138 research outputs found
Decohering localized waves
In the absence of confinement localization of waves takes place due to
randomness or nonlinearity and relies on their phase coherence. We
quantitatively probe the sensitivity of localized wave packets to random phase
fluctuations and confirm the necessity of phase coherence for localization.
Decoherence resulting from a dynamical random environment leads to diffusive
spreading and destroys linear and nonlinear localization. We find that maximal
spreading is achieved for optimal phase fluctuation characteristics which is a
consequence of the competition between diffusion due to decoherence and
ballistic transport within the mean free path distance.Comment: Updated affiliatio
New approaches for automated data processing of annually laminated sediments
International audienceLaminated sediments, like evaporites and biogenic lake sediments, provide high-resolution paleo-climate records. Yet detection and counting of laminae causes still problems because sedimentary structures are often disturbed. In the past laminated rocks often were analysed manually - a tedious and subjective work. The present study describes four automated approaches for lamina detection based on 1d grey-scale vectors. Best results are obtained with a newly developed algorithm, called Adaptive Template Method (ATM) in combination with the Hilbert transform. ATM improves the signal to noise ratio of the grey-value signal. Its basic idea is to extract first a characteristic waveform, the template, which describes the typical grey-value variation transverse to the laminae. This is a kind of "template learning" process, which in practice is done by an appropriate averaging method. This template is in a second step used for processing the whole sample. One calculates the overlap of the template with the actual signal, the grey-value variation along the core, as function of position in core direction. This method generates a new signal with maxima at positions, where the template optimally matches the original signal. The new time-series is called AT-transform. It is smoother than the initial data sequence. High frequency noise and local trend effects are suppressed. Afterwards, the AT-transform can be analysed with the Hilbert transformation for extracting phase information. The data processing methods are tested both on artificial data sequences and on a seasonally laminated sedimentary record of the Oligocene Baruth Maar (Germany). Although ATM is no panacea for highly disturbed signals, our comparison with other approaches shows that it provides the best results. The combination of ATM and the Hilbert transform allows to detect clearly long-term oscillations in the sedimentation patterns and thus cycles in climatic variations
Understanding highly excited states via parametric variations
Highly excited vibrational states of an isolated molecule encode the
vibrational energy flow pathways in the molecule. Recent studies have had
spectacular success in understanding the nature of the excited states mainly
due to the extensive studies of the classical phase space structures and their
bifurcations. Such detailed classical-quantum correspondence studies are
presently limited to two or quasi two dimensional systems. One of the main
reasons for such a constraint has to do with the problem of visualization of
relevant objects like surface of sections and Wigner or Husimi distributions
associated with an eigenstate. This neccesiates various alternative techniques
which are more algebraic than geometric in nature. In this work we introduce
one such method based on parametric variation of the eigenvalues of a
Hamiltonian. It is shown that the level velocities are correlated with the
phase space nature of the corresponding eigenstates. A semiclassical expression
for the level velocities of a single resonance Hamiltonian is derived which
provides theoretical support for the correlation. We use the level velocities
to dynamically assign the highly excited states of a model spectroscopic
Hamiltonian in the mixed phase space regime. The effect of bifurcations on the
level velocities is briefly discussed using a recently proposed spectroscopic
Hamiltonian for the HCP molecule.Comment: 12 pages, 9 figures, submitted to J. Chem. Phy
Analyzing intramolecular vibrational energy redistribution via the overlap intensity-level velocity correlator
Numerous experimental and theoretical studies have established that
intramolecular vibrational energy redistribution (IVR) in isolated molecules
has a heirarchical tier structure. The tier structure implies strong
correlations between the energy level motions of a quantum system and its
intensity-weighted spectrum. A measure, which explicitly accounts for this
correaltion, was first introduced by one of us as a sensitive probe of phase
space localization. It correlates eigenlevel velocities with the overlap
intensities between the eigenstates and some localized state of interest. A
semiclassical theory for the correlation is developed for systems that are
classically integrable and complements earlier work focusing exclusively on the
chaotic case. Application to a model two dimensional effective spectroscopic
Hamiltonian shows that the correlation measure can provide information about
the terms in the molecular Hamiltonian which play an important role in an
energy range of interest and the character of the dynamics. Moreover, the
correlation function is capable of highlighting relevant phase space structures
including the local resonance features associated with a specific bright state.
