21,989 research outputs found
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
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