Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.

An existence theorem for an analytic first order PDE in the framework of Colombeau's theory

We study the existence of a holomorphic generalized solution u of the PDE[GRAPHICS]where f is a given holomorphic generalized function and (alpha (1),...alpha (m)) is an element of C-m\{0}.

Synthesis, characterization and solution properties of amphiphilic N-isopropylacrylamide-poly(ethylene glycol)-dodecyl methacrylate thermosensitive polymers

Terpolymers of N-isopropylacrylamide, dodecyl methacrylate (DOMA) and poly(ethylene glycol) (PEG) methacrylate, were synthesized by random copolymerization, and the composition was controlled to achieve systems having different thermosensitivities. H-1 NMR spectra and gel permeation chromatography (GPC) were employed to characterize the different samples obtained. The solution properties were studied by employing spectrophotometry, fluorescence, and dynamic light scattering techniques. The chemical compositions in the final terpolymers are close to those in the feed. The polymers exhibited cloud point temperatures (T-es) varying from 17 to 52 degrees C. Micropolarity studies using I-1/I-3 ratio of the vibronic bands of pyrene show the formation of amphiphilic aggregates capable of incorporating hydrophobic drugs as the polymer concentration is increased. The critical aggregation concentration (CAC) increases from 3.6 x 10(-3) to 1 x 10(-2) g/l with the PEG content varying from 5 to 35 mol%. Anisotropy measurements confirm the results obtained by pyrene fluorescence and show that the aggregates resulting from intermolecular interactions present different organizations. The hydrodynamic diameters (Dh) of the aggregates determined by dynamic light scattering (DLS) vary from 40 to 150 nm depending on the terpolymer composition. The T-cs and Dh values decreased with the ionic strength, and this behavior was attributed to the dehydration of the polymeric micelles. The capacity of solubilization of the aggregates was evaluated by employing pyrene, and the obtained results confirm the ability to incorporate hydrophobic molecules. (c) 2005 Elsevier B.V All rights reserved.

Theory of small aspect ratio waves in deep water

In the limit of small values of the aspect ratio parameter (or wave steepness) which measures the amplitude of a surface wave in units of its wave-length, a model equation is derived from the Euler system in infinite depth (deep water) without potential flow assumption. The resulting equation is shown to sustain periodic waves which on the one side tend to the proper linear limit at small amplitudes, on the other side possess a threshold amplitude where wave crest peaking is achieved. An explicit expression of the crest angle at wave breaking is found in terms of the wave velocity. By numerical simulations, stable soliton-like solutions (experiencing elastic interactions) propagate in a given velocities range on the edge of which they tend to the peakon solution. (c) 2005 Elsevier B.V. All rights reserved.

Higher-derivative theory of (2+1)-dimensional gravity

Higher-derivative gravity in 2 + 1 dimensions is considered. The general solution of the linearized field equations in a three-dimensional version of the Teyssandier gauge is obtained, and from that the solution for a static pointlike source is found. The deflection of light rays is also analysed. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Cubic interaction term for Schnabl's solution using Pade approximants

We evaluate the cubic interaction term in the action of open bosonic string field theory for Schnabl's solution written in terms of Bernoulli numbers. This computation provides us with new evidence for the fact that the string field equation of motion is satisfied when it is contracted with the solution itself.

Weak-field approximation of effective gravitational theory with local Galilean invariance

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Looking for a Matrix model for ABJM theory

Encouraged by the recent construction of fuzzy sphere solutions in the Aharony, Bergman, Jafferis, and Maldacena (ABJM) theory, we re-analyze the latter from the perspective of a Matrix-like model. In particular, we argue that a vortex solution exhibits properties of a supergraviton, while a kink represents a 2-brane. Other solutions are also consistent with the Matrix-type interpretation. We study vortex scattering and compare with graviton scattering in the massive ABJM background, however our results are inconclusive. We speculate on how to extend our results to construct a Matrix theory of ABJM.

