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.

A similarity solution for a shock reflection problem in isentropic gas dynamics

A one-dimensional shock-reflection test problem in the case of slab, cylindrical, or spherical symmetry is discussed. The differential equations for a similarity solution are derived and solved numerically in conjunction with the Rankie-Hugoniot shock relations.

An efficient flux difference splitting algorithm for unsteady duct flows of a real gas

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This includes flow in a duct of variable cross-section, as well as flow with slab, cylindrical or spherical symmetry, as well as the case of an ideal gas, and can be useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The resulting scheme requires an average of the flow variables across the interface between cells, and this average is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual “square root” averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and for a number of equations of state. The results compare favourably with the results from other schemes.

An efficient shock capturing algorithm for compressible flows in a duct of variable cross-section

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co-ordinate. This includes flow in a duct of variable cross-section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two-dimensional problem with no sources.

Similarity solutions for multicomponent flows

A one-dimensional shock-reflection test problem in the case of slab, cylindrical or spherical symmetry is discussed for multi-component flows. The differential equations for a similarity solution are derived and then solved numerically in conjunction with the Rankine-Hugoniot shock relations.

Real gas flows in a duct

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This include flow in a duct of variable cross-section as well as flow with cylindrical or spherical symmetry, and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The scheme is applied with success to a problem involving the interaction of converging and diverging cylindrical shocks for four equations of state and to a problem involving the reflection of a converging shock.

Cylindrically symmetric flows in a Lagrangian frame

An approximate Riemann solver, in a Lagrangian frame of reference, is presented for the compressible flow equations with cylindrical and spherical symmetry, including flow in a duct of variable cross section. The scheme is applied to a cylindrically symmetric problem involving the interaction of shocks.

Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing

We study the numerical efficiency of solving the self-consistent field theory (SCFT) for periodic block-copolymer morphologies by combining the spectral method with Anderson mixing. Using AB diblock-copolymer melts as an example, we demonstrate that this approach can be orders of magnitude faster than competing methods, permitting precise calculations with relatively little computational cost. Moreover, our results raise significant doubts that the gyroid (G) phase extends to infinite $\chi N$. With the increased precision, we are also able to resolve subtle free-energy differences, allowing us to investigate the layer stacking in the perforated-lamellar (PL) phase and the lattice arrangement of the close-packed spherical (S$_{cp}$) phase. Furthermore, our study sheds light on the existence of the newly discovered Fddd (O$^{70}$) morphology, showing that conformational asymmetry has a significant effect on its stability.

Droplets of structured fluid on a flat substrate

We study the equilibrium morphology of droplets of symmetric AB diblock copolymer on a flat substrate. Using self-consistent field theory (SCFT), we provide the first predictions for the equilibrium droplet shape and its internal structure. When the sustrate affinity for the A component, $\eta_A$, is small, the droplet adopts a nearly spherical shape much like that of simple fluids. Inside the spherical droplet, however, concentric circular lamellar layers stack on top of each other; hence the thickness of the droplet is effectively quantized by a half-integer or integer number of layers. At larger $\eta_A$ and smaller contact angle, the area of the upper-most layer becomes relatively large, resulting in a nearly flat, faceted top surface, followed by a semi-spherical slope. This geometry is remarkably reminiscent of the droplet shapes observed with smetic liquid crystals.

NOx and O3 above a tropical rainforest: an analysis with a global and box model

A cross-platform field campaign, OP3, was conducted in the state of Sabah in Malaysian Borneo between April and July of 2008. Among the suite of observations recorded, the campaign included measurements of NOx and O3 – crucial outputs of any model chemistry mechanism. We describe the measurements of these species made from both the ground site and aircraft. We then use the output from two resolutions of the chemistry transport model p-TOMCAT to illustrate the ability of a global model chemical mechanism to capture the chemistry at the rainforest site. The basic model performance is good for NOx and poor for ozone. A box model containing the same chemical mechanism is used to explore the results of the global model in more depth and make comparisons between the two. Without some parameterization of the nighttime boundary layer – free troposphere mixing (i.e. the use of a dilution parameter), the box model does not reproduce the observations, pointing to the importance of adequately representing physical processes for comparisons with surface measurements. We conclude with a discussion of box model budget calculations of chemical reaction fluxes, deposition and mixing, and compare these results to output from p-TOMCAT. These show the same chemical mechanism behaves similarly in both models, but that emissions and advection play particularly strong roles in influencing the comparison to surface measurements.

