Non-parallel Geometry Research Articles

Green fluorescence from perylene liquid in the molten state

Green fluorescence from perylene liquid in the molten state was observed, which differed substantially from the orange fluorescence from the sandwich excimer generally observed in concentrated solutions and in stable α-phase crystals. The peak position of the green fluorescence was similar to those in unstable β-phase crystals and in densely doped polymer films. Results from analysis of spectral components indicate that the green fluorescence is emitted from an excimer with non-parallel geometry, populated by thermal activation of the excimer with sandwich geometry.

Axis-aligned filtering for interactive physically-based diffuse indirect lighting

We introduce an algorithm for interactive rendering of physically-based global illumination, based on a novel frequency analysis of indirect lighting. Our method combines adaptive sampling by Monte Carlo ray or path tracing, using a standard GPU-accelerated raytracer, with real-time reconstruction of the resulting noisy images. Our theoretical analysis assumes diffuse indirect lighting, with general Lambertian and specular receivers. In practice, we demonstrate accurate interactive global illumination with diffuse and moderately glossy objects, at 1-3 fps. We show mathematically that indirect illumination is a structured signal in the Fourier domain, with inherent band-limiting due to the BRDF and geometry terms. We extend previous work on sheared and axis-aligned filtering for motion blur and shadows, to develop an image-space filtering method for interreflections. Our method enables 5--8X reduced sampling rates and wall clock times, and converges to ground truth as more samples are added. To develop our theory, we overcome important technical challenges---unlike previous work, there is no light source to serve as a band-limit in indirect lighting, and we also consider non-parallel geometry of receiver and reflecting surfaces, without first-order approximations.

A SPECT reconstruction method for extending parallel to non-parallel geometries

Due to its simplicity, parallel-beam geometry is usually assumed for the development of image reconstruction algorithms. The established reconstruction methodologies are then extended to fan-beam, cone-beam and other non-parallel geometries for practical application. This situation occurs for quantitative SPECT (single photon emission computed tomography) imaging in inverting the attenuated Radon transform. Novikov reported an explicit parallel-beam formula for the inversion of the attenuated Radon transform in 2000. Thereafter, a formula for fan-beam geometry was reported by Bukhgeim and Kazantsev (2002 Preprint N. 99 Sobolev Institute of Mathematics). At the same time, we presented a formula for varying focal-length fan-beam geometry. Sometimes, the reconstruction formula is so implicit that we cannot obtain the explicit reconstruction formula in the non-parallel geometries. In this work, we propose a unified reconstruction framework for extending parallel-beam geometry to any non-parallel geometry using ray-driven techniques. Studies by computer simulations demonstrated the accuracy of the presented unified reconstruction framework for extending parallel-beam to non-parallel geometries in inverting the attenuated Radon transform.

Converging flow between coaxial cones

Fluid flow governed by the Navier–Stokes equation is considered in a domain bounded by two cones with the same axis. In the first, ‘non-parallel’ case, the two cones have the same apex and different angles θ=α and β in spherical polar coordinates (r, θ, ϕ). In the second, ‘parallel’ case, the two cones have the same opening angle α, parallel walls separated by a gap h and apices separated by a distance h/sin α. Flows are driven by a source Q at the origin, the apex of the lower cone in the parallel case. The Stokes solution for the non-parallel case is discussed and the angles (α, β) identified where it breaks down, analogously to flow in a wedge geometry. For the case of convergent flow, Q<0, solutions governed by the Navier–Stokes equation are discussed for both parallel and non-parallel geometries. At large distances the flow is in a viscous regime and takes a Poiseuille profile. As the origin is approached the inertial terms become important and a plug flow emerges, with constant radial velocity in the core, sandwiched between thin boundary layers. By systematic approximation, partial differential equations (PDEs) are derived that describe the transition from viscous to high Reynolds number flow, and solutions describing the plug flow and boundary layers are obtained using matched asymptotic expansions.

ABSTRACT: Evolution of Non-parallel Geometry of Detachment Folds in the Northeastern Brooks Range, Alaska

ABSTRACT: Evolution of Non-parallel Geometry of Detachment Folds in the Northeastern Brooks Range, Alaska

Influence of the Radiation Field and Track Shape on the Supralinear Response of TLD-100 to Heavy Charged Particles

A Monte Carlo simulation is presented of the supralinear behaviour of TLD-100 exposed to heavy charged particles (HCP) based on the Track Interaction Model. The simulation considers HCP tracks as cylinders or cones, either parallel or non-parallel. The most interesting features of this approach are that electrons are not restricted to travel up to the third neighbour and that it includes saturation effects. The Monte Carlo results are compared to TLD-100 experimental data obtained with 5.3 MeV 4 He ions in parallel irradiation geometry, and 5.3 MeV 241 Am α particles in non-parallel geometry. The comparison of the calculations and the supralinear functions of peaks 8 and 9 for the helium beam and peak 8 for the α particles shows excellent agreement.

