381 research outputs found
Asymmetric ac fluxon depinning in a Josephson junction array: A highly discrete limit
Directed motion and depinning of topological solitons in a strongly discrete
damped and biharmonically ac-driven array of Josephson junctions is studied.
The mechanism of the depinning transition is investigated in detail. We show
that the depinning process takes place through chaotization of an initially
standing fluxon periodic orbit. Detailed investigation of the Floquet
multipliers of these orbits shows that depending on the depinning parameters
(either the driving amplitude or the phase shift between harmonics) the
chaotization process can take place either along the period-doubling scenario
or due to the type-I intermittency.Comment: 12 pages, 9 figures. Submitted to Phys. Rev.
Generic coverings of plane with A-D-E-singularities
We generalize results of the paper math.AG/9803144, in which Chisini's
conjecture on the unique reconstruction of f by the curve B is investigated.
For this fibre products of generic coverings are studied. The main inequality
bounding the degree of a covering in the case of existence of two nonequivalent
coverings with the branch curve B is obtained. This inequality is used for the
proof of the Chisini conjecture for m-canonical coverings of surfaces of
general type for .Comment: 43 pages, 20 figures; to appear in Izvestiya Mat
Connections on modules over quasi-homogeneous plane curves
Let k be an algebraically closed field of characteristic 0, and let be a quasi-homogeneous plane curve. We show that for any graded
torsion free A-module M, there exists a natural graded integrable connection,
i.e. a graded A-linear homomorphism that satisfy the derivation property and preserves the
Lie product.
In particular, a torsion free module N over the complete local ring admits a natural integrable connection if A is a simple curve singularity,
or if A is irreducible and N is a gradable module.Comment: AMS-LaTeX, 12 pages, minor changes. To appear in Comm. Algebr
Hilbert's 16th Problem for Quadratic Systems. New Methods Based on a Transformation to the Lienard Equation
Fractionally-quadratic transformations which reduce any two-dimensional
quadratic system to the special Lienard equation are introduced. Existence
criteria of cycles are obtained
Revisiting the ABC flow dynamo
The ABC flow is a prototype for fast dynamo action, essential to the origin
of magnetic field in large astrophysical objects. Probably the most studied
configuration is the classical 1:1:1 flow. We investigate its dynamo properties
varying the magnetic Reynolds number Rm. We identify two kinks in the growth
rate, which correspond respectively to an eigenvalue crossing and to an
eigenvalue coalescence. The dominant eigenvalue becomes purely real for a
finite value of the control parameter. Finally we show that even for Rm =
25000, the dominant eigenvalue has not yet reached an asymptotic behaviour. Its
still varies very significantly with the controlling parameter. Even at these
very large values of Rm the fast dynamo property of this flow cannot yet be
established
Quasi-morphisms and L^p-metrics on groups of volume-preserving diffeomorphisms
Let M be a smooth compact connected oriented manifold of dimension at least
two endowed with a volume form. We show that every homogeneous quasi-morphism
on the identity component of the group of volume preserving
diffeomorphisms of M, which is induced by a quasi-morphism on the fundamental
group, is Lipschitz with respect to the L^p-metric on the group
. As a consequence, assuming certain conditions on the
fundamental group, we construct bi-Lipschitz embeddings of finite dimensional
vector spaces into .Comment: This is a published versio
General stability criterion of inviscid parallel flow
A more restrictively general stability criterion of two-dimensional inviscid
parallel flow is obtained analytically. First, a sufficient criterion for
stability is found as either or
in the flow, where is the velocity at inflection
point, is the eigenvalue of Poincar\'{e}'s problem. Second, this
criterion is generalized to barotropic geophysical flows in plane.
Based on the criteria, the flows are are divided into different categories of
stable flows, which may simplify the further investigations. And the
connections between present criteria and Arnol'd's nonlinear criteria are
discussed. These results extend the former criteria obtained by Rayleigh,
Tollmien and Fj{\o}rtoft and would intrigue future research on the mechanism of
hydrodynamic instability.Comment: Revtex4, 4 pages, 2 figures, extends the first part of
physics/0512208, Accepted, to be continue
Quenched and Negative Hall Effect in Periodic Media: Application to Antidot Superlattices
We find the counterintuitive result that electrons move in OPPOSITE direction
to the free electron E x B - drift when subject to a two-dimensional periodic
potential. We show that this phenomenon arises from chaotic channeling
trajectories and by a subtle mechanism leads to a NEGATIVE value of the Hall
resistivity for small magnetic fields. The effect is present also in
experimentally recorded Hall curves in antidot arrays on semiconductor
heterojunctions but so far has remained unexplained.Comment: 10 pages, 4 figs on request, RevTeX3.0, Europhysics Letters, in pres
Estimating long term behavior of flows without trajectory integration: the infinitesimal generator approach
The long-term distributions of trajectories of a flow are described by
invariant densities, i.e. fixed points of an associated transfer operator. In
addition, global slowly mixing structures, such as almost-invariant sets, which
partition phase space into regions that are almost dynamically disconnected,
can also be identified by certain eigenfunctions of this operator. Indeed,
these structures are often hard to obtain by brute-force trajectory-based
analyses. In a wide variety of applications, transfer operators have proven to
be very efficient tools for an analysis of the global behavior of a dynamical
system.
The computationally most expensive step in the construction of an approximate
transfer operator is the numerical integration of many short term trajectories.
In this paper, we propose to directly work with the infinitesimal generator
instead of the operator, completely avoiding trajectory integration. We propose
two different discretization schemes; a cell based discretization and a
spectral collocation approach. Convergence can be shown in certain
circumstances. We demonstrate numerically that our approach is much more
efficient than the operator approach, sometimes by several orders of magnitude
A Quantum-Classical Brackets from p-Mechanics
We provide an answer to the long standing problem of mixing quantum and
classical dynamics within a single formalism. The construction is based on
p-mechanical derivation (quant-ph/0212101, quant-ph/0304023) of quantum and
classical dynamics from the representation theory of the Heisenberg group. To
achieve a quantum-classical mixing we take the product of two copies of the
Heisenberg group which represent two different Planck's constants. In
comparison with earlier guesses our answer contains an extra term of analytical
nature, which was not obtained before in purely algebraic setup.
Keywords: Moyal brackets, Poisson brackets, commutator, Heisenberg group,
orbit method, representation theory, Planck's constant, quantum-classical
mixingComment: LaTeX, 7 pages (EPL style), no figures; v2: example of dynamics with
two different Planck's constants is added, minor corrections; v3: major
revion, a complete example of quantum-classic dynamics is given; v4: few
grammatic correction
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