5,237 research outputs found
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
Ultrashort pulses and short-pulse equations in dimensions
In this paper, we derive and study two versions of the short pulse equation
(SPE) in dimensions. Using Maxwell's equations as a starting point, and
suitable Kramers-Kronig formulas for the permittivity and permeability of the
medium, which are relevant, e.g., to left-handed metamaterials and dielectric
slab waveguides, we employ a multiple scales technique to obtain the relevant
models. General properties of the resulting -dimensional SPEs, including
fundamental conservation laws, as well as the Lagrangian and Hamiltonian
structure and numerical simulations for one- and two-dimensional initial data,
are presented. Ultrashort 1D breathers appear to be fairly robust, while rather
general two-dimensional localized initial conditions are transformed into
quasi-one-dimensional dispersing waveforms
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
Monte Carlo simulations of infinitely dilute solutions of amphiphilic diblock star copolymers
Single-chain Monte Carlo simulations of amphiphilic diblock star copolymers
were carried out in continuous space using implicit solvents. Two distinct
architectures were studied: stars with the hydrophobic blocks attached to the
core, and stars with the polar blocks attached to the core, with all arms being
of equal length. The ratio of the lengths of the hydrophobic block to the
length of the polar block was varied from 0 to 1. Stars with 3, 6, 9 or 12
arms, each of length 10, 15, 25, 50, 75 and 100 Kuhn segments were analysed.
Four distinct types of conformations were observed for these systems. These,
apart from studying the snapshots from the simulations, have been
quantitatively characterised in terms of the mean-squared radii of gyration,
mean-squared distances of monomers from the centre-of-mass, asphericity
indices, static scattering form factors in the Kratky representation as well as
the intra-chain monomer-monomer radial distribution functions.Comment: 12 pages, 11 ps figures. Accepted for publication in J. Chem. Phy
Backlund transformations for many-body systems related to KdV
We present Backlund transformations (BTs) with parameter for certain
classical integrable n-body systems, namely the many-body generalised
Henon-Heiles, Garnier and Neumann systems. Our construction makes use of the
fact that all these systems may be obtained as particular reductions
(stationary or restricted flows) of the KdV hierarchy; alternatively they may
be considered as examples of the reduced sl(2) Gaudin magnet. The BTs provide
exact time-discretizations of the original (continuous) systems, preserving the
Lax matrix and hence all integrals of motion, and satisfy the spectrality
property with respect to the Backlund parameter.Comment: LaTeX2e, 8 page
Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics
We discuss a conjecture saying that derived equivalence of smooth projective simply connected varieties implies that the difference of their classes in the Grothendieck ring of varieties is annihilated by a power of the affine line class. We support the conjecture with a number of known examples, and one new example. We consider a smooth complete intersection X of three quadrics in P5 and the corresponding double cover Y→P2 branched over a sextic curve. We show that as soon as the natural Brauer class on Y vanishes, so that X and Y are derived equivalent, the difference [X]−[Y] is annihilated by the affine line class
Baxter's Q-operator for the homogeneous XXX spin chain
Applying the Pasquier-Gaudin procedure we construct the Baxter's Q-operator
for the homogeneous XXX model as integral operator in standard representation
of SL(2). The connection between Q-operator and local Hamiltonians is
discussed. It is shown that operator of Lipatov's duality symmetry arises
naturally as leading term of the asymptotic expansion of Q-operator for large
values of spectral parameter.Comment: 23 pages, Late
Triggering rogue waves in opposing currents
We show that rogue waves can be triggered naturally when a stable wave train
enters a region of an opposing current flow. We demonstrate that the maximum
amplitude of the rogue wave depends on the ratio between the current velocity,
, and the wave group velocity, . We also reveal that an opposing
current can force the development of rogue waves in random wave fields,
resulting in a substantial change of the statistical properties of the surface
elevation. The present results can be directly adopted in any field of physics
in which the focusing Nonlinear Schrodinger equation with non constant
coefficient is applicable. In particular, nonlinear optics laboratory
experiments are natural candidates for verifying experimentally our results.Comment: 5 pages, 5 figure
Quantum Transparency of Barriers for Structure Particles
Penetration of two coupled particles through a repulsive barrier is
considered. A simple mechanism of the appearance of barrier resonances is
demonstrated that makes the barrier anomalously transparent as compared to the
probability of penetration of structureless objects. It is indicated that the
probabilities of tunnelling of two interacting particles from a false vacuum
can be considerably larger than it was assumed earlier.Comment: Revtex, 4 pages, 4 figure
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