Intrinsic noise-induced phase transitions: Beyond the noise interpretation

We discuss intrinsic noise effects in stochastic multiplicative-noise partial differential equations, which are qualitatively independent of the noise interpretation (Itô vs Stratonovich), in particular in the context of noise-induced ordering phase transitions. We study a model which, contrary to all cases known so far, exhibits such ordering transitions when the noise is interpreted not only according to Stratonovich, but also to Itô. The main feature of this model is the absence of a linear instability at the transition point. The dynamical properties of the resulting noise-induced growth processes are studied and compared in the two interpretations and with a reference Ginzburg-Landau-type model. A detailed discussion of a different numerical algorithm valid for both interpretations is also presented.

Phase-field approach to spatial perturbations in normal Saffman-Taylor fingers

We make a numerical study of the effect that spatial perturbations have in normal Saffman-Taylor fingers driven at constant pressure gradients. We use a phase field model that allows for spatial variations in the Hele-Shaw cell. We find that, regardless of the specific way in which spatial perturbations are introduced, a lateral instability develops on the sides of the propagating Saffman-Taylor finger. Moreover, the instability exists regardless of the intensity of spatial perturbations in the cell as long as the perturbations are felt by the finger tip. If, as the finger propagates, the spatial perturbations felt by the tip change, the instability is nonperiodic. If, as the finger propagates, the spatial perturbations felt by the tip are persistent, the instability developed is periodic. In the later case, the instability is symmetrical or asymmetrical depending on the intensity of the perturbation.

Fluctuations in Saffman-Taylor fingers with quenched disorder

We make an experimental characterization of the effect that static disorder has on the shape of a normal Saffman-Taylor finger. We find that static noise induces a small amplitude and long wavelength instability on the sides of the finger. Fluctuations on the finger sides have a dominant wavelength, indicating that the system acts as a selective amplifier of static noise. The dominant wavelength does not seem to be very sensitive to the intensity of static noise present in the system. On the other hand, at a given flow rate, rms fluctuations of the finger width, decrease with decreasing intensity of static noise. This might explain why the sides of the fingers are flat for typical Saffman-Taylor experiments. Comparison with previous numerical studies of the effect that temporal noise has on the Saffman-Taylor finger, leads to conclude that the effect of temporal noise and static noise are similar. The behavior of fluctuations of the finger width found in our experiments, is qualitatively similar to one recently reported, in the sense that, the magnitude of the width fluctuations decays as a power law of the capillary number, at low flow rates, and increases with capillary number for larger flow rates.

Viscous fingering as a paradigm of interfacial pattern formation: Recent results and new challenges

We review recent results on dynamical aspects of viscous fingering. The Saffman¿Taylor instability is studied beyond linear stability analysis by means of a weakly nonlinear analysis and the exact determination of the subcritical branch. A series of contributions pursuing the idea of a dynamical solvability scenario associated to surface tension in analogy with the traditional selection theory is put in perspective and discussed in the light of the asymptotic theory of Tanveer and co-workers. The inherently dynamical singular effects of surface tension are clarified. The dynamical role of viscosity contrast is explored numerically. We find that the basin of attraction of the Saffman¿Taylor finger depends on viscosity contrast, and that the sensitivity to this parameter is maximal in the usual limit of high viscosity contrast. The competing attractors are identified as closed bubble solutions. We briefly report on recent results and work in progress concerning rotating Hele-Shaw flows, topological singularities and wetting effects, and also discuss future directions in the context of viscous fingering

Design and construction of precision heat fluxmeters

The possibility of local elastic instabilities is considered in a first¿order structural phase transition, typically a thermoelastic martensitic transformation, with associated interfacial and volumic strain energy. They appear, for instance, as the result of shape change accommodation by simultaneous growth of different crystallographic variants. The treatment is phenomenological and deals with growth in both thermoelastic equilibrium and in nonequilibrium conditions produced by the elastic instability. Scaling of the transformed fraction curves against temperature is predicted only in the case of purely thermoelastic growth. The role of the transformation latent heat on the relaxation kinetics is also considered, and it is shown that it tends to increase the characteristic relaxation times as adiabatic conditions are approached, by keeping the system closer to a constant temperature. The analysis also reveals that the energy dissipated in the relaxation process has a double origin: release of elastic energy Wi and entropy production Si. The latter is shown to depend on both temperature rate and thermal conduction in the system.

Radial displacement of a fluid annulus in a rotating Hele¿Shaw cell

The radial displacement of a fluid annulus in a rotating circular Hele-Shaw cell has been investigated experimentally. It has been found that the flow depends sensitively on the wetting conditions at the outer interface. Displacements in a prewet cell are well described by Darcy's law in a wide range of experimental parameters, with little influence of capillary effects. In a dry cell, however, a more careful analysis of the interface motion is required; the interplay between a gradual loss of fluid at the inner interface, and the dependence of capillary forces at the outer interface on interfacial velocity and dynamic contact angle, result in a constant velocity for the interfaces. The experimental results in this case correlate in the form of an empirical scaling relation between the capillary number Ca and a dimensionless group, related to the ratio of centrifugal to capillary forces, which spans about three orders of magnitude in both quantities. Finally, the relative thickness of the coating film left by the inner interface, alpha i, is obtained as a function of Ca.

Low viscosity contrast fingering in a rotating Hele-Shaw cell

We study the fingering instability of a circular interface between two immiscible liquids in a radial Hele-Shaw cell. The cell rotates around its vertical symmetry axis, and the instability is driven by the density difference between the two fluids. This kind of driving allows studying the interfacial dynamics in the particularly interesting case of an interface separating two liquids of comparable viscosity. An accurate experimental study of the number of fingers emerging from the instability reveals a slight but systematic dependence of the linear dispersion relation on the gap spacing. We show that this result is related to a modification of the interface boundary condition which incorporates stresses originated from normal velocity gradients. The early nonlinear regime shows nearly no competition between the outgrowing fingers, characteristic of low viscosity contrast flows. We perform experiments in a wide range of experimental parameters, under conditions of mass conservation (no injection), and characterize the resulting patterns by data collapses of two characteristic lengths: the radius of gyration of the pattern and the interface stretching. Deep in the nonlinear regime, the fingers which grow radially outwards stretch and become gradually thinner, to a point that the fingers pinch and emit drops. We show that the amount of liquid emitted in the first generation of drops is a constant independent of the experimental parameters. Further on there is a sharp reduction of the amount of liquid centrifugated, punctuated by periods of no observable centrifugation.

The role of AUF1 in AU-rich interleukin-6 mRNA regulation

Abstract: The AU-rich elements (AREs) consisting of repeated AUUUA motifs confer rapid degradation to many cellular mRNAs when present in the 3' untranslated region (3'UTR). We have studied the instability of interleukin-6 mRNA by grafting its 3' untranslated region to a stable green fluorescent protein mRNA. Subsequent scanning mutagenesis identified two conserved elements, which taken together account for most of the instability. The first corresponds to a short non-canonical AU-rich element. The other comprises a sequence predicted to form astern-loop structure. Both elements need to be present in order to confer full instability (Paschoud et al. 2006). Destabilization of ARE-containing mRNAs is thought to involve ARE-binding proteins such as AUF1. We tested whether AUF1 binding to interleukin-6 mRNA correlates with decreased mRNA stability. Overexpression of myc-tagged p37AUFl and p42AUF1 as well as suppression of all four AUF1 isoforms by RNA interference stabilized the interleukin-6 mRNA. Furthermore, the interleukin-6 mRNA co-immunoprecipitated specifically with myc-tagged p37AUF1 and p42AUF1 in cell extracts. Both the stabilization and AUF1-binding required the non-canonical AU-rich sequence. These results indicate that AUF1 binds to the AU-rich element in vivo and promotes interleukin6 mRNA degradation. The combination of mRNA co-immunoprecipitation with microarray technology revealed that at least 500 cellular mRNAs associate with AUF1. Résumé: "La présence d'éléments riches en A et U (ARE), en particulier les motifs répétés d'AUUUA dans la région 3' non traduite, confère une dégradation rapide à beaucoup d'ARN cellulaires. Nous avons étudié l'instabilité de l'ARN codant pour l'interleukine 6 en greffant sa région 3' non traduite à un ARN stable codant pour la protéine fluorescente verte. La mutagenèse systématique des séquences non traduites a permis l'identification de deux éléments conservés qui confèrent l'instabilité à l'ARN. Le premier correspond à un élément AU-riche non canonique court. Le second comporte une structure en 'épingle à cheveux'. Tous les deux éléments doivent être présents afin de conférer une instabilité complète (Paschoud et al. 2006). On pense que des protéines telles que AUF1, pouvant se lier aux éléments ARE, sont impliquées dans la dégradation des ARN messagers. Nous avons examiné si la liaison de AUFl sur l'ARN de l'interleukine 6 corrèle avec une stabilité diminuée. La surexpression des protéines p37AUF1 et de p42AUF1 myc-étiquetées ainsi que la suppression de chacun des quatre isoformes de AUF1 par interférence d'ARN a stabilisé l'ARN messager d'interleukine 6. En outre, cet ARN co-immunoprécipite spécifiquement avec p37AUF1 et p42AUF1 dans des extraits cellulaires. La présence de l'élément AUriche non canonique est nécessaire pour la stabilisation de l'ARN et sa liaison avec AUFI. Ces résultats indiquent qu'AUF1 se lie à l'élément AU-riche in vivo et favorise la dégradation de l'ARN messager d'interleukine 6. La combinaison des techniques de coimmunoprécipitation des ARN messagers et des analyses par `microarray' indique qu'au moins 500 ARN cellulaires s'associent à AUF1.

Quantification of aluminium in soil of the Solimões Formation, Acre State, Brazil

The variety of soils in the State of Acre is wide and their chemical profiles are still not fully understood. The nature of the material of origin of these soils is indicated by the high aluminium (Al) content, commonly associated with high calcium (Ca) and magnesium (Mg) contents. The study objective was to use different methods to quantify Al in soils from toposequences formed from material of a sedimentary nature originating from the Solimões Formation, in Acre, Brazil. Trenches were opened at three distinct points in the landscape: shoulder, backslope and footslope positions. Soil samples were collected for physical, chemical, mineralogical analyses. The Al content was quantified using different methods. High Al contents were found in most of these horizons, associated with high Ca and Mg levels, representing the predominant cations in the sum of exchangeable bases. The mineralogy indicates that the soils are still in a low weathering phase, with the presence of significant quantities of 2:1 minerals. Similar Al contents were determined by the methods of NaOH titration, xylenol orange spectrometry and inductively coupled plasma optical emission spectrometry. However, no consistent data were obtained by the pyrocatechol violet method. Extraction with KCl overestimated the exchangeable Al content due to its ability to extract the non-exchangeable Al present in the smectite interlayers. It was observed that high Al contents are related to the instability of the hydroxyl-Al smectite interlayers.

Efficiency of nitrogen fertilizer applied at corn sowing in contrasting growing seasons in Paraguay

In order to select soil management practices that increase the nitrogen-use efficiency (NUE) in agro-ecosystems, the different indices of agronomic fertilizer efficiency must be evaluated under varied weather conditions. This study assessed the NUE indices in no-till corn in southern Paraguay. Nitrogen fertilizer rates from 0 to 180 kg ha-1 were applied in a single application at corn sowing and the crop response investigated in two growing seasons (2010 and 2011). The experimental design was a randomized block with three replications. Based on the data of grain yield, dry matter, and N uptake, the following fertilizer indices were assessed: agronomic N-use efficiency (ANE), apparent N recovery efficiency (NRE), N physiological efficiency (NPE), partial factor productivity (PFP), and partial nutrient balance (PNB). The weather conditions varied largely during the experimental period; the rainfall distribution was favorable for crop growth in the first season and unfavorable in the second. The PFP and ANE indices, as expected, decreased with increasing N fertilizer rates. A general analysis of the N fertilizer indices in the first season showed that the maximum rate (180 kg ha-1) obtained the highest corn yield and also optimized the efficiency of NPE, NRE and ANE. In the second season, under water stress, the most efficient N fertilizer rate (60 kg ha-1) was three times lower than in the first season, indicating a strong influence of weather conditions on NUE. Considering that weather instability is typical for southern Paraguay, anticipated full N fertilization at corn sowing is not recommended due the temporal variability of the optimum N fertilizer rate needed to achieve high ANE.

Fingerlike aggregates in thin-layer electrodeposition

Electrodeposition experiments conducted in a thin-layer horizontal cell containing a nonbinary aqueous electrolyte prepared with cupric sulfate and sodium sulfate gave rise to fingerlike deposits, a novel and unexpected growth mode in this context. Both the leading instability from which fingers emerge and some distinctive features of their steady evolution are interpreted in terms of a simple model based on the existing theory of fingering in fluids.

Influence of mineral fertilization on edaphic fauna in Acacia auriculiformis (A. Cunn) plantations

Fertilization and/or the accumulation of organic matter from plant residues can influence the composition of soil and litter community. The goal of this study was to evaluate the effects of P and K fertilization on total faunal and nematode faunal composition and richness in plant litter and soil for 360 days in an area reforested with Acacia auriculiformis (A. Cunn), located in the municipality of Conceição de Macabu in the State of Rio de Janeiro. For each treatment (fertilized and unfertilized plots), samples of litter and soil (to a depth of 5 cm) were collected and transferred into a Berlese-Tüllgren funnels for the extraction of fauna. Mesofauna and macrofauna were quantified, and the major taxa identified. Nematodes were extracted by centrifugal flotation in sucrose solution and identified according to feeding habits. Density (number of individuals m-2) of total fauna, microphages, social insects and saprophages varied significantly per treatment and sampling time in both litter and soil. The total number of individuals collected was 5,127, and the total number of nematodes 894. Phosphorus and potassium fertilization resulted in an increase in total fauna density and richness in the litter due to an increased abundance of social insects, saprophages and herbivores. In the soil, fertilization increased the saprophage and predator densities. Saprophages were the predominant taxa in the litter, while social insects (Formicidae) prevailed in the soil. Litter nematode populations were favored by mineral fertilization. Bacteriophages were the predominant nematode group in both litter and soil.

The 2006 Eiger rockslide, European Alps

In July 2006, approximately 2 million m3 of massive limestone began to move on the east flank of the Eiger in central Switzerland. For more than two years after the initial failure, the rock mass moved at rates of up to 70 cm per day. A detailed analysis of the structures and velocities of the different moving blocks was conducted with the aid of terrestrial laser scanning. The moving rock mass included a rear block that subsided, pushing a frontal block forward. Movement directions were controlled by discontinuity sets that formed wedges bounded on one side by sub-vertical bedding planes. The instability was, until recently, buttressed by a glacier. Slope observations and results of continuum and discontinuum modeling indicate that the structure of the rock mass and topography were the main causes of the instability. Progressive weathering and mechanical fatigue of the rock mass appear to have led to the failure. A dynamic analytical model further indicates that the rockslide was primarily controlled by a reduction in the strength of discontinuities, the effects of ice deformation, and ? to a limited extent ? groundwater flow. This study shows that realistic and simple instability models can be constructed for rock-slope failures if high-resolution data are available.

Statistical dynamics of dislocation systems: The influence of dislocation-dislocation correlations.

During plastic deformation of crystalline materials, the collective dynamics of interacting dislocations gives rise to various patterning phenomena. A crucial and still open question is whether the long range dislocation-dislocation interactions which do not have an intrinsic range can lead to spatial patterns which may exhibit well-defined characteristic scales. It is demonstrated for a general model of two-dimensional dislocation systems that spontaneously emerging dislocation pair correlations introduce a length scale which is proportional to the mean dislocation spacing. General properties of the pair correlation functions are derived, and explicit calculations are performed for a simple special case, viz pair correlations in single-glide dislocation dynamics. It is shown that in this case the dislocation system exhibits a patterning instability leading to the formation of walls normal to the glide plane. The results are discussed in terms of their general implications for dislocation patterning.

In defense of the "tunneling" wave function of the universe

The tunneling approach to the wave function of the Universe has been recently criticized by Bousso and Hawking who claim that it predicts a catastrophic instability of de Sitter space with respect to pair production of black holes. We show that this claim is unfounded. First, we argue that different horizon size regions in de Sitter space cannot be treated as independently created, as they contend. And second, the WKB tunneling wave function is not simply the inverse of the Hartle-Hawking one, except in very special cases. Applied to the related problem of pair production of massive particles, we argue that the tunneling wave function leads to a small constant production rate, and not to a catastrophe as the argument of Bousso and Hawking would suggest.