Quasi Monte Carlo approach with uniform separation for solving of the rendering equation, ICNAAM 2007

This paper is directed to the advanced parallel Quasi Monte Carlo (QMC) methods for realistic image synthesis. We propose and consider a new QMC approach for solving the rendering equation with uniform separation. First, we apply the symmetry property for uniform separation of the hemispherical integration domain into 24 equal sub-domains of solid angles, subtended by orthogonal spherical triangles with fixed vertices and computable parameters. Uniform separation allows to apply parallel sampling scheme for numerical integration. Finally, we apply the stratified QMC integration method for solving the rendering equation. The superiority our QMC approach is proved.

Alignment of a model amyloid peptide fragment in bulk and at a solid surface

The alignment of model amyloid peptide YYKLVFFC is investigated in bulk and at a solid surface using a range of spectroscopic methods employing polarized radiation. The peptide is based on a core sequence of the amyloid beta (A beta) peptide, KLVFF. The attached tyrosine and cysteine units are exploited to yield information on alignment and possible formation of disulfide or dityrosine links. Polarized Raman spectroscopy on aligned stalks provides information on tyrosine orientation, which complements data from linear dichroism (LD) on aqueous solutions subjected to shear in a Couette cell. LD provides a detailed picture of alignment of peptide strands and aromatic residues and was also used to probe the kinetics of self-assembly. This suggests initial association of phenylalanine residues, followed by subsequent registry of strands and orientation of tyrosine residues. X-ray diffraction (XRD) data from aligned stalks is used to extract orientational order parameters from the 0.48 nm reflection in the cross-beta pattern, from which an orientational distribution function is obtained. X-ray diffraction on solutions subject to capillary flow confirmed orientation in situ at the level of the cross-beta pattern. The information on fibril and tyrosine orientation from polarized Raman spectroscopy is compared with results from NEXAFS experiments on samples prepared as films on silicon. This indicates fibrils are aligned parallel to the surface, with phenyl ring normals perpendicular to the surface. Possible disulfide bridging leading to peptide dimer formation was excluded by Raman spectroscopy, whereas dityrosine formation was probed by fluorescence experiments and was found not to occur except under alkaline conditions. Congo red binding was found not to influence the cross-beta XRD pattern.

A non-uniform mesh scheme for compressible flow

A non-uniform mesh scheme is presented for the computation of compressible flows governed by the Euler equations of gas dynamics. The scheme is based on flux-difference splitting and represents an extension of a similar scheme designed for uniform meshes. The numerical results demonstrate that little, if any, spurious oscillation occurs as a result of the non-uniformity of the mesh; and importantly, shock speeds are computed correctly.

A TVD finite difference scheme with non-uniform meshes and without upstream weighting

We present a finite difference scheme, with the TVD (total variation diminishing) property, for scalar conservation laws. The scheme applies to non-uniform meshes, allowing for variable mesh spacing, and is without upstream weighting. When applied to systems of conservation laws, no scalar decomposition is required, nor are any artificial tuning parameters, and this leads to an efficient, robust algorithm.

Multiplexed quantitative proteomics using differential metabolic 15N-labeling

There are several advantages of using metabolic labeling in quantitative proteomics. The early pooling of samples compared to post-labeling methods eliminates errors from different sample processing, protein extraction and enzymatic digestion. Metabolic labeling is also highly efficient and relatively inexpensive compared to commercial labeling reagents. However, methods for multiplexed quantitation in the MS-domain (or ‘non-isobaric’ methods), suffer from signal dilution at higher degrees of multiplexing, as the MS/MS signal for peptide identification is lower given the same amount of peptide loaded onto the column or injected into the mass spectrometer. This may partly be overcome by mixing the samples at non-uniform ratios, for instance by increasing the fraction of unlabeled proteins. We have developed an algorithm for arbitrary degrees of nonisobaric multiplexing for relative protein abundance measurements. We have used metabolic labeling with different levels of 15N, but the algorithm is in principle applicable to any isotope or combination of isotopes. Ion trap mass spectrometers are fast and suitable for LC-MS/MS and peptide identification. However, they cannot resolve overlapping isotopic envelopes from different peptides, which makes them less suitable for MS-based quantitation. Fourier-transform ion cyclotron resonance (FTICR) mass spectrometry is less suitable for LC-MS/MS, but provides the resolving power required to resolve overlapping isotopic envelopes. We therefore combined ion trap LC-MS/MS for peptide identification with FTICR LC-MS for quantitation using chromatographic alignment. We applied the method in a heat shock study in a plant model system (A. thaliana) and compared the results with gene expression data from similar experiments in literature.

