Reactive dynamics on fractal sets: anomalous fluctuations and memory effects

We study the effect of fractal initial conditions in closed reactive systems in the cases of both mobile and immobile reactants. For the reaction $A+A\to A$, in the absence of diffusion, the mean number of particles $A$ is shown to decay exponentially to a steady state which depends on the details of the initial conditions. The nature of this dependence is demonstrated both analytically and numerically. In contrast, when diffusion is incorporated, it is shown that the mean number of particles $$ decays asymptotically as $t^{-d_f/2}$, the memory of the initial conditions being now carried by the dynamical power law exponent. The latter is fully determined by the fractal dimension $d_f$ of the initial conditions.Comment: 7 pages, 2 figures, uses epl.cl

Diversity-induced resonance

We present conclusive evidence showing that different sources of diversity, such as those represented by quenched disorder or noise, can induce a resonant collective behavior in an ensemble of coupled bistable or excitable systems. Our analytical and numerical results show that when such systems are subjected to an external subthreshold signal, their response is optimized for an intermediate value of the diversity. These findings show that intrinsic diversity might have a constructive role and suggest that natural systems might profit from their diversity in order to optimize the response to an external stimulus.Comment: 4 pages, 3 figure

Lifting of Ir{100} reconstruction by CO adsorption: An ab initio study

The adsorption of CO on unreconstructed and reconstructed Ir{100} has been studied, using a combination of density functional theory and thermodynamics, to determine the relative stability of the two phases as a function of CO coverage, temperature and pressure. We obtain good agreement with experimentaldata. At zero temperature, the (1X5) reconstruction becomes less stable than the unreconstructed (1X1) surface when the CO coverage exceeds a critical value of 0.09 ML. The interaction between CO molecules is found to be repulsive on the reconstructed surface, but attractive on the unreconstructed, explaining the experimental observation of high CO coverage on growing (1X1) islands. At all temperatures and pressures, we find only two possible stable states: 0.05 ML CO c(2X2) overlayer on the (1X1) substrate, and the clean (1$\times$5) reconstructed surface.Comment: 31 page

Probabilistic and thermodynamic aspects of dynamical systems

The probabilistic approach to dynamical systems giving rise to irreversible behavior at the macroscopic, mesoscopic, and microscopic levels of description is outlined. Signatures of the complexity of the underlying dynamics on the spectral properties of the Liouville, Frobenius-Perron, and Fokker-Planck operators are identified. Entropy and entropy production-like quantities are introduced and the connection between their properties in nonequilibrium steady states and the characteristics of the dynamics in phase space are explored.info:eu-repo/semantics/publishe

Comparison of Entropy Production Rates in Two Different Types of Self-organized Flows: B\'{e}nard Convection and Zonal flow

Entropy production rate (EPR) is often effective to describe how a structure is self-organized in a nonequilibrium thermodynamic system. The "minimum EPR principle" is widely applicable to characterizing self-organized structures, but is sometimes disproved by observations of "maximum EPR states." Here we delineate a dual relation between the minimum and maximum principles; the mathematical representation of the duality is given by a Legendre transformation. For explicit formulation, we consider heat transport in the boundary layer of fusion plasma [Phys. Plasmas {\bf 15}, 032307 (2008)]. The mechanism of bifurcation and hysteresis (which are the determining characteristics of the so-called H-mode, a self-organized state of reduced thermal conduction) is explained by multiple tangent lines to a pleated graph of an appropriate thermodynamic potential. In the nonlinear regime, we have to generalize Onsager's dissipation function. The generalized function is no longer equivalent to EPR; then EPR ceases to be the determinant of the operating point, and may take either minimum or maximum values depending on how the system is driven

Nonequilibrium stochastic processes: Time dependence of entropy flux and entropy production

Based on the Fokker-Planck and the entropy balance equations we have studied the relaxation of a dissipative dynamical system driven by external Ornstein-Uhlenbeck noise processes in absence and presence of nonequilibrium constraint in terms of the thermodynamically inspired quantities like entropy flux and entropy production. The interplay of nonequilibrium constraint, dissipation and noise reveals some interesting extremal nature in the time dependence of entropy flux and entropy production.Comment: RevTex, 17 pages, 9 figures. To appear in Phys. Rev.

Ratio control in a cascade model of cell differentiation

We propose a kind of reaction-diffusion equations for cell differentiation, which exhibits the Turing instability. If the diffusivity of some variables is set to be infinity, we get coupled competitive reaction-diffusion equations with a global feedback term. The size ratio of each cell type is controlled by a system parameter in the model. Finally, we extend the model to a cascade model of cell differentiation. A hierarchical spatial structure appears as a result of the cell differentiation. The size ratio of each cell type is also controlled by the system parameter.Comment: 13 pages, 7 figure

Secular increase of the Astronomical Unit and perihelion precessions as tests of the Dvali-Gabadadze-Porrati multi-dimensional braneworld scenario

An unexpected secular increase of the Astronomical Unit, the length scale of the Solar System, has recently been reported by three different research groups (Krasinsky and Brumberg, Pitjeva, Standish). The latest JPL measurements amount to 7+-2 m cy^-1. At present, there are no explanations able to accommodate such an observed phenomenon, neither in the realm of classical physics nor in the usual four-dimensional framework of the Einsteinian General Relativity. The Dvali-Gabadadze-Porrati braneworld scenario, which is a multi-dimensional model of gravity aimed to the explanation of the observed cosmic acceleration without dark energy, predicts, among other things, a perihelion secular shift, due to Lue and Starkman, of 5 10^-4 arcsec cy^-1 for all the planets of the Solar System. It yields a variation of about 6 m cy^-1 for the Earth-Sun distance which is compatible at 1-sigma level with the observed rate of the Astronomical Unit. The recently measured corrections to the secular motions of the perihelia of the inner planets of the Solar System are in agreement, at 1-sigma level, with the predicted value of the Lue-Starkman effect for Mercury and Mars and at 2-sigma level for the Earth.Comment: LaTex2e, 7 pages, no figures, no tables, 13 references. Minor correction