326 research outputs found
Forecasting confined spatiotemporal chaos with genetic algorithms
A technique to forecast spatiotemporal time series is presented. it uses a
Proper Ortogonal or Karhunen-Lo\`{e}ve Decomposition to encode large
spatiotemporal data sets in a few time-series, and Genetic Algorithms to
efficiently extract dynamical rules from the data. The method works very well
for confined systems displaying spatiotemporal chaos, as exemplified here by
forecasting the evolution of the onedimensional complex Ginzburg-Landau
equation in a finite domain.Comment: 4 pages, 5 figure
Turbulent spectrum of the Earth's ozone field
The Total Ozone Mapping Spectrometer (TOMS) database is subjected to an
analysis in terms of the Karhunen-Loeve (KL) empirical eigenfunctions. The
concentration variance spectrum is transformed into a wavenumber spectrum, . In terms of wavenumber is shown to be in the
inverse cascade regime, in the enstrophy cascade regime with the
spectral {\it knee} at the wavenumber of barotropic instability.The spectrum is
related to known geophysical phenomena and shown to be consistent with physical
dimensional reasoning for the problem. The appropriate Reynolds number for the
phenomena is .Comment: RevTeX file, 4 pages, 4 postscript figures available upon request
from Richard Everson <[email protected]
Independent Component Analysis of Spatiotemporal Chaos
Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear
oscillators are analyzed using independent component analysis (ICA). For
diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth
amplitude patterns, ICA extracts localized one-humped basis vectors that
reflect the characteristic hole structures of the system, and for nonlocally
coupled complex Ginzburg-Landau oscillators with fractal amplitude patterns,
ICA extracts localized basis vectors with characteristic gap structures.
Statistics of the decomposed signals also provide insight into the complex
dynamics of the spatiotemporal chaos.Comment: 5 pages, 6 figures, JPSJ Vol 74, No.
Unified Multifractal Description of Velocity Increments Statistics in Turbulence: Intermittency and Skewness
The phenomenology of velocity statistics in turbulent flows, up to now,
relates to different models dealing with either signed or unsigned longitudinal
velocity increments, with either inertial or dissipative fluctuations. In this
paper, we are concerned with the complete probability density function (PDF) of
signed longitudinal increments at all scales. First, we focus on the symmetric
part of the PDFs, taking into account the observed departure from scale
invariance induced by dissipation effects. The analysis is then extended to the
asymmetric part of the PDFs, with the specific goal to predict the skewness of
the velocity derivatives. It opens the route to the complete description of all
measurable quantities, for any Reynolds number, and various experimental
conditions. This description is based on a single universal parameter function
D(h) and a universal constant R*.Comment: 13 pages, 3 figures, Extended version, Publishe
Risk of prostate cancer after isolated high-grade prostatic intraepithelial neoplasia (HGPIN) detected on extended core needle biopsy : a UK hospital experience.
