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 $m\ge 5$.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 $A = k[x,y]/(f)$ 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 $\nabla: \operatorname{Der}_k(A) \to \operatorname{End}_k(M)$ that satisfy the derivation property and preserves the Lie product. In particular, a torsion free module N over the complete local ring $B = \hat A$ 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

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 $-\mu_1<\frac{U''}{U-U_s}<0$ or $0<\frac{U''}{U-U_s}$ in the flow, where $U_s$ is the velocity at inflection point, $\mu_1$ is the eigenvalue of Poincar\'{e}'s problem. Second, this criterion is generalized to barotropic geophysical flows in $\beta$ 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

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

Novel Topological Invariant in the U(1) Gauge Field Theory

Based on the decomposition of U(1) gauge potential theory and the $\phi$-mapping topological current theory, the three-dimensional knot invariant and a four-dimensional new topological invariant are discussed in the U(1) gauge field.Comment: 10 pages, 0 figures accepted by MPL

A Renormalization Proof of the KAM Theorem for Non-Analytic Perturbations

We shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non-analytic perturbation (the latter will be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which the perturbations are analytic approximations of the original one. We shall finally show that the sequence of the approximate solutions will converge to a differentiable solution of the original problem.Comment: 33 pages, no figure

Binary trees, coproducts, and integrable systems

We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.Comment: 15 pages, 6 figures, v2: minor correction in theorem 1, two new appendices adde