7,096 research outputs found
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 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
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