In addition to being ideally suited for multidimensional systems with a large
density of states, the measure can also be used to gain insights into the phase
space transport and localization. It is argued that the overlap intensity-level
velocity correlation function provides a novel way of studying vibrational
energy redistribution in isolated molecules. The correlation function is
ideally suited to analyzing the parametric spectra of molecules in external
fields.Comment: 16 pages, 13 figures (low resolution
Effect of time-correlation of input patterns on the convergence of on-line learning
We studied the effects of time correlation of subsequent patterns on the
convergence of on-line learning by a feedforward neural network with
backpropagation algorithm. By using chaotic time series as sequences of
correlated patterns, we found that the unexpected scaling of converging time
with learning parameter emerges when time-correlated patterns accelerate
learning process.Comment: 8 pages(Revtex), 5 figure
The randomly driven Ising ferromagnet, Part I: General formalism and mean field theory
We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics
under the influence of a fast switching, random external field. After
introducing a general formalism for describing such systems, we consider here
the mean-field theory. A novel type of first order phase transition related to
spontaneous symmetry breaking and dynamic freezing is found. The
non-equilibrium stationary state has a complex structure, which changes as a
function of parameters from a singular-continuous distribution with Euclidean
or fractal support to an absolutely continuous one.Comment: 12 pages REVTeX/LaTeX format, 12 eps/ps figures. Submitted to Journal
of Physics
Discrete model for laser driven etching and microstructuring of metallic surfaces
We present a unidimensional discrete solid-on-solid model evolving in time
using a kinetic Monte Carlo method to simulate micro-structuring of kerfs on
metallic surfaces by means of laser-induced jet-chemical etching. The precise
control of the passivation layer achieved by this technique is responsible for
the high resolution of the structures. However, within a certain range of
experimental parameters, the microstructuring of kerfs on stainless steel
surfaces with a solution of shows periodic ripples,
which are considered to originate from an intrinsic dynamics. The model mimics
a few of the various physical and chemical processes involved and within
certain parameter ranges reproduces some morphological aspects of the
structures, in particular ripple regimes. We analyze the range of values of
laser beam power for the appearance of ripples in both experimental and
simulated kerfs. The discrete model is an extension of one that has been used
previously in the context of ion sputtering and is related to a noisy version
of the Kuramoto-Sivashinsky equation used extensively in the field of pattern
formation.Comment: Revised version. Etching probability distribution and new simulations
adde
Convolution of multifractals and the local magnetization in a random field Ising chain
The local magnetization in the one-dimensional random-field Ising model is
essentially the sum of two effective fields with multifractal probability
measure. The probability measure of the local magnetization is thus the
convolution of two multifractals. In this paper we prove relations between the
multifractal properties of two measures and the multifractal properties of
their convolution. The pointwise dimension at the boundary of the support of
the convolution is the sum of the pointwise dimensions at the boundary of the
support of the convoluted measures and the generalized box dimensions of the
convolution are bounded from above by the sum of the generalized box dimensions
of the convoluted measures. The generalized box dimensions of the convolution
of Cantor sets with weights can be calculated analytically for certain
parameter ranges and illustrate effects we also encounter in the case of the
measure of the local magnetization. Returning to the study of this measure we
apply the general inequalities and present numerical approximations of the
D_q-spectrum. For the first time we are able to obtain results on multifractal
properties of a physical quantity in the one-dimensional random-field Ising
model which in principle could be measured experimentally. The numerically
generated probability densities for the local magnetization show impressively
the gradual transition from a monomodal to a bimodal distribution for growing
random field strength h.Comment: An error in figure 1 was corrected, small additions were made to the
introduction and the conclusions, some typos were corrected, 24 pages,
LaTeX2e, 9 figure
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