Seismic cycles, size of the largest events, and the avalanche size distribution in a model of seismicity

We address several questions on the behavior of a numerical model recently introduced to study seismic phenomena, that includes relaxation in the plates as a key ingredient. We make an analysis of the scaling of the largest events with system size, and show that when parameters are appropriately interpreted, the typical size of the largest events scale as the system size, without the necessity to tune any parameter. Secondly, we show that the temporal activity in the model is inherently non-stationary, and obtain from here justification and support for the concept of a "seismic cycle" in the temporal evolution of seismic activity. Finally, we ask for the reasons that make the model display a realistic value of the decaying exponent $b$ in the Gutenberg-Richter law for the avalanche size distribution. We explain why relaxation induces a systematic increase of $b$ from its value $b\simeq 0.4$ observed in the absence of relaxation. However, we have not been able to justify the actual robustness of the model in displaying a consistent $b$ value around the experimentally observed value $b\simeq 1$.Comment: 11 pages, 10 figure

Non-linear effects on Turing patterns: time oscillations and chaos.

We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space, produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, Turing patterns oscillate in time, a phenomenon which is expected to occur only in a three morphogen system. When varying a single parameter, a series of bifurcations lead to period doubling, quasi-periodic and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examined the Turing conditions for obtaining a diffusion driven instability and discovered that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. All this results demonstrates the limitations of the linear analysis for reaction-diffusion systems

Turing patterns resulting from a Sturm-Liouville problem

Pattern formation in reaction-diffusion systems where the diffusion terms correspond to a Sturm-Liouville problem are studied. These correspond to a problem where the diffusion coefficient depends on the spatial variable: $\nabla \cdot \left( \mathcal{D} ( {\mathbf x} ) \nabla {\mathbf u} \right)$. We found that the conditions for Turing instability are the same as in the case of homogeneous diffusion but the nonlinear analysis must be generalized to consider general orthogonal eigenfunctions instead of the standard Fourier approach. The particular case $\mathcal{D} (x)= 1-x^2$, where solutions are linear combinations of Legendre polynomials, is studied in detail. From the developed general nonlinear analysis, conditions for producing stripes and spots are obtained, which are numerically verified using the Schaneknberg system. Unlike to the case with homogeneous diffusion, and due to the properties of the Legendre polynomials, stripped and spotted patterns with variable wavelength are produced, and a change from stripes to spots is predicted when the wavelength increases. The patterns obtained can model biological systems where stripes or spots accumulate close to the boundaries and the theory developed here can be applied to study Turing patterns associated to other eigenfunctions related with Sturm-Liouville problems.Comment: 15 pages, 4 figure

Ensiling of Tannin-Containing Sorghum Grain

Sorghum is known as important feed-stuff in tropical regions where rainfall is insufficient for the cultivation of maize. Furthermore, those sorghum cultivars rich in tannins are naturally protected to a certain extent against bird damage, insect pests and moulds. Nevertheless, tannins impair the feed quality. Thus, the objectives of this study were to investigate whether ensiling could be a suitable preservation method for sorghum grain originally rich in tannins and if it is possible to reduce tannin content during fermentation

Ram pressure and dusty red galaxies - key factors in the evolution of the multiple cluster system Abell 901/902

We present spectroscopic observations of 182 disk galaxies (96 in the cluster and 86 in the field environment) in the region of the Abell 901/902 multiple cluster system, which is located at a redshift of $z\sim 0.165$. The presence of substructures and non-Gaussian redshift distributions indicate that the cluster system is dynamically young and not in a virialized state. We find evidence for two important galaxy populations. \textit{Morphologically distorted galaxies} are probably subject to increased tidal interactions. They show pronounced rotation curve asymmetries at intermediate cluster-centric radii and low rest-frame peculiar velocities. \textit{Morphologically undistorted galaxies} show the strongest rotation curve asymmetries at high rest-frame velocities and low cluster-centric radii. Supposedly, this group is strongly affected by ram-pressure stripping due to interaction with the intra-cluster medium. Among the morphologically undistorted galaxies, dusty red galaxies have particularly strong rotation curve asymmetries, suggesting ram pressure is an important factor in these galaxies. Furthermore, dusty red galaxies on average have a bulge-to-total ratio higher by a factor of two than cluster blue cloud and field galaxies. The fraction of kinematically distorted galaxies is 75% higher in the cluster than in the field environment. This difference mainly stems from morphological undistorted galaxies, indicating a cluster-specific interaction process that only affects the gas kinematics but not the stellar morphology. Also the ratio between gas and stellar scale length is reduced for cluster galaxies compared to the field sample. Both findings could be best explained by ram-pressure effects.Comment: Electronic version published in Astronomy and Astrophysics Volume 549, Page 0; 19 pages, 21 figure

Tully-Fisher analysis of the multiple cluster system Abell 901/902

We derive rotation curves from optical emission lines of 182 disk galaxies (96 in the cluster and 86 in the field) in the region of Abell 901/902 located at $z\sim 0.165$. We focus on the analysis of B-band and stellar-mass Tully-Fisher relations. We examine possible environmental dependencies and differences between normal spirals and "dusty red" galaxies, i.e. disk galaxies that have red colors due to relatively low star formation rates. We find no significant differences between the best-fit TF slope of cluster and field galaxies. At fixed slope, the field population with high-quality rotation curves (57 objects) is brighter by \Delta M_{B}=-0\fm42\pm0\fm15 than the cluster population (55 objects). We show that this slight difference is at least in part an environmental effect. The scatter of the cluster TFR increases for galaxies closer to the core region, also indicating an environmental effect. Interestingly, dusty red galaxies become fainter towards the core at given rotation velocity (i.e. total mass). This indicates that the star formation in these galaxies is in the process of being quenched. The luminosities of normal spiral galaxies are slightly higher at fixed rotation velocity for smaller cluster-centric radii. Probably these galaxies are gas-rich (compared to the dusty red population) and the onset of ram-pressure stripping increases their star-formation rates. The results from the TF analysis are consistent with and complement our previous findings. Dusty red galaxies might be an intermediate stage in the transformation of infalling field spiral galaxies into cluster S0s, and this might explain the well-known increase of the S0 fraction in galaxy clusters with cosmic time.Comment: Accepted for publication in Astronomy and Astrophysics; 16 pages, 14 figure