Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.     

Changes in defect concentration within polymer crystals: annealing of isotropic and drawn polyethylene

An estimation of the changes in the level of chain defects (branches) accommodated within crystals of undrawn and drawn branched polyethylene, subsequently annealed, is carried out in the light of unit cell expansion data. The results reveal that annealing affects the estimated crystalline defect concentration differently depending on whether the material was drawn or undrawn. Thus, annealing of drawn polyethylene with a defect concentration of 3 % results in a healing of crystal defects, due to a preferential rejection of branches from the crystals. In contrast, annealing of melt crystallized branched polyethylene does not influence the average concentration of chain defects within the crystal despite the increase in lamellar thickness. The branches are trapped into the much wider lamellar crystals with fewer grain boundaries available and defect sequences cannot diffuse out of the crystals.Cordially dedicated to Prof. Dr. H.-G. Kilian on the occasion of his 60th birthday.     

Dynamic mechanical and dielectric relaxations in poly(monoethylphenyl itaconate)

Dynamic mechanical and dielectric relaxational behavior of poly(monoethylphenyl itaconate) at different frequencies and temperatures was studied. Three relaxation zones are found. The dynamic mechanical response is dominated by a relaxation peak at room temperature, labeled β relaxation. Two prominent shoulders labelled as γ and α relaxations are observed. Because of the overlapping of the α and γ with the β relaxation, a deconvolution method to improve the understanding of these phenomena is proposed. In spite of the complexity of the experimental spectra, the proposed deconvolution method seems to be a convenient approach to interpret the relaxational behavior of this polymer. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2749–2756, 1997     

Probing multiple melting behaviors in poly(ethylene naphthalene 2,6‐dicarboxylate) with different thermal histories by simultaneous wide‐angle and small‐angle X‐ray scattering

A simultaneous wide‐angle and small‐angle X‐ray scattering study of two poly(ethylene naphthalene 2,6‐dicarboxylate) samples crystallized from the glassy state at different annealing temperatures for different annealing times was carried out with synchrotron radiation. Either single or dual melting was induced in the samples, as confirmed by differential scanning calorimetry (DSC). The correlation function and interface distribution function were calculated to evaluate microstructural parameters such as the long spacing, the thickness of the amorphous and crystalline phases, and the width of the size distributions. The sample with dual melting behavior exhibited an abrupt increase of all microstructural parameters at temperatures above the melting of the lowest endotherm, whereas the sample revealing a single melting endotherm did not show such a sudden change. This finding agrees with the concept that the appearance of two melting peaks in DSC traces can be explained by the dual lamellar stacking model. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 881–894, 2001     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.     

Resonant Raman scattering by N-related local modes in AlGaAs/InGaAsN multiquantum wells

We report resonant Raman scattering and secondary ion mass spectrometry measurements on InGaAsN/AlGaAs multiquantum wells grown by plasma-assisted molecular beam epitaxy. The appearance of a strong TO band at resonance with nitrogen (N)-related electronic levels has been observed. The N-induced vibration mode at 470 cm⁻¹ changes in intensity and shape with increasing N and In content. A new vibration mode has been observed at 320 cm⁻¹, whose intensity scales with the N concentration. This mode is not present in InGaAsN films, so it is linked to the presence of Al. Its frequency is close to the B₁ silent mode of wurtzite GaN. It is attributed to the formation of GaN pairs, near the MQW interfaces as a consequence of the preferential Al–N bonding.     

Microindentation Hardness of Nanostructured Thermoplastic Materials

Summary: The micromechanical behaviour of various thermoplastics based nanocomposites was investigated with the aid of the microindentation technique. The materials studied were microphase separated styrene-butadiene block copolymer systems and several thermoplastics reinforced with nano-sized fillers having variable dimensionality. It was found that the microhardness behaviour of the nanocomposites studied was strongly influenced by the dimensionalities of the filler. Due to large surface to volume-ratio one- and two-dimensional fillers exhibit a far better reinforcing behaviour than the three dimensional ones. In case of nanostructured block copolymers, the microhardness is not determined by the total polystyrene (PS)/polybutadiene (PB) composition alone but diminishes gradually in presence of freely standing dangling polybutadiene chains even if the morphology of the systems remains unaltered.     

Differential non-destructive image current detection in a fourier transform quadrupole ion trap

Dual-detector differential non-destructive Fourier transform detection in a quadrupole ion trap is shown to improve signal intensity and reduce noise compared with spectra recorded using a single detector. A larger area detector in each end-cap electrode is machined to fit its hyperbolic shape and so minimize field imperfections on the z-axis. Argon, acetophenone and bromobenzene spectra were recorded to allow a comparison between single- and dual-detector (differential) modes of detection and to demonstrate the improvement achieved with differential detection. Copyright 1999 John Wiley & Sons, Ltd.