Echoes in classical dynamical systems

Echoes arise when external manipulations to a system induce a reversal of its time evolution that leads to a more or less perfect recovery of the initial state. We discuss the accuracy with which a cloud of trajectories returns to the initial state in classical dynamical systems that are exposed to additive noise and small differences in the equations of motion for forward and backward evolution. The cases of integrable and chaotic motion and small or large noise are studied in some detail and many different dynamical laws are identified. Experimental tests in 2-d flows that show chaotic advection are proposed.Comment: to be published in J. Phys.

Tidal controls on trace gas dynamics in a seagrass meadow of the Ria Formosa lagoon (southern Portugal)

Coastal zones are important source regions for a variety of trace gases, including halocarbons and sulfur-bearing species. While salt marshes, macroalgae and phyto-plankton communities have been intensively studied, little is known about trace gas fluxes in seagrass meadows. Here we report results of a newly developed dynamic flux chamber system that can be deployed in intertidal areas over full tidal cycles allowing for highly time-resolved measurements. The fluxes of CO2, methane (CH4) and a range of volatile organic compounds (VOCs) showed a complex dynamic mediated by tide and light. In contrast to most previous studies, our data indicate significantly enhanced fluxes during tidal immersion relative to periods of air exposure. Short emission peaks occurred with onset of the feeder current at the sampling site. We suggest an overall strong effect of advective transport processes to explain the elevated fluxes during tidal immersion. Many emission estimates from tidally influenced coastal areas still rely on measurements carried out during low tide only. Hence, our results may have significant implications for budgeting trace gases in coastal areas. This dynamic flux chamber system provides intensive time series data of community respiration (at night) and net community production (during the day) of shallow coastal systems.German Federal Ministry of Education and Research (BMBF) [03F0611E, 03F0662E]; EU FP7 ASSEMBLE research infrastructure initiative

Shear-flow transition: the basin boundary

The structure of the basin of attraction of a stable equilibrium point is investigated for a dynamical system (W97) often used to model transition to turbulence in shear flows. The basin boundary contains not only an equilibrium point Xlb but also a periodic orbit P, and it is the latter that mediates the transition. Orbits starting near Xlb relaminarize. We offer evidence that this is due to the extreme narrowness of the region complementary to basin of attraction in that part of phase space near Xlb. This leads to a proposal for interpreting the 'edge of chaos' in terms of more familiar invariant sets.Comment: 11 pages; submitted for publication in Nonlinearit

A Trace Formula for Products of Diagonal Matrix Elements in Chaotic Systems

We derive a trace formula for $\sum_n A_{nn}B_{nn}...\delta(E-E_n)$, where $A_{nn}$ is the diagonal matrix element of the operator $A$ in the energy basis of a chaotic system. The result takes the form of a smooth term plus periodic-orbit corrections; each orbit is weighted by the usual Gutzwiller factor times $A_p B_p ...$, where $A_p$ is the average of the classical observable $A$ along the periodic orbit $p$. This structure for the orbit corrections was previously proposed by Main and Wunner (chao-dyn/9904040) on the basis of numerical evidence.Comment: 8 pages; analysis made more rigorous in the revised versio

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

On-the-fly memory compression for multibody algorithms.

Memory and bandwidth demands challenge developers of particle-based codes that have to scale on new architectures, as the growth of concurrency outperforms improvements in memory access facilities, as the memory per core tends to stagnate, and as communication networks cannot increase bandwidth arbitrary. We propose to analyse each particle of such a code to find out whether a hierarchical data representation storing data with reduced precision caps the memory demands without exceeding given error bounds. For admissible candidates, we perform this compression and thus reduce the pressure on the memory subsystem, lower the total memory footprint and reduce the data to be exchanged via MPI. Notably, our analysis and transformation changes the data compression dynamically, i.e. the choice of data format follows the solution characteristics, and it does not require us to alter the core simulation code

Anomalous power law of quantum reversibility for classically regular dynamics

The Loschmidt Echo M(t) (defined as the squared overlap of wave packets evolving with two slightly different Hamiltonians) is a measure of quantum reversibility. We investigate its behavior for classically quasi-integrable systems. A dominant regime emerges where M(t) ~ t^{-alpha} with alpha=3d/2 depending solely on the dimension d of the system. This power law decay is faster than the result ~ t^{-d} for the decay of classical phase space densities

A method to find unstable periodic orbits for the diamagnetic Kepler Problem

A method to determine the admissibility of symbolic sequences and to find the unstable periodic orbits corresponding to allowed symbolic sequences for the diamagnetic Kepler problem is proposed by using the ordering of stable and unstable manifolds. By investigating the unstable periodic orbits up to length 6, a one to one correspondence between the unstable periodic orbits and their corresponding symbolic sequences is shown under the system symmetry decomposition

A halocarbon survey from a seagrass dominated subtropical lagoon, Ria Formosa (Portugal): flux pattern and isotopic composition

In this study we report fluxes of chloromethane (CH3Cl), bromomethane (CH3Br), iodomethane (CH3I), and bromoform (CHBr3) from two sampling campaigns (summer and spring) in the seagrass dominated subtropical lagoon Ria Formosa, Portugal. Dynamic flux chamber measurements were performed when seagrass patches were either air-exposed or submerged. Overall, we observed highly variable fluxes from the seagrass meadows and attributed them to diurnal cycles, tidal effects, and the variety of possible sources and sinks in the seagrass meadows. The highest emissions with up to 130 nmol m−2 h−1 for CH3Br were observed during tidal changes, from air exposure to submergence and conversely. Furthermore, during the spring campaign, the emissions of halocarbons were significantly elevated during tidal inundation as compared to air exposure. Accompanying water sampling performed during both campaigns revealed elevated concentrations of CH3Cl and CH3Br, indicating productive sources within the lagoon. Stable carbon isotopes of halocarbons from the air and water phase along with source signatures were used to allocate the distinctive sources and sinks in the lagoon. Results suggest that CH3Cl was rather originating from seagrass meadows and water column than from salt marshes. Aqueous and atmospheric CH3Br was substantially enriched in 13C in comparison to source signatures for seagrass meadows and salt marshes. This suggests a significant contribution from the water phase on the atmospheric CH3Br in the lagoon. A rough global upscaling yields annual productions from seagrass meadows of 2.3–4.5 Gg yr−1, 0.5–1.0 Gg yr−1, 0.6–1.2 Gg yr−1, and 1.9–3.7 Gg yr−1 for CH3Cl, CH3Br, CH3I, and CHBr3 respectively. This suggests a minor contribution from seagrass meadows to the global production of CH3Cl and CH3Br with about 0.1 and 0.7%, respectively. In comparison to the known marine sources for CH3I and CHBr3, seagrass meadows are rather small sources