9,803 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
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
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
Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity
We examine the completeness of bi-orthogonal sets of eigenfunctions for
non-Hermitian Hamiltonians possessing a spectral singularity. The correct
resolutions of identity are constructed for delta like and smooth potentials.
Their form and the contribution of a spectral singularity depend on the class
of functions employed for physical states. With this specification there is no
obstruction to completeness originating from a spectral singularity.Comment: 25 pages, more refs adde
Spectral and Rotational Changes in the Isolated Neutron Star RX J0720.4-3125
RX J0720.4-3125 is an isolated neutron star that, uniquely in its class, has
shown changes in its thermal X-ray spectrum. We use new spectra taken with
Chandra's Low Energy Transmission Grating Spectrometer, as well as archival
observations, to try to understand the timescale and nature of these changes.
We construct lightcurves, which show both small, slow variations on a timescale
of years, and a larger event that occurred more quickly, within half a year.
From timing, we find evidence for a `glitch' coincident with this larger
event, with a fractional increase in spin frequency of 5x10^{-8}. We compare
the `before' and `after' spectra with those from RX J1308.6+2127, an isolated
neutron star with similar temperature and magnetic field strength, but with a
much stronger absorption feature in its spectrum. We find that the `after'
spectrum can be represented remarkably well by the superposition of the
`before' spectrum, scaled by two thirds, and the spectrum of RX J1308.6+2127,
thus suggesting that the event affected approximately one third of the surface.
We speculate the event reflects a change in surface composition caused by,
e.g., an accretion episode.Comment: 4 pages, 2 figures, 2 tables, emulateapj format. ApJL, accepte
Micro-displacement sensors based on plastic photonic bandgap Bragg fibers
We demonstrate an amplitude-based micro-displacement sensor that uses a
plastic photonic bandgap Bragg fiber with one end coated with a silver layer.
The reflection intensity of the Bragg fiber is characterized in response to
different displacements (or bending curvatures). We note that the Bragg
reflector of the fiber acts as an efficient mode stripper for the wavelengths
near the edge of the fiber bandgap, which makes the sensor extremely sensitive
to bending or displacements at these wavelengths. Besides, by comparison of the
Bragg fiber sensor to a sensor based on a regular multimode fiber with similar
outer diameter and length, we find that the Bragg fiber sensor is more
sensitive to bending due to presence of mode stripper in the form of the
multilayer reflector. Experimental results show that the minimum detection
limit of the Bragg fiber sensor can be smaller than 5 um for displacement
sensing
Underpriced Default Spread Exacerbates Market Crashes
In this paper, we develop a specific observable symptom of a banking system that underprices the default spread in non-recourse asset-backed lending. Using three different data sets for 18 countries and property types, we find that, following a negative demand shock, the âunderpricingâ economies experience far deeper asset market crashes than economies in which the put option is correctly priced. Furthermore, only one of the countries in our sample continues to exhibit the underpricing symptom following a market crash. This indicates that market crashes have a cleansing effect and eliminate underpricing at least for a period of time. This makes investing in such markets safer following a negative demand shock.real estate bubble, lender optimism, disaster myopia, Asian financial crisis
X-ray emission from PSR B1800-21, its wind nebula, and similar systems
We detected X-ray emission from PSR B1800-21 and its synchrotron nebula with
the Chandra X-ray Observatory. The pulsar's observed flux is (1.4+/-0.2)
10^{-14} ergs cm^{-2} s^{-1} in the 1-6 keV band. The spectrum can be described
by a two-component PL+BB model, suggesting a mixture of thermal and
magnetospheric emission. For a plausible hydrogen column density n_{H}=1.4
10^{22} cm^{-2}, the PL component has a slope Gamma=1.4+/-0.6 and a luminosity
L_{psr}^{nonth}=4 10^{31}(d/4 kpc)^2 ergs s^{-1}. The properties of the thermal
component (kT=0.1-0.3 keV, L^{bol}=10^{31}-10^{33} ergs s^{-1}) are very poorly
constrained because of the strong interstellar absorption. The compact,
7''\times4'', inner pulsar-wind nebula (PWN), elongated perpendicular to the
pulsar's proper motion, is immersed in a fainter asymmetric emission. The
observed flux of the PWN is (5.5+/-0.6) 10^{-14} ergs cm^{-2} s^{-1} in the 1-8
keV band. The PWN spectrum fits by a PL model with Gamma=1.6+/-0.3, L=1.6
10^{32} (d/4 kpc})^2 ergs s^{-1}. The shape of the inner PWN suggests that the
pulsar moves subsonically and X-ray emission emerges from a torus associated
with the termination shock in the equatorial pulsar wind. The inferred
PWN-pulsar properties (e.g., the PWN X-ray efficiency, L_{pwn}/\dot{E}~10^{-4};
the luminosity ratio, L_{pwn}/L_{psr}^{nonth}=4; the pulsar wind pressure at
the termination shock, p_s=10^{-9} ergs cm^{-3}) are very similar to those of
other subsonically moving Vela-like objects detected with Chandra
(L_{pwn}/\dot{E}=10^{-4.5}-10^{-3.5}, L_{pwn}/L_{psr}^{nonth}~5,
p_s=10^{-10}-10^{-8} ergs cm^{-1}).Comment: 11 pages, 10 figures, 2 tables; submitted to ApJ. Version with the
high-resolution figures is available at
http://www.astro.psu.edu/users/green/B1800/B1800_ApJ.pd
Algebro-geometric approach in the theory of integrable hydrodynamic type systems
The algebro-geometric approach for integrability of semi-Hamiltonian
hydrodynamic type systems is presented. This method is significantly simplified
for so-called symmetric hydrodynamic type systems. Plenty interesting and
physically motivated examples are investigated
Computing Economic Chaos
Existence theory in economics is usually in real domains such as the findings
of chaotic trajectories in models of economic growth, tatonnement, or
overlapping generations models. Computational examples, however, sometimes
converge rapidly to cyclic orbits when in theory they should be nonperiodic
almost surely. We explain this anomaly as the result of digital approximation
and conclude that both theoretical and numerical behavior can still illuminate
essential features of the real data
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