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 $N$-fold first order local Hamiltonian structure can be cast into variational form with $2N-1$ Lagrangians which will be local functionals of Clebsch potentials. This number increases to $3N-2$ when the Miura transformation is invertible. Furthermore we construct a new Lagrangian for polytropic gas dynamics in $1+1$ 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 “underpricing” 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