Noise and ultraviolet divergences in the dynamics of the chiral condensate in QCD

The time evolution of the matter produced in high energy heavy-ion collisions seems to be well described by relativistic viscous hydrodynamics. In addition to the hydrodynamic degrees of freedom related to energy-momentum conservation, degrees of freedom associated with order parameters of broken continuous symmetries must be considered because they are all coupled to each other. of particular interest is the coupling of degrees of freedom associated with the chiral symmetry of QCD. Quantum and thermal fluctuations of the chiral fields act as noise sources in the classical equations of motion, turning them into stochastic differential equations in the form of Ginzburg-Landau-Langevin (GLL) equations. Analytic solutions of GLL equations are attainable only in very special circumstances and extensive numerical simulations are necessary, usually by discretizing the equations on a spatial lattice. However, a not much appreciated issue in the numerical simulations of GLL equations is that ultraviolet divergences in the form of lattice-spacing dependence plague the solutions. The divergences are related to the well-known Rayleigh-Jeans catastrophe in classical field theory. In the present communication we present a systematic lattice renormalization method to control the catastrophe. We discuss the implementation of the method for a GLL equation derived in the context of a model for the QCD chiral phase transition and consider the nonequilibrium evolution of the chiral condensate during the hydrodynamic flow of the quark-gluon plasma.

Stability of differential equations with piecewise constant argument via discrete equations

Lyapunov stability for a class of differential equation with piecewise constant argument (EPCA) is considered by means of the stability of a discrete equation. Applications to some nonlinear autonomous equations are given improving some linear known cases.

Mass fractal characteristics of wet sonogels as determined by small-angle x-ray scattering and differential scanning calorimetry

Low density silica sonogels were prepared from acid sonohydrolysis of tetraethoxysilane. Wet gels were studied by small-angle x-ray scattering (SAXS) and differential scanning calorimetry (DSC). The DSC tests were carried out under a heating rate of 2 degrees C/min from -120 degrees C up to 30 degrees C. Aerogels were obtained by CO(2) supercritical extraction and characterized by nitrogen adsorption and SAXS. The DSC thermogram displays two distinct endothermic peaks. The first, a broad peak extending from about -80 degrees C up to practically 0 degrees C, was associated to the melting of ice nanocrystals with a crystal size distribution with pore diameter ranging from 1 or 2 nm up to about 60 nm, as estimated from Thomson's equation. The second, a sharp peak with onset temperature close to 0 degrees C, was attributed to the melting of macroscopic crystals. The DSC incremental nanopore volume distribution is in reasonable agreement with the incremental pore volume distribution of the aerogel as determined from nitrogen adsorption. No macroporosity was detected by nitrogen adsorption, probably because the adsorption method applies stress on the sample during measurement, leading to a underestimation of pore volume, or because often positive curvature of the solid surface is in aerogels, making the nitrogen condensation more difficult. According to the SAXS results, the solid network of the wet gels behaves as a mass fractal structure with mass fractal dimension D=2.20 +/- 0.01 in a characteristic length scale below xi=7.9 +/- 0.1 nm. The mass fractal characteristics of the wet gels have also been probed from DSC data by means of an earlier applied modeling for generation of a mass fractal from the incremental pore volume distribution curves. The results are shown to be in interesting agreement with the results from SAXS.

Simultaneous determination of quinoline and pyridine compounds in gasoline and diesel by differential pulse voltammetry