Background High-grade prostatic intraepithelial neoplasia (HGPIN) is a precursor lesion to prostate cancer (CaP). UK-based studies examining the occurrence of isolated HGPIN and subsequent risk of CaP are lacking. Our aim was to assess the occurrence of HGPIN in a regional UK population and to determine whether in a retrievable cohort of such patients that had repeat extended core biopsies, there was an elevated risk of CaP. Methods A retrospective analysis of the pathology database was conducted at our institution (Lancashire Teaching Hospitals NHS Foundation Trust) for prostate biopsies recorded between January 2001 and December 2005 (all extended core biopsies). Those patients with isolated HGPIN on 1st set of biopsies were identified and, their clinical characteristics and pathological findings from subsequent biopsies (if any) were determined. The risk of CaP on subsequent biopsies based on presenting baseline PSA was stratified. Results Of 2,192 biopsied patients, there were 88 cases of isolated HGPIN of which 67 patients underwent one or more repeat biopsies. In this repeat-biopsy group, 28 CaP diagnoses were made. Age at first biopsy (P 20 ng/ml – 87.5%. Conclusion Based on our results, we recommend delaying the 1st repeat biopsy at low PSA range but to have a shorter interval to repeat biopsies at intermediate and higher PSA ranges
Turbulence Time Series Data Hole Filling using Karhunen-Loeve and ARIMA methods
Measurements of optical turbulence time series data using unattended
instruments over long time intervals inevitably lead to data drop-outs or
degraded signals. We present a comparison of methods using both Principal
Component Analysis, which is also known as the Karhunen--Loeve decomposition,
and ARIMA that seek to correct for these event-induced and mechanically-induced
signal drop-outs and degradations. We report on the quality of the correction
by examining the Intrinsic Mode Functions generated by Empirical Mode
Decomposition. The data studied are optical turbulence parameter time series
from a commercial long path length optical anemometer/scintillometer, measured
over several hundred metres in outdoor environments.Comment: 8 pages, 9 figures, submitted to ICOLAD 2007, City University,
London, U
POD Analysis of Sound Generation by a Turbulent Jet
A Proper Orthogonal Decomposition (POD) is constructed for a Mach 0.9 turbulent jet using a well-validated direct numerical simulation database. Norms are defined based on near-field volume integrals of pressure, turbulence kinetic energy, streamwise velocity, and total enthalpy, two-dimensional integrals of streamswise velocity (to match experimental measurements), and far-field integrals of pressure over a sphere. We find substantially different POD modes for the different norms, and their efficiency at representing the full data is strongly dependent upon the norm and specifically which data we attempt to represent. To reproduce near-field turbulence statistics requires relatively few modes computed by a kinetic energy or pressure norm. However, a large number of the POD modes computed using a near-field norm are required to represent the sound field. The dominant near-field POD modes computed with either the near-field pressure norm or the sound field norm have the structure of wave packets
Model Order Reduction for Rotating Electrical Machines
The simulation of electric rotating machines is both computationally
expensive and memory intensive. To overcome these costs, model order reduction
techniques can be applied. The focus of this contribution is especially on
machines that contain non-symmetric components. These are usually introduced
during the mass production process and are modeled by small perturbations in
the geometry (e.g., eccentricity) or the material parameters. While model order
reduction for symmetric machines is clear and does not need special treatment,
the non-symmetric setting adds additional challenges. An adaptive strategy
based on proper orthogonal decomposition is developed to overcome these
difficulties. Equipped with an a posteriori error estimator the obtained
solution is certified. Numerical examples are presented to demonstrate the
effectiveness of the proposed method
Perturbation Theory Without Diagrams: The Polaron Case
Higher-order perturbative calculations in Quantum (Field) Theory suffer from
the factorial increase of the number of individual diagrams. Here I describe an
approach which evaluates the total contribution numerically for finite
temperature from the cumulant expansion of the corresponding observable
followed by an extrapolation to zero temperature. This method (originally
proposed by Bogolyubov and Plechko) is applied to the calculation of
higher-order terms for the ground-state energy of the polaron. Using
state-of-the-art multidimensional integration routines two new coefficients are
obtained corresponding to a four- and five-loop calculation. Several analytical
and numerical procedures have been implemented which were crucial for obtaining
reliable results.Comment: 32 pages, 7 figures, 4 tables, Latex, v2: misprints corrected, small
changes in text following referee comments and PR style conventions, matches
published versio
A Fokker-Planck formalism for diffusion with finite increments and absorbing boundaries
Gaussian white noise is frequently used to model fluctuations in physical
systems. In Fokker-Planck theory, this leads to a vanishing probability density
near the absorbing boundary of threshold models. Here we derive the boundary
condition for the stationary density of a first-order stochastic differential
equation for additive finite-grained Poisson noise and show that the response
properties of threshold units are qualitatively altered. Applied to the
integrate-and-fire neuron model, the response turns out to be instantaneous
rather than exhibiting low-pass characteristics, highly non-linear, and
asymmetric for excitation and inhibition. The novel mechanism is exhibited on
the network level and is a generic property of pulse-coupled systems of
threshold units.Comment: Consists of two parts: main article (3 figures) plus supplementary
text (3 extra figures
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