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 $\zeta(s)$ at $s=0$ 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 $\zeta(0)$ for the cases of Euclidean spaces and $N$-spheres. In the $N$-sphere case, we make use of the Euler-Maclaurin formula to develop asymptotic expansions for the required sums. The resulting $\zeta(0)$ 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

Spherically Symmetric Solutions in Macroscopic Gravity

Schwarzschild's solution to the Einstein Field Equations was one of the first and most important solutions that lead to the understanding and important experimental tests of Einstein's theory of General Relativity. However, Schwarzschild's solution is essentially based on an ideal theory of gravitation, where all inhomogeneities are ignored. Therefore, any generalization of the Schwarzschild solution should take into account the effects of small perturbations that may be present in the gravitational field. The theory of Macroscopic Gravity characterizes the effects of the inhomogeneities through a non-perturbative and covariant averaging procedure. With similar assumptions on the geometry and matter content, a solution to the averaged field equations as dictated by Macroscopic Gravity are derived. The resulting solution provides a possible explanation for the flattening of galactic rotation curves, illustrating that Dark Matter is not real but may only be the result of averaging inhomogeneities in a spherically symmetric background.Comment: 14 pages, added and updated references, some paragraphs rewritten for clarity, typographical errors fixed, results have not change