Sol phase and sol-gel transition in SnO2 colloidal suspensions

The effect of concentration on the structure of SnO2 colloids in aqueous suspension, on their spatial correlation and on the gelation process was studied by small angle x-ray scattering (SAXS). The shape of the experimental SAXS curves varies with suspension concentration. For diluted suspensions ([SnO2] less than or equal to 0.13 mol L-1), SAXS results indicate the presence of colloidal fractal aggregates with an internal correlation length xi congruent to 20 Angstrom, without any noticeable spatial correlation between them. This suggests that the aggregates are spatially arranged without any significant interaction like in ideal gas structures. For higher concentrations ([SnO2] = 0.16, 0.32, and 0.64 mol L-1), the colloidal aggregates are larger (xi = 24 Angstrom) and exhibit a certain degree of spatial correlation between them. The pair correlation function corresponding to the sol with the highest concentration (0.92 mol L-1) reveals a rather strong short range order between aggregates, characteristic of a fluid-like structure, with an average nearest-neighbor distance between aggregates d(1) = 125 Angstrom and an average second-neighbor distance d(2) = 283 Angstrom. The pair distribution function remains essentially invariant during the sol-gel transition, suggesting that gelation involves the formation of a few points of connection between the aggregates resulting in a gel network constituted by essentially linear chains of clusters..

Short term hydroelectric scheduling combining network flow and interior point approaches

In this paper, short term hydroelectric scheduling is formulated as a network flow optimization model and solved by interior point methods. The primal-dual and predictor-corrector versions of such interior point methods are developed and the resulting matrix structure is explored. This structure leads to very fast iterations since it avoids computation and factorization of impedance matrices. For each time interval, the linear algebra reduces to the solution of two linear systems, either to the number of buses or to the number of independent loops. Either matrix is invariant and can be factored off-line. As a consequence of such matrix manipulations, a linear system which changes at each iteration has to be solved, although its size is reduced to the number of generating units and is not a function of time intervals. These methods were applied to IEEE and Brazilian power systems, and numerical results were obtained using a MATLAB implementation. Both interior point methods proved to be robust and achieved fast convergence for all instances tested. (C) 2004 Elsevier Ltd. All rights reserved.

Dynamical scaling properties of nanoporous undoped and Sb-doped SnO2 supported thin films during tri- and bidimensional structure coarsening

The coarsening of the nanoporous structure developed in undoped and 3% Sb-doped SnO2 sol-gel dip-coated films deposited on a mica substrate was studied by time-resolved small-angle x-ray scattering (SAXS) during in situ isothermal treatments at 450 and 650 degrees C. The time dependence of the structure function derived from the experimental SAXS data is in reasonable agreement with the predictions of the statistical theory of dynamical scaling, thus suggesting that the coarsening process in the studied nanoporous structures exhibits dynamical self-similar properties. The kinetic exponents of the power time dependence of the characteristic scaling length of undoped SnO2 and 3% Sb-doped SnO2 films are similar (alpha approximate to 0.09), this value being invariant with respect to the firing temperature. In the case of undoped SnO2 films, another kinetic exponent, alpha('), corresponding to the maximum of the structure function was determined to be approximately equal to three times the value of the exponent alpha, as expected for the random tridimensional coarsening process in the dynamical scaling regime. Instead, for 3% Sb-doped SnO2 films fired at 650 degrees C, we have determined that alpha(')approximate to 2 alpha, thus suggesting a bidimensional coarsening of the porous structure. The analyses of the dynamical scaling functions and their asymptotic behavior at high q (q being the modulus of the scattering vector) provided additional evidence for the two-dimensional features of the pore structure of 3% Sb-doped SnO2 films. The presented experimental results support the hypotheses of the validity of the dynamic scaling concept to describe the coarsening process in anisotropic nanoporous systems.

Structural characterization of undoped and Sb-doped SnO2 thin films fired at different temperatures

SnO2 thin films were obtained by the sol-gel method starting from inorganic precursor solutions. In this work, we compare the structure of undoped and Sb-doped SnO2 films prepared by dip-coating. The films were deposited on quartz substrates and then fired at different temperatures ranging from 383 up to 1173 K. The density and the thickness of the films were determined by X-ray reflectivity (XRR) and their porous nanostructure was characterized by grazing-incidence small angle X-ray scattering (GISAXS). XRR results corresponding to undoped and Sb-doped samples indicate a monotonous decrease in film thickness when they are fired at increasing temperatures. At same time, the apparent density of undoped samples exhibits a progressive increase while for Sb-doped films it remains invariant up to 973 K and then increases for T = 1173 K. Anisotropic GISAXS patterns of both films, Sb-doped and undoped, fired above 573 K indicate the presence of elongated pores with their major axis perpendicular to the film surface. For all firing temperatures the nanopores in doped samples are larger than in undoped ones. This suggests that Sb-doping favours the pore growth hindering the film densification. At the highest firing temperature (1173 K) this effect is reversed.

