Arc-Length Continuation and Multigrid Techniques for Nonlinear Elliptic Eigenvalue Problems

We investigate multi-grid methods for solving linear systems arising from arc-length continuation techniques applied to nonlinear elliptic eigenvalue problems. We find that the usual multi-grid methods diverge in the neighborhood of singular points of the solution branches. As a result, the continuation method is unable to continue past a limit point in the Bratu problem. This divergence is analyzed and a modified multi-grid algorithm has been devised based on this analysis. In principle, this new multi-grid algorithm converges for elliptic systems, arbitrarily close to singularity and has been used successfully in conjunction with arc-length continuation procedures on the model problem. In the worst situation, both the storage and the computational work are only about a factor of two more than the unmodified multi-grid methods

Statistics Of The Burst Model At Super-critical Phase

We investigate the statistics of a model of type-I X-ray burst [Phys. Rev. E, {\bf 51}, 3045 (1995)] in its super-critical phase. The time evolution of the burnable clusters, places where fire can pass through, is studied using simple statistical arguments. We offer a simple picture for the time evolution of the percentage of space covered by burnable clusters. A relation between the time-average and the peak percentage of space covered by burnable clusters is also derived.Comment: 11 Pages in Revtex 3.0. Two figures available by sending request to [email protected]

Dressing a Naked Singularity: an Example

Considering the evolution of a perfect fluid with self-similarity of the second kind, we have found that an initial naked singularity can be trapped by an event horizon due to collapsing matter. The fluid moves along time-like geodesics with a self-similar parameter $\alpha = -3$. Since the metric obtained is not asymptotically flat, we match the spacetime of the fluid with a Schwarzschild spacetime. All the energy conditions are fulfilled until the naked singularity.Comment: 14 pages, 1 figure. This version corrects an error in the calculus of the pressure and in the conclusion

Gravastars and Black Holes of Anisotropic Dark Energy

Dynamical models of prototype gravastars made of anisotropic dark energy are constructed, in which an infinitely thin spherical shell of a perfect fluid with the equation of state $p = (1-\gamma)\sigma$ divides the whole spacetime into two regions, the internal region filled with a dark energy fluid, and the external Schwarzschild region. The models represent "bounded excursion" stable gravastars, where the thin shell is oscillating between two finite radii, while in other cases they collapse until the formation of black holes. Here we show, for the first time in the literature, a model of gravastar and formation of black hole with both interior and thin shell constituted exclusively of dark energy. Besides, the sign of the parameter of anisotropy ($p_t - p_r$) seems to be relevant to the gravastar formation. The formation is favored when the tangential pressure is greater than the radial pressure, at least in the neighborhood of the isotropic case ($\omega=-1$).Comment: 16 pages, 8 figures. Accepted for publication in Gen. Rel. Gra

Roles of the Bloom's syndrome helicase in the maintenance of genome stability

The RecQ family of DNA helicases is highly conserved in evolution from bacteria to humans. Of the five known human RecQ family members, three (BLM, WRN and RECQ4, which cause Bloom's syndrome, Werner's syndrome and Rothmund-Thomson syndrome respectively) are mutated in distinct clinical disorders associated with cancer predisposition and/or premature aging. BLM forms part of a multienzyme complex including topoisomerase IIIalpha, replication protein A and a newly identified factor called BLAP75. Together, these proteins play a role in the resolution of DNA structures that arise during the process of homologous recombination repair. In the absence of BLM, cells show genomic instability and a high incidence of sister-chromatid exchanges. In addition to a DNA structure-specific helicase activity, BLM also catalyses Holliday-junction branch migration and the annealing of complementary single-stranded DNA molecules

A Graph Theoretic Approach for Optimizing Key Pre-distribution in Wireless SensorNetworks

Finding an optimal key assignment (subject to given constraints) for a key predistribution scheme in wireless sensor networks is a difficult task. Hence, most of the practical schemes are based on probabilistic key assignment, which leads to sub-optimal schemes requiring key storage linear in the total number of nodes. A graph theoretic framework is introduced to study the fundamental tradeoffs between key storage, average key path length (directly related to the battery consumption) and resilience (to compromised nodes) of key predistribution schemes for wireless sensor networks. Based on the proposed framework, a lower bound on key storage is derived for a given average key path length. An upper bound on the compromising probability is also given. This framework also leads to the design of key assignment schemes with a storage complexity of the same order as the lower bound