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 (&approx;0.5 km vertically and 12.5 km horizontally) cross sections of ozone (O₃), nitric acid (HNO₃), 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 O₃ 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 (HNO₃ + PAN + ClONO₂) and O₃ 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 $W$. If $W$ 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 $W$ 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 $W$ 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 $\mathbf{cn}$ and $\mathbf{sn}$ 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