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

Behavior of tumors under nonstationary theraphy

We present a model for the interaction dynamics of lymphocytes-tumor cells population. This model reproduces all known states for the tumor. Futherly,we develop it taking into account periodical immunotheraphy treatment with cytokines alone. A detailed analysis for the evolution of tumor cells as a function of frecuency and theraphy burden applied for the periodical treatment is carried out. Certain threshold values for the frecuency and applied doses are derived from this analysis. So it seems possible to control and reduce the growth of the tumor. Also, constant values for cytokines doses seems to be a succesful treatment.Comment: 6 pages, 7 figure

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

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

Dynamics of the Free Surface of a Conducting Liquid in a Near-Critical Electric Field

Near-critical behavior of the free surface of an ideally conducting liquid in an external electric field is considered. Based on an analysis of three-wave processes using the method of integral estimations, sufficient criteria for hard instability of a planar surface are formulated. It is shown that the higher-order nonlinearities do not saturate the instability, for which reason the growth of disturbances has an explosive character.Comment: 19 page

Low Temperature Electronic Transport through Macromolecules and Characteristics of Intramolecular Electron Transfer

A theory of electronic transport through molecular wires is applied to analyze characteristics of a long-range electron transfer (ET) through molecular bridges in macromolecules with complex donor/acceptor subsystems. Assuming a coherent electron tunneling through the bridge to be the predominant mechanism of ET at low temperatures it is shown that low temperature current-voltage curves can exhibit a step-like structure, which contains information concerning intrinsic features of ET processes such as the effect of donor/acceptor coupling to the bridge and primary pathways of electrons tunneling through the bridge. By contacting the proposed theoretical analysis with such experimental data a variety of valuable characteristics of long-range intramolecular ET can be identified. Analytical and numerical results are presented. Using the Buttiker dephasing model within the scattering matrix formalism we analyze dephasing effects, and we show that these effects could be reduced enough to allow the structure of the electron transmission function to be exposed in the experiments on the electronic transport through macromolecules.Comment: 9 pages, 2 figures, text revise

Breathers on quantized superfluid vortices

We consider the propagation of breathers along a quantized superfluid vortex. Using the correspondence between the local induction approximation (LIA) and the nonlinear Schrödinger equation, we identify a set of initial conditions corresponding to breather solutions of vortex motion governed by the LIA. These initial conditions, which give rise to a long-wavelength modulational instability, result in the emergence of large amplitude perturbations that are localized in both space and time. The emergent structures on the vortex filament are analogous to loop solitons but arise from the dual action of bending and twisting of the vortex. Although the breather solutions we study are exact solutions of the LIA equations, we demonstrate through full numerical simulations that their key emergent attributes carry over to vortex dynamics governed by the Biot-Savart law and to quantized vortices described by the Gross-Pitaevskii equation. The breather excitations can lead to self-reconnections, a mechanism that can play an important role within the crossover range of scales in superfluid turbulence. Moreover, the observation of breather solutions on vortices in a field model suggests that these solutions are expected to arise in a wide range of other physical contexts from classical vortices to cosmological strings

Dark matter-wave solitons in the dimensionality crossover

We consider the statics and dynamics of dark matter-wave solitons in the dimensionality crossover regime from 3D to 1D. There, using the nonpolynomial Schr\"{o}dinger mean-field model, we find that the anomalous mode of the Bogoliubov spectrum has an eigenfrequency which coincides with the soliton oscillation frequency obtained by the 3D Gross-Pitaevskii model. We show that substantial deviations (of order of 10% or more) from the characteristic frequency $\omega_{z}/\sqrt{2}$ ($\omega_{z}$ being the longitudinal trap frequency) are possible even in the purely 1D regime.Comment: Phys. Rev. A, in pres

Formation of singularities on the surface of a liquid metal in a strong electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is establish that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time.Comment: 14 page

Interaction of a vortex ring with the free surface of ideal fluid

The interaction of a small vortex ring with the free surface of a perfect fluid is considered. In the frame of the point ring approximation the asymptotic expression for the Fourier-components of radiated surface waves is obtained in the case when the vortex ring comes from infinity and has both horizontal and vertical components of the velocity. The non-conservative corrections to the equations of motion of the ring, due to Cherenkov radiation, are derived.Comment: LaTeX, 15 pages, 1 eps figur