Convective instability of 3-D fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the convective instability of 3-D fluid-saturated geological fault zones when they are heated uniformly from below. In particular, we have derived exact analytical solutions for the critical Rayleigh numbers of different convective flow structures. Using these critical Rayleigh numbers, three interesting convective flow structures have been identified in a geological fault zone system. It has been recognized that the critical Rayleigh numbers of the system have a minimum value only for the fault zone of infinite length, in which the corresponding convective flow structure is a 2-D slender-circle flow. However, if the length of the fault zone is finite, the convective flow in the system must be 3-D. Even if the length of the fault zone is infinite, since the minimum critical Rayleigh number for the 2-D slender-circle flow structure is so close to that for the 3-D convective flow structure, the system may have almost the same chance to pick up the 3-D convective flow structures. Also, because the convection modes are so close for the 3-D convective flow structures, the convective flow may evolve into the 3-D finger-like structures, especially for the case of the fault thickness to height ratio approaching zero. This understanding demonstrates the beautiful aspects of the present analytical solution for the convective instability of 3-D geological fault zones, because the present analytical solution is valid for any value of the ratio of the fault height to thickness. Using the present analytical solution, the conditions, under which different convective flow structures may take place, can be easily determined.

High resolution 3-D imaging via multi-pass SAR

Spaceborne/airborne synthetic aperture radar (SAR) systems provide high resolution two-dimensional terrain imagery. The paper proposes a technique for combining multiple SAR images, acquired on flight paths slightly separated in the elevation direction, to generate high resolution three-dimensional imagery. The technique could be viewed as an extension to interferometric SAR (InSAR) in that it generates topographic imagery with an additional dimension of resolution. The 3-D multi-pass SAR imaging system is typically characterised by a relatively short ambiguity length in the elevation direction. To minimise the associated ambiguities we exploit the relative phase information within the set of images to track the terrain landscape. The SAR images are then coherently combined, via a nonuniform DFT, over a narrow (in elevation) volume centred on the 'dominant' terrain ground plane. The paper includes a detailed description of the technique, background theory, including achievable resolution, and the results of an experimental study.

The 3-D Structure of Polycrystalline Diamond Film by Electron Backscattering Diffraction (EBSD)

A lithographic method was used to produce polycrystalline diamond films having highly defined surface geometry, showing an array of diamond tips for possible application as a field emitter device. The films grown in this study used microwave plasma assisted chemical vapour deposition (MACVD) on a silicon substrate; the substrate was then dissolved away to reveal the surface features on the diamond film. It is possible to align the crystallite direction and affect the electron emission properties using a voltage bias to enhance the nucleation process and influence the nuclei to a preferred orientation. This study focuses on the identification of the distribution of crystal directions in the film, using electron backscattering diffraction (EBSD) to identify the crystallographic character of the film surface. EBSD allows direct examination of the individual diamond grains, grains boundaries and the crystal orientation of each individual crystallite. The EBSD maps of the bottom (nucleation side) of the films, following which a layer of film is ion-milled away and the mapping process repeated. The method demonstrates experimentally that oriented nucleation occurs and the thin sections allow the crystal texture to be reconstructed in 3-D. (C) 2003 Elsevier B.V. All rights reserved.

3-D magnetic resonance angiography versus conventional angiography in peripheral arterial disease: Pilot study

Angiography is usually performed as the preoperative road map for those requiring revascularization for lower extremity peripheral arterial disease (PAD). The alternative investigations are ultrasound, 3-D magnetic resonance angiography (3-D MRA) and computed tomography angiography. This pilot study aimed to assess whether 3-D MRA could replace the gold standard angiography in preoperative planning. Eight patients considered for aortoiliac or infrainguinal arterial bypass surgery were recruited. All underwent both imaging modalities within 7 days. A vascular surgeon and a radiologist each reported on the images from both the 3-D MRA and the angiography, with blinding to patient details and each others reports. Comparisons were made between the reports for the angiographic and the 3-D MRA images, and between the reports of the vascular surgeon and the radiologist. Compared to the gold standard angiogram, 3-D MRA had a sensitivity of 77% and specificity of 94% in detecting occlusion, and a sensitivity of 72% and specificity of 90% in differentiating high grade (> 50%) versus low grade (< 50%) stenoses. There was an overall concordance of 78% between the two investigations with a range of 62% in the peroneal artery to 94% in the aorta. 3-D MRA showed flow in 23% of cases where conventional angiography showed no flow. In the present pilot study, 3-D MRA had reasonable concordance with the gold standard angiography, depending on the level of the lesion. At times it showed vessel flow where occlusion was shown on conventional angiogram. 3-D MRA in peripheral vascular disease is challenging the gold standard, but is inconsistent at present.