The presence of trace basic organonitrogen compounds such as quinoline and pyridine in derivative petroleum fuels plays an important role in maintaining the engines of vehicles. However, these substances can contaminate the environment and so must be controlled because most of them are potentially carcinogenic and mutagenic. For these reasons, a reliable and sensitive method was developed for the determination of basic nitrogen compounds in fuel samples such as gasoline and diesel. This method utilizes preconcentration on an ion-exchange resin (Amberlyte IR - 120 H) followed by differential pulse voltammetry (DPV) on a glassy carbon electrode. The electrochemical behavior of quinoline and pyridine as studied by cyclic voltammetry (CV) suggests that their reduction occurs via a reversible electron transfer followed by an irreversible chemical reaction. Very well resolved diffusion-controlled voltammetric peaks were obtained in dimethylformamide (DMF) with tetrabutylammonium tetrafluoroborate (TBAF(4) 0.1 mol L-1) for quinoline (-1.95 V) and pyridine (-2.52 V) vs. Ag vertical bar AgCl vertical bar KClsat reference electrode. The proposed DPV method displayed a good linear response from 0.10 to 300 mg L-1 and a limit of detection (LOD) of 5.05 and 0.25 mu g L-1 for quinoline and pyridine, respectively. Using the method of standard additions, the simultaneous determination of quinoline and pyridine in gasoline samples yielded 25.0 +/- 0.3 and 33.0 +/- 0.7 mg L-1 and in diesel samples yielded 80.3 +/- 0.2 and 131 +/- 0.4 mg L-1, respectively. Spike recoveries were 94.4 +/- 0.3% and 10 +/- 0.5% for quinoline and pyridine, respectively, in the fuel determinations. This proposed method was also compared with UV-vis spectrophotometric measurements. Results obtained for the two methods agreed well based on F and t student's tests.

Simultaneous determination of neutral nitrogen compounds in gasoline and diesel by differential pulse voltammetry

The presence of trace neutral organonitrogen compounds as carbazole and indole in derivative petroleum fuels plays an important role in the car's engine maintenance. In addition, these substances contribute to the environmental contamination and their control is necessary because most of them are potentially carcinogenic and mutagenic. For those reasons, a reliable and sensitive method was proposed for the determination of neutral nitrogen compounds in fuel samples, such as gasoline and diesel using preconcentration with modified silica gel (Merck 70-230 mesh ASTM) followed by differential pulse voltammetry (DPV) technique on a glassy carbon electrode. The electrochemical behavior of carbazole and indole studied by cyclic voltammetry (CV) suggests that their reduction occurs via a reversible electron transfer followed by an irreversible chemical reaction. Very well resolved diffusion controlled voltammetric peaks were obtained in dimethylformamide (DMF) with tetrabutylammonium tetrafluoroborate (TBAF(4) 0.1 mol L-1) for indole (-2.27 V) and carbazole (-2.67 V) versus Ag vertical bar AgCl vertical bar KClsat reference electrode. The proposed DPV method showed a good linear response range from 0.10 to 300 mg L-1 and a limit of detection (L.O.D) of 7.48 and 2.66 mu g L-1 for indole and carbazole, respectively. The results showed that simultaneous determination of indole and carbazole presents in spiked gasoline samples were 15.8 +/- 0.3 and 64.6 +/- 0.9 mg L-1 and in spiked diesel samples were 9.29 +/- 1 and 142 +/- 1 mg L-1, respectively. The recovery was evaluated and the results shown the values of 88.9 +/- 0.4 and 90.2 +/- 0.8% for carbazole and indole in fuel determinations. The proposed method was also compared with UV-vis spectrophotometric measures and the results obtained for the two methods were in good agreement according to the F and t Student's tests. (C) 2007 Elsevier B.V. All rights reserved.

On the limit cycles of a class of piecewise linear differential systems in R-4 with two zones

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Group A T-loop for differential moment mechanics: An implant study

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Some results on stability of retarded functional differential equations using dichotomic map techniques

This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation x′(t) = -b(t)x(t - r) and of its nonlinear generalization x′(t) = b(t) f (x(t - r)) are established. © 1998 Kluwer Academic Publishers.

Lamé differential equations and electrostatics

The problem of existence and uniqueness of polynomial solutions of the Lamé differential equation A(x)y″ + 2B(x)y′ + C(x)y = 0, where A(x),B(x) and C(x) are polynomials of degree p + 1,p and p - 1, is under discussion. We concentrate on the case when A(x) has only real zeros aj and, in contrast to a classical result of Heine and Stieltjes which concerns the case of positive coefficients rj in the partial fraction decomposition B(x)/A(x) = ∑j p=0 rj/(x - aj), we allow the presence of both positive and negative coefficients rj. The corresponding electrostatic interpretation of the zeros of the solution y(x) as points of equilibrium in an electrostatic field generated by charges rj at aj is given. As an application we prove that the zeros of the Gegenbauer-Laurent polynomials are the points of unique equilibrium in a field generated by two positive and two negative charges. © 2000 American Mathematical Society.

