14,680 research outputs found
On Sasaki-Einstein manifolds in dimension five
We prove the existence of Sasaki-Einstein metrics on certain simply connected
5-manifolds where until now existence was unknown. All of these manifolds have
non-trivial torsion classes. On several of these we show that there are a
countable infinity of deformation classes of Sasaki-Einstein structures.Comment: 18 pages, Exposition was expanded and a reference adde
Rotating gravity currents: small-scale and large-scale laboratory experiments and a geostrophic model
Laboratory experiments simulating gravity-driven coastal surface currents produced by estuarine fresh-water discharges into the ocean are discussed. The currents are generated inside a rotating tank filled with salt water by the continuous release of buoyant fresh water from a small source at the fluid surface. The height, the width and the length of the currents are studied as a function of the background rotation rate, the volumetric discharge rate and the density difference at the source. Two complementary experimental data sets are discussed and compared with each other. One set of experiments was carried out in a tank of diameter 1 m on a small-scale rotating turntable. The second set of experiments was conducted at the large-scale Coriolis Facility (LEGI, Grenoble) which has a tank of diameter 13 m. A simple geostrophic model predicting the current height, width and propagation velocity is developed. The experiments and the model are compared with each other in terms of a set of non-dimensional parameters identified in the theoretical analysis of the problem. These parameters enable the corresponding data of the large-scale and the small-scale experiments to be collapsed onto a single line. Good agreement between the model and the experiments is found
Self-organization, scaling and collapse in a coupled automaton model of foragers and vegetation resources with seed dispersal
We introduce a model of traveling agents ({\it e.g.} frugivorous animals) who
feed on randomly located vegetation patches and disperse their seeds, thus
modifying the spatial distribution of resources in the long term. It is assumed
that the survival probability of a seed increases with the distance to the
parent patch and decreases with the size of the colonized patch. In turn, the
foraging agents use a deterministic strategy with memory, that makes them visit
the largest possible patches accessible within minimal travelling distances.
The combination of these interactions produce complex spatio-temporal patterns.
If the patches have a small initial size, the vegetation total mass (biomass)
increases with time and reaches a maximum corresponding to a self-organized
critical state with power-law distributed patch sizes and L\'evy-like movement
patterns for the foragers. However, this state collapses as the biomass sharply
decreases to reach a noisy stationary regime characterized by corrections to
scaling. In systems with low plant competition, the efficiency of the foraging
rules leads to the formation of heterogeneous vegetation patterns with
frequency spectra, and contributes, rather counter-intuitively,
to lower the biomass levels.Comment: 11 pages, 5 figure
Gravitational Chern-Simons and the adiabatic limit
We compute the gravitational Chern-Simons term explicitly for an adiabatic
family of metrics using standard methods in general relativity. We use the fact
that our base three-manifold is a quasi-regular K-contact manifold heavily in
this computation. Our key observation is that this geometric assumption
corresponds exactly to a Kaluza-Klein Ansatz for the metric tensor on our three
manifold, which allows us to translate our problem into the language of general
relativity. Similar computations have been performed in a paper of Guralnik,
Iorio, Jackiw and Pi (2003), although not in the adiabatic context.Comment: 17 page
Some Heuristic Semiclassical Derivations of the Planck Length, the Hawking Effect and the Unruh Effect
The formulae for Planck length, Hawking temperature and Unruh-Davies
temperature are derived by using only laws of classical physics together with
the Heisenberg principle. Besides, it is shown how the Hawking relation can be
deduced from the Unruh relation by means of the principle of equivalence; the
deep link between Hawking effect and Unruh effect is in this way clarified.Comment: LaTex file, 6 pages, no figure
Hydrodynamic reductions of the heavenly equation
We demonstrate that Pleba\'nski's first heavenly equation decouples in
infinitely many ways into a triple of commuting (1+1)-dimensional systems of
hydrodynamic type which satisfy the Egorov property. Solving these systems by
the generalized hodograph method, one can construct exact solutions of the
heavenly equation parametrized by arbitrary functions of a single variable. We
discuss explicit examples of hydrodynamic reductions associated with the
equations of one-dimensional nonlinear elasticity, linearly degenerate systems
and the equations of associativity.Comment: 14 page
On the supersymmetries of anti de Sitter vacua
We present details of a geometric method to associate a Lie superalgebra with
a large class of bosonic supergravity vacua of the type AdS x X, corresponding
to elementary branes in M-theory and type II string theory.Comment: 16 page
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