371 research outputs found
Possible quantum kinematics. II. Non-minimal case
The quantum analogs of the N-dimensional Cayley-Klein spaces with different
combinations of quantum and Cayley-Klein structures are described for
non-minimal multipliers, which include the first and the second powers of
contraction parameters in the transformation of deformation parameter. The
noncommutative analogs of (N-1)-dimensional constant curvature spaces are
introduced. Part of these spaces for N=5 are interpreted as the noncommutative
analogs of (1+3) space-time models. As a result the wide variety of the quantum
deformations of realistic kinematics are suggested.Comment: 13 pages, no figure
Delayed feedback control of self-mobile cavity solitons
Control of the motion of cavity solitons is one the central problems in
nonlinear optical pattern formation. We report on the impact of the phase of
the time-delayed optical feedback and carrier lifetime on the self-mobility of
localized structures of light in broad area semiconductor cavities. We show
both analytically and numerically that the feedback phase strongly affects the
drift instability threshold as well as the velocity of cavity soliton motion
above this threshold. In addition we demonstrate that non-instantaneous carrier
response in the semiconductor medium is responsible for the increase in
critical feedback rate corresponding to the drift instability
Numerical methods for solving a hereditary equation of hyperbolic type
A family of grid methods is constructed for the numerical solution of a wave equation with delay of general form; the methods are based on the idea of separating the current state and the history function. A theorem on the order of convergence of the methods is obtained by means of embedding into a general difference scheme with aftereffect. Results of calculating test examples with constant and variable delays are presented. © 2013 Pleiades Publishing, Ltd
Numerical studies for fractional functional differential equations with delay based on BDF-type shifted Chebyshev approximations
Fractional functional differential equations with delay (FDDEs) have recently played a significant role in modeling of many real areas of sciences such as physics, engineering, biology, medicine, and economics. FDDEs often cannot be solved analytically so the approximate and numerical methods should be adapted to solve these types of equations. In this paper we consider a new method of backward differentiation formula-(BDF-) type for solving FDDEs. This approach is based on the interval approximation of the true solution using the Clenshaw and Curtis formula that is based on the truncated shifted Chebyshev polynomials. It is shown that the new approach can be reformulated in an equivalent way as a Runge-Kutta method and the Butcher tableau of this method is given. Estimation of local and global truncating errors is deduced and this leads to the proof of the convergence for the proposed method. Illustrative examples of FDDEs are included to demonstrate the validity and applicability of the proposed approach. © 2015 V. G. Pimenov and A. S. Hendy
Evidence of electro-active excitation of the spin cycloid in TbMnO3
Terahertz electromagnetic excitations in the multiferroic TbMnO3 at the
field-induced magnetic transition are investigated for different orientations
of the magnetic cycloid. In addition to the electromagnon along the a-axis, the
detailed polarization analysis of the experimental spectra suggests the
existence of an electro-active excitation for ac electric fields along the
crystallographic c-axis. This excitation is possibly the electro-active
eigenmode of the spin cycloid in TbMnO3, which has been predicted within the
inverse Dzyaloshinskii-Moriya mechanism of magnetoelectric coupling.Comment: 5 page
Optical conductivity and penetration depth in MgB2
The complex conductivity of a MgB2 film has been investigated in the
frequency range 4 cm^{-1}< nu < 30 cm^{-1} and for temperatures 2.7 K < T <300
K. The overall temperature dependence of both components of the complex
conductivity is reminiscent of BCS-type behavior, although a detailed analysis
reveals a number of discrepancies. No characteristic feature of the isotropic
BCS gap temperature evolution is observed in the conductivity spectra in the
superconducting state. A peak in the temperature dependence of the real part of
the conductivity is detected for frequencies below 9 cm^{-1}. The
superconducting penetration depth follows a T^2 behavior at low temperatures.Comment: 4 pages, 4 figure
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