Dynamic rupture in a 3-D particle-based simulation of a rough planar fault

An appreciation of the physical mechanisms which cause observed seismicity complexity is fundamental to the understanding of the temporal behaviour of faults and single slip events. Numerical simulation of fault slip can provide insights into fault processes by allowing exploration of parameter spaces which influence microscopic and macroscopic physics of processes which may lead towards an answer to those questions. Particle-based models such as the Lattice Solid Model have been used previously for the simulation of stick-slip dynamics of faults, although mainly in two dimensions. Recent increases in the power of computers and the ability to use the power of parallel computer systems have made it possible to extend particle-based fault simulations to three dimensions. In this paper a particle-based numerical model of a rough planar fault embedded between two elastic blocks in three dimensions is presented. A very simple friction law without any rate dependency and no spatial heterogeneity in the intrinsic coefficient of friction is used in the model. To simulate earthquake dynamics the model is sheared in a direction parallel to the fault plane with a constant velocity at the driving edges. Spontaneous slip occurs on the fault when the shear stress is large enough to overcome the frictional forces on the fault. Slip events with a wide range of event sizes are observed. Investigation of the temporal evolution and spatial distribution of slip during each event shows a high degree of variability between the events. In some of the larger events highly complex slip patterns are observed.

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.

Novel solitons in parametric amplifiers and atom lasers

We review recent developments in quantum and classical soliton theory, leading to the possibility of observing both classical and quantum parametric solitons in higher-dimensional environments. In particular, we consider the theory of three bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical medium this corresponds to the process of sum frequency generation (via chi((2)) nonlinearity) modified by the chi((3)) nonlinearity. Potential applications include an ultrafast photonic AND-gate. The simplest quantum solitons or energy eigenstates (bound-state solutions) of the interacting field Hamiltonian are obtained exactly in three space dimensions. They have a point-like structure-even though the corresponding classical theory is nonsingular. We show that the solutions can be regularized with the imposition of a momentum cut-off on the nonlinear couplings. The case of three-dimensional matter-wave solitons in coupled atomic/molecular Bose-Einstein condensates is discussed.

Mathematical models in percutaneous absorption

A number of mathematical models have been used to describe percutaneous absorption kinetics. In general, most of these models have used either diffusion-based or compartmental equations. The object of any mathematical model is to a) be able to represent the processes associated with absorption accurately, b) be able to describe/summarize experimental data with parametric equations or moments, and c) predict kinetics under varying conditions. However, in describing the processes involved, some developed models often suffer from being of too complex a form to be practically useful. In this chapter, we attempt to approach the issue of mathematical modeling in percutaneous absorption from four perspectives. These are to a) describe simple practical models, b) provide an overview of the more complex models, c) summarize some of the more important/useful models used to date, and d) examine sonic practical applications of the models. The range of processes involved in percutaneous absorption and considered in developing the mathematical models in this chapter is shown in Fig. 1. We initially address in vitro skin diffusion models and consider a) constant donor concentration and receptor conditions, b) the corresponding flux, donor, skin, and receptor amount-time profiles for solutions, and c) amount- and flux-time profiles when the donor phase is removed. More complex issues, such as finite-volume donor phase, finite-volume receptor phase, the presence of an efflux. rate constant at the membrane-receptor interphase, and two-layer diffusion, are then considered. We then look at specific models and issues concerned with a) release from topical products, b) use of compartmental models as alternatives to diffusion models, c) concentration-dependent absorption, d) modeling of skin metabolism, e) role of solute-skin-vehicle interactions, f) effects of vehicle loss, a) shunt transport, and h) in vivo diffusion, compartmental, physiological, and deconvolution models. We conclude by examining topics such as a) deep tissue penetration, b) pharmacodynamics, c) iontophoresis, d) sonophoresis, and e) pitfalls in modeling.

Characterization of mouse Frizzled-3 expression in hair follicle development and identification of the human homolog in keratinocytes

