26,890 research outputs found
Study of Growth in Recent and Fossil Invertebrate Exoskeletons and Its Relationship to Tidal Cycles in the Earth-moon System Semiannual Report, May 1 - Oct. 31, 1966
Growth cycles in fossil pelecypod shells and relationship to tidal cycles in earth-moon syste
Critical random graphs: limiting constructions and distributional properties
We consider the Erdos-Renyi random graph G(n,p) inside the critical window,
where p = 1/n + lambda * n^{-4/3} for some lambda in R. We proved in a previous
paper (arXiv:0903.4730) that considering the connected components of G(n,p) as
a sequence of metric spaces with the graph distance rescaled by n^{-1/3} and
letting n go to infinity yields a non-trivial sequence of limit metric spaces C
= (C_1, C_2, ...). These limit metric spaces can be constructed from certain
random real trees with vertex-identifications. For a single such metric space,
we give here two equivalent constructions, both of which are in terms of more
standard probabilistic objects. The first is a global construction using
Dirichlet random variables and Aldous' Brownian continuum random tree. The
second is a recursive construction from an inhomogeneous Poisson point process
on R_+. These constructions allow us to characterize the distributions of the
masses and lengths in the constituent parts of a limit component when it is
decomposed according to its cycle structure. In particular, this strengthens
results of Luczak, Pittel and Wierman by providing precise distributional
convergence for the lengths of paths between kernel vertices and the length of
a shortest cycle, within any fixed limit component.Comment: 30 pages, 4 figure
Late Wenlock (middle Silurian) bio-events: Caused by volatile boloid impact/s
Late Wenlockian (late mid-Silurian) life is characterized by three significant changes or bioevents: sudden development of massive carbonate reefs after a long interval of limited reef growth; sudden mass mortality among colonial zooplankton, graptolites; and origination of land plants with vascular tissue (Cooksonia). Both marine bioevents are short in duration and occur essentially simultaneously at the end of the Wenlock without any recorded major climatic change from the general global warm climate. These three disparate biologic events may be linked to sudden environmental change that could have resulted from sudden infusion of a massive amount of ammonia into the tropical ocean. Impact of a boloid or swarm of extraterrestrial bodies containing substantial quantities of a volatile (ammonia) component could provide such an infusion. Major carbonate precipitation (formation), as seen in the reefs as well as, to a more limited extent, in certain brachiopods, would be favored by increased pH resulting from addition of a massive quantity of ammonia into the upper ocean. Because of the buffer capacity of the ocean and dilution effects, the pH would have returned soon to equilibrium. Major proliferation of massive reefs ceased at the same time. Addition of ammonia as fertilizer to terrestrial environments in the tropics would have created optimum environmental conditions for development of land plants with vascular, nutrient-conductive tissue. Fertilization of terrestrial environments thus seemingly preceded development of vascular tissue by a short time interval. Although no direct evidence of impact of a volatile boloid may be found, the bioevent evidence is suggestive that such an impact in the oceans could have taken place. Indeed, in the case of an ammonia boloid, evidence, such as that of the Late Wenlockian bioevents may be the only available data for impact of such a boloid
Critical random graphs : limiting constructions and distributional properties
We consider the Erdos-Renyi random graph G(n, p) inside the critical window, where p = 1/n + lambda n(-4/3) for some lambda is an element of R. We proved in Addario-Berry et al. [2009+] that considering the connected components of G(n, p) as a sequence of metric spaces with the graph distance rescaled by n(-1/3) and letting n -> infinity yields a non-trivial sequence of limit metric spaces C = (C-1, C-2,...). These limit metric spaces can be constructed from certain random real trees with vertex-identifications. For a single such metric space, we give here two equivalent constructions, both of which are in terms of more standard probabilistic objects. The first is a global construction using Dirichlet random variables and Aldous' Brownian continuum random tree. The second is a recursive construction from an inhomogeneous Poisson point process on R+. These constructions allow us to characterize the distributions of the masses and lengths in the constituent parts of a limit component when it is decomposed according to its cycle structure. In particular, this strengthens results of Luczak et al. [1994] by providing precise distributional convergence for the lengths of paths between kernel vertices and the length of a shortest cycle, within any fixed limit component
A simple and surprisingly accurate approach to the chemical bond obtained from dimensional scaling
We present a new dimensional scaling transformation of the Schrodinger
equation for the two electron bond. This yields, for the first time, a good
description of the two electron bond via D-scaling. There also emerges, in the
large-D limit, an intuitively appealing semiclassical picture, akin to a
molecular model proposed by Niels Bohr in 1913. In this limit, the electrons
are confined to specific orbits in the scaled space, yet the uncertainty
principle is maintained because the scaling leaves invariant the
position-momentum commutator. A first-order perturbation correction,
proportional to 1/D, substantially improves the agreement with the exact ground
state potential energy curve. The present treatment is very simple
mathematically, yet provides a strikingly accurate description of the potential
energy curves for the lowest singlet, triplet and excited states of H_2. We
find the modified D-scaling method also gives good results for other molecules.
