Aggregation of chemotactic organisms in a differential flow

We study the effect of advection on the aggregation and pattern formation in chemotactic systems described by Keller-Segel type models. The evolution of small perturbations is studied analytically in the linear regime complemented by numerical simulations. We show that a uniform differential flow can significantly alter the spatial structure and dynamics of the chemotactic system. The flow leads to the formation of anisotropic aggregates that move following the direction of the flow, even when the chemotactic organisms are not directly advected by the flow. Sufficiently strong advection can stop the aggregation and coarsening process that is then restricted to the direction perpendicular to the flow

From brain to earth and climate systems: Small-world interaction networks or not?

We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With numerical simulations that mimic typical experimental situations we have identified an important constraint when characterizing such networks: indications of a small-world topology can be expected solely due to the spatial sampling of the system along with commonly used time series analysis based approaches to network characterization

Buchbesprechungen

Besprochen werden die beiden folgenden Werke: (1) Handbuch der Bodenkunde - Grundwerk. Von H. P. Blume , P. Felix-Henningsen, W.R. Fischer, H.-G. Frede, R. Horn u. K. Stahr. (2) Thienemann, Johannes: Rossitten - drei Jahrzehnte auf der Kurischen Nehrung. Reprint der Ausgabe Melsungen, Neumann-Neudamm von 1930 (3.Aufl.)

Absolute instabilities of travelling wave solutions in a Keller-Segel model

We investigate the spectral stability of travelling wave solutions in a Keller-Segel model of bacterial chemotaxis with a logarithmic chemosensitivity function and a constant, sublinear, and linear consumption rate. Linearising around the travelling wave solutions, we locate the essential and absolute spectrum of the associated linear operators and find that all travelling wave solutions have essential spectrum in the right half plane. However, we show that in the case of constant or sublinear consumption there exists a range of parameters such that the absolute spectrum is contained in the open left half plane and the essential spectrum can thus be weighted into the open left half plane. For the constant and sublinear consumption rate models we also determine critical parameter values for which the absolute spectrum crosses into the right half plane, indicating the onset of an absolute instability of the travelling wave solution. We observe that this crossing always occurs off of the real axis

Hawking Radiation on an Ion Ring in the Quantum Regime

This paper discusses a recent proposal for the simulation of acoustic black holes with ions. The ions are rotating on a ring with an inhomogeneous, but stationary velocity profile. Phonons cannot leave a region, in which the ion velocity exceeds the group velocity of the phonons, as light cannot escape from a black hole. The system is described by a discrete field theory with a nonlinear dispersion relation. Hawking radiation is emitted by this acoustic black hole, generating entanglement between the inside and the outside of the black hole. We study schemes to detect the Hawking effect in this setup.Comment: 42 pages (one column), 17 figures, published revised versio

The one-dimensional Keller-Segel model with fractional diffusion of cells

We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent $0<\alpha\leq 2$. We prove some features related to the classical two-dimensional Keller-Segel system: blow-up may or may not occur depending on the initial data. More precisely a singularity appears in finite time when $\alpha<1$ and the initial configuration of cells is sufficiently concentrated. On the opposite, global existence holds true for $\alpha\leq1$ if the initial density is small enough in the sense of the $L^{1/\alpha}$ norm.Comment: 12 page

Geometric gradient-flow dynamics with singular solutions

The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcy's Law. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification of fluid mechanics. Eulerian equations for self-organization of scalars, 1-forms and 2-forms are shown to reduce to nonlocal characteristic equations. We identify singular solutions of these equations corresponding to collapsed (clumped) states and discuss their evolution.Comment: 28 pages, 1 figure, to appear on Physica

A carbonate-banded iron formation transition in the Early Protorezoicum of South Africa

Seven new and two resurveyed stratigraphic sections through the important carbonate-BIF transition in Griqualand West are presented and compared with six published sections. Lateral correlation within this zone is attempted but the variability was found to be too great for meaningful subdivision. Substantial lithological irregularity is the only unifying character of this zone, for which the new name Finsch Member (Formation) is proposed. Vertical and lateral lithological variations as well as chemical changes across this zone are discussed with reference to environmental aspects. Local and regional considerations lead to the conclusion that fresh water-sea water mixing occurred in a shallowing basin

Critical dynamics of self-gravitating Langevin particles and bacterial populations

We study the critical dynamics of the generalized Smoluchowski-Poisson system (for self-gravitating Langevin particles) or generalized Keller-Segel model (for the chemotaxis of bacterial populations). These models [Chavanis & Sire, PRE, 69, 016116 (2004)] are based on generalized stochastic processes leading to the Tsallis statistics. The equilibrium states correspond to polytropic configurations with index $n$ similar to polytropic stars in astrophysics. At the critical index $n_{3}=d/(d-2)$ (where $d\ge 2$ is the dimension of space), there exists a critical temperature $\Theta_{c}$ (for a given mass) or a critical mass $M_{c}$ (for a given temperature). For $\Theta>\Theta_{c}$ or $M<M_{c}$ the system tends to an incomplete polytrope confined by the box (in a bounded domain) or evaporates (in an unbounded domain). For $\Theta<\Theta_{c}$ or $M>M_{c}$ the system collapses and forms, in a finite time, a Dirac peak containing a finite fraction $M_c$ of the total mass surrounded by a halo. This study extends the critical dynamics of the ordinary Smoluchowski-Poisson system and Keller-Segel model in $d=2$ corresponding to isothermal configurations with $n_{3}\to +\infty$. We also stress the analogy between the limiting mass of white dwarf stars (Chandrasekhar's limit) and the critical mass of bacterial populations in the generalized Keller-Segel model of chemotaxis

The ZEUS Forward Plug Calorimeter with Lead-Scintillator Plates and WLS Fiber Readout

A Forward Plug Calorimeter (FPC) for the ZEUS detector at HERA has been built as a shashlik lead-scintillator calorimeter with wave length shifter fiber readout. Before installation it was tested and calibrated using the X5 test beam facility of the SPS accelerator at CERN. Electron, muon and pion beams in the momentum range of 10 to 100 GeV/c were used. Results of these measurements are presented as well as a calibration monitoring system based on a $^{60}$Co source.Comment: 38 pages (Latex); 26 figures (ps