Correlations of electromagnetic fields in chaotic cavities

We consider the fluctuations of electromagnetic fields in chaotic microwave cavities. We calculate the transversal and longitudinal correlation function based on a random wave assumption and compare the predictions with measurements on two- and three-dimensional microwave cavities.Comment: Europhys style, 8 pages, 3 figures (included

Axiomatic Digital Topology

The paper presents a new set of axioms of digital topology, which are easily understandable for application developers. They define a class of locally finite (LF) topological spaces. An important property of LF spaces satisfying the axioms is that the neighborhood relation is antisymmetric and transitive. Therefore any connected and non-trivial LF space is isomorphic to an abstract cell complex. The paper demonstrates that in an n-dimensional digital space only those of the (a, b)-adjacencies commonly used in computer imagery have analogs among the LF spaces, in which a and b are different and one of the adjacencies is the "maximal" one, corresponding to 3n\"i1 neighbors. Even these (a, b)-adjacencies have important limitations and drawbacks. The most important one is that they are applicable only to binary images. The way of easily using LF spaces in computer imagery on standard orthogonal grids containing only pixels or voxels and no cells of lower dimensions is suggested

Statistical analysis of coherent structures in transitional pipe flow

Numerical and experimental studies of transitional pipe flow have shown the prevalence of coherent flow structures that are dominated by downstream vortices. They attract special attention because they contribute predominantly to the increase of the Reynolds stresses in turbulent flow. In the present study we introduce a convenient detector for these coherent states, calculate the fraction of time the structures appear in the flow, and present a Markov model for the transition between the structures. The fraction of states that show vortical structures exceeds 24% for a Reynolds number of about Re=2200, and it decreases to about 20% for Re=2500. The Markov model for the transition between these states is in good agreement with the observed fraction of states, and in reasonable agreement with the prediction for their persistence. It provides insight into dominant qualitative changes of the flow when increasing the Reynolds number.Comment: 11 pages, 26 (sub)figure

Intraspecific diversity of the rhizodeposition of Lupinus angustifolius L. regarding the phosphorus mobilization in the soil

The cropping of lupines (Lupinus spp.) for protein production is rising worldwide. The growth of lupines is often limited by P deficiency, caused by low P bioavailability in soils. The rhizodeposition is a leading control of the P mobilization in the soil, i.e. especially by the release of phosphatases and organic acids. In the present study 20 genotypes of L. angustifolius (19 accessions from different geographic origins and the cultivar Boruta) were tested on their molecular-chemical composition of the rhizodeposition in P-deficiency by pyrolysis-field ionisation mass spectrometry (Py-FIMS) and on the phosphatase and ß-glucosidase activities in the rhizosphere soil. The intraspecific diversity of the composition of the rhizodeposits was especially large for the relative abundance of carbohydrates and in this way in a specific impact on the microbial activity in the rhizosphere by selective promotion under some genotypes by easily available C sources for the microbial rhizosphere community. This was confirmed by a large variation in the thermal stability of the rhizodeposits of different genotypes, a varying pH level in identical cultivation conditions and in varying activities of alkaline and acid phosphomonoesterases and ß-glucosidase in the rhizosphere. Furthermore, the data revealed a strong variation in the release of alkaloids into the rhizosphere during the growth with a further impact on the microbial activity. In conclusion, the use of the quality of the rhizodeposition as an indicator of the potential for P mobilization in P-deficient soils highlighted a broad intraspecific diversity within L. angustifolius. This is a promising basis for a selection of highly P efficient genotypes within this species for further breeding strategies of productive cultivars

Approach to ergodicity in quantum wave functions

According to theorems of Shnirelman and followers, in the semiclassical limit the quantum wavefunctions of classically ergodic systems tend to the microcanonical density on the energy shell. We here develop a semiclassical theory that relates the rate of approach to the decay of certain classical fluctuations. For uniformly hyperbolic systems we find that the variance of the quantum matrix elements is proportional to the variance of the integral of the associated classical operator over trajectory segments of length $T_H$, and inversely proportional to $T_H^2$, where $T_H=h\bar\rho$ is the Heisenberg time, $\bar\rho$ being the mean density of states. Since for these systems the classical variance increases linearly with $T_H$, the variance of the matrix elements decays like $1/T_H$. For non-hyperbolic systems, like Hamiltonians with a mixed phase space and the stadium billiard, our results predict a slower decay due to sticking in marginally unstable regions. Numerical computations supporting these conclusions are presented for the bakers map and the hydrogen atom in a magnetic field.Comment: 11 pages postscript and 4 figures in two files, tar-compressed and uuencoded using uufiles, to appear in Phys Rev E. For related papers, see http://www.icbm.uni-oldenburg.de/icbm/kosy/ag.htm

Quantum Chaos in the Yang-Mills-Higgs System at Finite Temperature

The quantum chaos in the finite-temperature Yang-Mills-Higgs system is studied. The energy spectrum of a spatially homogeneous SU(2) Yang-Mills-Higgs is calculated within thermofield dynamics. Level statistics of the spectra is studied by plotting nearest-level spacing distribution histograms. It is found that finite temperature effects lead to a strengthening of chaotic effects, i.e. spectrum which has Poissonian distribution at zero temperature has Gaussian distribution at finite-temperature.Comment: 6 pages, 5 figures, Revte

How does flow in a pipe become turbulent?