Frizzled genes encode a family of Wnt ligand receptors, which have a conserved cysteine-rich Wnt binding domain and include both transmembrane and secreted forms. Work by others has shown that experimental perturbation of Wnt signaling results in aberrant hair formation, hair growth, and hair structure. To date, however, there is no information on the contribution of individual Frizzled proteins to hair development. We now report that Frizzled-3 expression in skin is restricted to the epidermis and to the developing hair follicle. Northern analysis on total mouse skin mRNA revealed a single Frizzled-3 transcript of 3.7 kb. Reverse transcription-polymerase chain reaction and in situ hybridization analysis revealed Frizzled-3 expression in epidermal and hair follicle keratinocytes. Frizzled-3 transcripts are first detected in discrete foci in the developing epidermis of 13 d embryos and later in the hair follicle placodes of 15 d embryos, suggesting a role for this Frizzled isoform in follicle development. In 17 d embryos and id old newborn mice Frizzled-3 expression is limited to suprabasal keratinocytes and is not seen in pelage follicles until 3 d postpartum. In 7 d old neonatal skin, Frizzled-3 is expressed throughout the epidermis and in the outer cell layers of hair follicles. We have also identified the mRNA encoding human Frizzled-3 in epidermal keratinocytes and in the HaCaT keratinocyte cell line. Human Frizzled-3 mRNA encodes a 666 amino acid protein with 97.8% identity to the mouse protein. The human Frizzled-3 gene was mapped using a radiation-hybrid cell line panel to the short arm of chromosome 8 between the markers WI-1172 and WI-8496 near the loci for the Hypotrichosis of Marie Unna and Hairless genes.

An FDTD model for calculation of gradient-induced eddy currents in MRI system

In most magnetic resonance imaging (MRI) systems, pulsed magnetic gradient fields induce eddy currents in the conducting structures of the superconducting magnet. The eddy currents induced in structures within the cryostat are particularly problematic as they are characterized by long time constants by virtue of the low resistivity of the conductors. This paper presents a three-dimensional (3-D) finite-difference time-domain (FDTD) scheme in cylindrical coordinates for eddy-current calculation in conductors. This model is intended to be part of a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The singularity apparent in the governing equations is removed by using a series expansion method and the conductor-air boundary condition is handled using a variant of the surface impedance concept. The numerical difficulty due to the asymmetry of Maxwell equations for low-frequency eddy-current problems is circumvented by taking advantage of the known penetration behavior of the eddy-current fields. A perfectly matched layer absorbing boundary condition in 3-D cylindrical coordinates is also incorporated. The numerical method has been verified against analytical solutions for simple cases. Finally, the algorithm is illustrated by modeling a pulsed field gradient coil system within an MRI magnet system. The results demonstrate that the proposed FDTD scheme can be used to calculate large-scale eddy-current problems in materials with high conductivity at low frequencies.

Multigradient field-active contour model for multilayer boundary detection of ultrasound rectal wall image

Extraction and reconstruction of rectal wall structures from an ultrasound image is helpful for surgeons in rectal clinical diagnosis and 3-D reconstruction of rectal structures from ultrasound images. The primary task is to extract the boundary of the muscular layers on the rectal wall. However, due to the low SNR from ultrasound imaging and the thin muscular layer structure of the rectum, this boundary detection task remains a challenge. An active contour model is an effective high-level model, which has been used successfully to aid the tasks of object representation and recognition in many image-processing applications. We present a novel multigradient field active contour algorithm with an extended ability for multiple-object detection, which overcomes some limitations of ordinary active contour models—"snakes." The core part in the algorithm is the proposal of multigradient vector fields, which are used to replace image forces in kinetic function for alternative constraints on the deformation of active contour, thereby partially solving the initialization limitation of active contour for rectal wall boundary detection. An adaptive expanding force is also added to the model to help the active contour go through the homogenous region in the image. The efficacy of the model is explained and tested on the boundary detection of a ring-shaped image, a synthetic image, and an ultrasound image. The experimental results show that the proposed multigradient field-active contour is feasible for multilayer boundary detection of rectal wall

Parallel 3D Simulation of a Fault Gouge using the Lattice Solid Model

Despite the insight gained from 2-D particle models, and given that the dynamics of crustal faults occur in 3-D space, the question remains, how do the 3-D fault gouge dynamics differ from those in 2-D? Traditionally, 2-D modeling has been preferred over 3-D simulations because of the computational cost of solving 3-D problems. However, modern high performance computing architectures, combined with a parallel implementation of the Lattice Solid Model (LSM), provide the opportunity to explore 3-D fault micro-mechanics and to advance understanding of effective constitutive relations of fault gouge layers. In this paper, macroscopic friction values from 2-D and 3-D LSM simulations, performed on an SGI Altix 3700 super-cluster, are compared. Two rectangular elastic blocks of bonded particles, with a rough fault plane and separated by a region of randomly sized non-bonded gouge particles, are sheared in opposite directions by normally-loaded driving plates. The results demonstrate that the gouge particles in the 3-D models undergo significant out-of-plane motion during shear. The 3-D models also exhibit a higher mean macroscopic friction than the 2-D models for varying values of interparticle friction. 2-D LSM gouge models have previously been shown to exhibit accelerating energy release in simulated earthquake cycles, supporting the Critical Point hypothesis. The 3-D models are shown to also display accelerating energy release, and good fits of power law time-to-failure functions to the cumulative energy release are obtained.