Stirring in 3-d spherical models of convection in the Earth's mantle

On a global scale basalts from mid-ocean ridges are strikingly more homogeneous than basalts from intraplate volcanism. The observed geochemical heterogeneity argues strongly for the existence of distinct reservoirs in the Earth's mantle. It is an unresolved problem of Geodynamics as to how these findings can be reconciled with large-scale convection. We review observational constraints, and investigate stirring properties of numerical models of mantle convection. Conditions in the early Earth may have supported layered convection with rapid stirring in the upper layers. Material that has been altered near the surface is transported downwards by small-scale convection. Thereby a layer of homogeneous depleted material develops above pristine mantle. As the mantle cools over Earth history, the effects leading to layering become reduced and models show the large-scale convection favoured for the Earth today. Laterally averaged, the upper mantle below the lithosphere is least affected by material that has experienced near-surface differentiation. The geochemical signature obtained during the previous episode of small-scale convection may be preserved there for the longest time. Additionally, stirring is less effective in the high viscosity layer of the central lower mantle [1, 2], supporting the survival of medium-scale heterogeneities there. These models are the first, using 3-d spherical geometry and mostly Earth-like parameters, to address the suggested change of convective style. Although the models are still far from reproducing our planet, we find that proposal might be helpful towards reconciling geochemical and geophysical constraints.

Implementation of particle-scale rotation in the 3-d Lattice Solid Model

In this study, 3-D Lattice Solid Model (LSMearth or LSM) was extended by introducing particle-scale rotation. In the new model, for each 3-D particle, we introduce six degrees of freedom: Three for translational motion, and three for orientation. Six kinds of relative motions are permitted between two neighboring particles, and six interactions are transferred, i.e., radial, two shearing forces, twisting and two bending torques. By using quaternion algebra, relative rotation between two particles is decomposed into two sequence-independent rotations such that all interactions due to the relative motions between interactive rigid bodies can be uniquely decided. After incorporating this mechanism and introducing bond breaking under torsion and bending into the LSM, several tests on 2-D and 3-D rock failure under uni-axial compression are carried out. Compared with the simulations without the single particle rotational mechanism, the new simulation results match more closely experimental results of rock fracture and hence, are encouraging. Since more parameters are introduced, an approach for choosing the new parameters is presented.

Depth propagation and surface construction in 3-D vision

In stereo vision, regions with ambiguous or unspecified disparity can acquire perceived depth from unambiguous regions. This has been called stereo capture, depth interpolation or surface completion. We studied some striking induced depth effects suggesting that depth interpolation and surface completion are distinct stages of visual processing. An inducing texture (2-D Gaussian noise) had sinusoidal modulation of disparity, creating a smooth horizontal corrugation. The central region of this surface was replaced by various test patterns whose perceived corrugation was measured. When the test image was horizontal 1-D noise, shown to one eye or to both eyes without disparity, it appeared corrugated in much the same way as the disparity-modulated (DM) flanking regions. But when the test image was 2-D noise, or vertical 1-D noise, little or no depth was induced. This suggests that horizontal orientation was a key factor. For a horizontal sine-wave luminance grating, strong depth was induced, but for a square-wave grating, depth was induced only when its edges were aligned with the peaks and troughs of the DM flanking surface. These and related results suggest that disparity (or local depth) propagates along horizontal 1-D features, and then a 3-D surface is constructed from the depth samples acquired. The shape of the constructed surface can be different from the inducer, and so surface construction appears to operate on the results of a more local depth propagation process.

Depth propagation and surface construction in 3-D vision

Motion discontinuities can signal object boundaries where few or no other cues, such as luminance, colour, or texture, are available. Hence, motion-defined contours are an ecologically important counterpart to luminance contours. We developed a novel motion-defined Gabor stimulus to investigate the nature of neural operators analysing visual motion fields in order to draw parallels with known luminance operators. Luminance-defined Gabors have been successfully used to discern the spatial-extent and spatial-frequency specificity of possible visual contour detectors. We now extend these studies into the motion domain. We define a stimulus using limited-lifetime moving dots whose velocity is described over 2-D space by a Gabor pattern surrounded by randomly moving dots. Participants were asked to determine whether the orientation of the Gabor pattern (and hence of the motion contours) was vertical or horizontal in a 2AFC task, and the proportion of correct responses was recorded. We found that with practice participants became highly proficient at this task, able in certain cases to reach 90% accuracy with only 12 limited-lifetime dots. However, for both practised and novice participants we found that the ability to detect a single boundary saturates with the size of the Gaussian envelope of the Gabor at approximately 5 deg full-width at half-height. At this optimal size we then varied spatial frequency and found the optimum was at the lowest measured spatial frequency (0.1 cycle deg-1 ) and then steadily decreased with higher spatial frequencies, suggesting that motion contour detectors may be specifically tuned to a single, isolated edge.

