6,824 research outputs found
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
with a geometric collection . We define the notion of regularity of a
coherent sheaf \cF on with respect to . 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} ( 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 ( 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
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