It can be combined advantageously with Hartree-Fock and other conventional
methods.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Letter
Uniform WKB approximation of Coulomb wave functions for arbitrary partial wave
Coulomb wave functions are difficult to compute numerically for extremely low
energies, even with direct numerical integration. Hence, it is more convenient
to use asymptotic formulas in this region. It is the object of this paper to
derive analytical asymptotic formulas valid for arbitrary energies and partial
waves. Moreover, it is possible to extend these formulas for complex values of
parameters.Comment: 5 pages, 2 figure
Parametrically excited "Scars" in Bose-Einstein condensates
Parametric excitation of a Bose-Einstein condensate (BEC) can be realized by
periodically changing the interaction strength between the atoms. Above some
threshold strength, this excitation modulates the condensate density. We show
that when the condensate is trapped in a potential well of irregular shape,
density waves can be strongly concentrated ("scarred") along the shortest
periodic orbits of a classical particle moving within the confining potential.
While single-particle wave functions of systems whose classical counterpart is
chaotic may exhibit rich scarring patterns, in BEC, we show that nonlinear
effects select mainly those scars that are locally described by stripes.
Typically, these are the scars associated with self retracing periodic orbits
that do not cross themselves in real space. Dephasing enhances this behavior by
reducing the nonlocal effect of interference
Spectral fluctuations and 1/f noise in the order-chaos transition regime
Level fluctuations in quantum system have been used to characterize quantum
chaos using random matrix models. Recently time series methods were used to
relate level fluctuations to the classical dynamics in the regular and chaotic
limit. In this we show that the spectrum of the system undergoing order to
chaos transition displays a characteristic noise and is
correlated with the classical chaos in the system. We demonstrate this using a
smooth potential and a time-dependent system modeled by Gaussian and circular
ensembles respectively of random matrix theory. We show the effect of short
periodic orbits on these fluctuation measures.Comment: 4 pages, 5 figures. Modified version. To appear in Phys. Rev. Let
Gravitational wave energy spectrum of a parabolic encounter
We derive an analytic expression for the energy spectrum of gravitational
waves from a parabolic Keplerian binary by taking the limit of the Peters and
Matthews spectrum for eccentric orbits. This demonstrates that the location of
the peak of the energy spectrum depends primarily on the orbital periapse
rather than the eccentricity. We compare this weak-field result to strong-field
calculations and find it is reasonably accurate (~10%) provided that the
azimuthal and radial orbital frequencies do not differ by more than ~10%. For
equatorial orbits in the Kerr spacetime, this corresponds to periapse radii of
rp > 20M. These results can be used to model radiation bursts from compact
objects on highly eccentric orbits about massive black holes in the local
Universe, which could be detected by LISA.Comment: 5 pages, 3 figures. Minor changes to match published version; figure
1 corrected; references adde
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