36 research outputs found
Control of potato late blight by caraway oil in organic farming
Caraway (Carum carvi) seeds contain biologically active essential oils, which have shown potential in controlling Phytophthora infestans (P.i.). An attempt is being made to develop a P.i. control strategy for organic farming based on caraway oil
Universal criterion for the breakup of invariant tori in dissipative systems
The transition from quasiperiodicity to chaos is studied in a two-dimensional
dissipative map with the inverse golden mean rotation number. On the basis of a
decimation scheme, it is argued that the (minimal) slope of the critical
iterated circle map is proportional to the effective Jacobian determinant.
Approaching the zero-Jacobian-determinant limit, the factor of proportion
becomes a universal constant. Numerical investigation on the dissipative
standard map suggests that this universal number could become observable in
experiments. The decimation technique introduced in this paper is readily
applicable also to the discrete quasiperiodic Schrodinger equation.Comment: 13 page
Screening current effects in Josephson junction arrays
The purpose of this work is to compare the dynamics of arrays of Josephson
junctions in presence of magnetic field in two different frameworks: the so
called XY frustrated model with no self inductance and an approach that takes
into account the screening currents (considering self inductances only). We
show that while for a range of parameters the simpler model is sufficiently
accurate, in a region of the parameter space solutions arise that are not
contained in the XY model equations.Comment: Figures available from the author
Wave transmission, phonon localization and heat conduction of 1D Frenkel-Kontorova chain
We study the transmission coefficient of a plane wave through a 1D finite
quasi-periodic system -- the Frenkel-Kontorova (FK) model -- embedding in an
infinite uniform harmonic chain. By varying the mass of atoms in the infinite
uniform chain, we obtain the transmission coefficients for {\it all}
eigenfrequencies. The phonon localization of the incommensurated FK chain is
also studied in terms of the transmission coefficients and the Thouless
exponents. Moreover, the heat conduction of Rubin-Greer-like model for FK chain
at low temperature is calculated. It is found that the stationary heat flux
, and depends on the strength of the external
potential.Comment: 15 pages in Revtex, 8 EPS figure
Fractal Spin Glass Properties of Low Energy Configurations in the Frenkel-Kontorova chain
We study numerically and analytically the classical one-dimensional
Frenkel-Kontorova chain in the regime of pinned phase characterized by phonon
gap. Our results show the existence of exponentially many static equilibrium
configurations which are exponentially close to the energy of the ground state.
The energies of these configurations form a fractal quasi-degenerate band
structure which is described on the basis of elementary excitations. Contrary
to the ground state, the configurations inside these bands are disordered.Comment: revtex, 9 pages, 9 figure
A Nonperturbative Eliasson's Reducibility Theorem
This paper is concerned with discrete, one-dimensional Schr\"odinger
operators with real analytic potentials and one Diophantine frequency. Using
localization and duality we show that almost every point in the spectrum admits
a quasi-periodic Bloch wave if the potential is smaller than a certain constant
which does not depend on the precise Diophantine conditions. The associated
first-order system, a quasi-periodic skew-product, is shown to be reducible for
almost all values of the energy. This is a partial nonperturbative
generalization of a reducibility theorem by Eliasson. We also extend
nonperturbatively the genericity of Cantor spectrum for these Schr\"odinger
operators. Finally we prove that in our setting, Cantor spectrum implies the
existence of a -set of energies whose Schr\"odinger cocycle is not
reducible to constant coefficients
The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results
The problem of finding the exact energies and configurations for the
Frenkel-Kontorova model consisting of particles in one dimension connected to
their nearest-neighbors by springs and placed in a periodic potential
consisting of segments from parabolas of identical (positive) curvature but
arbitrary height and spacing, is reduced to that of minimizing a certain convex
function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6
Postscript figures, accepted by Phys. Rev.
Renormalization analysis of correlation properties in a quasiperiodically forced two-level system
This pre-print has been submitted, and accepted, to the journal, Journal of Mathematical Physics [© American Institute of Physics]. The definitive version: MESTEL, B.D. and OSBALDESTIN, A.H., 2002. Renormalization analysis of correlation properties in a quasiperiodically forced two-level system. Journal of Mathematical Physics, 43(7), pp. 3458-3483, is available at: http://jmp.aip.org/jmp/.We give a rigorous renormalization analysis of the self-similarity of correlation functions in a quasiperiodically forced two-level system. More precisely, the system considered is a quantum two-level system in a time-dependent field consisting of periodic kicks with amplitude given by a discontinuous modulation function driven in a quasiperiodic manner at golden mean frequency. Mathematically, our analysis consists of a description of all piecewise-constant periodic orbits of an additive functional recurrence. We further establish a criterion for such orbits to be globally bounded functions. In a particular example, previously only treated numerically, we further calculate explicitly the asymptotic height of the main peaks in the correlation function