Solutions for a class of integro-differential equations with time periodic coefficients

In this work, a series solution is found for the integro-differential equation y″ (t) = -(ω2 c + ω2 f sin2 ωpt)y(t) + ωf (sin ωpt) z′ (0) + ω2 fωp sin ωpt ∫t 0 (cos ωps) y(s)ds, which describes the charged particle motion for certain configurations of oscillating magnetic fields. As an interesting feature, the terms of the solution are related to distinct sequences of prime numbers.

Maturity degree of composts from municipal solid wastes evaluated by differential scanning calorimetry

Differential scanning calorimetry (DSC) in association with chemical analysis was applied to assess the maturity reached by the organic fraction of Municipal Solid Wastes (MSW) subjected to composting processes with manual and fixed aeration and sampled at different composting times. Thermograms showed that the difference in the treatments, i.e., the manual aeration and the fixed aeration, had no relevant effect on the stabilization and maturation of OM in the substrates. Common thermal effects observed were: a low temperature endotherm assigned to dehydration and/or loss of peripheral polysaccharides chains; a medium temperature exotherm assigned to loss of peptidic structures, and a high temperature exotherm assigned to oxydation and polycondensation of aromatic nuclei of the molecule. Results obtained suggest that in the experimental conditions used, a shorter time of composting (about 30 d) appears adequate, in order to limit the extended mineralization of OM, whereas a prolonged composting time (up to 132 d) would produce a compost of poor quality with high ash content and low OM content.

Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event

This paper is concerned with the stability of discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, a stopping time τ Δ is associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to pure infinite horizon problems. Using the concept named stochastic τ-stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of τ Δ is obtained. In addition, an intermediary and mixed case for which τ represents the minimum between the occurrence of a fix number N of failures and the occurrence of a crucial failure τ Δ is also considered. Necessary and sufficient conditions to ensure the stochastic τ-stability are provided in this setting that are auxiliary to the main result.

Stable two-dimensional dispersion-managed soliton

The existence of a dispersion-managed soliton in two-dimensional nonlinear Schrodinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct partial differential equation (PDE) and ordinary differential equation (ODE) simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown.

Analytical/numerical hybrid solution for one-dimensional ablation problem

Ablation is a thermal protection process with several applications in engineering, mainly in the field of airspace industry. The use of conventional materials must be quite restricted, because they would suffer catastrophic flaws due to thermal degradation of their structures. However, the same materials can be quite suitable once being protected by well-known ablative materials. The process that involves the ablative phenomena is complex, could involve the whole or partial loss of material that is sacrificed for absorption of energy. The analysis of the ablative process in a blunt body with revolution geometry will be made on the stagnation point area that can be simplified as a one-dimensional plane plate problem, hi this work the Generalized Integral Transform Technique (GITT) is employed for the solution of the non-linear system of coupled partial differential equations that model the phenomena. The solution of the problem is obtained by transforming the non-linear partial differential equation system to a system of coupled first order ordinary differential equations and then solving it by using well-established numerical routines. The results of interest such as the temperature field, the depth and the rate of removal of the ablative material are presented and compared with those ones available in the open literature.

A preliminary differential proteomic analysis of the periplasmic fraction in Acidithiobacillus ferrooxidans planktonic and attached cells exposed to chalcopyrite

The Acidithiobacillus ferrooxidans periplasmic space is known to have proteins involved in the respiratory chains. There are no reports about the expression of the periplasmic proteins in A. ferrooxidans cells attached to chalcopyrite. In this preliminary work, it was compared the periplasmic protein profiles of A. ferrooxidans planktonic and attached cells after exposure to chalcopyrite for 2 hours. The bacterial response to chalcopyrite was investigated by a proteomic approach (two- dimensional gel electrophoresis and mass spectrometry). Four proteins differentially expressed between planktonic and attached cells after exposure to chalcopyrite were identified. Two of these proteins, repressed in chalcopyrite- attached cells, were both identified as superoxide dismutase, whereas the single strand binding protein (SSB) and the PspA/IM30 protein were induced. These results showed that A. ferrooxidans chalcopyrite- attached and planktonic cells show differential expression of the periplasmic proteins and that a proteomic approach can provide a valuable tool to detect proteins related to the A. ferrooxidans response to attachment to the mineral substrates. © (2009) Trans Tech Publications.