Localization of the optimal solution and a posteriori bounds for aggregation

After an aggregated problem has been solved, it is often desirable to estimate the accuracy loss due to the fact that a simpler problem than the original one has been solved. One way of measuring this loss in accuracy is the difference in objective function values. To get the bounds for this difference, Zipkin (Operations Research 1980;28:406) has assumed, that a simple (knapsack-type) localization of an original optimal solution is known. Since then various extensions of Zipkin's bound have been proposed, but under the same assumption. A method to compute the bounds for variable aggregation for convex problems, based on general localization of the original solution is proposed. For some classes of the original problem it is shown how to construct the localization. Examples are given to illustrate the main constructions and a small numerical study is presented.

O processo sol-gel: uma visão físico-química

The aim of this work was to revise the main concepts involved in the physical-chemistry of the sol-gel process. First, the preparation and its influence on the gel's structure are focalized; the sol-gel transition is revised under the thermodynamics of crytical phenomena point of view and by considering the kinetic models of aggregation. Second, the experimental methods usually used to characterize the sol-gel transition are discussed.

Aggregation in the generalized transportation problem

Aggregation disaggregation is used to reduce the analysis of a large generalized transportation problem to a smaller one. Bounds for the actual difference between the aggregated objective and the original optimal value are used to quantify the error due to aggregation and estimate the quality of the aggregation. The bounds can be calculated either before optimization of the aggregated problem (a priori) or after (a posteriori). Both types of the bounds are derived and numerically compared. A computational experiment was designed to (a) study the correlation between the bounds and the actual error and (b) quantify the difference of the error bounds from the actual error. The experiment shows a significant correlation between some a priori bounds, the a posteriori bounds and the actual error. These preliminary results indicate that calculating the a priori error bound is a useful strategy to select the appropriate aggregation level, since the a priori bound varies in the same way that the actual error does. After the aggregated problem has been selected and optimized, the a posteriori bound provides a good quantitative measure for the error due to aggregation.

Aggregation behaviour of hydrophobically modified poly(allylammonium) chloride

The behaviour of hydrophobically modified poly(allylammonium) chloride having octyl, decyl, dodecyl and hexadecyl side chains has been studied in aqueous solution using fluorescence emission techniques. Micropolarity studies using the I-1/I-3 ratio of the vibronic bands of pyrene show that the formation of hydrophobic microdomains depends on both the length of the side chain and the polymer concentration. The I-1/I-3 ratio of the polymers with low hydrophobe content (less than 5% mel) changes substantially when reaching a certain concentration. These changes are assigned to aggregation originating from interchain interactions. This behaviour is also confirmed by the behaviour of the monomer/excimer emission intensities of pyrene- dodecanoic acid used as a probe. For polymers having dodecyl side chains and hydrophobe contents higher than 10%, aggregates are formed independently of the polymer concentration. Anisotropy measurements show that microdomains resulting from the inter- and/or intramolecular interactions are similar to those observed for cationic surfactants. Viscosity measurements show that the coil dimensions are substantially decreased for the polymers having high hydrophobe contents, indicating intramolecular associations.

A SAXS study of kinetics of aggregation of TEOS-derived sonogels at different temperatures

The kinetics of aggregation of tetraethoxysilane (TEOS)-derived silica sols, produced by acid-catalyzed and ultrasound-stimulated hydrolysis, were studied by 'in situ' measurements of small-angle X-ray scattering (SAXS) at the temperatures 40 degreesC, 60 degreesC and 70 degreesC. The results were analyzed in terms of the evolution with time (t) of the SAXS intensity probing the mass fractal characteristics of the system, the average radius of gyration (Rc,) of the clusters and the number of primary particles per cluster. The aggregation process yields mass fractal structures which exhibit a scattering exponent (alpha) practically equal to 2, in the probed length scale range (5.3 nm < 1/q < 0.22 nm), beneath and even far beyond the gel point. This suggests that a is a direct measure of the real mass fractal dimension (D) of the structure. The precursor sol (pH = 2) exhibits I nm mean sized clusters with mass fractal dimension D similar to 1.9. Increasing the pH to 4.5, the cluster mean size and the number of primary particles per cluster increase but the system keeps a more opened structure (D similar to 1.4). In the first aggregation stages, D increases up to similar to2 by incorporating primary particles to the clusters without changing their mean size. From this stage, the aggregation progresses following a thermally activated scaling law well described by R-G similar tot(1/D) in all cases. This is indicative of a diffusion-controlled cluster-cluster aggregation process. The activation energy of the process was found to be 91.7 kJ/mol. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Use of spin label EPR spectra to monitor peptide chain aggregation inside resin beads.

