5,233 research outputs found
High energy processes in the vicinity of the Kerr's black hole horizon
Two particle collisions close to the horizon of the rotating nonextremal
black hole are analyzed. It is shown that high energy of the order of the Grand
Unification scale in the centre of mass of colliding particles can be obtained
when there is a multiple collision - the particle from the accretion disc gets
the critical momentum in first collision with the other particle close to the
horizon and then there is a second collision of the critical particle with the
ordinary one. High energy occurs due to a great relative velocity of two
particles and a large Lorentz factor. The dependence of the relative velocity
on the distance to horizon is analyzed, the time of movement from the point in
the accretion disc to the point of scattering with large energy as well as the
time of back movement to the Earth are calculated. It is shown that they have
reasonable order.Comment: 13 pages, 2 figures, added some formulas and one referenc
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
Integrable Systems and Metrics of Constant Curvature
In this article we present a Lagrangian representation for evolutionary
systems with a Hamiltonian structure determined by a differential-geometric
Poisson bracket of the first order associated with metrics of constant
curvature. Kaup-Boussinesq system has three local Hamiltonian structures and
one nonlocal Hamiltonian structure associated with metric of constant
curvature. Darboux theorem (reducing Hamiltonian structures to canonical form
''d/dx'' by differential substitutions and reciprocal transformations) for
these Hamiltonian structures is proved
Hydrodynamic chains and a classification of their Poisson brackets
Necessary and sufficient conditions for an existence of the Poisson brackets
significantly simplify in the Liouville coordinates. The corresponding
equations can be integrated. Thus, a description of local Hamiltonian
structures is a first step in a description of integrable hydrodynamic chains.
The concept of Poisson bracket is introduced. Several new Poisson brackets
are presented
A note on condensations of onto compacta
summary:A condensation is a one-to-one continuous mapping onto. It is shown that the space of real-valued continuous functions on in the topology of pointwise convergence very often cannot be condensed onto a compact Hausdorff space. In particular, this is so for any non-metrizable Eberlein compactum (Theorem 19). However, there exists a non-metrizable compactum such that condenses onto a metrizable compactum (Theorem 10). Several curious open problems are formulated
Two-Photon Excitation of Low-Lying Electronic Quadrupole States in Atomic Clusters
A simple scheme of population and detection of low-lying electronic
quadrupole modes in free small deformed metal clusters is proposed. The scheme
is analyzed in terms of the TDLDA (time-dependent local density approximation)
calculations. As test case, the deformed cluster is considered.
Long-living quadrupole oscillations are generated via resonant two-photon
(two-dipole) excitation and then detected through the appearance of satellites
in the photoelectron spectra generated by a probe pulse. Femtosecond pump and
probe pulses with intensities and
pulse duration fs are found to be optimal. The modes of
interest are dominated by a single electron-hole pair and so their energies,
being combined with the photoelectron data for hole states, allow to gather new
information about mean-field spectra of valence electrons in the HOMO-LUMO
region. Besides, the scheme allows to estimate the lifetime of electron-hole
pairs and hence the relaxation time of electronic energy into ionic heat.Comment: 4 pages, 4 figure
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