Molecular t-matrices for low-energy electron diffraction (TMOL v1.1)*1

We describe a FORTRAN-90 program that computes scattering t-matrices for a molecule. These can be used in a Low-Energy Electron Diffraction program to solve the molecular structural problem very efficiently. The intramolecular multiple scattering is computed within a Dyson-like approach, using free space Green propagators in a basis of spherical waves. The advantage of this approach is related to exploiting the chemical identity of the molecule, and to the simplicity to translate and rotate these t-matrices without performing a new multiple-scattering calculation for each configuration. FORTRAN-90 routines for rotating the resulting t-matrices using Wigner matrices are also provided.

A FORTRAN-90 low-energy electron diffraction program (LEED90 v1.1)

We describe a FORTRAN-90 program to compute low-energy electron diffraction I(V) curves. Plane-waves and layer doubling are used to compute the inter-layer multiple-scattering, while the intra-layer multiple-scattering is computed in the standard way expanding the wavefield on a basis of spherical waves. The program is kept as general as possible, in order to allow testing different parts of multiple-scattering calculations. In particular, it can handle non-diagonal t-matrices describing the scattering of non-spherical potentials, anisotropic vibrations, anharmonicity, etc. The program does not use old FORTRAN flavours, and has been written keeping in mind the advantage for parallelism brought forward by FORTRAN-90.

Cavity-enhanced absorption: detection of nitrogen dioxide and iodine monoxide using a violet laser diode

We present an application of cavity-enhanced absorption spectroscopy with an off-axis alignment of the cavity formed by two spherical mirrors and with time integration of the cavity-output intensity for detection of nitrogen dioxide (NO2) and iodine monoxide (IO) radicals using a violet laser diode at lambda = 404.278 nm. A noise-equivalent (1sigma = root-mean-square variation of the signal) fractional absorption for one optical pass of 4.5x10(-8) was demonstrated with a mirror reflectivity of similar to0.99925, a cavity length of 0.22 m and a lock-in-amplifier time constant of 3 s. Noise-equivalent detection sensitivities towards nitrogen dioxide of 1.8x10(10) molecule cm(-3) and towards the IO radical of 3.3x10(9) molecule cm(-3) were achieved in flow tubes with an inner diameter of 4 cm for a lock-in-amplifier time constant of 3 s. Alkyl peroxy radicals were detected using chemical titration with excess nitric oxide (RO2 + NO --> RO + NO2). Measurement of oxygen-atom concentrations was accomplished by determining the depletion of NO2 in the reaction NO2 + O --> NO + O-2. Noise-equivalent concentrations of alkyl peroxy radicals and oxygen atoms were 3x10(10) molecule cm(-3) in the discharge-flow-tube experiments.

The International Urban Energy Balance Models Comparison Project: First Results from Phase 1

A large number of urban surface energy balance models now exist with different assumptions about the important features of the surface and exchange processes that need to be incorporated. To date, no com- parison of these models has been conducted; in contrast, models for natural surfaces have been compared extensively as part of the Project for Intercomparison of Land-surface Parameterization Schemes. Here, the methods and first results from an extensive international comparison of 33 models are presented. The aim of the comparison overall is to understand the complexity required to model energy and water exchanges in urban areas. The degree of complexity included in the models is outlined and impacts on model performance are discussed. During the comparison there have been significant developments in the models with resulting improvements in performance (root-mean-square error falling by up to two-thirds). Evaluation is based on a dataset containing net all-wave radiation, sensible heat, and latent heat flux observations for an industrial area in Vancouver, British Columbia, Canada. The aim of the comparison is twofold: to identify those modeling ap- proaches that minimize the errors in the simulated fluxes of the urban energy balance and to determine the degree of model complexity required for accurate simulations. There is evidence that some classes of models perform better for individual fluxes but no model performs best or worst for all fluxes. In general, the simpler models perform as well as the more complex models based on all statistical measures. Generally the schemes have best overall capability to model net all-wave radiation and least capability to model latent heat flux.

Strong-segregation limit of the self-consistent field theory for diblock copolymer melts

The self-consistent field theory (SCFT) introduced by Helfand for diblock copolymer melts is expected to converge to the strong-segregation theory (SST) of Semenov in the asymptotic limit, $\chi N \rightarrow \infty$. However, past extrapolations of the lamellar/cylinder and cylinder/sphere phase boundaries, within the standard unit-cell approximation, have cast some doubts on whether or not this is actually true. Here we push the comparison further by extending the SCFT calculations to $\chi N = 512,000$, by accounting for exclusion zones in the coronae of the cylindrical and spherical unit cells, and by examining finite-segregation corrections to SST. In doing so, we provide the first compelling evidence that SCFT does indeed reduce to SST.