Features of pulsed synchronization of a systems with a tree-dimensional phase space

Features of synchronization picture in the system with the limit cycle embedded in a three-dimensional phase space are considered. By the example of Ressler system and Dmitriev - Kislov generator under the action of a periodic sequence of delta - function it is shown, that synchronization picture significantly depends on the direction of pulse action. Features of synchronization tons appeared in these models are observed.Comment: 16 pages, 11 figure

Nonlinear mirror modes in the presence of hot electrons

A non-perturbative calculation of the gyrotropic pressures associated with large-scale mirror modes is performed, taking into account a finite, possibly anisotropic electron temperature. In the small-amplitude limit, this leads to an extension of an asymptotic model previously derived for cold electrons. A model equation for the profile of subcritical finite-amplitude large-scale structures is also presented

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

Peltier effect in normal metal-insulator-heavy fermion metal junctions

A theoretical study has been undertaken of the Peltier effect in normal metal - insulator - heavy fermion metal junctions. The results indicate that, at temperatures below the Kondo temperature, such junctions can be used as electronic microrefrigerators to cool the normal metal electrode and are several times more efficient in cooling than the normal metal - heavy fermion metal junctions.Comment: 3 pages in REVTeX, 2 figures, to be published in Appl. Phys. Lett., April 7, 200

Geometric collections and Castelnuovo-Mumford Regularity

The paper begins by overviewing the basic facts on geometric exceptional collections. Then, we derive, for any coherent sheaf \cF on a smooth projective variety with a geometric collection, two spectral sequences: the first one abuts to \cF and the second one to its cohomology. The main goal of the paper is to generalize Castelnuovo-Mumford regularity for coherent sheaves on projective spaces to coherent sheaves on smooth projective varieties $X$ with a geometric collection $\sigma$. We define the notion of regularity of a coherent sheaf \cF on $X$ with respect to $\sigma$. We show that the basic formal properties of the Castelnuovo-Mumford regularity of coherent sheaves over projective spaces continue to hold in this new setting and we show that in case of coherent sheaves on \PP^n and for a suitable geometric collection of coherent sheaves on \PP^n both notions of regularity coincide. Finally, we carefully study the regularity of coherent sheaves on a smooth quadric hypersurface Q_n \subset \PP^{n+1} ($n$ odd) with respect to a suitable geometric collection and we compare it with the Castelnuovo-Mumford regularity of their extension by zero in \PP^{n+1}.Comment: To appear in Math. Proc. Cambridg