Constrained Reductions of 2D dispersionless Toda Hierarchy, Hamiltonian Structure and Interface Dynamics

Finite-dimensional reductions of the 2D dispersionless Toda hierarchy, constrained by the ``string equation'' are studied. These include solutions determined by polynomial, rational or logarithmic functions, which are of interest in relation to the ``Laplacian growth'' problem governing interface dynamics. The consistency of such reductions is proved, and the Hamiltonian structure of the reduced dynamics is derived. The Poisson structure of the rationally reduced dispersionless Toda hierarchies is also derivedComment: 18 pages LaTex, accepted to J.Math.Phys, Significantly updated version of the previous submissio

Mediation, arbitration and negotiation

We compare three common dispute resolution processes { negotiation, mediation, and arbitration { in the framework of Crawford and Sobel (1982). Under negotiation, the two parties engage in (possibly arbitrarily long) face-to-face cheap talk. Under mediation, the parties communicate with a neutral third party who makes a non-binding recommendation. Under arbitration, the two parties commit to conform to the third party recommendation. We characterize and compare the optimal mediation and arbitration procedures. Both mediators and arbitrators should optimally filter information, but mediators should also add noise to it. We find that unmediated negotiation performs as well as mediation if and only if the degree of conflict between the parties is low

Tsunami generation by ocean floor rupture front propagation: Hamiltonian description

The Hamiltonian method is applied to the problem of tsunami generation caused by a propagating rupture front and deformation of the ocean floor. The method establishes an alternative framework for analyzing the tsunami generation process and produces analytical expressions for the power and directivity of tsunami radiation (in the far-field) for two illustrative cases, with constant and gradually varying speeds of rupture front propagation

X-ray Pulsations from the Central Source in Puppis A

There are several supernova remnants which contain unresolved X-ray sources close to their centers, presumably radio-quiet neutron stars. To prove that these objects are indeed neutron stars, to understand the origin of their X-ray radiation, and to explain why they are radio-quiet, one should know their periods and period derivatives. We searched for pulsations of the X-ray flux from the radio-quiet neutron star candidate RX J0822-4300 near the center of the Puppis A supernova remnant observed with the ROSAT PSPC and HRI. A standard timing analysis of the separate PSPC and HRI data sets does not allow one to detect the periodicity unequivocally. However, a thorough analysis of the two observations separated by 4.56 yr enabled us to find a statistically significant period $P\simeq 75.3$ ms and its derivative $\dot{P}\simeq 1.49\times 10^{-13}$ s s$^{-1}$. The corresponding characteristic parameters of the neutron star, age $\tau=P/(2\dot{P})=8.0$ kyr, magnetic field $B=3.4\times 10^{12}$ G, and rotational energy loss $\dot{E}=1.4\times 10^{37}$ erg s$^{-1}$, are typical for young radio pulsars. Since the X-ray radiation has a thermal-like spectrum, its pulsations may be due to a nonuniform temperature distribution over the neutron star surface caused by anisotropy of the heat conduction in the strongly magnetized crust.Comment: 9 pages, 2 postscript figures, to appear in ApJ Letters; an acknowledgment is adde

Discovery of a 112 ms X-ray Pulsar in Puppis A: Further Evidence of Neutron Stars Weakly Magnetized at Birth

We report the discovery of 112-ms X-ray pulsations from RX J0822-4300, the compact central object (CCO) in the supernova remnant Puppis A, in two archival Newton X-Ray Multi-Mirror Mission observations taken in 2001. The sinusoidal light curve has a pulsed fraction of 11% with an abrupt 180 deg. change in phase at 1.2 keV. The observed phase shift and modulation are likely the result of emission from opposing thermal hot spots of distinct temperatures. Phase-resolved spectra reveal an emission feature at E(line) = 0.8 keV associated with the cooler region, possibly due to an electron cyclotron resonance effect similar to that seen in the spectrum of the CCO pulsar 1E 1207.4-5209. No change in the spin period of PSR J0821-4300 is detected in 7 months, with a 2 sigma upper limit on the period derivative less than 8.3E-15. This implies limits on the spin-down energy loss rate of less than 2.3E35 erg/s, the surface magnetic dipole field strength B_s < 9.8E11 G, and the spin-down age tau > 220 kyr. The latter is much longer than the SNR age, indicating that PSR J0821-4300 was born spinning near its present period. Its properties are remarkably similar to those of the two other known CCO pulsars, demonstrating the existence of a class of neutron stars born with weak magnetic fields related to a slow original spin. These results are also of importance in understanding the extreme transverse velocity of PSR J0821-4300, favoring the hydrodynamic instability mechanism in the supernova explosion.Comment: 5 pages, 4 figure, Latex, emulateapj style. To appear in the Astrophysical Journa

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 $(\gamma=1)$ for which we found new non homogenious solutions expressed in terms of the elementary functions.Comment: 11 pages, 1 figur

Detection of X-ray Emission from the Very Old Pulsar J0108-1431

PSR J0108-1431 is a nearby, 170 Myr old, very faint radio pulsar near the "pulsar death line" in the P-Pdot diagram. We observed the pulsar field with the Chandra X-ray Observatory and detected a point source (53 counts in a 30 ks exposure, energy flux (9+/-2)\times 10^{-15} ergs cm^{-2} s^{-1} in the 0.3-8 keV band) close to the radio pulsar position. Based on the large X-ray/optical flux ratio at the X-ray source position, we conclude that the source is the X-ray counterpart of PSR J0108-1431.The pulsar spectrum can be described by a power-law model with photon index Gamma \approx 2.2 and luminosity L_{0.3-8 keV} \sim 2\times 10^{28} d_{130}^2 ergs s^{-1}, or by a blackbody model with the temperature kT\approx 0.28 keV and bolometric luminosity L_{bol} \sim 1.3\times 10^{28} d_{130}^2 ergs s^{-1}, for a plausible hydrogen column density NH = 7.3\times 10^{19} cm^{-2} (d_{130}=d/130 pc). The pulsar converts \sim 0.4% of its spin-down power into the X-ray luminosity, i.e., its X-ray efficiency is higher than for most younger pulsars. From the comparison of the X-ray position with the previously measured radio positions, we estimated the pulsar proper motion of 0.2 arcsec yr^{-1} (V_\perp \sim 130 d_{130} km s^{-1}), in the south-southeast direction.Comment: 8 pages, 9 figures, accepted to ApJ; minor revisions in Sections 2.2 and 3.