19 research outputs found
Electromagnetic field near cosmic string
The retarded Green function of the electromagnetic field in spacetime of a
straight thin cosmic string is found. It splits into a geodesic part
(corresponding to the propagation along null rays) and to the field scattered
on the string. With help of the Green function the electric and magnetic fields
of simple sources are constructed. It is shown that these sources are
influenced by the cosmic string through a self-interaction with their field.
The distant field of static sources is studied and it is found that it has a
different multipole structure than in Minkowski spacetime. On the other hand,
the string suppresses the electric and magnetic field of distant sources--the
field is expelled from regions near the string.Comment: 12 pages, 8 figures (low-resolution figures; for the version with
high-resolution figures see http://utf.mff.cuni.cz/~krtous/papers/), v2: two
references added, typos correcte
Scaling and self-similarity in an unforced flow of inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell
We investigate quasi-two-dimensional relaxation, by surface tension, of a
long straight stripe of inviscid fluid trapped inside a viscous fluid in a
Hele-Shaw cell. Combining analytical and numerical solutions, we describe the
emergence of a self-similar dumbbell shape and find non-trivial dynamic
exponents that characterize scaling behavior of the dumbbell dimensions.Comment: 4 pages, 5 figures, to appear in PR
Quantum superintegrability and exact solvability in N dimensions
A family of maximally superintegrable systems containing the Coulomb atom as
a special case is constructed in N-dimensional Euclidean space. Two different
sets of N commuting second order operators are found, overlapping in the
Hamiltonian alone. The system is separable in several coordinate systems and is
shown to be exactly solvable. It is solved in terms of classical orthogonal
polynomials. The Hamiltonian and N further operators are shown to lie in the
enveloping algebra of a hidden affine Lie algebra