3,232 research outputs found
Scale-free Universal Spectrum for Atmospheric Aerosol Size Distribution for Davos, Mauna Loa and Izana
Atmospheric flows exhibit fractal fluctuations and inverse power law form for
power spectra indicating an eddy continuum structure for the selfsimilar
fluctuations. A general systems theory for fractal fluctuations developed by
the author is based on the simple visualisation that large eddies form by
space-time integration of enclosed turbulent eddies, a concept analogous to
Kinetic Theory of Gases in Classical Statistical Physics. The ordered growth of
atmospheric eddy continuum is in dynamical equilibrium and is associated with
Maximum Entropy Production. The model predicts universal (scale-free) inverse
power law form for fractal fluctuations expressed in terms of the golden mean.
Atmospheric particulates are held in suspension in the fractal fluctuations of
vertical wind velocity. The mass or radius (size) distribution for homogeneous
suspended atmospheric particulates is expressed as a universal
scale-independent function of the golden mean, the total number concentration
and the mean volume radius. Model predicted spectrum is in agreement (within
two standard deviations on either side of the mean) with total averaged radius
size spectra for the AERONET (aerosol inversions) stations Davos and Mauna Loa
for the year 2010 and Izana for the year 2009 daily averages. The general
systems theory model for aerosol size distribution is scale free and is derived
directly from atmospheric eddy dynamical concepts. At present empirical models
such as the log normal distribution with arbitrary constants for the size
distribution of atmospheric suspended particulates are used for quantitative
estimation of earth-atmosphere radiation budget related to climate
warming/cooling trends. The universal aerosol size spectrum will have
applications in computations of radiation balance of earth-atmosphere system in
climate models.Comment: 18 pages, 5 figures. arXiv admin note: substantial text overlap with
arXiv:1105.0172, arXiv:1005.1336, arXiv:0908.2321, arXiv:1002.3230,
arXiv:0704.211
Analyzing stability of a delay differential equation involving two delays
Analysis of the systems involving delay is a popular topic among applied
scientists. In the present work, we analyze the generalized equation
involving two delays
viz. and . We use the the stability conditions to
propose the critical values of delays. Using examples, we show that the chaotic
oscillations are observed in the unstable region only. We also propose a
numerical scheme to solve such equations.Comment: 10 pages, 7 figure
"0-1" test chaosu
The goal of this thesis is to research the 0-1 test for chaos, its application in Matlab, and testing on suitable models. Elementary tools of the dynamical systems analysis are introduced, that are later used in the main results part of the thesis. The 0-1 test for chaos is introduced in detail, defined, and implemented in Matlab. The application is then performed on two one-dimensional discrete models where the first one is in explicit and the second one in implicit form. In both cases, simulations in dependence of the state parameter were done and main results are given - the 0-1 test for chaos, phase, and bifurcation diagrams.Hlavním cílem bakalářské práce je studium 0-1 testu chaosu, jeho implementace v Matlabu a následné testování na vhodných modelech. V práci jsou zavedeny základní nástroje analýzy dynamických systémů, které jsou později použity v části hlavních výsledků. 0-1 test chaosu je podrobně uveden, řádně definován a implementován v Matlabu. Aplikace je provedena na dvou jednodimenzionálních diskrétních modelech z nichž jeden je v explicitním a druhý v implicitním tvaru. V obou případech byly provedeny simulace v závislosti na stavovém parametru a hlavní výsledky byly demonstrovány formou 0-1 testu chaosu, fázových a bifurkačních diagramů.470 - Katedra aplikované matematikyvýborn
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