Morse-Novikov theory, Heegaard splittings and closed orbits of gradient flows

The works of Donaldson and Mark make the structure of the Seiberg-Witten invariant of 3-manifolds clear. It corresponds to certain torsion type invariants counting flow lines and closed orbits of a gradient flow of a circle-valued Morse map on a 3-manifold. We study these invariants using the Morse-Novikov theory and Heegaard splitting for sutured manifolds, and make detailed computations for knot complements.Comment: 27 pages, 12 figure

The Dust Mantle of Comet 9P/Tempel 1: Dynamical Constraints on Physical Properties

The trajectories of dust particles ejected from a comet are affected by solar radiation pressure as a function of their ratios of radiation pressure cross section to mass. Therefore, a study on the orbital evolution of the particles caused by the radiation pressure reveals the physical properties of dust on the surface of the comet nucleus. In the course of NASA's Deep Impact mission, the ejecta plume evolved under the influence of the radiation pressure. From the evolution and shape of the plume, we have succeeded in obtaining $\beta \approx 0.4$, where $\beta$ is the ratio of the radiation pressure to the solar gravity. Taking into account $\beta \approx 0.4$ as well as the observational constraints of a high color temperature and a small silicate-feature strength, dust particles ejected from the surface of comet 9P/Tempel 1 are likely compact dust aggregates of sizes $\approx 20\,\mu$m (mass $\sim 10^{-8}$\,g). This is comparable to the major dust on the surface of comet 1P/Halley ($\sim 10\mu$m) inferred from in-situ measurements and theoretical considerations. Since such dust aggregates with $\beta \approx 0.4$ must have survived on the surface against jets due to ice sublimation, the temperature of ice in the nucleus must be kept below 145\,K, which is much lower than equilibrium temperature determined by solar irradiation and thermal emission. These facts indicate that 9P/Tempel 1 has a dust mantle composed of $20\,\mu$m-sized dust aggregates with low thermal conductivities $\sim 1 \, {\rm erg\, cm}^{-1} \, {\rm K}^{-1}\,{\rm s}^{-1}$.Comment: 4 pages, 3 figures, accepted for publication in Astronomy and Astrophysic

Labour Productivity Superstatistics

We discuss superstatistics theory of labour productivity. Productivity distribution across workers, firms and industrial sectors are studied empirically and found to obey power-distributions, in sharp contrast to the equilibrium theories of mainstream economics. The Pareto index is found to decrease with the level of aggregation, {\it i.e.}, from workers to firms and to industrial sectors. In order to explain these phenomenological laws, we propose a superstatistics framework, where the role of the fluctuating temperature is played by the fluctuating demand.Comment: 13 pages including figure