Mean flow instabilities of two-dimensional convection in strong magnetic fields

The interaction of magnetic fields with convection is of great importance in astrophysics. Two well-known aspects of the interaction are the tendency of convection cells to become narrow in the perpendicular direction when the imposed field is strong, and the occurrence of streaming instabilities involving horizontal shears. Previous studies have found that the latter instability mechanism operates only when the cells are narrow, and so we investigate the occurrence of the streaming instability for large imposed fields, when the cells are naturally narrow near onset. The basic cellular solution can be treated in the asymptotic limit as a nonlinear eigenvalue problem. In the limit of large imposed field, the instability occurs for asymptotically small Prandtl number. The determination of the stability boundary turns out to be surprisingly complicated. At leading order, the linear stability problem is the linearisation of the same nonlinear eigenvalue problem, and as a result, it is necessary to go to higher order to obtain a stability criterion. We establish that the flow can only be unstable to a horizontal mean flow if the Prandtl number is smaller than order , where B0 is the imposed magnetic field, and that the mean flow is concentrated in a horizontal jet of width in the middle of the layer. The result applies to stress-free or no-slip boundary conditions at the top and bottom of the layer

Patterns of convection in rotating spherical shells

Patterns of convection in internally heated, self-gravitating rotating spherical fluid shells are investigated through numerical simulations. While turbulent states are of primary interest in planetary and stellar applications the present paper emphasizes more regular dynamical features at Rayleigh numbers not far above threshold which are similar to those which might be observed in laboratory or space experiments. Amplitude vacillations and spatial modulations of convection columns are common features at moderate and large Prandtl numbers. In the low Prandtl number regime equatorially attached convection evolves differently with increasing Rayleigh number and exhibits an early transition into a chaotic state. Relationships of the dynamical features to coherent structures in fully turbulent convection states are emphasized

Haemoglobin and size dependent constraints on swimbladder inflation in fish larvae

In developmental studies of fish species (especially physostomians) it could be demonstrated, that the lack of haemoglobin during larval and juvenile stages is a relatively common phenomenon. Generally it is linked with body translucency. In representatives of the families Galaxiidae, Osmeridae and Clupeidae, partly reared, partly observed immediately after being caught in the wild, it turned out, that this condition coincides with a considerable delay in swimbladder inflation. To determine the moment of its first inflation, larvae placed in a hermetic chamber were observed under a dissecting microscope. While lowering the pressure, the expanding swimbladder showed whether or not its content is really gaseous. The reason postulated to be responsible for the delayed inflation is that larvae lacking haemoglobin do not have the possibility of oxygen transport to their buoyancy organ by means of the blood. Apart of this, capillarity force calculations and body force estimations show that with decreasing size the constraints linked with surface tension increase overproportionally. While in larger sized larvae like trout we could demonstrate inflation by swallowing air, in species with small larvae this was not the case. Below a certain size, even in physostomians, the ductus pneumaticus is no alternative to the blood pathway for swimbladder inflation

Detection of fixed points in spatiotemporal signals by clustering method

We present a method to determine fixed points in spatiotemporal signals. A 144-dimensioanl simulated signal, similar to a Kueppers-Lortz instability, is analyzed and its fixed points are reconstructed.Comment: 3 pages, 3 figure

Of gene expression and cell division time: a mathematical framework for advanced differential gene expression and data analysis

Estimating fold changes of average mRNA and protein molecule counts per cell is the most common way to perform differential expression analysis. However, these gene expression data may be affected by cell division, an often-neglected phenomenon. Here, we develop a quantitative framework that links population-based mRNA and protein measurements to rates of gene expression in single cells undergoing cell division. The equations we derive are easy-to-use and widely robust against biological variability. They integrate multiple "omics" data into a coherent, quantitative description of single-cell gene expression and improve analysis when comparing systems or states with different cell division times. We explore these ideas in the context of resting versus activated B cells. Analyzing differences in protein synthesis rates enables to account for differences in cell division times. We demonstrate that this improves the resolution and hit rate of differential gene expression analysis when compared to analyzing population protein abundances alone

Hysteresis phenomenon in turbulent convection

Coherent large-scale circulations of turbulent thermal convection in air have been studied experimentally in a rectangular box heated from below and cooled from above using Particle Image Velocimetry. The hysteresis phenomenon in turbulent convection was found by varying the temperature difference between the bottom and the top walls of the chamber (the Rayleigh number was changed within the range of $10^7 - 10^8$). The hysteresis loop comprises the one-cell and two-cells flow patterns while the aspect ratio is kept constant ($A=2 - 2.23$). We found that the change of the sign of the degree of the anisotropy of turbulence was accompanied by the change of the flow pattern. The developed theory of coherent structures in turbulent convection (Elperin et al. 2002; 2005) is in agreement with the experimental observations. The observed coherent structures are superimposed on a small-scale turbulent convection. The redistribution of the turbulent heat flux plays a crucial role in the formation of coherent large-scale circulations in turbulent convection.Comment: 10 pages, 9 figures, REVTEX4, Experiments in Fluids, 2006, in pres

Localized transverse bursts in inclined layer convection

We investigate a novel bursting state in inclined layer thermal convection in which convection rolls exhibit intermittent, localized, transverse bursts. With increasing temperature difference, the bursts increase in duration and number while exhibiting a characteristic wavenumber, magnitude, and size. We propose a mechanism which describes the duration of the observed bursting intervals and compare our results to bursting processes in other systems.Comment: 4 pages, 8 figure

Generation and Structure of Solitary Rossby Vortices in Rotating Fluids

The formation of zonal flows and vortices in the generalized Charney-Hasegawa-Mima equation is studied. We focus on the regime when the size of structures is comparable to or larger than the deformation (Rossby) radius. Numerical simulations show the formation of anticyclonic vortices in unstable shear flows and ring-like vortices with quiescent cores and vorticity concentrated in a ring. Physical mechanisms that lead to these phenomena and their relevance to turbulence in planetary atmospheres are discussed.Comment: 3 pages in REVTeX, 5 postscript figures separately, submitted to Phys. Rev.