Dynamics of fingering convection II: The formation of thermohaline staircases

Regions of the ocean's thermocline unstable to salt fingering are often observed to host thermohaline staircases, stacks of deep well-mixed convective layers separated by thin stably-stratified interfaces. Decades after their discovery, however, their origin remains controversial. In this paper we use 3D direct numerical simulations to shed light on the problem. We study the evolution of an analogous double-diffusive system, starting from an initial statistically homogeneous fingering state and find that it spontaneously transforms into a layered state. By analysing our results in the light of the mean-field theory developed in Paper I, a clear picture of the sequence of events resulting in the staircase formation emerges. A collective instability of homogeneous fingering convection first excites a field of gravity waves, with a well-defined vertical wavelength. However, the waves saturate early through regular but localized breaking events, and are not directly responsible for the formation of the staircase. Meanwhile, slower-growing, horizontally invariant but vertically quasi-periodic gamma-modes are also excited and grow according to the gamma-instability mechanism. Our results suggest that the nonlinear interaction between these various mean-field modes of instability leads to the selection of one particular gamma-mode as the staircase progenitor. Upon reaching a critical amplitude, this progenitor overturns into a fully-formed staircase. We conclude by extending the results of our simulations to real oceanic parameter values, and find that the progenitor gamma-mode is expected to grow on a timescale of a few hours, and leads to the formation of a thermohaline staircase in about one day with an initial spacing of the order of one to two metres.Comment: 18 pages, 9 figures, associated mpeg file at http://earth.uni-muenster.de/~stellma/movie_small.mp4, submitted to JF

Scale Transformations on the Noncommutative Plane and the Seiberg-Witten Map

We write down three kinds of scale transformations {\tt i-iii)} on the noncommutative plane. {\tt i)} is the analogue of standard dilations on the plane, {\tt ii)} is a re-scaling of the noncommutative parameter $\theta$, and {\tt iii)} is a combination of the previous two, whereby the defining relations for the noncommutative plane are preserved. The action of the three transformations is defined on gauge fields evaluated at fixed coordinates and $\theta$. The transformations are obtained only up to terms which transform covariantly under gauge transformations. We give possible constraints on these terms. We show how the transformations {\tt i)} and {\tt ii)} depend on the choice of star product, and show the relation of {\tt ii)} to Seiberg-Witten transformations. Because {\tt iii)} preserves the fundamental commutation relations it is a symmetry of the algebra. One has the possibility of implementing it as a symmetry of the dynamics, as well, in noncommutative field theories where $\theta$ is not fixed.Comment: 20 page

Space station integrated wall design and penetration damage control

A methodology was developed to allow a designer to optimize the pressure wall, insulation, and meteoroid/debris shield system of a manned spacecraft for a given spacecraft configuration and threat environment. The threat environment consists of meteoroids and orbital debris, as specified for an arbitrary orbit and expected lifetime. An overall probability of no penetration is calculated, as well as contours of equal threat that take into account spacecraft geometry and orientation. Techniques, tools, and procedures for repairing an impacted and penetrated pressure wall were developed and tested. These techniques are applied from the spacecraft interior and account for the possibility of performing the repair in a vacuum. Hypervelocity impact testing was conducted to: (1) develop and refine appropriate penetration functions, and (2) determine the internal effects of a penetration on personnel and equipment

Space station integrated wall design and penetration damage control

The analysis code BUMPER executes a numerical solution to the problem of calculating the probability of no penetration (PNP) of a spacecraft subject to man-made orbital debris or meteoroid impact. The codes were developed on a DEC VAX 11/780 computer that uses the Virtual Memory System (VMS) operating system, which is written in FORTRAN 77 with no VAX extensions. To help illustrate the steps involved, a single sample analysis is performed. The example used is the space station reference configuration. The finite element model (FEM) of this configuration is relatively complex but demonstrates many BUMPER features. The computer tools and guidelines are described for constructing a FEM for the space station under consideration. The methods used to analyze the sensitivity of PNP to variations in design, are described. Ways are suggested for developing contour plots of the sensitivity study data. Additional BUMPER analysis examples are provided, including FEMs, command inputs, and data outputs. The mathematical theory used as the basis for the code is described, and illustrates the data flow within the analysis

The Role of Interactions in an Electronic Fabry-Perot Interferometer Operating in the Quantum Hall Effect Regime

Interference of edge channels is expected to be a prominent tool for studying statistics of charged quasiparticles in the quantum Hall effect (QHE) [A. Stern (2008), Ann. Phys. 1:204; C. Chamon et al. (1997), Phys. Rev. B, 55:2331]. We present here a detailed study of an electronic Fabry-Perot interferometer (FPI) operating in the QHE regime [C. Chamon et al. (1997), Phys. Rev. B, 55:2331], with the phase of the interfering quasiparticles controlled by the Aharonov-Bohm (AB) effect. Our main finding is that Coulomb interactions among the electrons dominate the interference, even in a relatively large area FPI, leading to a strong dependence of the area enclosed by the interference loop on the magnetic field. In particular, for a composite edge structure, with a few independent edge channels propagating along the edge, interference of the outmost edge channel (belonging to the lowest Landau level) was insensitive to magnetic field; suggesting a constant enclosed flux. However, when any of the inner edge channels interfered, the enclosed flux decreased when the magnetic field increased. By intentionally varying the enclosed area with a biased metallic gate and observing the periodicity of the interference pattern, charges e (for integer filling factors) and e/3 (for a fractional filling factor) were found to be expelled from the FPI. Moreover, these observations provided also a novel way of detecting the charge of the interfering quasiparticles.Comment: 8 pages, 8 figure