An effective use of 3-D CAD/CAM withing an overall C.I.M. framework

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A new 3-D polymeric spin transition compound: [tris(1,4-bis-(tetrazol-1-yl) butane-N1,N1′)iron(II)] bis(perchlorate)

A series of novel polymeric compounds of formula [M(btzb)3][ClO4]2 (Mll = Fe, Ni or Cu) with btzb = 1,4-bis-(tetrazol-1-yl)butane have been prepared and their physical properties investigated. The btzb ligand has been prepared and its crystal structure determined, together with a tentative crystal structure of the 3-D compound [Fe(btzb)3][ClO4]2. The model of the latter shows two symmetry-related, interpenetrating Fe-btzb networks in which the iron(II) ions approach each other as close as 8.3 and 9.1 Å. This supramolecular catenane undergoes a sharp thermal spin transition around 160 K with hysteresis (20 K) along with a pronounced thermochromic effect. The spin crossover behaviour has been followed by magnetic, DSC, optical spectroscopy and 57Fe Mössbauer spectroscopy measurements. Irradiation with green light at low temperature leads to population of the metastable high-spin state for the thermally active iron(ll) ions. The nature of the spin crossover behaviour has been discussed in detail.

Simultaneous strain and temperature measurement of advanced 3-D braided composite materials using an improved EFPI/FBG system

Simultaneous strain and temperature measurement for advanced 3-D braided composite materials using fibre-optic sensor technology is demonstrated, for the first time. These advanced 3-D braided composites can virtually eliminate the most serious problem of delamination for conventional composites. A tandem in-fibre Bragg-grating (FBG)/extrinsic Fabry-Perot interferometric sensor (EFPI) system with improved accuracy has been used to facilitate simultaneous temperature and strain measurement in this work. The non-symmetric distortion of the optical spectrum of the FBG, due to the combination of the FBG and the EFPI, is observed for the first time. Experimental and theoretical studies indicate that this type of distortion can affect the measurement accuracy seriously and it is mainly caused by the modulation of the periodic output of the EFPI. A simple method has been demonstrated to improve the accuracy for detection of the wavelength-shift of the FBG induced by temperature change. A strain accuracy of ∼ ±20 με and a temperature accuracy of ∼ ±1 °C have been achieved, which can meet the requirements for practical applications of 3-D braided composites. © 2002 Elsevier Science Ltd. All rights reserved.

The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations

Недю Попиванов, Цветан Христов - Изследвани са някои тримерни аналози на задачата на Дарбу в равнината. През 1952 М. Протер формулира нови тримерни гранични задачи както за клас слабо хиперболични уравнения, така и за някои хиперболично-елиптични уравнения. За разлика от коректността на двумерната задача на Дарбу, новите задачи са некоректни. За слабо хиперболични уравнения, съдържащи младши членове, ние намираме достатъчни условия както за съществуване и единственост на обобщени решения с изолирана степенна особеност, така и за единственост на квази-регулярни решения на задачата на Протер.

Singular Solutions of Protter’s Problem for a Class of 3-D Hyperbolic Equations

Недю Иванов Попиванов, Алексей Йорданов Николов - През 1952 г. М. Протър формулира нови гранични задачи за вълновото уравнение, които са тримерни аналози на задачите на Дарбу в равнината. Задачите са разгледани в тримерна област, ограничена от две характеристични конуса и равнина. Сега, след като са минали повече от 50 години, е добре известно, че за безброй гладки функции в дясната страна на уравнението тези задачи нямат класически решения, а обобщеното решение има силна степенна особеност във върха на характеристичния конус, която е изолирана и не се разпространява по конуса. Тук ние разглеждаме трета гранична задача за вълновото уравнение с младши членове и дясна страна във формата на тригонометричен полином. Дадена е по-нова от досега известната априорна оценка за максимално възможната особеност на решенията на тази задача. Оказва се, че при по-общото уравнение с младши членове възможната сингулярност е от същия ред като при чисто вълновото уравнение.

