308 research outputs found
Approximate renormalization for the break-up of invariant tori with three frequencies
We construct an approximate renormalization transformation for Hamiltonian
systems with three degrees of freedom in order to study the break-up of
invariant tori with three incommensurate frequencies which belong to the cubic
field , where . This renormalization has two
fixed points~: a stable one and a hyperbolic one with a codimension one stable
manifold. We compute the associated critical exponents that characterize the
universality class for the break-up of the invariant tori we consider.Comment: 5 pages, REVTe
Geology of the Engigstciak Archaeological Site, Yukon Territory
Reports geological investigations is 1956-1957 to aid in dating the archeological finds. Quaternary sediments in a clay and a sand sequence are described; their stratigraphic relationships have been disrupted by soil movements resulting from freezing and thawing and from downslope creep. These soil movements, their mechanisms and rates postulated, apparently buried an organic layer containing artifacts progressively between two layers of marine clay. Due to overturning and mixing of layers of different ages, further complicated by a possible upthrust of the marine clay by glacier ice, the artifacts cannot be dated by geological means. From evidence indicating only one marine invasion coincident with glacial advance however, the archeological material is concluded to postdate the last Pleistocene glaciation
Renormalization and Quantum Scaling of Frenkel-Kontorova Models
We generalise the classical Transition by Breaking of Analyticity for the
class of Frenkel-Kontorova models studied by Aubry and others to non-zero
Planck's constant and temperature. This analysis is based on the study of a
renormalization operator for the case of irrational mean spacing using
Feynman's functional integral approach. We show how existing classical results
extend to the quantum regime. In particular we extend MacKay's renormalization
approach for the classical statistical mechanics to deduce scaling of low
frequency effects and quantum effects. Our approach extends the phenomenon of
hierarchical melting studied by Vallet, Schilling and Aubry to the quantum
regime.Comment: 14 pages, 1 figure, submitted to J.Stat.Phy
Ulam method for the Chirikov standard map
We introduce a generalized Ulam method and apply it to symplectic dynamical
maps with a divided phase space. Our extensive numerical studies based on the
Arnoldi method show that the Ulam approximant of the Perron-Frobenius operator
on a chaotic component converges to a continuous limit. Typically, in this
regime the spectrum of relaxation modes is characterized by a power law decay
for small relaxation rates. Our numerical data show that the exponent of this
decay is approximately equal to the exponent of Poincar\'e recurrences in such
systems. The eigenmodes show links with trajectories sticking around stability
islands.Comment: 13 pages, 13 figures, high resolution figures available at:
http://www.quantware.ups-tlse.fr/QWLIB/ulammethod/ minor corrections in text
and fig. 12 and revised discussio
An approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom
We construct an approximate renormalization transformation that combines
Kolmogorov-Arnold-Moser (KAM)and renormalization-group techniques, to analyze
instabilities in Hamiltonian systems with three degrees of freedom. This scheme
is implemented both for isoenergetically nondegenerate and for degenerate
Hamiltonians. For the spiral mean frequency vector, we find numerically that
the iterations of the transformation on nondegenerate Hamiltonians tend to
degenerate ones on the critical surface. As a consequence, isoenergetically
degenerate and nondegenerate Hamiltonians belong to the same universality
class, and thus the corresponding critical invariant tori have the same type of
scaling properties. We numerically investigate the structure of the attracting
set on the critical surface and find that it is a strange nonchaotic attractor.
We compute exponents that characterize its universality class.Comment: 10 pages typeset using REVTeX, 7 PS figure
Discrete breathers in dc biased Josephson-junction arrays
We propose a method to excite and detect a rotor localized mode
(rotobreather) in a Josephson-junction array biased by dc currents. In our
numerical studies of the dynamics we have used experimentally realizable
parameters and included self-inductances. We have uncovered two families of
rotobreathers. Both types are stable under thermal fluctuations and exist for a
broad range of array parameters and sizes including arrays as small as a single
plaquette. We suggest a single Josephson-junction plaquette as an ideal system
to experimentally investigate these solutions.Comment: 5 pages, 5 figure, to appear June 1, 1999 in PR
Seasonal forecasting of groundwater levels in principal aquifers of the United Kingdom
To date, the majority of hydrological forecasting studies have focussed on using medium-range (3–15 days) weather forecasts to drive hydrological models and make predictions of future river flows. With recent developments in seasonal (1–3 months) weather forecast skill, such as those from the latest version of the UK Met Office global seasonal forecast system (GloSea5), there is now an opportunity to use similar methodologies to forecast groundwater levels in more slowly responding aquifers on seasonal timescales. This study uses seasonal rainfall forecasts and a lumped groundwater model to simulate groundwater levels at 21 locations in the United Kingdom up to three months into the future. The results indicate that the forecasts have skill; outperforming a persistence forecast and demonstrating reliability, resolution and discrimination. However, there is currently little to gain from using seasonal rainfall forecasts over using site climatology for this type of application. Furthermore, the forecasts are not able to capture extreme groundwater levels, primarily because of inadequacies in the driving rainfall forecasts. The findings also show that the origin of forecast skill, be it from the meteorological input, groundwater model or initial condition, is site specific and related to the groundwater response characteristics to rainfall and antecedent hydro-meteorological conditions
Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential
Coupled-mode systems are used in physical literature to simplify the
nonlinear Maxwell and Gross-Pitaevskii equations with a small periodic
potential and to approximate localized solutions called gap solitons by
analytical expressions involving hyperbolic functions. We justify the use of
the one-dimensional stationary coupled-mode system for a relevant elliptic
problem by employing the method of Lyapunov--Schmidt reductions in Fourier
space. In particular, existence of periodic/anti-periodic and decaying
solutions is proved and the error terms are controlled in suitable norms. The
use of multi-dimensional stationary coupled-mode systems is justified for
analysis of bifurcations of periodic/anti-periodic solutions in a small
multi-dimensional periodic potential.Comment: 18 pages, no figure
Discrete breathers in polyethylene chain
The existence of discrete breathers (DBs), or intrinsic localized modes
(localized periodic oscillations of transzigzag) is shown. In the localization
region periodic contraction-extension of valence C-C bonds occurs which is
accompanied by decrease-increase of valence angles. It is shown that the
breathers present in thermalized chain and their contribution dependent on
temperature has been revealed.Comment: 5 pages, 6 figure
Multidimensional continued fractions, dynamical renormalization and KAM theory
The disadvantage of `traditional' multidimensional continued fraction
algorithms is that it is not known whether they provide simultaneous rational
approximations for generic vectors. Following ideas of Dani, Lagarias and
Kleinbock-Margulis we describe a simple algorithm based on the dynamics of
flows on the homogeneous space SL(2,Z)\SL(2,R) (the space of lattices of
covolume one) that indeed yields best possible approximations to any irrational
vector. The algorithm is ideally suited for a number of dynamical applications
that involve small divisor problems. We explicitely construct renormalization
schemes for (a) the linearization of vector fields on tori of arbitrary
dimension and (b) the construction of invariant tori for Hamiltonian systems.Comment: 51 page
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