On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

We consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and impedance infinite rough surfaces.Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A→∞ of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ‘flattened’ in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd.

LARGE ATOMIC and NUCLEAR THREE-BODY SYSTEMS: SCATTERING and BINDING

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

Signature of the scattering between dark sectors in large scale cosmic microwave background anisotropies

We study the interaction between dark sectors by considering the momentum transfer caused by the dark matter scattering elastically within the dark energy fluid. Describing the dark scattering analogy to the Thomson scattering which couples baryons and photons, we examine the impact of the dark scattering in CMB observations. Performing global fitting with the latest observational data, we find that for a dark energy equation of state w < -1, the CMB gives tight constraints on dark matter-dark energy elastic scattering. Assuming a dark matter particle of proton mass, we derive an elastic scattering cross section of sigma(D) < 3.295 x 10(-10)sigma(T) where sigma(T) is the cross section of Thomson scattering. For w > -1, however, the constraints are poor. For w = -1, sigma(D) can formally take any value.

High frequency acoustics in colloid-based meso- and nanostructures by spontaneous Brillouin light scattering

Materials that can mold the flow of elastic waves of certain energy in certain directions are called phononic materials. The present thesis deals essentially with such phononic systems, which are structured in the mesoscale (<1 µm), and with their individual components. Such systems show interesting phononic properties in the hypersonic region, i.e., at frequencies in the GHz range. It is shown that colloidal systems are excellent model systems for the realization of such phononic materials. Therefore, different structures and particle architectures are investigated by Brillouin light scattering, the inelastic scattering of light by phonons.rnThe experimental part of this work is divided into three chapters: Chapter 4 is concerned with the localized mechanical waves in the individual spherical colloidal particles, i.e., with their resonance- or eigenvibrations. The investigation of these vibrations with regard to the environment of the particles, their chemical composition, and the influence of temperature on nanoscopically structured colloids allows novel insights into the physical properties of colloids at small length scales. Furthermore, some general questions concerning light scattering on such systems, in dispute so far, are convincingly addressed.rnChapter 5 is a study of the traveling of mechanical waves in colloidal systems, consisting of ordered and disordered colloids in liquid or elastic matrix. Such systems show acoustic band gaps, which can be explained geometrically (Bragg gap) or by the interaction of the acoustic band with the eigenvibrations of the individual spheres (hybridization gap).rnWhile the latter has no analogue in photonics, the presence of strong phonon scatterers, when a large elastic mismatch between the composite components exists, can largely impact phonon propagation in analogy to strong multiple light scattering systems. The former is exemplified in silica based phononic structures that opens the door to new ways of sound propagation manipulation.rnChapter 6 describes the first measurement of the elastic moduli in newly fabricated by physical vapor deposition so-called ‘stable organic glasses’. rnIn brief, this thesis explores novel phenomena in colloid-based hypersonic phononic structures, utilizing a versatile microfabrication technique along with different colloid architectures provided by material science, and applying a non-destructive optical experimental tool to record dispersion diagrams.rn

From large polycyclic aromatic hydrocarbons to extended aromate-rich networks

The common ground of this study is the development of novel synthetic strategies to extended one-, two- and three-dimensional aromate-rich systems for which a number of applications are envisaged. rnThe point of departure is the synthesis and characterization of highly symmetric macrocyclic PAHs (polycyclic aromatic hydrocarbons) for which various aspects of supramolecular chemistry will be investigated. The versatility of the Yamamoto macrocyclization will be demonstrated on the basis of a set of cyclic trimers that exhibit a rich supramolecular chemistry. 1,10-phenanthroline, triphenylene and ortho-terphenyl building blocks have been successfully assembled to the corresponding macrocycles following the newly developed synthetic route. Scanning-tunneling microscopy (STM) and two-dimensional wide-angle X-ray scattering (2D-WAXS) were used to study the two- and three-dimensional self-assembly, respectively.rnSecondly, the development of chemical approaches to highly shape-anisotropic graphene nanoribbons (GNRs) and related nanographene molecules shall be discussed. Aryl-aryl coupling was used for the bottom-up fabrication of dendronized monomers, polymers and model compounds. Subsequently, these structures were converted into the final graphene material using oxidative (Scholl-type) cyclodehydrogenation. The GNRs thus obtained are characterized by an unprecedented length and lateral extension. The relevance of structural tailoring in the field of well-defined graphene materials is discussed in detail as only the chemical approach provides full geometry control. rnLastly, novel pathways towards the synthesis of extended three-dimensional networks that are dominated by nitrogen-rich motifs will be presented. If porous, these materials hold a great potential in the fields of gas and energy storage as well as for applications in catalysis. Hence, poly(aminal) networks based on melamine as crosslinking unit were synthesized and characterized with respect to the applications mentioned above. As set of conjugated poly(azomethine) networks was investigated regarding their use as a novel class of organic semiconductors for photocatalytic water splitting. The network structures described in this chapter can also be subjected to a controlled pyrolysis yielding mesoporous, nitrogen-rich carbon materials that were evaluated as active component for supercapacitors.rn

