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Periodic solutions of a many-rotator problem in the plane. II. Analysis of various motions
Various solutions are displayed and analyzed (both analytically and
numerically) of arecently-introduced many-body problem in the plane which
includes both integrable and nonintegrable cases (depending on the values of
the coupling constants); in particular the origin of certain periodic behaviors
is explained. The light thereby shone on the connection among
\textit{integrability} and \textit{analyticity} in (complex) time, as well as
on the emergence of a \textit{chaotic} behavior (in the guise of a sensitive
dependance on the initial data) not associated with any local exponential
divergence of trajectories in phase space, might illuminate interesting
phenomena of more general validity than for the particular model considered
herein.Comment: Published by JNMP at http://www.sm.luth.se/math/JNMP
A solvable many-body problem in the plane
A solvable many-body problem in the plane is exhibited. It is characterized
by rotation-invariant Newtonian (``acceleration equal force'') equations of
motion, featuring one-body (``external'') and pair (``interparticle'') forces.
The former depend quadratically on the velocity, and nonlinearly on the
coordinate, of the moving particle. The latter depend linearly on the
coordinate of the moving particle, and linearly respectively nonlinearly on the
velocity respectively the coordinate of the other particle. The model contains
arbitrary coupling constants, being the number of particles. The
behaviour of the solutions is outlined; special cases in which the motion is
confined (multiply periodic), or even completely periodic, are identified
Black branes in asymptotically Lifshitz spacetime and viscosity/entropy ratios in Horndeski gravity
We investigate black brane solutions in asymptotically Lifshitz spacetime in
3+1-dimensional Horndeski gravity, which admit a critical exponent fixed at
. The cosmological constant depends on as .
We compute the shear viscosity in the 2+1-dimensional dual boundary field
theory via holographic correspondence. We investigate the violation of the
bound for viscosity to entropy density ratio of at
.Comment: 7 pages, no figures, 1 table. Version published in EP
Comparative performance of twenty-three types of flat plate solar energy collectors
Report compares efficiencies of 23 solar collectors for four different purposes: operating a Rankine-cycle engine, heating or absorption air conditioning, heating hot water, and heating a swimming pool
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