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

Systems of conservation laws with third-order Hamiltonian structures

We investigate $n$-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 $\mathbb{P}^{n+2}$ satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space $W$ of dimension $n+2$, classify $n$-tuples of skew-symmetric 2-forms $A^{\alpha} \in \Lambda^2(W)$ such that $$\phi_{\beta \gamma}A^{\beta}\wedge A^{\gamma}=0,$$ for some non-degenerate symmetric $\phi$.Comment: 31 page

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

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

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

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

Multicolor Photometry of the Vela Pulsar

Multicolor photometry of the Vela pulsar (PSR B0833-45), updated by recent HST/WFPC2 observations obtained in the 555W, 675W and 814W filters, is presented. The available data provide the best characterization so far of the pulsar spectral shape, which is dominated by a flat power law continuum with spectral index \alpha = -0.2 +/- 0.2, consistent with the extrapolation in the optical domain of the power law component of the X-ray spectrum detected by Chandra. In addition, a marginally significant dip (~ 3 sigma) seems to be present at about 6500 AA. Spectroscopic observations with the VLT, now in progress, will undoubtly provide a much better assessment of the reality and characteristics of this feature.Comment: 4 pages, LaTex, 2 Postscript figures. Astronomy & Astrophysics, accepte