2,317 research outputs found
Formal Solution of the Fourth Order Killing equations for Stationary Axisymmetric Vacuum Spacetimes
An analytic understanding of the geodesic structure around non-Kerr
spacetimes will result in a powerful tool that could make the mapping of
spacetime around massive quiescent compact objects possible. To this end, I
present an analytic closed form expression for the components of a the fourth
order Killing tensor for Stationary Axisymmetric Vacuum (SAV) Spacetimes. It is
as yet unclear what subset of SAV spacetimes admit this solution. The solution
is written in terms of an integral expression involving the metric functions
and two specific Greens functions. A second integral expression has to vanish
in order for the solution to be exact. In the event that the second integral
does not vanish it is likely that the best fourth order approximation to the
invariant has been found. This solution can be viewed as a generalized Carter
constant providing an explicit expression for the fourth invariant, in addition
to the energy, azimuthal angular momentum and rest mass, associated with
geodesic motion in SAV spacetimes, be it exact or approximate. I further
comment on the application of this result for the founding of a general
algorithm for mapping the spacetime around compact objects using gravitational
wave observatories.Comment: 5 Page
Application of p-adic analysis to models of spontaneous breaking of the replica symmetry
Methods of p-adic analysis are applied to the investigation of the
spontaneous symmetry breaking in the models of spin glasses. A p-adic
expression for the replica matrix is given and moreover the replica matrix in
the models of spontaneous breaking of the replica symmetry in the simplest case
is expressed in the form of the Vladimirov operator of p-adic fractional
differentiation. Also the model of hierarchical diffusion (that was proposed to
describe relaxation of spin glasses) investigated using p-adic analysis.Comment: Latex, 8 page
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
Dynamics of a class A nonlinear mirror mode-locked laser
Using a delay differential equation model we study theoretically the dynamics
of a unidirectional class-A ring laser with a nonlinear amplifying loop mirror.
We perform linear stability analysis of the CW regimes in the large delay limit
and demonstrate that these regimes can be destabilized via modulational and
Turing-type instabilities, as well as by an instability leading to the
appearance of square-waves. We investigate the formation of square-waves and
mode-locked pulses in the system. We show that mode-locked pulses are
asymmetric with exponential decay of the trailing edge in positive time and
faster-than-exponential (super-exponential) decay of the leading edge in
negative time. We discuss asymmetric interaction of these pulses leading to a
formation of harmonic mode-locked regimes.Comment: 9 pages
Metal-insulator transition in a two-dimensional electron system: the orbital effect of in-plane magnetic field
The conductance of an open quench-disordered two-dimensional (2D) electron
system subject to an in-plane magnetic field is calculated within the framework
of conventional Fermi liquid theory applied to actually a three-dimensional
system of spinless electrons confined to a highly anisotropic (planar)
near-surface potential well. Using the calculation method suggested in this
paper, the magnetic field piercing a finite range of infinitely long system of
carriers is treated as introducing the additional highly non-local scatterer
which separates the circuit thus modelled into three parts -- the system as
such and two perfect leads. The transverse quantization spectrum of the inner
part of the electron waveguide thus constructed can be effectively tuned by
means of the magnetic field, even though the least transverse dimension of the
waveguide is small compared to the magnetic length. The initially finite
(metallic) value of the conductance, which is attributed to the existence of
extended modes of the transverse quantization, decreases rapidly as the
magnetic field grows. This decrease is due to the mode number reduction effect
produced by the magnetic field. The closing of the last current-carrying mode,
which is slightly sensitive to the disorder level, is suggested as the origin
of the magnetic-field-driven metal-to-insulator transition widely observed in
2D systems.Comment: 19 pages, 7 eps figures, the extension of cond-mat/040613
Direct observation of mode-coupling instability in two-dimensional plasma crystals
Dedicated experiments on melting of 2D plasma crystals were carried out. The
melting was always accompanied by spontaneous growth of the particle kinetic
energy, suggesting a universal plasma-driven mechanism underlying the process.
By measuring three principal dust-lattice (DL) wave modes simultaneously, it is
unambiguously demonstrated that the melting occurs due to the resonance
coupling between two of the DL modes. The variation of the wave modes with the
experimental conditions, including the emergence of the resonant (hybrid)
branch, reveals exceptionally good agreement with the theory of mode-coupling
instability.Comment: 4 pages, submitted to Physical Review Letter
The fundamental solution of the unidirectional pulse propagation equation
The fundamental solution of a variant of the three-dimensional wave equation
known as "unidirectional pulse propagation equation" (UPPE) and its paraxial
approximation is obtained. It is shown that the fundamental solution can be
presented as a projection of a fundamental solution of the wave equation to
some functional subspace. We discuss the degree of equivalence of the UPPE and
the wave equation in this respect. In particular, we show that the UPPE, in
contrast to the common belief, describes wave propagation in both longitudinal
and temporal directions, and, thereby, its fundamental solution possesses a
non-causal character.Comment: accepted to J. Math. Phy
Oscillations of cometary tails: a vortex shedding phenomenon?
Context. During their journey to perihelion, comets may appear in the
field-of-view of space-borne optical instruments, showing in some cases a
nicely developed plasma tail extending from their coma and exhibiting an
oscillatory behaviour. Aims. The oscillations of cometary tails may be
explained in terms of vortex shedding because of the interaction of the comet
with the solar wind streams. Therefore, it is possible to exploit these
oscillations in order to infer the value of the Strouhal number , which
quantifies the vortex shedding phenomenon, and the physical properties of the
local medium. Methods. We used the Heliospheric Imager (HI) data of the Solar
TErrestrial Relations Observatory (STEREO) mission to study the oscillations of
the tails of the comets 2P/Encke and C/2012 S1 (ISON) during their perihelion
in Nov 2013, determining the Strouhal numbers from the estimates of the halo
size, the relative speed of the solar wind flow and the period of the
oscillations. Results. We found that the estimated Strouhal numbers are very
small, and the typical value of would be extrapolated for size of
the halo larger than km. Conclusions. Despite the vortex shedding
phenomenon has not been unambiguously revealed, the findings suggest that some
MHD instability process is responsible for the observed behaviour of cometary
tails, which can be exploited for probing the physical conditions of the
near-Sun region.Comment: 10 pages, 9 figures, accepted for publication in A&A, Sect. 1
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