A canonical UTD solution for electromagnetic scattering by an electrically large impedance circular cylinder illuminated by an obliquely incident plane wave

A uniform geometrical theory of diffraction (UTD) solution is developed for the canonical problem of the electromagnetic (EM) scattering by an electrically large circular cylinder with a uniform impedance boundary condition (IBC), when it is illuminated by an obliquely incident high frequency plane wave. A solution to this canonical problem is first constructed in terms of an exact formulation involving a radially propagating eigenfunction expansion. The latter is converted into a circumferentially propagating eigenfunction expansion suited for large cylinders, via the Watson transform, which is expressed as an integral that is subsequently evaluated asymptotically, for high frequencies, in a uniform manner. The resulting solution is then expressed in the desired UTD ray form. This solution is uniform in the sense that it has the important property that it remains continuous across the transition region on either side of the surface shadow boundary. Outside the shadow boundary transition region it recovers the purely ray optical incident and reflected ray fields on the deep lit side of the shadow boundary and to the modal surface diffracted ray fields on the deep shadow side. The scattered field is seen to have a cross-polarized component due to the coupling between the TEz and TMz waves (where z is the cylinder axis) resulting from the IBC. Such cross-polarization vanishes for normal incidence on the cylinder, and also in the deep lit region for oblique incidence where it properly reduces to the geometrical optics (GO) or ray optical solution. This UTD solution is shown to be very accurate by a numerical comparison with an exact reference solution.

Effect of the average soft-segment length on the morphology and properties of segmented polyurethane nanocomposites

Two organically modified layered silicates (with small and large diameters) were incorporated into three segmented polyurethanes with various degrees of microphase separation. Microphase separation increased with the molecular weight of the poly(hexamethylene oxide) soft segment. The molecular weight of the soft segment did not influence the amount of polyurethane intercalating the interlayer spacing. Small-angle neutron scattering and differential scanning calorimetry data indicated that the layered silicates did not affect the microphase morphology of any host polymer, regardless of the particle diameter. The stiffness enhancement on filler addition increased as the microphase separation of the polyurethane decreased, presumably because a greater number of urethane linkages were available to interact with the filler. For comparison, the small nanofiller was introduced into a polyurethane with a poly(tetramethylene oxide) soft segment, and a significant increase in the tensile strength and a sharper upturn in the stress-strain curve resulted. No such improvement occurred in the host polymers with poly(hexamethylene oxide) soft segments. It is proposed that the nanocomposite containing the more hydrophilic and mobile poly(tetramethylene oxide) soft segment is capable of greater secondary bonding between the polyurethane chains and the organosilicate surface, resulting in improved stress transfer to the filler and reduced molecular slippage. (c) 2006 Wiley Periodicals, Inc.

