Percolation transition in quantum Ising and rotor models with sub-Ohmic dissipation

We investigate the influence of sub-Ohmic dissipation on randomly diluted quantum Ising and rotor models. The dissipation causes the quantum dynamics of sufficiently large percolation clusters to freeze completely. As a result, the zero-temperature quantum phase transition across the lattice percolation threshold separates an unusual super-paramagnetic cluster phase from an inhomogeneous ferromagnetic phase. We determine the low-temperature thermodynamic behavior in both phases, which is dominated by large frozen and slowly fluctuating percolation clusters. We relate our results to the smeared transition scenario for disordered quantum phase transitions, and we compare the cases of sub-Ohmic, Ohmic, and super-Ohmic dissipation.

Influence of the initial condition in equilibrium last-passage percolation models

In this paper we consider an equilibrium last-passage percolation model on an environment given by a compound two-dimensional Poisson process. We prove an L-2-formula relating the initial measure with the last-passage percolation time. This formula turns out to be a useful tool to analyze the fluctuations of the last-passage times along non-characteristic directions.

Burrow ventilation and associated porewater irrigation by the polychaete Marenzelleria viridis

Burrow ventilation of benthic infauna generates water currents that irrigate the interstices of the sediments surrounding the burrow walls. Such activities have associated effects on biogeochemical processes affecting ultimately important ecosystem processes. In this study, the ventilation and irrigation behavior of Marenzelleria viridis, an invasive polychaete species in Europe, was analyzed using different approaches. M. viridis showed to perform two types of ventilation: (1) muscular pumping of water out of the burrow and (2) cilia pumping of water into the burrow. Flowmeter measurements presented muscular pumping in time averaged rates of 0.15 ml min(-1). Oxygen needle electrodes positioned above the burrow openings revealed that muscular undulation of the worm body pumps anoxic water out of the burrow. On the other hand, microscope observations of the animal showed that ventilation of oxygen-rich water in the burrow occurs by ciliary action. The volume of water irrigated by M. viridis appears to vary linearly within the first 24 h incubation, with rates ranging from 0.003 to 0.01 ml min(-1). From those rates we could estimate that the time averaged rate of cilia ventilation should be about 0.16 ml min(-1). Since the cilia pumping into the burrow occurs in periods of 24 +/- 12 min and at 50-70% of the measured time, considerable amounts of water from deeper sediments may percolate upwards to the sediment surface. This water is rich in reduced compounds and nutrients and may have important associated ecological implications in the ecosystem (e.g. affecting redox conditions, organic matter degradation, benthic recruitment and primary production). (C) 2010 Elsevier B.V. All rights reserved.

Percolated non-Newtonian flow for silicone obtained from exfoliated bioinorganic layered double hydroxide intercalated with amino acid

A simple and scalable procedure was used to obtain thin, stable, homogeneous, and easy-to-handle films composed of silicone derived from dimethicones containing dispersed hydrotalcite-type materials previously organo-modified with amino acids. The absence of the typical X-ray pattern of the bioinorganic LDH filler suggested an exfoliation process that was further indirectly evidenced by a drastic change in the rheological behavior, which turned from a quasi-Newtonian behavior for the silicone free of LDH filler to an extensive developed gel-like structure for the nanocomposite derivatives. Visualized by the shear-thinning exponent of the complex viscosity in the low-frequency range, the percolation threshold was evident for filler loading as low as <5 w/W%, suggesting the presence of a largely developed interface between the filler and the polymer. The increase of more than one order of magnitude in viscosity was explained by the rather strong attrition phenomenon between the tethered amino acid anions and the silicone chains. UVB radiation absorption profiles make such bioinorganic polymer nanocomposites potentially applicable in skin protection. Thermo-gravimetric analysis revealed significant improvement in the thermal stability, especially in the final step of the polymer combustion, thus underlining the role of the hybrid material as a thermal retardant agent. (C) 2011 Elsevier B.V. All rights reserved.

