Neumann and Bargmann systems associated with an extension of the coupled KdV hierarchy

An eigenvalue problem with a reference function and the corresponding hierarchy of nonlinear evolution equations are proposed. The bi-Hamiltonian structure of the hierarchy is established by using the trace identity. The isospectral problem is nonlinearized as to be finite-dimensional completely integrable systems in Liouville sense under Neumann and Bargmann constraints

Strongly interacting neutrinos as the highest energy cosmic rays

We show that all features of the ultrahigh energy cosmic ray spectrum from 10^{17} eV to 10^{21} eV can be described with a simple power-like injection spectrum of protons under the assumption that the neutrino-nucleon cross-section is significantly enhanced at center of mass energies above \approx 100 TeV. In our scenario, the cosmogenic neutrinos produced during the propagation of protons through the cosmic microwave background initiate air showers in the atmosphere, just as the protons. The total air shower spectrum induced by protons and neutrinos shows excellent agreement with the observations. A particular possibility for a large neutrino-nucleon cross-section exists within the Standard Model through electroweak instanton-induced processes.Comment: 8 pages, 4 figures, talk given at Beyond the Desert '03, Castle Ringberg, 9-14 June, 200

Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor

The integrability of an m-component system of hydrodynamic type, u_t=V(u)u_x, by the generalized hodograph method requires the diagonalizability of the mxm matrix V(u). This condition is known to be equivalent to the vanishing of the corresponding Haantjes tensor. We generalize this approach to hydrodynamic chains -- infinite-component systems of hydrodynamic type for which the infinite matrix V(u) is `sufficiently sparse'. For such systems the Haantjes tensor is well-defined, and the calculation of its components involves finite summations only. We illustrate our approach by classifying broad classes of conservative and Hamiltonian hydrodynamic chains with the zero Haantjes tensor. We prove that the vanishing of the Haantjes tensor is a necessary condition for a hydrodynamic chain to possess an infinity of semi-Hamiltonian hydrodynamic reductions, thus providing an easy-to-verify necessary condition for the integrability.Comment: 36 pages, the classification results and proofs are refined. A section on generating functions is adde

Radiance and Doppler shift distributions across the network of the quiet Sun

The radiance and Doppler-shift distributions across the solar network provide observational constraints of two-dimensional modeling of transition-region emission and flows in coronal funnels. Two different methods, dispersion plots and average-profile studies, were applied to investigate these distributions. In the dispersion plots, we divided the entire scanned region into a bright and a dark part according to an image of Fe xii; we plotted intensities and Doppler shifts in each bin as determined according to a filtered intensity of Si ii. We also studied the difference in height variations of the magnetic field as extrapolated from the MDI magnetogram, in and outside network. For the average-profile study, we selected 74 individual cases and derived the average profiles of intensities and Doppler shifts across the network. The dispersion plots reveal that the intensities of Si ii and C iv increase from network boundary to network center in both parts. However, the intensity of Ne viii shows different trends, namely increasing in the bright part and decreasing in the dark part. In both parts, the Doppler shift of C iv increases steadily from internetwork to network center. The average-profile study reveals that the intensities of the three lines all decline from the network center to internetwork region. The binned intensities of Si ii and Ne viii have a good correlation. We also find that the large blue shift of Ne viii does not coincide with large red shift of C iv. Our results suggest that the network structure is still prominent at the layer where Ne viii is formed in the quiet Sun, and that the magnetic structures expand more strongly in the dark part than in the bright part of this quiet Sun region.Comment: 10 pages,9 figure