Pseudorotations of the 2-disc and Reeb flows on the 3-sphere

We use Lerman's contact cut construction to find a sufficient condition for Hamiltonian diffeomorphisms of compact surfaces to embed into a closed 3-manifold as Poincar\'e return maps on a global surface of section for a Reeb flow. In particular, we show that the irrational pseudorotations of the 2-disc constructed by Fayad-Katok embed into the Reeb flow of a dynamically convex contact form on the 3-sphere.Comment: 30 pages; v2: Section 2 rewritten; v3: small changes to the exposition, some references adde

Properties of a Luttinger Liquid with Boundaries at Finite Temperature and Size

We use bosonization methods to calculate the exact finite-temperature single-electron Green's function of a spinful Luttinger liquid confined by open boundaries. The corresponding local spectral density is constructed and analyzed in detail. The interplay between boundary, finite-size and thermal effects are shown to dramatically influence the low-energy properties of the system. In particular, the well-known zero-temperature critical behavior in the bulk always crosses over to a boundary dominated regime in the vicinity of the Fermi level. Thermal fluctuations cause an enhanced depletion of spectral weight for small energies E, with the spectral density scaling as E^2 for E much less than the temperature. Consequences for photoemission experiments are discussed.Comment: 18 pages in revtex format including 5 embedded figures (using epsf). The latest complete postscript file is available from http://fy.chalmers.se/~eggert/papers/longlutt.ps or by request from [email protected]. To appear in Phys. Rev. B (Dec. 1997

Mathemagix User Guide

101 pagesThis manual describes the Mathemagix programming language (http://www.mathemagix.org)

Systems Biology Markup Language (SBML) Level 2: Structures and Facilities for Model Definitions

With the rise of Systems Biology as a new paradigm for understanding biological processes, the development of quantitative models is no longer restricted to a small circle of theoreticians. The dramatic increase in the number of these models precipitates the need to exchange and reuse both existing and newly created models. The Systems Biology Markup Language (SBML) is a free, open, XML-based format for representing quantitative models of biological interest that advocates the consistent specification of such models and thus facilitates both software development and model exchange.

Principally oriented towards describing systems of biochemical reactions, such as cell signalling pathways, metabolic networks and gene regulation etc., SBML can also be used to encode any kinetic model. SBML offers mechanisms to describe biological components by means of compartments and reacting species, as well as their dynamic behaviour, using reactions, events and arbitrary mathematical rules. SBML also offers all the housekeeping structures needed to ensure an unambiguous understanding of quantitative descriptions.

This is Release 1 of the specification for SBML Level 2 Version 4, describing the structures of the language and the rules used to build a valid model. SBML XML Schema and other related documents and software are also available from the SBML project web site, "http://sbml.org/":http://sbml.org/

Systems Biology Markup Language (SBML) Level 2: Structures and Facilities for Model Definitions

Not applicabl

Torus knot filtered embedded contact homology of the tight contact 3-sphere

Knot filtered embedded contact homology was first introduced by Hutchings in 2015; it has been computed for the standard transverse unknot in irrational ellipsoids by Hutchings and for the Hopf link in lens spaces L(n,n-1) via a quotient by Weiler. While straightforward toric constructions can be used to understand the ECH chain complexes of open books along the unknot and Hopf link, they do not readily adapt to general torus knots and links. In this paper, we generalize the definition and invariance of knot filtered embedded contact homology to allow for degenerate knots with rational rotation numbers. We then develop new methods for understanding the embedded contact homology chain complex of positive torus knotted fibrations of the standard tight contact 3-sphere in terms of their presentation as open books and as Seifert fibered spaces. We provide Morse-Bott methods, using a doubly filtered complex and the energy filtered perturbed Seiberg-Witten theory developed by Hutchings and Taubes, and use them to compute the T(2,q) knot filtered embedded contact homology, for q odd and positive. In the sequel we complete the computation for positive T(p,q) knots (where there is a nonvanishing differential) and use our results to deduce quantitative existence results for torus knotted Reeb dynamics on the tight 3-sphere and the mean action of area preserving diffeomorphisms of once punctured surfaces of arbitrary genus arising as Seifert surfaces of positive torus knots.Comment: 85 pages, arXiv insists the primary is GT rather than S