3,937 research outputs found
Stochastic stability versus localization in chaotic dynamical systems
We prove stochastic stability of chaotic maps for a general class of Markov
random perturbations (including singular ones) satisfying some kind of mixing
conditions. One of the consequences of this statement is the proof of Ulam's
conjecture about the approximation of the dynamics of a chaotic system by a
finite state Markov chain. Conditions under which the localization phenomenon
(i.e. stabilization of singular invariant measures) takes place are also
considered. Our main tools are the so called bounded variation approach
combined with the ergodic theorem of Ionescu-Tulcea and Marinescu, and a random
walk argument that we apply to prove the absence of ``traps'' under the action
of random perturbations.Comment: 27 pages, LaTe
Hysteresis phenomenon in deterministic traffic flows
We study phase transitions of a system of particles on the one-dimensional
integer lattice moving with constant acceleration, with a collision law
respecting slower particles. This simple deterministic ``particle-hopping''
traffic flow model being a straightforward generalization to the well known
Nagel-Schreckenberg model covers also a more recent slow-to-start model as a
special case. The model has two distinct ergodic (unmixed) phases with two
critical values. When traffic density is below the lowest critical value, the
steady state of the model corresponds to the ``free-flowing'' (or ``gaseous'')
phase. When the density exceeds the second critical value the model produces
large, persistent, well-defined traffic jams, which correspond to the
``jammed'' (or ``liquid'') phase. Between the two critical values each of these
phases may take place, which can be interpreted as an ``overcooled gas'' phase
when a small perturbation can change drastically gas into liquid. Mathematical
analysis is accomplished in part by the exact derivation of the life-time of
individual traffic jams for a given configuration of particles.Comment: 22 pages, 6 figures, corrected and improved version, to appear in the
Journal of Statistical Physic
Filamentary structure in chemical tracer distributions near the subtropical jet following a wave breaking event
This paper presents a set of observations and analyses of trace gas cross sections in the extratropical upper troposphere/lower stratosphere (UTLS). The spatially highly resolved (≈0.5 km vertically and 12.5 km horizontally) cross sections of ozone (O<sub>3</sub>), nitric acid (HNO<sub>3</sub>), and peroxyacetyl nitrate (PAN), retrieved from the measurements of the CRISTA-NF infrared limb sounder flown on the Russian M55-Geophysica, revealed intricate layer structures in the region of the subtropical tropopause break. The chemical structure in this region shows an intertwined stratosphere and troposphere. The observed filaments in all discussed trace gases are of a spatial scale of less than 0.8 km vertically and about 200 km horizontally across the jet stream. Backward trajectory calculations confirm that the observed filaments are the result of a breaking Rossby wave in the preceding days. An analysis of the trace gas relationships between PAN and O<sub>3</sub> identifies four distinct groups of air mass: polluted subtropical tropospheric air, clean tropical upper-tropospheric air, the lowermost stratospheric air, and air from the deep stratosphere. The tracer relationships further allow the identification of tropospheric, stratospheric, and the transitional air mass made of a mixture of UT and LS air. Mapping of these air mass types onto the geo-spatial location in the cross sections reveals a highly structured extratropical transition layer (ExTL). Finally, the ratio between the measured reactive nitrogen species (HNO<sub>3</sub> + PAN + ClONO<sub>2</sub>) and O<sub>3</sub> is analysed to estimate the influence of tropospheric pollution on the extratropical UTLS. <br><br> In combination, these diagnostics provide the first example of a multi-species two-dimensional picture of the inhomogeneous distribution of chemical species within the UTLS region. Since Rossby wave breaking occurs frequently in the region of the tropopause break, these observed fine-scale filaments are likely ubiquitous in the region. The implications of the layered structure for chemistry and radiation need to be examined, and the representation of this structure in chemistry-climate models is discussed
Magnetic transport in a straight parabolic channel
We study a charged two-dimensional particle confined to a straight
parabolic-potential channel and exposed to a homogeneous magnetic field under
influence of a potential perturbation . If is bounded and periodic along
the channel, a perturbative argument yields the absolute continuity of the
bottom of the spectrum. We show it can have any finite number of open gaps
provided the confining potential is sufficiently strong. However, if
depends on the periodic variable only, we prove by Thomas argument that the
whole spectrum is absolutely continuous, irrespectively of the size of the
perturbation. On the other hand, if is small and satisfies a weak
localization condition in the the longitudinal direction, we prove by Mourre
method that a part of the absolutely continuous spectrum persists
Magnetic strip waveguides
We analyze the spectrum of the "local" Iwatsuka model, i.e. a two-dimensional
charged particle interacting with a magnetic field which is homogeneous outside
a finite strip and translationally invariant along it. We derive two new
sufficient conditions for absolute continuity of the spectrum. We also show
that in most cases the number of open spectral gaps of the model is finite. To
illustrate these results we investigate numerically the situation when the
field is zero in the strip being screened, e.g. by a superconducting mask.Comment: 22 pages, a LaTeX source file with three eps figure
Variation in Emission and Absorption Lines and Continuum Flux by Orbital Phase in Vela X-1
High resolution spectral studies were undertaken at orbital phases 0, 0.25
and 0.5 on the high-mass X-ray binary (HMXB) Vela X-1 using archival Chandra
data. We present (a) the first detailed analysis of the multiple strong narrow
emission lines present in phase 0.5 (b) an analysis of the absorption of the
continuum in phase 0.5, and (c) the first detection of narrow emission and
absorption lines in phase 0.25. Multiple fluorescent and H-and He-like emission
lines in the band 1.6 - 20 Angstrom in eclipse are partially obscured at phase
0.25 by the X-ray continuum. The phase 0.25 spectrum displays 3 triplets, 2
with a blue-shifted resonance (r) line in absorption and the intercombination
(i) and forbidden (f) lines in emission, and shows in absorption other
blue-shifted lines seen in emission in eclipse. At phase 0.5 the soft X-ray
continuum diminishes revealing an "eclipse-like" spectrum, however line flux
values are around 13-fold those in eclipse. We conclude the narrow emission
lines in Vela X-1 become apparent when the continuum is blocked from line of
sight, either by eclipse or by scattering and/or absorption from a wake or
cloud. The H-and He-like lines arise in warm photoionised regions in the
stellar wind, while the fluorescent lines (including a Ni K alpha line) are
produced in cooler clumps of gas outside these regions. Absorption of the 5-13
Angstrom continuum at phase 0.5 may be caused by an accretion wake comprised of
dense stagnant photoionized plasma inside a Stromgren zone. Multiple
fluorescent emission lines may be a common feature of the supergiant category
of HMXBs.Comment: 29 pages, 7 figures, accepted for publication in the Astronomical
Journa
Hierarchy of piecewise non-linear maps with non-ergodicity behavior
We study the dynamics of hierarchy of piecewise maps generated by
one-parameter families of trigonometric chaotic maps and one-parameter families
of elliptic chaotic maps of and types, in detail.
We calculate the Lyapunov exponent and Kolmogorov-Sinai entropy of the these
maps with respect to control parameter. Non-ergodicity of these piecewise maps
is proven analytically and investigated numerically . The invariant measure of
these maps which are not equal to one or zero, appears to be characteristic of
non-ergodicity behavior. A quantity of interest is the Kolmogorov-Sinai
entropy, where for these maps are smaller than the sum of positive Lyapunov
exponents and it confirms the non-ergodicity of the maps.Comment: 18 pages, 8 figure
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