A new conceptual model for fluid flow in discrete fractures: An experimental and numerical study

A fundamental understanding of flow within single, or discrete, fractures is necessary so that fluid flow and chemical transport in fractured rocks can be accurately characterized. To explore discrete fracture flow, we conducted a series of experiments to study the movement of water through four artificial fractures, each with a different two‐dimensional surface topography. We then performed fluid flow simulations using a lattice gas automata (LGA) numerical model to compare with the experimental results and to obtain detailed pictures of the fluid velocity fields within these fractures. The flow experiments and LGA simulations, all performed under fully saturated and laminar flow conditions, used fracture aperture values ranging from 0.25 to 1.80 mm. Our main focus was to determine how the cubic law, derived for fluid flow through parallel plates, could be modified to accommodate a tortuous fracture geometry. Our experimental and numerical results led to the proposal of a new conceptual model. This model states that when the aperture is measured normal to the flow path and is harmonically averaged and when the tortuosity of the flow path is included in the calculation of the pressure gradient, the cubic law can adequately predict the flow rate through fractures with a nonparallel geometry. Our study has implications for interpreting laboratory fracture flow data and for improving predictive numerical models.

Optimization of interstitial volume implants

For interstitial applications of high dose rate (HDR) afterloading brachytherapy, generally a single stepping iridium-192 source is used, enabling optimization of the dose distribution by optimization of the relative time (dwell time) that the source remains at a certain position (dwell position). We analysed the effects of geometric optimization in a regular volume implant, with strictly parallel catheters, and in an irregular volume implant, such as an implant for tumours of the base of the tongue characterized by a non-parallel geometry and varying catheter separations. In both examples the reference dose is specified at 85% of the mean central dose (as is done in the Paris system for dose specification) in the non-optimized as well as the optimized plan. The irradiated volume, the dose uniformity, and the choice of the reference dose of optimized and non-optimized dose distributions were compared. This was done by isodose plots for representative planes, volume dose histograms (distributed, contiguous, and natural), and dose non-uniformity ratios (DNRs). For the regular implant, optimization results in a 28% increase in the treated volume with a similar increase in the overdosed volumes. In order to keep the treated volume comparable with the non-optimized dose distribution, 90–95% of the mean central dose should be chosen as a reference dose or the range of active dwell positions should be shortened in case of optimization. In the case of the irregular volume implant at the base of the tongue, the method for dose specification should be kept unchanged after geometric optimization as the volume enclosed by the reference isodose does not increase. It is clear from the volume-dose histograms that there is a reduction of the overdosed volume due to optimization. This is accompanied by an increase in the uniformity index and a decrease of the DNR. In conclusion, geometric optimization appears to be an effective tool to improve the dose distribution of interstitial volume implants. Contiguous and natural volume dose histograms appear, apart from planar dose plots, valuable methods for evaluating the dose distribution of an implant.

Eigenmodes for an elastic halfspace surrounding a semi-rigid cylinder

The elastodynamics of a halfspace with a cylindrical hole belongs to a class of problems which involve solving the elastic wave equation in a geometry that is bounded by nonparallel surfaces. Integral transform techniques are not very suitable for the solution of such problems because the transform approach yields solutions in terms of wavefronts (or rays). For a nonparallel geometry one may need a large collection of such terms and this may be an inconvenient description. So, we have taken an approach to construct the eigenmodes (normal modes) for this geometry for a given set of boundary conditions. A set of linearly independent solutions, without any reference to sources or receivers, is developed and completeness of this set is verified explicitly. Using this complete set of eigenmodes the displacement field for any source problem in this geometry can be expressed following standard mathematical procedures.

Electronic structure of bis(cyclopentadienyl) lanthanide compounds: photoelectron spectra and molecular orbital calculations

Gas phase He-I and He-II photoelectron (p.e.) spectra have been obtained for Ln(η-C5Me5)2, where Ln = Sm, Eu, Yb, and bands associated with ionization of f-electrons are identified for the Sm and Yb compounds; ionization energies calculated from quasi-relativistic Xα-SW calculations are in good agreement with the experimental values showing the compounds to be highly ionic in nature, but providing no orbital reason for the established non-parallel geometry of the rings.