On the electrical conductivity of Ti-implanted alumina

Ion implantation of metal species into insulators provides a tool for the formation of thin, electrically conducting, surface layers with experimenter-controlled resistivity. High energy implantation of Pt and Ti into alumina accelerator components has been successfully employed to control high voltage surface breakdown in a number of cases. In the work described here we have carried out some basic investigations related to the origin of this phenomenon. By comparison of the results of alumina implanted with Ti at 75 keV with the results of prior investigations of polymers implanted with Pt at 49 eV and Au at 67 eV, we describe a physical model of the effect based on percolation theory and estimate the percolation parameters for the Ti-alumina composite. We estimate that the percolation dose threshold is about 4 x 10(16) cm(-2) and the maximum dose for which the system remains an insulator-conductor composite is about 10 x 10(16) cm(-2). The saturation electrical conductivity is estimated to be about 50 S/m. We conclude that the observed electrical conductivity properties of Ti-implanted alumina can be satisfactorily described by percolation theory. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3697900]

Two versions of the threshold contact model in two dimensions

Two versions of the threshold contact process ordinary and conservative - are studied on a square lattice. In the first, particles are created on active sites, those having at least two nearest neighbor sites occupied, and are annihilated spontaneously. In the conservative version, a particle jumps from its site to an active site. Mean-field analysis suggests the existence of a first-order phase transition, which is confirmed by Monte Carlo simulations. In the thermodynamic limit, the two versions are found to give the same results. (C) 2012 Elsevier B.V. All rights reserved.

Harmonic deformation of Delaunay triangulations

We construct harmonic functions on random graphs given by Delaunay triangulations of ergodic point processes as the limit of the zero-temperature harness process. (C) 2012 Elsevier B.V All rights reserved.

A spatial stochastic model for rumor transmission

We consider an interacting particle system representing the spread of a rumor by agents on the d-dimensional integer lattice. Each agent may be in any of the three states belonging to the set {0,1,2}. Here 0 stands for ignorants, 1 for spreaders and 2 for stiflers. A spreader tells the rumor to any of its (nearest) ignorant neighbors at rate lambda. At rate alpha a spreader becomes a stifler due to the action of other (nearest neighbor) spreaders. Finally, spreaders and stiflers forget the rumor at rate one. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.

Subcritical fatigue in fuse networks

We obtain the Paris law of fatigue crack propagation in a fuse network model where the accumulated damage in each resistor increases with time as a power law of the local current amplitude. When a resistor reaches its fatigue threshold, it burns irreversibly. Over time, this drives cracks to grow until the system is fractured into two parts. We study the relation between the macroscopic exponent of the crack-growth rate -entering the phenomenological Paris law-and the microscopic damage accumulation exponent, gamma, under the influence of disorder. The way the jumps of the growing crack, Delta a, and the waiting time between successive breaks, Delta t, depend on the type of material, via gamma, are also investigated. We find that the averages of these quantities, <Delta a > and <Delta t >/< t(r)>, scale as power laws of the crack length a, <Delta a > proportional to a(alpha) and <Delta t >/< t(r)> proportional to a(-beta), where < t(r)> is the average rupture time. Strikingly, our results show, for small values of gamma, a decrease in the exponent of the Paris law in comparison with the homogeneous case, leading to an increase in the lifetime of breaking materials. For the particular case of gamma = 0, when fatigue is exclusively ruled by disorder, an analytical treatment confirms the results obtained by simulation. Copyright (C) EPLA, 2012

Mean-Field critical behavior and ergodicity break in a nonequilibrium one-dimensional RSOS growth model

We investigate the nonequilibrium roughening transition of a one-dimensional restricted solid-on-solid model by directly sampling the stationary probability density of a suitable order parameter as the surface adsorption rate varies. The shapes of the probability density histograms suggest a typical Ginzburg-Landau scenario for the phase transition of the model, and estimates of the "magnetic" exponent seem to confirm its mean-field critical behavior. We also found that the flipping times between the metastable phases of the model scale exponentially with the system size, signaling the breaking of ergodicity in the thermodynamic limit. Incidentally, we discovered that a closely related model not considered before also displays a phase transition with the same critical behavior as the original model. Our results support the usefulness of off-critical histogram techniques in the investigation of nonequilibrium phase transitions. We also briefly discuss in the appendix a good and simple pseudo-random number generator used in our simulations.

