48,614 research outputs found
Eleven spherically symmetric constant density solutions with cosmological constant
Einstein's field equations with cosmological constant are analysed for a
static, spherically symmetric perfect fluid having constant density. Five new
global solutions are described.
One of these solutions has the Nariai solution joined on as an exterior
field. Another solution describes a decreasing pressure model with exterior
Schwarzschild-de Sitter spacetime having decreasing group orbits at the
boundary. Two further types generalise the Einstein static universe.
The other new solution is unphysical, it is an increasing pressure model with
a geometric singularity.Comment: 19 pages, 5 figures, 1 table, revised bibliography, corrected eqn.
(3.11), typos corrected, two new reference
A Business Entity By Any Other Name: Corporation, Community and Kinship
Forty-five years ago, the Alaska Native Claims Settlement Act resolved outstanding land claims between the federal and state government and Alaska Natives. The fund created by the settlement was used as seed money to establish the Alaska Native Corporations. The Native corporations have particular features which make them distinct from other business entities, these differences have been lauded by some shareholders but have simultaneously drawn ire from others. In 2015 the Alaska legislature introduced H.B. 49, a benefit corporation bill that would allow entrepreneurs to pursue both profits and social ends. This note traces the rise of the modern Alaska Native Corporation. It then weighs the merits of each business entity and assesses which is best aligned to improve the lives of Alaska Natives
Large Deviations for Nonlocal Stochastic Neural Fields
We study the effect of additive noise on integro-differential neural field
equations. In particular, we analyze an Amari-type model driven by a -Wiener
process and focus on noise-induced transitions and escape. We argue that
proving a sharp Kramers' law for neural fields poses substanial difficulties
but that one may transfer techniques from stochastic partial differential
equations to establish a large deviation principle (LDP). Then we demonstrate
that an efficient finite-dimensional approximation of the stochastic neural
field equation can be achieved using a Galerkin method and that the resulting
finite-dimensional rate function for the LDP can have a multi-scale structure
in certain cases. These results form the starting point for an efficient
practical computation of the LDP. Our approach also provides the technical
basis for further rigorous study of noise-induced transitions in neural fields
based on Galerkin approximations.Comment: 29 page
Bounds on M/R for static objects with a positive cosmological constant
We consider spherically symmetric static solutions of the Einstein equations
with a positive cosmological constant which are regular at the
centre, and we investigate the influence of on the bound of M/R,
where M is the ADM mass and R is the area radius of the boundary of the static
object. We find that for any solution which satisfies the energy condition
where and are the radial and
tangential pressures respectively, and is the energy density, and
for which the inequality
\frac{M}{R}\leq\frac29-\frac{\Lambda R^2}{3}+\frac29 \sqrt{1+3\Lambda R^2},
holds. If it is known that infinitely thin shell solutions uniquely
saturate the inequality, i.e. the inequality is sharp in that case. The
situation is quite different if Indeed, we show that infinitely
thin shell solutions do not generally saturate the inequality except in the two
degenerate situations and . In the latter
situation there is also a constant density solution, where the exterior
spacetime is the Nariai solution, which saturates the inequality, hence, the
saturating solution is non-unique. In this case the cosmological horizon and
the black hole horizon coincide. This is analogous to the charged situation
where there is numerical evidence that uniqueness of the saturating solution is
lost when the inner and outer horizons of the Reissner-Nordstr\"{o}m solution
coincide.Comment: 14 pages; Improvements and corrections, published versio
Environmental Superstatistics
A thermodynamic device placed outdoors, or a local ecosystem, is subject to a
variety of different temperatures given by short-tem (daily) and long-term
(seasonal) variations. In the long term a superstatistical description makes
sense, with a suitable distribution function f(beta) of inverse temperature
beta over which ordinary statistical mechanics is averaged. We show that
f(beta) is very different at different geographic locations, and typically
exhibits a double-peak structure for long-term data. For some of our data sets
we also find a systematic drift due to global warming. For a simple
superstatistical model system we show that the response to global warming is
stronger if temperature fluctuations are taken into account.Comment: 37 figures. Significantly extended version, to appear in Physica A.
Added new material in section 6 quantifying the stronger response to global
warming if temperature fluctuations are taken into account. Concluding
section 7 and several new references adde
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