Wave propagation over a beach within a nonlinear theory

Wave propagation over a beach is considered within a nonlinear theory in shallow water. Lagrangian coordinates are used to describe the problem. The solution is expanded in double series involving a small parameter and local oscillations. Two cases are treated: The beach with appreciable inclination on the horizontal (cliff) and the beach of small inclination. We show that finite solutions are obtained, in contrast to the linear theory which involves a logarithmic singularity at the shoreline. For the cliff, it is shown that local oscillations do not appear in the first two orders of approximation, and the incident wave is totally reflected without loss of energy at this order of approximation. The case of an incident wave on the beach is considered. The deformation of this wave is investigated and explicit formulae are obtained for the reflected wave and for the local oscillations, to shed light on the energy transfer due to interaction with the beach

Leadership Statistics in Random Structures

The largest component (``the leader'') in evolving random structures often exhibits universal statistical properties. This phenomenon is demonstrated analytically for two ubiquitous structures: random trees and random graphs. In both cases, lead changes are rare as the average number of lead changes increases quadratically with logarithm of the system size. As a function of time, the number of lead changes is self-similar. Additionally, the probability that no lead change ever occurs decays exponentially with the average number of lead changes.Comment: 5 pages, 3 figure

Kepler Eclipsing Binary Stars. V. Identification of 31 Eclipsing Binaries in the K2 Engineering Data-set

Over 2500 eclipsing binaries were identified and characterized from the ultra-precise photometric data provided by the Kepler space telescope. Kepler is now beginning its second mission, K2, which is proving to again provide ultra-precise photometry for a large sample of eclipsing binary stars. In the 1951 light curves covering 12 days in the K2 engineering data-set, we have identified and determined the ephemerides for 31 eclipsing binaries that demonstrate the capabilities for eclipsing binary science in the upcoming campaigns in K2. Of those, 20 are new discoveries. We describe both manual and automated approaches to harvesting the complete set of eclipsing binaries in the K2 data, provide identifications and details for the full set of eclipsing binaries present in the engineering data-set, and discuss the prospects for application of eclipsing binary searches in the K2 mission.Comment: 12 pages, 2 figures, submitted to PAS

Entanglement in squeezed two-level atom

In the previous paper, we adopted the method using quantum mutual entropy to measure the degree of entanglement in the time development of the Jaynes-Cummings model. In this paper, we formulate the entanglement in the time development of the Jaynes-Cummings model with squeezed states, and then show that the entanglement can be controlled by means of squeezing.Comment: 6 pages, 5 figures, to be published in J.Phys.

Long and short paths in uniform random recursive dags

In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \sigma such that S_n/log(n) tends to \sigma in probability as n tends to infinity. We also show that max_{1 \le i \le n} S_i/log(n) tends to \sigma in probability.Comment: 16 page

Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

The complexity of the neutron transport phenomenon throws its shadows on every physical system wherever neutron is produced or used. In the current study, an ab initio derivation of the neutron self-shielding factor to solve the problem of the decrease of the neutron flux as it penetrates into a material placed in an isotropic neutron field. We have employed the theory of steady-state neutron transport, starting from Stuart's formula. Simple formulae were derived based on the integral cross-section parameters that could be adopted by the user according to various variables, such as the neutron flux distribution and geometry of the simulation at hand. The concluded formulae of the self-shielding factors comprise an inverted sigmoid function normalized with a weight representing the ratio between the macroscopic total and scattering cross-sections of the medium. The general convex volume geometries are reduced to a set of chord lengths, while the neutron interactions probabilities within the volume are parameterized to the epithermal and thermal neutron energies. The arguments of the inverted-sigmoid function were derived from a simplified version of neutron transport formulation. Accordingly, the obtained general formulae were successful in giving the values of the experimental neutron self-shielding factor for different elements and different geometries.Comment: 14 pages, 5 figures, 1 graphical abstract, 73 references, and 2 tables, include improvement of illustration and story-telling writing styl

Phase Transition in a Random Fragmentation Problem with Applications to Computer Science

We study a fragmentation problem where an initial object of size x is broken into m random pieces provided x>x_0 where x_0 is an atomic cut-off. Subsequently the fragmentation process continues for each of those daughter pieces whose sizes are bigger than x_0. The process stops when all the fragments have sizes smaller than x_0. We show that the fluctuation of the total number of splitting events, characterized by the variance, generically undergoes a nontrivial phase transition as one tunes the branching number m through a critical value m=m_c. For m<m_c, the fluctuations are Gaussian where as for m>m_c they are anomalously large and non-Gaussian. We apply this general result to analyze two different search algorithms in computer science.Comment: 5 pages RevTeX, 3 figures (.eps

Stimulated perturbation on the neutron flux distribution in the mutually-dependent source-to-absorber geometry

The complexity of the neutron transport phenomenon throws its shadows on every physical system wherever neutron is produced or absorbed. The Monte Carlo N-Particle Transport Code (MCNP) was used to investigate the flux perturbations in the neutron field caused by an absorber. The geometry of the present experiment was designed to reach a simulation of an isotopic neutron field. The neutron source was a ${}^{241}$AmBe with the production physics of neutrons is dependent only on alpha-beryllium interaction and is independent of what happened to the neutron after it was generated. The geometries have been designed to get a volume of uniform neutron densities within a spherical volume of radius 15 cm in every neutron energy group up to 10 MeV. Absorbers of different dimensions were placed within the volume to investigate the field perturbation. Different neutron absorbers were used to correlate the phenomenon to the integral cross-section of the absorber. Flux density inside and outside the absorber samples was determined, while the spatial neutron flux distribution produced by the AmBe source without an absorber was taken as a reference. This study displayed that absorbers of various dimensions perturb the neutron field in a way that is dependent on the absorption and scattering cross-sections, particularly in the neutron resonance region. Unlike the simple picture of reducing the number density of neutrons, the perturbation was found to influence the moderation of neutrons in the medium, significantly above 1 MeV.Comment: 10 pages, 13 figures, 26 reference