8,298 research outputs found
On the bi-Hamiltonian Geometry of WDVV Equations
We consider the WDVV associativity equations in the four dimensional case.
These nonlinear equations of third order can be written as a pair of six
component commuting two-dimensional non-diagonalizable hydrodynamic type
systems. We prove that these systems possess a compatible pair of local
homogeneous Hamiltonian structures of Dubrovin--Novikov type (of first and
third order, respectively).Comment: 21 pages, revised published version; exposition substantially
improve
Phase and Power Control in the RF Magnetron Power Stations of Superconducting Accelerators
Phase and power control methods that satisfy the requirements of
superconducting accelerators to magnetron RF sources were considered by a
simplified kinetic model of a magnetron driven by a resonant injected signal.
The model predicting and explaining stable, low noise operation of the tube
below the threshold of self-excitation (the Hatrree voltage in free run mode)
at a highest efficiency, a wide range of power control and a wide-band phase
control was well verified in experiments demonstrating capabilities of the
magnetron transmitters for powering of state of the art superconducting
accelerators. Descriptions of the kinetic model, the experimental verification
and a conceptual scheme of the highly-efficient magnetron RF transmitter for
the accelerators are presented and discussed.Comment: 10 pages, 15 figure
Systems of conservation laws with third-order Hamiltonian structures
We investigate -component systems of conservation laws that possess
third-order Hamiltonian structures of differential-geometric type. The
classification of such systems is reduced to the projective classification of
linear congruences of lines in satisfying additional
geometric constraints. Algebraically, the problem can be reformulated as
follows: for a vector space of dimension , classify -tuples of
skew-symmetric 2-forms such that for some non-degenerate symmetric
.Comment: 31 page
X-ray emission from the old pulsar B0950+08
We present the timing and spectral analyses of theXMM-newton data on the
17-Myr-old, nearby radio pulsar B0950+08. This observation revealed pulsations
of the X-ray flux of the pulsar at its radio period. The pulse shape and pulsed
fraction are apparently different at lower and higher energies of the observed
0.2-10 keV energy range, which suggests that the radiation cannot be explained
by a single emission mechanism. The X-ray spectrum of the pulsar can be fitted
with a power-law model with a photon index about 1.75 and an (isotropic)
luminosity about 9.8e29 erg/s in the 0.2-10 keV. Better fits are obtained with
two-component, power-law plus thermal, models with index of 1.30 and 9.7e29
erg/s for the power-law component that presumably originates from the pulsar's
magnetosphere. The thermal component, dominating at E>0.7 keV, can be
interpreted as radiation from heated polar caps on the neutron star surface
covered with a hydrogen atmosphere. The inferred effective temperature, radius,
and bolometric luminosity of the polar caps are about 1 MK, 250 m, and 3e29
erg/s. Optical through X-ray nonthermal spectrum of the pulsar can be described
as a single power-law with index 1.3-1.4 for the two-component X-ray fit. The
ratio of the nonthermal X-ray (1-10 keV) luminosity to the nonthermal optical
(4000-9000 \AA) luminosity is within the range of 1e2-1e3 observed for younger
pulsars, which suggests that the magnetospheric X-ray and optical emissions are
powered by the same mechanism in all pulsars. An upper limit on the temperature
of the bulk of the neutron star surface, inferred from the optical and X-ray
data, is about 0.15 MK. We also analyze X-ray observations of several other old
pulsars, B2224+65, J2043+2740, B0628-28, B1813-36, B1929+10, and B0823+26.Comment: To be published in ApJ. Nonthermal optical and X-ray luminosities of
seven radio pulsars are updated and presented in a new Table. Figure 6
showing the ratios of the luminosities vs. spin-down energy is also update
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
Mass-to-Radius Ratio for the Millisecond Pulsar J0437-4715
Properties of X-ray radiation emitted from the polar caps of a radio pulsar
depend not only on the cap temperature, size, and position, but also on the
surface chemical composition, magnetic field, and neutron star's mass and
radius. Fitting the spectra and the light curves with neutron star atmosphere
models enables one to infer these parameters. As an example, we present here
results obtained from the analysis of the pulsed X-ray radiation of a nearby
millisecond pulsar J0437-4715. In particular, we show that stringent
constraints on the mass-to-radius ratio can be obtained if orientations of the
magnetic and rotation axes are known, e.g., from the radio polarization data.Comment: 2 figures, aasms4.sty; accepted for publication in ApJLetter
Polarization of Thermal X-rays from Isolated Neutron Stars
Since the opacity of a magnetized plasma depends on polarization of
radiation, the radiation emergent from atmospheres of neutron stars with strong
magnetic fields is expected to be strongly polarized. The degree of linear
polarization, typically ~10-30%, depends on photon energy, effective
temperature and magnetic field. The spectrum of polarization is more sensitive
to the magnetic field than the spectrum of intensity. Both the degree of
polarization and the position angle vary with the neutron star rotation period
so that the shape of polarization pulse profiles depends on the orientation of
the rotational and magnetic axes. Moreover, as the polarization is
substantially modified by the general relativistic effects, observations of
polarization of X-ray radiation from isolated neutron stars provide a new
method for evaluating the mass-to-radius ratio of these objects, which is
particularly important for elucidating the properties of the superdense matter
in the neutron star interiors.Comment: 7 figures, to be published in Ap
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