On the coupling of the self-dual field to dynamical U(1) matter and its dual theory

We consider arbitrary U (1) charged matter non-minimally coupled to the self-dual field in d = 2 + 1. The coupling includes a linear and a rather general quadratic term in the self-dual field. By using both Lagragian gauge embedding and master action approaches we derive the dual Maxwell Chern-Simons-type model and show the classical equivalence between the two theories. At the quantum level the master action approach in general requires the addition of an awkward extra term to the Maxwell Chern-Simons-type theory. Only in the case of a linear coupling in the self-dual field can the extra term be dropped and we are able to establish the quantum equivalence of gauge invariant correlation functions in both theories.

Multiloop superstring amplitudes from non-minimal pure spinor formalism

Using the non-minimal version of the pure spinor formalism, manifestly super-Poincare covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picture-changing operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRST-invariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to ten-dimensional F-terms, i.e. terms in the ten-dimensional superspace action which do not involve integration over the maximum number of theta's.

DERIVATION OF THE ENERGY-TIME UNCERTAINTY RELATION

A derivation from first principles is given of the energy-time uncertainty relation in quantum mechanics. A canonical transformation is made in classical mechanics to a new canonical momentum, which is energy E, and a new canonical coordinate T, which is called tempus, conjugate to the energy. Tempus T, the canonical coordinate conjugate to the energy, is conceptually different from the time t in which the system evolves. The Poisson bracket is a canonical invariant, so that energy and tempus satisfy the same Poisson bracket as do p and q. When the system is quantized, we find the energy-time uncertainty relation DELTAEDELTAT greater-than-or-equal-to HBAR/2. For a conservative system the average of the tempus operator T is the time t plus a constant. For a free particle and a particle acted on by a constant force, the tempus operators are constructed explicitly, and the energy-time uncertainty relation is explicitly verified.

Influence of agricultural biomass burning on aerosol size distribution and dry deposition in southeastern Brazil

The size distributed composition of ambient aerosols is used to explore seasonal differences in particle chemistry and to show that dry deposition fluxes of soluble species, including important plant nutrients, increase during periods of biomass (sugar cane trash) burning in São Paulo State, Brazil. Measurements were made at a single site centrally located in the State's sugar cane growing region but away from the immediate vicinity of burns, so that the air sampled was representative of the regional background. Calculation of ion equivalent balances showed that during burning periods smaller particles (Aitken and accumulation modes) were more acidic, containing higher concentrations of SO(4)(2-), oxalate, NO(3)(-), HCOO(-), CH(3)COO(-), and Cl(-), but insufficient NH(4)(+) and K(+) to achieve neutrality. Larger particles showed an anion deficit due to the presence of unmeasured ions and comprised resuspended dusts modified by accumulation of nitrate, chloride, and organic anions. Increases of resuspended particles during the burning season were attributed to release of earlier deposits from the surfaces of burning vegetation as well as increased vehicle movement on unsurfaced roads. During winter months the relative contribution of combined emissions from road transport and industry diminished due to increased emissions from biomass combustion and other activities specifically associated with the harvest period. Positive increments in annual particulate dry deposition fluxes due to higher fluxes during the sugar cane harvest were 44.3% (NH(4)(+)), 42.1 % (K(+)), 31.8% (Mg(2+)), 30.4% (HCOO(-)), 12.8% (Cl(-)), 6.6% (CH(3)COO(-)), 5.2% (Ca(2+)), 3.8% (SO(4)(2-)), and 2.3% (NO(3)(-)). Na(+) and oxalate fluxes were seasonally invariant. Annual aerosol dry deposition fluxes (kg ha(-1)) were 0.5 (Na(+)), 0.25 (NH(4)(+)), 0.39 (K(+)), 0.51 (Mg(2+)), 3.19 (Ca(2+)), 1.34 (Cl(-)), 4.47 (NO(3)(-)), 3.59 (SO(4)(2-)), 0.58 (oxalate), 0.71 (HCOO(-)), and 1.38 (CH(3)COO(-)). Contributions of this mechanism to combined aerosol dry deposition and precipitation scavenging (inorganic species, excluding gaseous dry deposition) were 31% (Na(+)), 8% (NH(4)(+)), 26% (K(+)), 63% (Mg(2+)), 66% (Ca(2+)), 32% (Cl(-)), 33% (NO(3)(-)), and 36% (SO(4)(2-)).