Prominent Effect of Soil Network Heterogeneity on Microbial Invasion

Using a network representation for real soil samples and mathematical models for microbial spread, we show that the structural heterogeneity of the soil habitat may have a very significant influence on the size of microbial invasions of the soil pore space. In particular, neglecting the soil structural heterogeneity may lead to a substantial underestimation of microbial invasion. Such effects are explained in terms of a crucial interplay between heterogeneity in microbial spread and heterogeneity in the topology of soil networks. The main influence of network topology on invasion is linked to the existence of long channels in soil networks that may act as bridges for transmission of microorganisms between distant parts of soil.

Phase Transition for the Ising Model on the Critical Lorentzian Triangulation

The ferromagnetic Ising model without external field on an infinite Lorentzian triangulation sampled from the uniform distribution is considered. We prove uniqueness of the Gibbs measure in the high temperature region and coexistence of at least two Gibbs measures at low temperature. The proofs are based on the disagreement percolation method and on a variant of the Peierls contour method. The critical temperature is shown to be constant a.s.

On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, da parts per thousand yen1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.

Linking origin of the electric field-assisted beta-PbF2 crystallization in lead oxyfluoroborate glasses below T (g) to simultaneous cathode/anode-compensated electrochemical reactions

Full validation of the electrochemical mechanisms so far postulated as driving force of electric field-assisted non-spontaneous crystallization development in given glasses has suffered experimental restrictions. In this work, we looked into origin of this phenomenon in lead oxyfluoroborate glasses, resulting in beta-PbF2 growth even below the corresponding glass transition temperatures, through achieving a systematic study of not only Pt,Ag/Glass/Ag,Pt- but also Pt,Ag/Glass/YSZ:PbF2/Ag,Pt-type cells, where YSZ:PbF2 represents a two-phase system (formed by Y2O3-doped ZrO2 and PbF2). It is demonstrated that crystallization induction in these glasses involves Pb2+ ions reduction at the cathode, the phenomenon being, however, confirmed only when the F- ions were simultaneously also able to reach the anode for oxidation, after assuring either a direct glass-anode contact or percolation pathways for free fluoride migration across the YSZ:PbF2 mixtures. A further support of this account is that the electrochemically induced beta-PbF2 phase crystallizes showing ramified-like microstructure morphology that arises, accordingly, from development of electroconvective diffusion processes under electric field action.

Applying design of experiments (DOE) to flavonoid extraction from Passiflora alata and P. edulis

The Passifloraceae family is extensively used in native Brazilian folk medicine to treat a wide variety of diseases. The problem of flavonoid extraction from Passiflora was treated by application of design of experiments (DOE), as an experiment with mixture including one categorical process variable. The components of the binary mixture were: ethanol (component A) and water (component B); the categorical process variable: extraction method (factor C) was varied at two levels: (+1) maceration and (-1) percolation. ANOVA suggested a cubic model for P. edulis extraction and a quadratic model for P. alata.These results indicate that the proportion of components A and B in the mixture is the main factor involved in significantly increasing flavonoid extraction. In regard to the extraction methods, no important differences were observed, which indicates that these two traditional extraction methods could be effectively used to extract flavonoids from both medicinal plants. The evaluation of antioxidant activity of the extract by ORAC method showed that P. edulis displays twice as much antioxidant activity as P. alata. Considering that maceration is a simple, rapid and environmentally friendly extraction method, in this study, the optimized conditions for flavonoid extraction from these Passiflora species is maceration with 75% ethanol for P. edulis and 50% ethanol for P. alata.