Small-angle x-ray scattering study of flow alignment of a thermotropic liquid crystal in the nematic and smectic phases

WThe capillary flow alignment of the thermotropic liquid crystal 4-n-octyl-4′-cyanobiphenyl in the nematic and smectic phases is investigated using time-resolved synchrotron small-angle x-ray scattering. Samples were cooled from the isotropic phase to erase prior orientation. Upon cooling through the nematic phase under Poiseuille flow in a circular capillary, a transition from the alignment of mesogens along the flow direction to the alignment of layers along the flow direction (mesogens perpendicular to flow) appears to occur continuously at the cooling rate applied. The transition is centered on a temperature at which the Leslie viscosity coefficient α3 changes sign. The configuration with layers aligned along the flow direction is also observed in the smectic phase. The transition in the nematic phase on cooling has previously been ascribed to an aligning-nonaligning or tumbling transition. At high flow rates there is evidence for tumbling around an average alignment of layers along the flow direction. At lower flow rates this orientation is more clearly defined. The layer alignment is ascribed to surface-induced ordering propagating into the bulk of the capillary, an observation supported by the parallel alignment of layers observed for a static sample at low temperatures in the nematic phase.

Uniform versus discriminatory tariffs

We analyze the non-cooperative interaction between two exporting countries producing differentiated products and one importing country when governments use optimal policies to maximize welfare. The analysis includes product differentiation, asymmetric costs, and Bertrand competition. For identical exporting countries we demonstrate that the importing country always prefers a uniform tariff regime while both exporting countries prefer a discriminatory tariff regime for any degree of product differentiation. If countries are asymmetric in terms of production cost then the higher-cost exporter always prefers the discriminatory regime but the lower-cost exporter prefers the uniform regime if there is a significant cost differential. With cost asymmetry the announcement of a uniform tariff regime by the importer is not a credible strategy since there is an incentive to deviate to discrimination. This implies an international body can play a role in ensuring that tariff agreements are respected.

Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field

A unified view on the interfacial instability in a model of aluminium reduction cells in the presence of a uniform, vertical, background magnetic field is presented. The classification of instability modes is based on the asymptotic theory for high values of parameter β, which characterises the ratio of the Lorentz force based on the disturbance current, and gravity. It is shown that the spectrum of the travelling waves consists of two parts independent of the horizontal cross-section of the cell: highly unstable wall modes and stable or weakly unstable centre, or Sele’s modes. The wall modes with the disturbance of the interface being localised at the sidewalls of the cell dominate the dynamics of instability. Sele’s modes are characterised by a distributed disturbance over the whole horizontal extent of the cell. As β increases these modes are stabilized by the field.

Thermal comfort assessment in a non-uniform thermal environment

This paper presents results for thermal comfort assessment in non-uniform thermal environments. Three types of displacement ventilation (DV) units that created stratified condition in an environmental test chamber have been selected to carry out the thermal comfort assessment: a flat diffuser (DV1), semi-circular diffuser (DV2), and floor swirl diffuser (DV3). The CBE (Center for the Built Environment at Berkeley) comfort model was implemented in this study to assess the occupant’s thermal comfort for the three DV types. The CBE model predicted the occupant’s mean skin as well as local skin temperatures very well when compared with measurements found in the literature, while it underestimated the occupant’s core temperature. The predicted occupant’s thermal sensation and thermal comfort for the case of (DV2) were the best. Therefore, the semi-circular diffuser (DV2) provided better thermal comfort for the occupant in comparison with the other two DV types.

A new frequency-uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L2(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star-combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second-kind integral operator for which convergence of the Galerkin method in L2(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star-combined operator implies frequency-explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high-frequency case. The proof of coercivity of the star-combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains.