Renormalisation-theoretic analysis of non-equilibrium phase transitions II: The effect of perturbations on rate coefficients in the Becker-Doring equations

We study in detail the application of renormalisation theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes. In particular, we investigate the Becker-Doring (BD) equations, originally formulated to describe and analyse non-equilibrium phase transitions, but more recently generalised to describe a wide range of physicochemical problems. We consider here rate coefficients which depend on the cluster size in a power-law fashion, but now perturbed by small amplitude random noise. Power-law rate coefficients arise naturally in the theory of surface-controlled nucleation and growth processes. The noisy perturbations on these rates reflect the effect of microscopic variations in such mean-field coefficients, thermal fluctuations and/or experimental uncertainties. In the present paper we generalise our earlier work that identified the nine classes into which all dynamical behaviour must fall by investigating how random perturbations of the rate coefficients influence the steady-state and kinetic behaviour of the coarse-grained, renormalised system. We are hence able to confirm the existence of a set of up to nine universality classes for such BD systems.Comment: 30 pages, to appear in J Phys A Math Ge

Renormalisation-theoretic analysis of non-equilibrium phase transitions I: The Becker-Doring equations with power law rate coefficients

We study in detail the application of renormalisation theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes. We investigate the Becker-Dorging equations, originally formulated to describe and analyse non-equilibrium phase transitions, and more recently generalised to describe a wide range of physicochemical problems. In the present paper we analyse how the systematic coarse-graining renormalisation of the \BD system of equations affects the aggregation and fragmentation rate coefficients. We consider the case of power-law size-dependent cluster rate coefficients which we show lead to only three classes of system that require analysis: coagulation-dominated systems, fragmentation-dominated systems and those where coagulation and fragmentation are exactly balanced. We analyse the late-time asymptotics associated with each class.Comment: 18 pages, to appear in J Phys A Math Ge

Evaluation of Synthetic and Semi- synthetic Culture Media for Endo-1,4-β- Glucanases Secretion by Trichoderma koningiopsis

AbstractThe actual demand of energy and the environmental concerns together with the reduced fossil fuel reserves have played an important role to convert the second generation bioethanol production into an attractive research area. To convert lignocellulosic biomass to bioethanol the cellulosic components must be hydrolyzed to fermentable sugars. Trichoderma fungi secrete large amounts of enzymes of industrial interest such as cellulases, able to degrade holocellulose in the saccharification of lignocellulosic biomass. In this work we evaluated endo-1.4-β-glucanases enzymatic secretion of Trichoderma koningiopsis from Misiones province, in synthetic medium, with carboxymethylcellulose as carbon source; and semi-synthetic medium, with pine sawdust as carbon source. Higher values of endo-1.4-β-glucanases were reached when the semi-synthetic medium was used. It could be concluded that pine sawdust seems to be a good candidate for utilization as carbon source in culture media aiming to obtain good enzyme secretion, being also an economic and easily available substrate

Mean field approximation of two coupled populations of excitable units

The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by replacing each population with the corresponding mean-field model. In the exact system, one has the units within an ensemble communicating via the time-delayed linear couplings, whereas the inter-ensemble terms involve the nonlinear time-delayed interaction mediated by the appropriate global variables. The aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system, governed by a set of 4N stochastic delay-differential equations for the microscopic dynamics, can accurately be reproduced by a flow containing just four deterministic delay-differential equations which describe the evolution of the mean-field based variables. In particular, the considered issues include determining the parameter domains where the stationary state is stable, the scenarios for the onset and the time-delay induced suppression of the collective mode, as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state. We show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations, like those with symmetrical or asymmetrical inter-population couplings.Comment: 5 figure

Gradual transition from insulator to semimetal of Ca1−x_{1-x}Eux_{x}B6_{6} with increasing Eu concentration

The local environment of Eu$^{2+}$ ($4f^{7}$, $S=7/2$) in Ca$_{1-x}$Eu$_{x}$B$_{6}$ ($0.003\leqslant x\leqslant 1.00$) is investigated by means of electron spin resonance (ESR). For $x\lesssim 0.003$ the spectra show resolved \textit{fine} and \textit{hyperfine} structures due to the cubic crystal \textit{electric} field and nuclear \textit{hyperfine} field, respectively. The resonances have Lorentzian line shape, indicating an \textit{insulating} environment for the Eu$^{2+}$ ions. For $0.003\lesssim x\lesssim 0.07$, as $x$ increases, the ESR lines broaden due to local distortions caused by the Eu/Ca ions substitution. For $0.07\lesssim x\lesssim 0.30$, the lines broaden further and the spectra gradually change from Lorentzian to Dysonian resonances, suggesting a coexistence of both \textit{insulating} and \textit{metallic} environments for the Eu$^{2+}$ ions. In contrast to Ca$_{1-x}$Gd$_{x}$B$_{6}$, the \textit{fine} structure is still observable up to $x\approx 0.15$. For $x\gtrsim 0.30$ the \textit{fine} and \textit{hyperfine} structures are no longer observed, the line width increases, and the line shape is purely Dysonian anticipating the \textit{semimetallic} character of EuB$_{6}$. This broadening is attributed to a spin-flip scattering relaxation process due to the exchange interaction between conduction and Eu$^{2+}$ $4f$ electrons. High field ESR measurements for $x\gtrsim 0.15$ reveal smaller and anisotropic line widths, which are attributed to magnetic polarons and Fermi surface effects, respectively.Comment: Submitted to PR

Proper motions of the HH1 jet

We describe a new method for determining proper motions of extended objects, and a pipeline developed for the application of this method. We then apply this method to an analysis of four epochs of [S~II] HST images of the HH~1 jet (covering a period of $\sim 20$~yr). We determine the proper motions of the knots along the jet, and make a reconstruction of the past ejection velocity time-variability (assuming ballistic knot motions). This reconstruction shows an "acceleration" of the ejection velocities of the jet knots, with higher velocities at more recent times. This acceleration will result in an eventual merging of the knots in $\sim 450$~yr and at a distance of $\sim 80"$ from the outflow source, close to the present-day position of HH~1.Comment: 12 pages, 8 figure

Numerical Modeling of Eta Carinae Bipolar Outflows

In this paper, we present two-dimensional gas dynamic simulations of the formation and evolution of the eta-Car bipolar outflows. Adopting the interacting nonspherical winds model, we have carried out high-resolution numerical simulations, which include explicitly computed time-dependent radiative cooling, for different possible scenarios of the colliding winds. In our simulations, we consider different degrees of non-spherical symmetry for the pre-outburst wind and the great eruption of the 1840s presented by the eta-Car wind. From these models, we obtain important differences in the shape and kinematical properties of the Homunculus structure. In particular, we find an appropriate combination of the wind parameters (that control the degree of non-spherical symmetry) and obtain numerical experiments that best match both the observed morphology and the expansion velocity of the eta-Car bipolar shell. In addition, our numerical simulations show the formation of a bipolar nebula embedded within the Homunculus (the little Homunculus) developed from a secondary eruptive event suffered by the star in the 1890s, and also the development of tenuous, high velocity ejections in the equatorial region that result from the impact of the eruptive wind of the 1840s with the pre-outburst wind and that could explain some of the high speed features observed in the equatorial ejecta. The models were, however, unable to produce equatorial ejections associated to the second eruptive event.Comment: 33 pages, 9 figures, accepted by the Astrophysical Journa

Alternative model of the Antonov problem

Astrophysical systems will never be in a real Thermodynamic equilibrium: they undergo an evaporation process due to the fact that the gravity is not able to confine the particles. Ordinarily, this difficulty is overcome by enclosing the system in a rigid container which avoids the evaporation. We proposed an energetic prescription which is able to confine the particles, leading in this way to an alternative version of the Antonov isothermal model which unifies the well-known isothermal and polytropic profiles. Besides of the main features of the isothermal sphere model: the existence of the gravitational collapse and the energetic region with a negative specific heat, this alternative model has the advantage that the system size naturally appears as a consequence of the particles evaporation.Comment: RevTex4, 9 pages, 10 figures, Version Submitted to PR

Charge-Fluctuation-Induced Non-analytic Bending Rigidity

In this Letter, we consider a neutral system of mobile positive and negative charges confined on the surface of curved films. This may be an appropriate model for: i) a highly charged membrane whose counterions are confined to a sheath near its surface; ii) a membrane composed of an equimolar mixture of anionic and cationic surfactants in aqueous solution. We find that the charge fluctuations contribute a non-analytic term to the bending rigidity that varies logarithmically with the radius of curvature. This may lead to spontaneous vesicle formation, which is indeed observed in similar systems.Comment: Revtex, 9 pages, no figures, submitted to PR

Charge Fluctuations on Membrane Surfaces in Water

We generalize the predictions for attractions between over-all neutral surfaces induced by charge fluctuations/correlations to non-uniform systems that include dielectric discontinuities, as is the case for mixed charged lipid membranes in an aqueous solution. We show that the induced interactions depend in a non-trivial way on the dielectric constants of membrane and water and show different scaling with distance depending on these properties. The generality of the calculations also allows us to predict under which dielectric conditions the interaction will change sign and become repulsive