Fluorescence-enhanced optical imaging on three-dimensional phantoms using a hand-held probe based frequency-domain intensified charge coupled device (ICCD) optical imager

Fluorescence-enhanced optical imaging is an emerging non-invasive and non-ionizing modality towards breast cancer diagnosis. Various optical imaging systems are currently available, although most of them are limited by bulky instrumentation, or their inability to flexibly image different tissue volumes and shapes. Hand-held based optical imaging systems are a recent development for its improved portability, but are currently limited only to surface mapping. Herein, a novel optical imager, consisting primarily of a hand-held probe and a gain-modulated intensified charge coupled device (ICCD) detector, is developed towards both surface and tomographic breast imaging. The unique features of this hand-held probe based optical imager are its ability to; (i) image large tissue areas (5×10 sq. cm) in a single scan, (ii) reduce overall imaging time using a unique measurement geometry, and (iii) perform tomographic imaging for tumor three-dimensional (3-D) localization. Frequency-domain based experimental phantom studies have been performed on slab geometries (650 ml) under different target depths (1-2.5 cm), target volumes (0.45, 0.23 and 0.10 cc), fluorescence absorption contrast ratios (1:0, 1000:1 to 5:1), and number of targets (up to 3), using Indocyanine Green (ICG) as fluorescence contrast agents. An approximate extended Kalman filter based inverse algorithm has been adapted towards 3-D tomographic reconstructions. Single fluorescence target(s) was reconstructed when located: (i) up to 2.5 cm deep (at 1:0 contrast ratio) and 1.5 cm deep (up to 10:1 contrast ratio) for 0.45 cc-target; and (ii) 1.5 cm deep for target as small as 0.10 cc at 1:0 contrast ratio. In the case of multiple targets, two targets as close as 0.7 cm were tomographically resolved when located 1.5 cm deep. It was observed that performing multi-projection (here dual) based tomographic imaging using a priori target information from surface images, improved the target depth recovery over using single projection based imaging. From a total of 98 experimental phantom studies, the sensitivity and specificity of the imager was estimated as 81-86% and 43-50%, respectively. With 3-D tomographic imaging successfully demonstrated for the first time using a hand-held based optical imager, the clinical translation of this technology is promising upon further experimental validation from in-vitro and in-vivo studies.

A novel 3-D segmentation algorithm for anatomic liver and tumor volume calculations for liver cancer treatment planning

Three-Dimensional (3-D) imaging is vital in computer-assisted surgical planning including minimal invasive surgery, targeted drug delivery, and tumor resection. Selective Internal Radiation Therapy (SIRT) is a liver directed radiation therapy for the treatment of liver cancer. Accurate calculation of anatomical liver and tumor volumes are essential for the determination of the tumor to normal liver ratio and for the calculation of the dose of Y-90 microspheres that will result in high concentration of the radiation in the tumor region as compared to nearby healthy tissue. Present manual techniques for segmentation of the liver from Computed Tomography (CT) tend to be tedious and greatly dependent on the skill of the technician/doctor performing the task. ^ This dissertation presents the development and implementation of a fully integrated algorithm for 3-D liver and tumor segmentation from tri-phase CT that yield highly accurate estimations of the respective volumes of the liver and tumor(s). The algorithm as designed requires minimal human intervention without compromising the accuracy of the segmentation results. Embedded within this algorithm is an effective method for extracting blood vessels that feed the tumor(s) in order to plan effectively the appropriate treatment. ^ Segmentation of the liver led to an accuracy in excess of 95% in estimating liver volumes in 20 datasets in comparison to the manual gold standard volumes. In a similar comparison, tumor segmentation exhibited an accuracy of 86% in estimating tumor(s) volume(s). Qualitative results of the blood vessel segmentation algorithm demonstrated the effectiveness of the algorithm in extracting and rendering the vasculature structure of the liver. Results of the parallel computing process, using a single workstation, showed a 78% gain. Also, statistical analysis carried out to determine if the manual initialization has any impact on the accuracy showed user initialization independence in the results. ^ The dissertation thus provides a complete 3-D solution towards liver cancer treatment planning with the opportunity to extract, visualize and quantify the needed statistics for liver cancer treatment. Since SIRT requires highly accurate calculation of the liver and tumor volumes, this new method provides an effective and computationally efficient process required of such challenging clinical requirements.^