616 research outputs found
Trapping structures in the three-dimensional water-wave problem
Trapped modes in the linearized water-wave problem are free oscillations of the fluid
which have finite energy. They are known to exist at isolated frequencies in the presence
of certain special structures. The existence of a trapped mode implies the
non-uniqueness, or non-existence, of the solution to physically relevant radiation and
diffraction problems for such a structure.
Previous work on the three-dimensional problem has established the existence of
vertically axisymmetric structures that support trapped modes with either a single
interior free surface, or two concentric interior free surfaces. In the present work
the existence of several new types of trapping structures is established. These include
non-axisymmetric structures with a single interior free surface and various structures
with multiple interior free surfaces. The method used is an indirect one in which flow
fields without wave radiation are specified, and corresponding structures are found by
constructing suitable stream surfaces. Computations of the added-mass coefficients
for these structures provide independent support for the existence of a trapping mode
and illustrate their hydrodynamic characteristics at other wavenumbers
Electromagnetic sources distributed on shells in a Schwarzschild background
In the Introduction we briefly recall our previous results on stationary
electromagnetic fields on black-hole backgrounds and the use of spin-weighted
spherical harmonics. We then discuss static electric and magnetic test fields
in a Schwarzschild background using some of these results. As sources we do not
consider point charges or current loops like in previous works, rather, we
analyze spherical shells with smooth electric or magnetic charge distributions
as well as electric or magnetic dipole distributions depending on both angular
coordinates. Particular attention is paid to the discontinuities of the field,
of the 4-potential, and their relation to the source.Comment: dedicated to Professor Goldberg's 86th birthday, accepted for
publication in Gen. Relat. Gravit., 12 page
Self-optimization, community stability, and fluctuations in two individual-based models of biological coevolution
We compare and contrast the long-time dynamical properties of two
individual-based models of biological coevolution. Selection occurs via
multispecies, stochastic population dynamics with reproduction probabilities
that depend nonlinearly on the population densities of all species resident in
the community. New species are introduced through mutation. Both models are
amenable to exact linear stability analysis, and we compare the analytic
results with large-scale kinetic Monte Carlo simulations, obtaining the
population size as a function of an average interspecies interaction strength.
Over time, the models self-optimize through mutation and selection to
approximately maximize a community fitness function, subject only to
constraints internal to the particular model. If the interspecies interactions
are randomly distributed on an interval including positive values, the system
evolves toward self-sustaining, mutualistic communities. In contrast, for the
predator-prey case the matrix of interactions is antisymmetric, and a nonzero
population size must be sustained by an external resource. Time series of the
diversity and population size for both models show approximate 1/f noise and
power-law distributions for the lifetimes of communities and species. For the
mutualistic model, these two lifetime distributions have the same exponent,
while their exponents are different for the predator-prey model. The difference
is probably due to greater resilience toward mass extinctions in the food-web
like communities produced by the predator-prey model.Comment: 26 pages, 12 figures. Discussion of early-time dynamics added. J.
Math. Biol., in pres
Analysis of CMB polarization on an incomplete sky
The full sky cosmic microwave background polarization field can be decomposed
into 'electric' and 'magnetic' components. Working in harmonic space we
construct window functions that allow clean separation of the electric and
magnetic modes from observations over only a portion of the sky. Our
construction is exact for azimuthally symmetric patches, but should continue to
perform well for arbitrary patches. From the window functions we obtain
variables that allow for robust estimation of the magnetic component without
risk of contamination from the probably much larger electric signal. For
isotropic, uncorrelated noise the variables have a very simple diagonal noise
correlation, and further analysis using them should be no harder than analysing
the temperature field. For an azimuthally-symmetric patch, such as that
obtained from survey missions when the galactic region is removed, the
exactly-separated variables are fast to compute allowing us to estimate the
magnetic signal that could be detected by the Planck satellite in the absence
of non-galactic foregrounds. We also discuss the sensitivity of future
experiments to tensor modes in the presence of a magnetic signal generated by
weak lensing, and give lossless methods for analysing the electric polarization
field in the case that the magnetic component is negligible.Comment: 27 pages, 8 figures. New appendix on weak signal detection and
revised plots using a better statistic. Other changes to match version
accepted by PRD. Sample source code now available at
http://cosmologist.info/pola
CMB Lensing Reconstruction on the Full Sky
Gravitational lensing of the microwave background by the intervening dark
matter mainly arises from large-angle fluctuations in the projected
gravitational potential and hence offers a unique opportunity to study the
physics of the dark sector at large scales. Studies with surveys that cover
greater than a percent of the sky will require techniques that incorporate the
curvature of the sky. We lay the groundwork for these studies by deriving the
full sky minimum variance quadratic estimators of the lensing potential from
the CMB temperature and polarization fields. We also present a general
technique for constructing these estimators, with harmonic space convolutions
replaced by real space products, that is appropriate for both the full sky
limit and the flat sky approximation. This also extends previous treatments to
include estimators involving the temperature-polarization cross-correlation and
should be useful for next generation experiments in which most of the
additional information from polarization comes from this channel due to
sensitivity limitations.Comment: Accepted for publication in Phys. Rev. D; typos correcte
Water wave propagation and scattering over topographical bottoms
Here I present a general formulation of water wave propagation and scattering
over topographical bottoms. A simple equation is found and is compared with
existing theories. As an application, the theory is extended to the case of
water waves in a column with many cylindrical steps
Reconstruction of Black Hole Metric Perturbations from Weyl Curvature
Perturbation theory of rotating black holes is usually described in terms of
Weyl scalars and , which each satisfy Teukolsky's complex
master wave equation and respectively represent outgoing and ingoing radiation.
On the other hand metric perturbations of a Kerr hole can be described in terms
of (Hertz-like) potentials in outgoing or ingoing {\it radiation
gauges}. In this paper we relate these potentials to what one actually computes
in perturbation theory, i.e and . We explicitly construct
these relations in the nonrotating limit, preparatory to devising a
corresponding approach for building up the perturbed spacetime of a rotating
black hole. We discuss the application of our procedure to second order
perturbation theory and to the study of radiation reaction effects for a
particle orbiting a massive black hole.Comment: 6 Pages, Revtex
Dynamics in online social networks
An increasing number of today's social interactions occurs using online
social media as communication channels. Some online social networks have become
extremely popular in the last decade. They differ among themselves in the
character of the service they provide to online users. For instance, Facebook
can be seen mainly as a platform for keeping in touch with close friends and
relatives, Twitter is used to propagate and receive news, LinkedIn facilitates
the maintenance of professional contacts, Flickr gathers amateurs and
professionals of photography, etc. Albeit different, all these online platforms
share an ingredient that pervades all their applications. There exists an
underlying social network that allows their users to keep in touch with each
other and helps to engage them in common activities or interactions leading to
a better fulfillment of the service's purposes. This is the reason why these
platforms share a good number of functionalities, e.g., personal communication
channels, broadcasted status updates, easy one-step information sharing, news
feeds exposing broadcasted content, etc. As a result, online social networks
are an interesting field to study an online social behavior that seems to be
generic among the different online services. Since at the bottom of these
services lays a network of declared relations and the basic interactions in
these platforms tend to be pairwise, a natural methodology for studying these
systems is provided by network science. In this chapter we describe some of the
results of research studies on the structure, dynamics and social activity in
online social networks. We present them in the interdisciplinary context of
network science, sociological studies and computer science.Comment: 17 pages, 4 figures, book chapte
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