Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories

Dynamical equations are formulated and a numerical study is provided for self-oscillatory model systems based on the triple linkage hinge mechanism of Thurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomic mechanical constraint of three rotators as well as systems, where three rotators interact by potential forces. We present and discuss some quantitative characteristics of the chaotic regimes (Lyapunov exponents, power spectrum). Chaotic dynamics of the models we consider are associated with hyperbolic attractors, at least, at relatively small supercriticality of the self-oscillating modes; that follows from numerical analysis of the distribution for angles of intersection of stable and unstable manifolds of phase trajectories on the attractors. In systems based on rotators with interacting potential the hyperbolicity is violated starting from a certain level of excitation.Comment: 30 pages, 18 figure

SUSY vertex algebras and supercurves

This article is a continuation of math.QA/0603633 Given a strongly conformal SUSY vertex algebra V and a supercurve X we construct a vector bundle V_X on X, the fiber of which, is isomorphic to V. Moreover, the state-field correspondence of V canonically gives rise to (local) sections of these vector bundles. We also define chiral algebras on any supercurve X, and show that the vector bundle V_X, corresponding to a SUSY vertex algebra, carries the structure of a chiral algebra.Comment: 50 page

Modeling of some nonstationary processes in tokamak plasmas

The results of modeling of shots from two series of experiments in two tokamaks with rather different geometric parameters are presented. The first one includes two shots from the spherical tokamak MAST with current ramp up, and the second one, a number of T-10 shots with periodic gas puffing. The modeling was performed with the ASTRA code in the framework of Canonical Profiles Transport Model (CPTM).Представлены результаты моделирования импульсов из двух серий экспериментов на двух разных токамаках, существенно отличающихся геометрическими параметрами. Первая серия включает два импульса с нарастанием тока сферического токамака MAST, а вторая – несколько импульсов Т-10 с периодическим газонапуском. Моделирование осуществлялось с помощью кода ASTRA в рамках транспортной модели канонических профилей (ТМКП).Представлені результати моделювання імпульсів з двох серій експериментів на двох різних токамаках, що істотно відрізняються геометричними параметрами. Перша серія включає два імпульси з наростанням струму сферичного токамака МАST, а друга – декілька імпульсів Т-10 з періодичним газонапуском. Моделювання здійснювалося за допомогою коду ASTRA в рамках транспортної моделі канонічних профілів (ТМКП)