An EPR approach to monitor peptide chain aggregation inside resin beads is introduced. Model low and highly peptide-loaded resins containing an aggregating sequence were labeled with a paramagnetic amino acid derivative and studied with regard to their solvation behavior in different solvent systems. For the first time in the peptide synthesis, EPR spectroscopic has allowed the detection of differentiated levels of peptide chain aggregation as a function of solvent and resin loading. (C) 1997, Elsevier B.V. Ltd. All rights reserved.

Photoinduced phenomena in layer-by-layer films of poly(allylamine hydrochloride) and Brilliant Yellow azodye

The nanoscale interactions between adjacent layers of layer-by-layer (LBL) films from poly(allylamine hydrochloride) (PAH) and azodye Brilliant Yellow (BY) have been investigated, with the films employed for optical storage and the formation of surface-relief gratings. Using Fourier transform infrared spectroscopy, we identified interactions involving SO3- groups from BY and NH3+ groups from PAH. These electrostatic interactions were responsible for the slow kinetics of writing in the optical storage experiments, due to a tendency to hinder photoisomerization and the subsequent reorientation of the azochromophores. The photoinduced birefringence did not saturate after one hour of exposure to the writing laser, whereas in azopolymer films, saturation is normally reached within a few minutes. on the other hand, the presence of such interactions prevented thermal relaxation of the chromophores after the writing laser was switched off, leading to a very stable written pattern. Moreover, the nanoscale interactions promoted mass transport for photoinscription of surface-relief gratings on PAH/BY LBL films, with the azochromophores being able to drag the inert PAH chains when undergoing the trans-cis-trans photoisomerization cycles. A low level of chromophore degradation was involved in the SRG photoinscription, which was confirmed with micro-Raman and fluorescence spectroscopies.

Adsorption processes in layer-by-layer films of poly(o-methoxyaniline): the role of aggregation

In this work we investigate the effect from the solution concentration on aggregation in layer-by-layer (LBL) films of poly(omethoxyaniline) (POMA) alternated with poly(vinyl sulfonic acid). Films are adsorbed on hydrophilized glass substrates and characterized with UV-Vis spectroscopy and atomic force microscopy. The formation of aggregates is favored in more concentrated solutions, leading to an increase in the diameter of the domains. This is caused by stronger polymer-polymer interactions under high concentrations. The size of POMA aggregates in solution is estimated to be larger than in LBL films, which is surprising because one should expect aggregates from solution to coalesce into larger aggregates in the deposited films. This unexpected result may be explained by a swelling effect of aggregates in the aqueous POMA solutions, consistent with other reports in the literature which consider the aggregates in solution to be made up of smaller aggregates. Upon adsorption on a solid substrate to form the LBL film, a molecular reorganization probably takes place, resulting in smaller aggregates. It is also found that the size distribution of the POMA domains in the LBL films is determined by the concentration of the solution. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Aggregation-based decomposition for multi-divisional models

The aggregation theory of mathematical programming is used to study decentralization in convex programming models. A two-level organization is considered and a aggregation-disaggregation scheme is applied to such a divisionally organized enterprise. In contrast to the known aggregation techniques, where the decision variables/production planes are aggregated, it is proposed to aggregate resources allocated by the central planning department among the divisions. This approach results in a decomposition procedure, in which the central unit has no optimization problem to solve and should only average local information provided by the divisions.