Cluster Approximation for the Farey Fraction Spin Chain

We consider the Farey fraction spin chain in an external field $h$. Utilising ideas from dynamical systems, the free energy of the model is derived by means of an effective cluster energy approximation. This approximation is valid for divergent cluster sizes, and hence appropriate for the discussion of the magnetizing transition. We calculate the phase boundaries and the scaling of the free energy. At $h=0$ we reproduce the rigorously known asymptotic temperature dependence of the free energy. For $h \ne 0$, our results are largely consistent with those found previously using mean field theory and renormalization group arguments.Comment: 17 pages, 3 figure

Chaotic quasi-collision trajectories in the 3-centre problem

We study a particular kind of chaotic dynamics for the planar 3-centre problem on small negative energy level sets. We know that chaotic motions exist, if we make the assumption that one of the centres is far away from the other two (see Bolotin and Negrini, J. Diff. Eq. 190 (2003), 539--558): this result has been obtained by the use of the Poincar\'e-Melnikov theory. Here we change the assumption on the third centre: we do not make any hypothesis on its position, and we obtain a perturbation of the 2-centre problem by assuming its intensity to be very small. Then, for a dense subset of possible positions of the perturbing centre on the real plane, we prove the existence of uniformly hyperbolic invariant sets of periodic and chaotic almost collision orbits by the use of a general result of Bolotin and MacKay (see Cel. Mech. & Dyn. Astr. 77 (2000), 49--75). To apply it, we must preliminarily construct chains of collision arcs in a proper way. We succeed in doing that by the classical regularisation of the 2-centre problem and the use of the periodic orbits of the regularised problem passing through the third centre.Comment: 22 pages, 6 figure

Symbolic dynamics for the NN-centre problem at negative energies

We consider the planar $N$-centre problem, with homogeneous potentials of degree -\a<0, \a \in [1,2). We prove the existence of infinitely many collisions-free periodic solutions with negative and small energy, for any distribution of the centres inside a compact set. The proof is based upon topological, variational and geometric arguments. The existence result allows to characterize the associated dynamical system with a symbolic dynamics, where the symbols are the partitions of the $N$ centres in two non-empty sets

Double exponential stability of quasi-periodic motion in Hamiltonian systems

We prove that generically, both in a topological and measure-theoretical sense, an invariant Lagrangian Diophantine torus of a Hamiltonian system is doubly exponentially stable in the sense that nearby solutions remain close to the torus for an interval of time which is doubly exponentially large with respect to the inverse of the distance to the torus. We also prove that for an arbitrary small perturbation of a generic integrable Hamiltonian system, there is a set of almost full positive Lebesgue measure of KAM tori which are doubly exponentially stable. Our results hold true for real-analytic but more generally for Gevrey smooth systems

Factors determining human-to-human transmissibility of zoonotic pathogens via contact.

The pandemic potential of zoonotic pathogens lies in their ability to become efficiently transmissible amongst humans. Here, we focus on contact-transmitted pathogens and discuss the factors, at the pathogen, host and environmental levels that promote or hinder their human-to-human transmissibility via the following modes of contact transmission: skin contact, sexual contact, respiratory contact and multiple route contact. Factors common to several modes of transmission were immune evasion, high viral load, low infectious dose, crowding, promiscuity, and co-infections; other factors were specific for a pathogen or mode of contact transmission. The identification of such factors will lead to a better understanding of the requirements for human-to-human spread of pathogens, as well as improving risk assessment of newly emerging pathogens

Linear Sigma Models with Torsion

Gauged linear sigma models with (0,2) supersymmetry allow a larger choice of couplings than models with (2,2) supersymmetry. We use this freedom to find a fully linear construction of torsional heterotic compactifications, including models with branes. As a non-compact example, we describe a family of metrics which correspond to deformations of the heterotic conifold by turning on H-flux. We then describe compact models which are gauge-invariant only at the quantum level. Our construction gives a generalization of symplectic reduction. The resulting spaces are non-Kahler analogues of familiar toric spaces like complex projective space. Perturbatively conformal models can be constructed by considering intersections.Comment: 40 pages, LaTeX, 1 figure; references added; a new section on supersymmetry added; quantization condition revisite

Hamiltonian dynamics of the two-dimensional lattice phi^4 model

The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the presence of the continuous phase transition at a finite energy density and are consistent both qualitatively and quantitatively with the predictions of equilibrium statistical mechanics. The Hamiltonian microscopic dynamics also exhibits critical slowing down close to the transition. Moreover, the relationship between chaos and the phase transition is considered, and interpreted in the light of a geometrization of dynamics.Comment: REVTeX, 24 pages with 20 PostScript figure