The transition to turbulence in pipe flow does not follow the scenario familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even when the flow speed is high enough and the perturbation sufficiently strong such that turbulent flow is established, it can return to the laminar state without any indication of the imminent decay. In this parameter range, the lifetimes of perturbations show a sensitive dependence on initial conditions and an exponential distribution. The turbulence seems to be supported by three-dimensional travelling waves which appear transiently in the flow field. The boundary between laminar and turbulent dynamics is formed by the stable manifold of an invariant chaotic state. We will also discuss the relation between observations in short, periodically continued domains, and the dynamics in fully extended puffs.Comment: for the proceedings of statphys 2

Travelling waves in pipe flow

A family of three-dimensional travelling waves for flow through a pipe of circular cross section is identified. The travelling waves are dominated by pairs of downstream vortices and streaks. They originate in saddle-node bifurcations at Reynolds numbers as low as 1250. All states are immediately unstable. Their dynamical significance is that they provide a skeleton for the formation of a chaotic saddle that can explain the intermittent transition to turbulence and the sensitive dependence on initial conditions in this shear flow.Comment: 4 pages, 5 figure

Die Rolle biologischer Bodenkrusten im C-, N- und P-Kreislauf

Biologische Bodenkrusten (BSCs) sind Organismengemeinschaften, die an der Bodenoberfläche leben. Ihre Hauptkomponenten sind neben heterotrophen Bakterien, Cyanobakterien, Grünalgen, Mikropilze, Moose und Flechten. Um die ökologische Rolle von BSCs in den oft verknüpften biogeochemischen Kreisläufen von C, N und P zu analysieren und zudem den Einfluss von Landnutzungsintensität zu untersuchen, beprobten wir BSCs aus Kiefer- bzw. Buche-dominierten Wäldern des Biodiversitätsexploratoriums Schorfheide-Chorin (DFG SPP 1374). Gesamt-C, -N und -P der Kompartimente Kruste, Krusten-anhängender (KA) Boden und Krusten-freier (KF) Boden wurden quantifiziert und der Gehalt an anorgischem und organischem P in fünf verschiedenen P-Fraktionen der unterschiedlichen Kompartimente bestimmt. P-Formen wurden mit Hilfe von P-XANES (x-ray absorbance near edge structure) analysiert. Py-FIMS (pyrolysis field ionization mass spectrometry) wurde zur Charakterisierung von C- und N-Verbindungen der organischen Substanz (OS) eingesetzt. Die Biodiversität der abundanten Grünalgen in der Kruste wurde morphologisch nach Anreicherungskultur bestimmt. Unabhängig von der Baumart waren Gesamt-C, -N und -P in der Kruste angereichert. P-Fraktionierungs- und XANES-Ergebnisse deuteten auf eine Verwitterung von resistentem P in Kruste und KA-Boden hin. Die OS war primär von der dominierenden Baumart geprägt. Auf Kompartiment-Ebene war Kruste durch hohe Anteile an Kohlenhydraten und freien Fettsäuren gekennzeichnet, während Lipid-Anteile in KA- und KF-Boden höher waren. Die Thermostabilität der OS der Kruste war am geringsten. Die Grünalgen-Zusammensetzung war von der Landnutzungsintensität beeinflusst und hatte Auswirkungen auf den Anteil an Alkylaromaten und labilem anorganischem P in den Krusten. Wir schlussfolgern, dass BSCs eine besondere Rolle bei der Umwandlung von anorganischem zu organischem P zukommt und sie an der Verwitterung P-haltiger Minerale in Böden beteiligt sein können. Die OS von Böden wird durch BSCs beeinflusst, ist jedoch v.a. durch die dominierende Baumart, wahrscheinlich durch deren Blätter und Exudate, geprägt

Fractal Stability Border in Plane Couette Flow

We study the dynamics of localised perturbations in plane Couette flow with periodic lateral boundary conditions. For small Reynolds number and small amplitude of the initial state the perturbation decays on a viscous time scale $t \propto Re$. For Reynolds number larger than about 200, chaotic transients appear with life times longer than the viscous one. Depending on the type of the perturbation isolated initial conditions with infinite life time appear for Reynolds numbers larger than about 270--320. In this third regime, the life time as a function of Reynolds number and amplitude is fractal. These results suggest that in the transition region the turbulent dynamics is characterised by a chaotic repeller rather than an attractor.Comment: 4 pages, Latex, 4 eps-figures, submitted to Phys. Rev. Le