Influence of the Solvent Evaporation Rate on the Crystalline Phases of Solution-Cast Poly(Vinylidene Fluoride) Films

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Biomimetic apatite formation on Ultra-High Molecular Weight Polyethylene (UHMWPE) using modified biomimetic solution

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

Removal of metal ions from aqueous solution by chelating polymeric hydrogel

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

Dynamic scale theory for characterizing surface morphology of layer-by-layer films of poly(o-methoxyaniline)

The dynamic scale theory and fractal concepts are employed in the characterization of surface morphological properties of layer-by-layer (LBL) films from poly(o-methoxyaniline) (POMA) alternated with poly(vinyl sulfonic acid) (PVS). The fractal dimensions are found to depend on the procedures to fabricate the POMA/PVS multilayers, particularly with regard to the drying procedures. LBL films obtained via drying in ambient air show a more homogeneous surface, compared to films dried under vacuum or a flow of nitrogen, due to a uniform rearrangement of polymer molecules during solvent evaporation.

Determination of site-site distance and site concentration within polymer beads: A combined swelling-electron paramagnetic resonance study

[GRAPHICS]This work proposes a combined swelling-electron paramagnetic resonance (EPR) approach aiming at determining some unusual polymer solvation parameters relevant for chemical processes occurring inside beads. Batches of benzhydrylamine-resin (BHAR), a copolymer of styrene-1% divinylbenzene containing phenylmethylamine groups were, labeled with the paramagnetic amino acid 2,2,6,6-tetramethylpiperidine-1-oxyl-4-amine-4-carboxylic acid (TOAC), and their swelling properties and EPR spectra were examined in DCM and DMF. By taking into account the BHARs labeling degrees, the corresponding swelling values, and some polymer structural characteristics, it was possible to calculate polymer swelling parameters, among them, the volume and the number of sites per bead, site-site distances and site concentration. The latter values ranged from 17 to 170 angstrom and from 0.4 to 550 mM, respectively. EPR spectroscopy was applied to validate the multistep calculation strategy of these swelling parameters. Spin-spin interaction was detected in the labeled resins at site-site distances less than approximately 60 A or probe concentrations higher than approximately 1 x 10(-2) M, in close agreement with the values obtained for the spin probe free in solution. Complementarily, the yield of coupling reactions in different resins indicated that the greater the inter-site distance or the lower the site concentration, the faster the reaction. The results suggested that the model and the experimental measurements developed for the determination of solvation parameters represent a relevant step forward for the deeper understanding and improvement of polymer-related processes.

Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre-Polya class and the Riemann xi -function.

Aqueous solution behavior of thermosensitive (N-isopropylacrylamide-acrylic acid-ethyl methacrylate) terpolymers

A series of N-isopropylacrylamide (NIPAM)-acrylic acid-ethyl methacrylate terpolymers with varied monomer compositions was prepared by radical polymerization. The solution behavior of these polymers was studied in dilute aqueous solution using spectrophotometry, fluorescence spectroscopy and high-sensitivity differential scanning calorimetry. The results obtained revealed that the lower critical solution temperatures depend strongly on the copolymer composition, solution pH and ionic strength. At a high pH, the ionization of acrylic acid (AA) units leads to an increase in solution cloud points (T-c). Solutions of polymers containing 10% or less of AA display a constant T-c for pH above 5.5, with 15% there is a continuous increase in T-c with pH and, for higher AA contents, no clouding was observed within the studied temperature range. Fluorescence probe studies were conducted by following the I (1)/I (3) ratio of pyrene vibronic bands and the emission of anilinonaphtalene sulfonic acid, sodium salt (ANS), both approaches revealing the existence of hydrophobic domains for polymers with higher ethyl methacrylate content at temperatures lower than T-c, suggesting some extent of aggregation and/or a coil-to-globule transition. Scanning calorimetry measurements showed an endothermic transition at temperatures agreeing with the previously detected cloud points. Moreover, the transition curves became broader and with a smaller transition enthalpy, as both the AA content and the solution pH were increased. These broader transitions were interpreted to be the result of a wider molecular distribution upon polymer ionization, hence, displaying varied solution properties. The decrease in transition enthalpy was rationalized as a consequence of reminiscent hydration of NIPAM units, even after phase separation, owing to the presence of electric charges along the polymer chain.