Glassy states in the stochastic Potts model

We have studied by numerical simulations the relaxation of the stochastic seven-state Potts model after a quench from a high temperature down to a temperature below the first-order transition. For quench temperatures just below the transition temperature the phase ordering occurs by simple coarsening under the action of surface tension. For sufficient low temperatures however the straightening of the interface between domains drives the system toward a metastable disordered state, identified as a glassy state. Escaping from this state occurs, if the quench temperature is nonzero, by a thermal activated dynamics that eventually drives the system toward the equilibrium state. (C) 2009 Elsevier B.V. All rights reserved.

The stochastic nature of predator-prey cycles

We study by numerical simulations the time correlation function of a stochastic lattice model describing the dynamics of coexistence of two interacting biological species that present time cycles in the number of species individuals. Its asymptotic behavior is shown to decrease in time as a sinusoidal exponential function from which we extract the dominant eigenvalue of the evolution operator related to the stochastic dynamics showing that it is complex with the imaginary part being the frequency of the population cycles. The transition from the oscillatory to the nonoscillatory behavior occurs when the asymptotic behavior of the time correlation function becomes a pure exponential, that is, when the real part of the complex eigenvalue equals a real eigenvalue. We also show that the amplitude of the undamped oscillations increases with the square root of the area of the habitat as ordinary random fluctuations. (C) 2009 Elsevier B.V. All rights reserved.

Mean Motion in Stochastic Plasmas With a Space-Dependent Diffusion Coefficient

Radial transport in the tokamap, which has been proposed as a simple model for the motion in a stochastic plasma, is investigated. A theory for previous numerical findings is presented. The new results are stimulated by the fact that the radial diffusion coefficients is space-dependent. The space-dependence of the transport coefficient has several interesting effects which have not been elucidated so far. Among the new findings are the analytical predictions for the scaling of the mean radial displacement with time and the relation between the Fokker-Planck diffusion coefficient and the diffusion coefficient from the mean square displacement. The applicability to other systems is also discussed. (c) 2009 WILEY-VCH GmbH & Co. KGaA, Weinheim

Pseudo-nonlinear and athermal lensing effects on transverse properties of Cr(3+) based solid-state lasers

Several experiments (time-resolved Z-scan experiments based on pulsed and CW pump lasers, time-resolved divergence diagnostics) have been performed to examine and clarify the question of the converging or diverging population lensing effect occurring in a Cr(3+):Al(2)O(3) ruby laser. The dynamics of the laser far-field divergence of such a laser indeed indicated initially a diverging effect while Z-scan measurements conclude to a converging one. The origin of this discrepancy is thus analysed and elucidated here by introducing the general concept of correlation collapse between the centre and the wings of a laser beam having some clipping. (C) 2010 Elsevier B.V. All rights reserved.

Conflicting structural and geochronological data from the Ibituruna quartz-syenite (SE Brazil): Effect of protracted ""hot"" orogeny and slow cooling rate?

The Ibituruna quartz-syenite was emplaced as a sill in the Ribeira-Aracuai Neoproterozoic belt (Southeastern Brazil) during the last stages of the Gondwana supercontinent amalgamation. We have measured the Anisotropy of Magnetic Susceptibility (AMS) in samples from the Ibituruna sill to unravel its magnetic fabric that is regarded as a proxy for its magmatic fabric. A large magnetic anisotropy, dominantly due to magnetite, and a consistent magnetic fabric have been determined over the entire Ibituruna massif. The magmatic foliation and lineation are strikingly parallel to the solid-state mylonitic foliation and lineation measured in the country-rock. Altogether, these observations suggest that the Ibituruna sill was emplaced during the high temperature (similar to 750 degrees C) regional deformation and was deformed before full solidification coherently with its country-rock. Unexpectedly, geochronological data suggest a rather different conclusion. LA-ICP-MS and SHRIMP ages of zircons from the Ibituruna quartz-syenite are in the range 530-535 Ma and LA-ICP-MS ages of zircons and monazites from synkinematic leucocratic veins in the country-rocks suggest a crystallization at similar to 570-580 Ma, i.e., an HT deformation >35My older than the emplacement of the Ibituruna quartz-syenite. Conclusions from the structural and the geochronological studies are therefore conflicting. A possible explanation arises from (40)Ar-(39)Ar thermochronology. We have dated amphiboles from the quartz-syenite, and amphiboles and biotites from the country-rock. Together with the ages of monazites and zircons in the country-rock, (40)Ar-(39)Ar mineral ages suggest a very low cooling rate: <3 degrees C/My between 570 and similar to 500 Ma and similar to 5 degrees C/My between 500 and 460 Ma. Assuming a protracted regional deformation consistent over tens of My, under such stable thermal conditions the fabric and microstructure of deformed rocks may remain almost unchanged even if they underwent and recorded strain pulses separated by long periods of time. This may be a characteristic of slow cooling ""hot orogens"" that rocks deformed at significantly different periods during the orogeny, but under roughly unchanged temperature conditions, may display almost indiscernible microstructure and fabric. (C) 2009 Elsevier B.V. All rights reserved.

Columnar joints in the Patino Formation sandstones, Eastern Paraguay: a dynamic interaction between dyke intrusion, quartz dissolution and cooling-induced fractures

The Patino Formation sandstones, which crop out in Aregua neighborhood in Eastern Paraguay and show columnar joints near the contact zone with a nephelinite dyke, have as their main characteristics the high proportion of syntaxial quartz overgrowth and a porosity originated from different processes, initially by dissolution and later by partial filling and fracturing. Features like the presence of floating grains in the syntaxial cement, the transitional interpenetrative contact between the silica-rich cement and grains as well as the intense fracture porosity are strong indications that the cement has been formed by dissolution and reprecipitation of quartz from the framework under the effect of thermal expansion followed by rapid contraction. The increase of the silica-rich cement towards the dyke in association with the orthogonal disposition of the columns relative to dyke walls are indicative that the igneous body may represent the main heat source for the interstitial aqueous solutions previously existing in the sediments. At macroscopic scale, the increasing of internal tensions in the sandstones is responsible for the nucleation of polygons, leading to the individualization of prisms, which are interconnected by a system of joints, formed firstly on isotherm surfaces of low temperature and later on successive adjacent planes towards the dyke heat source.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Symmetry in biology: from genetic code to stochastic gene regulation

Mathematical models, as instruments for understanding the workings of nature, are a traditional tool of physics, but they also play an ever increasing role in biology - in the description of fundamental processes as well as that of complex systems. In this review, the authors discuss two examples of the application of group theoretical methods, which constitute the mathematical discipline for a quantitative description of the idea of symmetry, to genetics. The first one appears, in the form of a pseudo-orthogonal (Lorentz like) symmetry, in the stochastic modelling of what may be regarded as the simplest possible example of a genetic network and, hopefully, a building block for more complicated ones: a single self-interacting or externally regulated gene with only two possible states: ` on` and ` off`. The second is the algebraic approach to the evolution of the genetic code, according to which the current code results from a dynamical symmetry breaking process, starting out from an initial state of complete symmetry and ending in the presently observed final state of low symmetry. In both cases, symmetry plays a decisive role: in the first, it is a characteristic feature of the dynamics of the gene switch and its decay to equilibrium, whereas in the second, it provides the guidelines for the evolution of the coding rules.