary requirement for the energy conversion is the decay of internal magnetic field. In this case the loss of vibration energy of the star causes its vibration period, equal to period of pulsating emission, to lengthen at a rate proportional to the rate of magnetic field decay. These prediction of the model of vibration powered neutron star are discussed in juxtaposition with data on pulsating emission of magnetars whose radiative activity is generally associated with the decay of ultra strong magnetic field.Comment: Accepted for publication in Astrophysics & Space Scienc

Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models

A computation scheme for solving elliptic boundary value problems with axially symmetric confining potentials using different sets of one-parameter basis functions is presented. The efficiency of the proposed symbolic-numerical algorithms implemented in Maple is shown by examples of spheroidal quantum dot models, for which energy spectra and eigenfunctions versus the spheroid aspect ratio were calculated within the conventional effective mass approximation. Critical values of the aspect ratio, at which the discrete spectrum of models with finite-wall potentials is transformed into a continuous one in strong dimensional quantization regime, were revealed using the exact and adiabatic classifications.Comment: 6 figures, Submitted to Proc. of The 12th International Workshop on Computer Algebra in Scientific Computing (CASC 2010) Tsakhkadzor, Armenia, September 5 - 12, 201

On Spectra of Linearized Operators for Keller-Segel Models of Chemotaxis

We consider the phenomenon of collapse in the critical Keller-Segel equation (KS) which models chemotactic aggregation of micro-organisms underlying many social activities, e.g. fruiting body development and biofilm formation. Also KS describes the collapse of a gas of self-gravitating Brownian particles. We find the fluctuation spectrum around the collapsing family of steady states for these equations, which is instrumental in derivation of the critical collapse law. To this end we develop a rigorous version of the method of matched asymptotics for the spectral analysis of a class of second order differential operators containing the linearized Keller-Segel operators (and as we argue linearized operators appearing in nonlinear evolution problems). We explain how the results we obtain are used to derive the critical collapse law, as well as for proving its stability.Comment: 22 pages, 1 figur

Frequency spectrum of toroidal Alfv\'en mode in a neutron star with Ferraro's form of nonhomogeneous poloidal magnetic field

Using the energy variational method of magneto-solid-mechanical theory of a perfectly conducting elastic medium threaded by magnetic field, the frequency spectrum of Lorentz-force-driven global torsional nodeless vibrations of a neutron star with Ferraro's form of axisymmetric poloidal nonhomogeneous internal and dipole-like external magnetic field is obtained and compared with that for this toroidal Alfv\'en mode in a neutron star with homogeneous internal and dipolar external magnetic field. The relevance of considered asteroseismic models to quasi-periodic oscillations of the X-ray flux during the ultra powerful outbursts of SGR 1806-20 and SGR 1900+14 is discussed.Comment: Accepted for publication in Astrophysics & Space Scienc

Fluorescence spectrum of a two-level atom driven by a multiple modulated field

We investigate the fluorescence spectrum of a two-level atom driven by a multiple amplitude-modulated field. The driving held is modeled as a polychromatic field composed of a strong central (resonant) component and a large number of symmetrically detuned sideband fields displaced from the central component by integer multiples of a constant detuning. Spectra obtained here differ qualitatively from those observed for a single pair of modulating fields [B. Blind, P.R. Fontana, and P. Thomann, J. Phys. B 13, 2717 (1980)]. In the case of a small number of the modulating fields, a multipeaked spectrum is obtained with the spectral features located at fixed frequencies that are independent of the number of modulating fields and their Rabi frequencies. As the number of the modulating fields increases, the spectrum ultimately evolves to the well-known Mellow triplet with the sidebands shifted from the central component by an effective Rabi frequency whose magnitude depends on the initial relative phases of the components of the driving held. For equal relative phases, the effective Rabi frequency of the driving field can be reduced to zero resulting in the disappearance of fluorescence spectrum, i.e., the atom can stop interacting with the field. When the central component and the modulating fields are 180 degrees out of phase, the spectrum retains its triplet structure with the sidebands located at frequencies equal to the sum of the Rabi frequencies of the component of the driving field. Moreover, we shaw that the frequency of spontaneous emission can be controlled and switched from one frequency to another when the Rabi frequency or initial phase of the modulating fields are varied