A study of the scattering of fast neutrons in large samples

In the present work, the elastic scattering of fast neutrons from iron and concrete samples were studied at incident neutron energies of 14.0 and 14.4 Mev, using a neutron spectrometer based on the associated particle time-of-flight technique. These samples were chosen because of their importance in the design of fusion reactor shielding and construction. Using the S.A.M.E.S. accelerator and the 3 M v Dynamitron accelerator at the Radiation Centre, 14.0 and 14.4 Mev neutrons were produced by the T(d, n)4He reaction at incident deuteron energies of 140 keV and 900 keV mass III ions respectively. The time of origin of the neutron was determined by detecting the associated alpha particles. The samples used were extended flat plates of thicknesses up to 1.73 mean free paths for iron and 2.3 mean free paths for concrete. The associated alpha particles and fast neutrons were detected by means of a plastic scintillator mounted on a fast focused photomultiplier tube. The differential neutron elastic scattering cross-sections were measured for 14 Mev neutrons in various thicknesses of iron and concrete in the angular range from zero to 90°. In addition, the angular distributions of 14.4 Mev neutrons after passing through extended samples of iron were measured at several scattering angles in the same angular range. The measurements obtained for the thin sample of iron were compared with the results of Coon et al. The differential cross-sections for the thin iron sample were also analyzed on the optical model using the computer code RAROMP. For the concrete sample, the angular distribution of the thin sample was compared with the cross-sections calculated from the major constituent elements of concrete, and with the predicted values of the optical model for those elements. No published data could be found to compare with the results of the concrete differential cross-sections. In the case of thick samples of iron and concrete, the number of scattered neutrons were compared with a phenomological calculation based on the continuous slowing down model. The variation of measured cross-sections with sample thickness were found to follow the empirical relation σ = σ0 eαx. By using the universal constant "K", good fits were obtained to the experimental data. In parallel with the work at 14.0 and 14.4 Mev, an associated particle time-of-flight spectrometer was investigated which used the 2H(d,n)3He reaction for 3.02 Mev neutron energy at the incident deuteron energy of 1 Mev.

Supramolecular polymorphism of DNA in non-cationic L(alpha) lipid phases

The structure of a complex between hydrated DNA and a non-cationic lipid is studied, including its phase diagram. The complex is spontaneously formed by adding DNA fragments (ca. 150 base pairs in length) to non-cationic lipids and water. The self-assembly process often leads to highly ordered structures. The structures were studied by combining X-ray scattering, fluorescence and polarized microscopy, as well as freeze-fracture experiments with transmission electron microscopy. We observe a significant increase of the smectic order as DNA is incorporated into the water layers of the lamellar host phase, and stabilization of single phase domains for large amounts of DNA. The effect of confinement on DNA ordering is investigated by varying the water content, following three dilution lines. A rich polymorphism is found, ranging from weakly correlated DNA-DNA in-plane organizations to highly ordered structures, where transmembrane correlations lead to the formation of columnar rectangular and columnar hexagonal superlattices of nucleotides embedded between lipid lamellae. From these observations, we suggest that addition of DNA to the lamellar phase significantly restricts membrane fluctuations above a certain concentration and helps the formation of the lipoplex. The alteration of membrane steric interactions, together with the appearance of interfacial interactions between membranes and DNA molecules may be a relevant mechanism for the emergence of highly ordered structures in the concentrated regime.

Thermally activated intersubband scattering and oscillating magnetoresistance in quantum wells

Experimental studies of magnetoresistance in high-mobility wide quantum wells reveal oscillations which appear with an increase in temperature to 10 K and whose period is close to that of Shubnikov-de Haas oscillations. The observed phenomenon is identified as magnetointersubband oscillations caused by the scattering of electrons between two occupied subbands and the third subband which becomes occupied as a result of thermal activation. These small-period oscillations are less sensitive to thermal suppression than the large-period magnetointersubband oscillations caused by the scattering between the first and the second subbands. Theoretical study, based on consideration of electron scattering near the edge of the third subband, gives a reasonable explanation of our experimental findings.

alpha plus alpha scattering reexamined in the context of the Sao Paulo potential

We have analyzed a large set of alpha + alpha elastic scattering data for bombarding energies ranging from 0.6 to 29.5 MeV. Because of the complete lack of open reaction channels, the optical interaction at these energies must have a vanishing imaginary part. Thus, this system is particularly important because the corresponding elastic scattering cross sections are very sensitive to the real part of the interaction. The data were analyzed in the context of the velocity-dependent Sao Paulo potential, which is a successful theoretical model for the description of heavy-ion reactions from sub-barrier to intermediate energies. We have verified that, even in this low-energy region, the velocity dependence of the model is quite important for describing the data of the alpha + alpha system.

Scattering of massless scalar waves by Reissner-Nordstrom black holes

We present a study of scattering of massless planar scalar waves by a charged nonrotating black hole. Partial wave methods are applied to compute scattering and absorption cross sections, for a range of incident wavelengths. We compare our numerical results with semiclassical approximations from a geodesic analysis, and find excellent agreement. The glory in the backward direction is studied, and its properties are shown to be related to the properties of the photon orbit. The effects of the black hole charge upon scattering and absorption are examined in detail. As the charge of the black hole is increased, we find that the absorption cross section decreases, and the angular width of the interference fringes of the scattering cross section at large angles increases. In particular, the glory spot in the backward direction becomes wider. We interpret these effects under the light of our geodesic analysis.

