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 $2n^2$ arbitrary coupling constants, $n$ 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

Fermion Systems in Discrete Space-Time

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.Comment: 8 pages, LaTeX, few typos corrected (published version

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 $z=1/2$. The cosmological constant depends on $z$ as $\Lambda=-(1+2z)/L^{2}$. 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 $\eta/s\geq1/(4\pi)$ at $z=1/2$.Comment: 7 pages, no figures, 1 table. Version published in EP

Braneworlds in Horndeski gravity

In this paper we address the issue of finding braneworld solutions in a five-dimensional Horndeski gravity and the mechanism of gravity localization into the brane via `almost massless modes' for suitable values of the Horndeski parameters. We compute the corrections to the Newtonian potential and discuss the limit where four-dimensional gravity is recovered.Comment: 14 pages, 6 figure

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