Patterns in parabolic problems with nonlinear boundary conditions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Small-angle X-ray scattering study of gelation and aging of Eu3+-doped sol-gel-derived siloxane-poly(oxyethylene) nanocomposites

The aggregation, gelation, and aging of urea-cross-linked siloxane-poly(oxyethylene) nanohybrids [(U600)-n] containing two different amounts of europium triflate initially dissolved in an ethanol-water mixture were investigated by in situ small-angle X-ray scattering (SAXS). For both low (n = [O]/[Eu] = 80) and high (n = 25) europium contents, the SAXS intensity was attributed to the formation of siloxane clusters of about 8-11 Angstrom in size. Siloxane cluster formation and growth is a rapid process in hybrids with low Eu contents and slow in Eu-rich hybrids. An additional contribution to the scattering intensity at very low angles was attributed to the formation of a coarse structure level. At this secondary level, the structure can be described as a set of dense domains containing siloxane clusters embedded in a depleted matrix composed of unfolded polymer chains and solvent. By fitting a theoretical function for this model to the experimental SAXS curves, relevant structural parameters were determined as functions of time during the sol-gel transition and gel aging. For hybrids with low europium contents (n = 80), the size of the siloxane clusters remains essentially invariant, whereas the dense segregation domains progressively grow. In hybrids with high doping contents (n = 25), the preponderant structure variation during the first stages of the sol-gel transformation is the slow growth of siloxane clusters. For these hybrids, the segregation of siloxane clusters forming dense domains occurs only during advanced stages of the process.

BFFT formalism applied to the minimal chiral Schwinger model

We consider the minimal chiral Schwinger model, by embedding the gauge non-invariant formulation into a gauge theory following the Batalin-Fradkin-Fradkina-Tyutin point of view. Within the BFFT procedure, the second-class constraints are converted into strongly involutive first-class ones, leading to an extended gauge-invariant formulation. We also show that, like the standard chiral model, in the minimal chiral model the Wess-Zumino action can be obtained by performing a q-number gauge transformation into the effective gauge non-invariant action.

Periodic orbits for a class of reversible quadratic vector field on R-3

For a class of reversible quadratic vector fields on R-3 we study the periodic orbits that bifurcate from a heteroclinic loop having two singular points at infinity connected by an invariant straight line in the finite part and another straight line at infinity in the local chart U-2. More specifically, we prove that for all n is an element of N, there exists epsilon(n) > 0 such that the reversible quadratic polynomial differential systemx = a(0) + a(1y) + a(3y)(2) + a(4Y)(2) + epsilon(a(2x)(2) + a(3xz)),y = b(1z) + b(3yz) + epsilon b(2xy),z = c(1y) +c(4az)(2) + epsilon c(2xz)in R-3, with a(0) < 0, b(1)c(1) < 0, a(2) < 0, b(2) < a(2), a(4) > 0, c(2) < a(2) and b(3) is not an element of (c(4), 4c(4)), for epsilon is an element of (0, epsilon(n)) has at least n periodic orbits near the heteroclinic loop. (c) 2007 Elsevier B.V. All rights reserved.

SAXS study of the kinetics of formation of ZnO colloidal suspensions

We have investigated, by in situ small-angle X-ray scattering (SAXS), the kinetics of formation of zinc oxide colloidal suspensions obtained after refluxing alcoholic solution of zinc acetate and catalysed by lithium hydroxide. The experimental results demonstrate that the suspensions are composed of colloidal spheroidal particles with a multimodal size distribution. The average radius of the main mode, approximately 2 nm, is invariant but the number of these basic particles continuously increases for increasing hydrolysis reaction time. The other two modes correspond to particles with average radii close to 6 and 10 nm, respectively. The larger particles are formed by coagulation of the smaller ones. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Manifest electromagnetic duality in closed superstring field theory

The free action for massless Ramond-Ramond fields is derived from closed superstring field theory using the techniques of Siegel and Zwiebach. For the uncompactified Type IIB superstring, this gives a manifestly Lorentz-covariant action for a self-dual five-form field strength. Upon compactification to four dimensions, the action depends on a U(1) field strength from 4D N = 2 supergravity. However, unlike the standard Maxwell action, this action is manifestly invariant under the electromagnetic duality transformation which rotates F-mn into epsilon(mnpq)F(pq).

Relating propelinear and binary G-linear codes

In this paper we establish the connections between two different extensions of Z(4)-linearity for binary Hamming spaces, We present both notions - propelinearity and G-linearity - in the context of isometries and group actions, taking the viewpoint of geometrically uniform codes extended to discrete spaces. We show a double inclusion relation: binary G-linear codes are propelinear codes, and translation-invariant propelinear codes are G-linear codes. (C) 2002 Elsevier B.V. B.V. All rights reserved.