Dynamic light scattering and optical absorption spectroscopy study of pH and temperature stabilities of the extracellular hemoglobin of Glossoscolex paulistus

The extracellular hemoglobin of Glossoscolex paulistus (HbGp) is constituted of subunits containing heme groups, monomers and trimers, and nonheme structures, called linkers, and the whole protein has a minimum molecular mass near 3.1 x 10(6) Da. This and other proteins of the same family are useful model systems for developing blood substitutes due to their extracellular nature, large size, and resistance to oxidation. HbGp samples were studied by dynamic light scattering (DLS). In the pH range 6.0-8.0, HbGp is stable and has a monodisperse size distribution with a z-average hydrodynamic diameter (D-h) of 27 +/- 1 nm. A more alkaline pH induced an irreversible dissociation process, resulting in a smaller D-h of 10 +/- 1 nm. The decrease in D-h suggests a complete hemoglobin dissociation. Gel filtration chromatography was used to show unequivocally the oligomeric dissociation observed at alkaline pH. At pH 9.0, the dissociation kinetics is slow, taking a minimum of 24 h to be completed. Dissociation rate constants progressively increase at higher pH, becoming, at pH 10.5, not detectable by DILS. Protein temperature stability was also pH-dependent. Melting curves for HbGp showed oligomeric dissociation and protein denaturation as a function of pH. Dissociation temperatures were lower at higher pH. Kinetic studies were also performed using ultraviolet-visible absorption at the Soret band. Optical absorption monitors the hemoglobin autoxidation while DLS gives information regarding particle size changes in the process of protein dissociation. Absorption was analyzed at different pH values in the range 9.0-9.8 and at two temperatures, 25 degrees C and 38 degrees C. At 25 degrees C, for pH 9.0 and 9.3, the kinetics monitored by ultraviolet-visible absorption presents a monoexponential behavior, whereas for pH 9.6 and 9.8, a biexponential behavior was observed, consistent with heme heterogeneity at more alkaline pH. The kinetics at 38 degrees C is faster than that at 25 degrees C and is biexponential in the whole pH range. DLS dissociation rates are faster than the autoxidation dissociation rates at 25 degrees C. Autoxiclation and dissociation processes are intimately related, so that oligomeric protein dissociation promotes the increase of autoxidation rate and vice versa. The effect of dissociation is to change the kinetic character of the autoxidation of hemes from monoexponential to biexponential, whereas the reverse change is not as effective. This work shows that DLS can be used to follow, quantitatively and in real time, the kinetics of changes in the oligomerization of biologic complex supramolecular systems. Such information is relevant for the development of mimetic systems to be used as blood substitutes.

An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations

The applicability of a meshfree approximation method, namely the EFG method, on fully geometrically exact analysis of plates is investigated. Based on a unified nonlinear theory of plates, which allows for arbitrarily large rotations and displacements, a Galerkin approximation via MLS functions is settled. A hybrid method of analysis is proposed, where the solution is obtained by the independent approximation of the generalized internal displacement fields and the generalized boundary tractions. A consistent linearization procedure is performed, resulting in a semi-definite generalized tangent stiffness matrix which, for hyperelastic materials and conservative loadings, is always symmetric (even for configurations far from the generalized equilibrium trajectory). Besides the total Lagrangian formulation, an updated version is also presented, which enables the treatment of rotations beyond the parameterization limit. An extension of the arc-length method that includes the generalized domain displacement fields, the generalized boundary tractions and the load parameter in the constraint equation of the hyper-ellipsis is proposed to solve the resulting nonlinear problem. Extending the hybrid-displacement formulation, a multi-region decomposition is proposed to handle complex geometries. A criterium for the classification of the equilibrium`s stability, based on the Bordered-Hessian matrix analysis, is suggested. Several numerical examples are presented, illustrating the effectiveness of the method. Differently from the standard finite element methods (FEM), the resulting solutions are (arbitrary) smooth generalized displacement and stress fields. (c) 2007 Elsevier Ltd. All rights reserved.