17,978 research outputs found
Existence and stability of hole solutions to complex Ginzburg-Landau equations
We consider the existence and stability of the hole, or dark soliton,
solution to a Ginzburg-Landau perturbation of the defocusing nonlinear
Schroedinger equation (NLS), and to the nearly real complex Ginzburg-Landau
equation (CGL). By using dynamical systems techniques, it is shown that the
dark soliton can persist as either a regular perturbation or a singular
perturbation of that which exists for the NLS. When considering the stability
of the soliton, a major difficulty which must be overcome is that eigenvalues
may bifurcate out of the continuous spectrum, i.e., an edge bifurcation may
occur. Since the continuous spectrum for the NLS covers the imaginary axis, and
since for the CGL it touches the origin, such a bifurcation may lead to an
unstable wave. An additional important consideration is that an edge
bifurcation can happen even if there are no eigenvalues embedded in the
continuous spectrum. Building on and refining ideas first presented in Kapitula
and Sandstede (Physica D, 1998) and Kapitula (SIAM J. Math. Anal., 1999), we
show that when the wave persists as a regular perturbation, at most three
eigenvalues will bifurcate out of the continuous spectrum. Furthermore, we
precisely track these bifurcating eigenvalues, and thus are able to give
conditions for which the perturbed wave will be stable. For the NLS the results
are an improvement and refinement of previous work, while the results for the
CGL are new. The techniques presented are very general and are therefore
applicable to a much larger class of problems than those considered here.Comment: 41 pages, 4 figures, submitte
Domain Bubbles of Extra Dimensions
``Dimension bubbles'' of the type previously studied by Blau and Guendelman
[S.K. Blau and E.I. Guendelman, Phys. Rev. D40, 1909 (1989)], which effectively
enclose a region of 5d spacetime and are surrounded by a region of 4d
spacetime, can arise in a 5d theory with a compact extra dimension that is
dimensionally reduced to give an effective 4d theory. These bubbles with thin
domain walls can be stabilized against total collapse in a rather natural way
by a scalar field which, as in the case with ``ordinary'' nontopological
solitons, traps light scalar particles inside the bubble.Comment: 13 pages, no figures; to appear in Phys.Rev.
Zeta-Functions for Non-Minimal Operators
We evaluate zeta-functions at for invariant non-minimal
2nd-order vector and tensor operators defined on maximally symmetric even
dimensional spaces. We decompose the operators into their irreducible parts and
obtain their corresponding eigenvalues. Using these eigenvalues, we are able to
explicitly calculate for the cases of Euclidean spaces and
-spheres. In the -sphere case, we make use of the Euler-Maclaurin formula
to develop asymptotic expansions for the required sums. The resulting
values for dimensions 2 to 10 are given in the Appendix.Comment: 26 pages, additional reference
The Nature and Frequency of Outflows from Stars in the Central Orion Nebula Cluster
Recent Hubble Space Telescope images have allowed the determination with
unprecedented accuracy of motions and changes of shocks within the inner Orion
Nebula. These originate from collimated outflows from very young stars, some
within the ionized portion of the nebula and others within the host molecular
cloud. We have doubled the number of Herbig-Haro objects known within the inner
Orion Nebula. We find that the best-known Herbig-Haro shocks originate from a
relatively few stars, with the optically visible X-ray source COUP 666 driving
many of them.
While some isolated shocks are driven by single collimated outflows, many
groups of shocks are the result of a single stellar source having jets oriented
in multiple directions at similar times. This explains the feature that shocks
aligned in opposite directions in the plane of the sky are usually blue shifted
because the redshifted outflows pass into the optically thick Photon Dominated
Region behind the nebula. There are two regions from which optical outflows
originate for which there are no candidate sources in the SIMBAD data base.Comment: 152 pages, 46 figures, 7 tables. Accepted by A
An Investigation of a Method for the Analysis of Smokes According to Particle Size
An electrical precipitation method for the analysis of smokes according to particle size has been investigated. A thin stream of smoke particles moving under laminar conditions in a wind tunnel of rectangular cross section is electrically charged in a small region. The charged particles are then precipitated by the uniform field existing between the charged upper plate and the grounded lower plate of the wind tunnel as a long track along the lower plate. The size-frequency distributions of the particles precipitated at various points on the lower plate were determined from measurements on enlargements of electron-microscope photographs of samples of the smoke precipitated at various points. The agreement between theory and experiment is fair, but the range of sizes of the particles precipitated at a given point is rather large
Possible Signature of Low Scale Gravity in Ultra High Enegry Cosmic Rays
We show that the existence of low scale gravity at TeV scale could lead to a
direct production of photons with energies above 10^22 eV due to annihilation
of ultra high energy neutrinos on relic massive neutrinos of the galactic halo.
Air showers initialized in the terrestrial atmosphere by these ultra energetic
photons could be collected in near future by the new generation of cosmic ray
experiments.Comment: 5 pages, 3 figure
Sensitivity of synchrotron radiation to the superthermal electron population in mildly relativistic plasma
Synchrotron radiation has markedly different behavior in and in plasma. We show that
high-energy electrons which occupy the tail of velocity distribution function
have disproportionate impact on power loss of plasma.
If electrons with energy more than a cutoff energy are redistributed while
keeping the Maxwellian distribution function below cutoff energy intact, both
emission and absorption of synchrotron radiation act to decrease the lost
power. These novel radiation transport effects in non-equilibrium plasma
suggest large utility in the deconfinement of high-energy electrons to reduce
synchrotron radiation in applications where the radiation is deleterious.Comment: 6 pages, 5 figures, submitted to Po
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