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

How to generate pentagonal symmetry using Turing systems

We explore numerically the formation of Turing patterns in a confined circular domain with small aspect ratio. Our results show that stable fivefold patterns are formed over a well defined range of disk sizes, offering a possible mechanism for inducing the fivefold symmetry observed in early development of regular echinoids. Using this pattern as a seed, more complex biological structures can be mimicked, such as the pigmentation pattern of sea urchins and the plate arrangements of the calyxes of primitive camerate crinoids

Conformal mapping of ultrasonic crystals: confining ultrasound and cochlear-like wave guiding

Conformal mapping of a slab of a two-dimensional ultrasonic crystal generate a closed geometrical arrangement of ultrasonic scatterers with appealing acoustic properties. This acoustic shell is able to confine ultrasonic modes. Some of these internal resonances can be induced from an external wave source. The mapping of a linear defect produces a wave-guide that exhibits a spatial-frequency selection analogous to that characteristic of a synthetic "cochlea". Both, experimental and theoretical results are reported here.Comment: 4 pages, 4 figure

A 3D geological model of Campo de Cartagena, SE Spain : Hydrogeological implications

Knowledge and understanding of geologic basins for hydrogeologic purposes requires an accurate 3D geological architecture representation. For model building, surface and subsurface data integration with the interpretation of geophysical survey and lithologic logs is needed. A methodology to reconstruct the geometric architecture of the sedimentary basin and relationships among stratigraphic formations, as well as to define hydrostratigraphic units, has been applied to the Campo de Cartagena Neogene formations. Data analysis included seismic reflection profiles and gravimetric data from oil exploration, electric resistivity surveys and 491 lithologic logs. The 3D model obtained from a close integration of stratigraphic and geophysical data was generated through a computerbased tool. It presents a common framework and a good starting point for hydrogeologic applications

Brillouin scattering studies in Fe3_3O4_4 across the Verwey transition

Brillouin scattering studies have been carried out on high quality single crystals of Fe$_3$O$_4$ with [100] and [110] faces in the temperature range of 300 to 30 K. The room temperature spectrum shows a surface Rayleigh wave (SRW) mode at 8 GHz and a longitudinal acoustic (LA) mode at 60 GHz. The SRW mode frequency shows a minimum at the Verwey transition temperature $T_V$ of 123 K. The softening of the SRW mode frequency from about 250 K to $T_V$ can be quantitatively understood as a result of a decrease in the shear elastic constant C$_{44}$, arising from the coupling of shear strain to charge fluctuations. On the other hand, the LA mode frequency does not show any significant change around $T_V$, but shows a large change in its intensity. The latter shows a maximum at around 120 K in the cooling run and at 165 K in the heating run, exhibiting a large hysteresis of 45 K. This significant change in intensity may be related to the presence of stress-induced ordering of Fe$^{3+}$ and Fe$^{2+}$ at the octahedral sites, as well as to stress-induced domain wall motion.Comment: 14 pages, 3 figures, accepted in Physical Review B 200