5,977 research outputs found
Multi-Lagrangians for Integrable Systems
We propose a general scheme to construct multiple Lagrangians for completely
integrable non-linear evolution equations that admit multi- Hamiltonian
structure. The recursion operator plays a fundamental role in this
construction. We use a conserved quantity higher/lower than the Hamiltonian in
the potential part of the new Lagrangian and determine the corresponding
kinetic terms by generating the appropriate momentum map. This leads to some
remarkable new developments. We show that nonlinear evolutionary systems that
admit -fold first order local Hamiltonian structure can be cast into
variational form with Lagrangians which will be local functionals of
Clebsch potentials. This number increases to when the Miura
transformation is invertible. Furthermore we construct a new Lagrangian for
polytropic gas dynamics in dimensions which is a {\it local} functional
of the physical field variables, namely density and velocity, thus dispensing
with the necessity of introducing Clebsch potentials entirely. This is a
consequence of bi-Hamiltonian structure with a compatible pair of first and
third order Hamiltonian operators derived from Sheftel's recursion operator.Comment: typos corrected and a reference adde
Non polynomial conservation law densities generated by the symmetry operators in some hydrodynamical models
New extra series of conserved densities for the polytropic gas model and
nonlinear elasticity equation are obtained without any references to the
recursion operator or to the Lax operator formalism. Our method based on the
utilization of the symmetry operators and allows us to obtain the densities of
arbitrary homogenuity dimensions. The nonpolynomial densities with logarithmics
behaviour are presented as an example. The special attention is paid for the
singular case for which we found new non homogenious solutions
expressed in terms of the elementary functions.Comment: 11 pages, 1 figur
Variability of the Vela Pulsar-wind Nebula Observed with Chandra
The observations of the pulsar-wind nebula (PWN) around the Vela pulsar with
the Advanced CCD Imaging Spectrometer aboard the Chandra X-ray Observatory,
taken on 2000 April 30 and November 30, reveal its complex morphology
reminiscent of that of the Crab PWN. Comparison of the two observations shows
changes up to 30% in the surface brightness of the PWN features. Some of the
PWN elements show appreciable shifts, up to a few arcseconds (about 10^{16}
cm), and/or spectral changes. To elucidate the nature of the observed
variations, further monitoring of the Vela PWN is needed.Comment: 7 pages (incl. 3 embedded PS figures), AASTEX, uses emulateapj5.sty.
Submitted to ApJ Lett. For a high-resolution color PS image of Figure 3 (6.3
Mby), see http://www.astro.psu.edu/users/divas/velaneb_fig3.p
Discrete Lie Advection of Differential Forms
In this paper, we present a numerical technique for performing Lie advection
of arbitrary differential forms. Leveraging advances in high-resolution finite
volume methods for scalar hyperbolic conservation laws, we first discretize the
interior product (also called contraction) through integrals over Eulerian
approximations of extrusions. This, along with Cartan's homotopy formula and a
discrete exterior derivative, can then be used to derive a discrete Lie
derivative. The usefulness of this operator is demonstrated through the
numerical advection of scalar fields and 1-forms on regular grids.Comment: Accepted version; to be published in J. FoC
Particles with negative energies in black holes
The problem of the existence of particles with negative energies inside and
outside of Schwarzschild, charged and rotating black holes is investigated.
Different definitions of the energy of the particle inside the Schwarzschild
black hole are analyzed and it is shown in what cases this energy can be
negative. A comparison is made for the cases of rotating black holes described
by the Kerr metric when the energy of the particle can be negative in the
ergosphere and the Reissner-Nordstrom metric.Comment: 10 pages, 2 figures, typos correction to match published versio
Absorption Features in Spectra of Magnetized Neutron Stars
The X-ray spectra of some magnetized isolated neutron stars (NSs) show
absorption features with equivalent widths (EWs) of 50 - 200 eV, whose nature
is not yet well known. To explain the prominent absorption features in the soft
X-ray spectra of the highly magnetized (B ~ 10^{14} G) X-ray dim isolated NSs
(XDINSs), we theoretically investigate different NS local surface models,
including naked condensed iron surfaces and partially ionized hydrogen model
atmospheres, with semi-infinite and thin atmospheres above the condensed
surface. We also developed a code for computing light curves and integral
emergent spectra of magnetized neutron stars with various temperature and
magnetic field distributions over the NS surface. We compare the general
properties of the computed and observed light curves and integral spectra for
XDINS RBS\,1223 and conclude that the observations can be explained by a thin
hydrogen atmosphere above the condensed iron surface, while the presence of a
strong toroidal magnetic field component on the XDINS surface is unlikely. We
suggest that the harmonically spaced absorption features in the soft X-ray
spectrum of the central compact object (CCO) 1E 1207.4-5209 (hereafter 1E 1207)
correspond to peaks in the energy dependence of the free-free opacity in a
quantizing magnetic field, known as quantum oscillations. To explore observable
properties of these quantum oscillations, we calculate models of hydrogen NS
atmospheres with B ~ 10^{10} - 10^{11} G (i.e., electron cyclotron energy
E_{c,e} ~ 0.1 - 1 keV) and T_eff = 1 - 3 MK. Such conditions are thought to be
typical for 1E 1207. We show that observable features at the electron cyclotron
harmonics with EWs \approx 100 - 200 eV can arise due to these quantum
oscillations.Comment: 4 pages, 3 figures, conference "Astrophysics of Neutron Stars - 2010"
in honor of M. Ali Alpar, Izmir, Turke
Ergatic dynamic control systems
Synthesis and analysis of systems containing a man in their control circuits are considered. The concepts of ergonomics and ergatic systems are defined, and tasks and problems of ergonomics are outlined. The synthesis of the structure of an astronautic ergatic organism is presented, as well as the synthesis of nonstationary ergatic systems. Problems of selecting the criteria for complex systems are considered, and the results are presented from a study of ergatic control systems with any degree of human participation
Gurevich-Zybin system
We present three different linearizable extensions of the Gurevich-Zybin
system. Their general solutions are found by reciprocal transformations. In
this paper we rewrite the Gurevich-Zybin system as a Monge-Ampere equation. By
application of reciprocal transformation this equation is linearized.
Infinitely many local Hamiltonian structures, local Lagrangian representations,
local conservation laws and local commuting flows are found. Moreover, all
commuting flows can be written as Monge-Ampere equations similar to the
Gurevich-Zybin system. The Gurevich-Zybin system describes the formation of a
large scale structures in the Universe. The second harmonic wave generation is
known in nonlinear optics. In this paper we prove that the Gurevich-Zybin
system is equivalent to a degenerate case of the second harmonic generation.
Thus, the Gurevich-Zybin system is recognized as a degenerate first negative
flow of two-component Harry Dym hierarchy up to two Miura type transformations.
A reciprocal transformation between the Gurevich-Zybin system and degenerate
case of the second harmonic generation system is found. A new solution for the
second harmonic generation is presented in implicit form.Comment: Corrected typos and misprint
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