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.

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.

A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.

A Novel Method for the 3-D Reconstruction of Scoliotic Ribs From Frontal and Lateral Radiographs

Among the external manifestations of scoliosis, the rib hump, which is associated with the ribs' deformities and rotations, constitutes the most disturbing aspect of the scoliotic deformity for patients. A personalized 3-D model of the rib cage is important for a better evaluation of the deformity, and hence, a better treatment planning. A novel method for the 3-D reconstruction of the rib cage, based only on two standard radiographs, is proposed in this paper. For each rib, two points are extrapolated from the reconstructed spine, and three points are reconstructed by stereo radiography. The reconstruction is then refined using a surface approximation. The method was evaluated using clinical data of 13 patients with scoliosis. A comparison was conducted between the reconstructions obtained with the proposed method and those obtained by using a previous reconstruction method based on two frontal radiographs. A first comparison criterion was the distances between the reconstructed ribs and the surface topography of the trunk, considered as the reference modality. The correlation between ribs axial rotation and back surface rotation was also evaluated. The proposed method successfully reconstructed the ribs of the 6th-12th thoracic levels. The evaluation results showed that the 3-D configuration of the new rib reconstructions is more consistent with the surface topography and provides more accurate measurements of ribs axial rotation.

Structural studies of proteinase entrapment by human alpha 2-macroglobulin using 3-D electron microscopy

Human a2 -macroglobulin ( a2 M; homotetramer, Mr 720 kDa) is an essential scavenger of proteinases in the serum. Each of its four subunits has a ‘bait region’, with cleavage sequences for almost all endo-proteinases, an unusual thiol ester moiety and a receptor-binding domain (RBD). Bait region cleavage in native a2 M ( a2 M-N) by a proteinase results in rapid thiol ester breakage, with a large-scale structural transformation, in which a2 M uniquely entraps the proteinase in a cage-like structure and exposes receptor-binding domains for rapid endocytosis. Transformed a2 M ( a2 M-TR) contains up to two proteinases, which remain active to small substrates. 3-D electron microscopy is optimally suited to study this unusual structural change at resolutions near (1/30) Å−1. ^ The structural importance of the thiol esters was demonstrated by a genetically-engineered a2 M, with the cysteines involved in thiol ester formation mutated to serines, which appeared structurally homologous to a2 M-TR. This demonstrates that the four highly labile thiol esters alone maintain the a2 M-N structure, while the ‘closed trap’ formed by a2 M-TR is a more stable structural form. ^ Half-transformed a2 M ( a2 M-HT), with cleaved bait regions and thiol esters in only two of its four subunits, provides an important structural link between a2 M-N and a2 M-TR. A comparison with a2 M-N showed the two proteinase-entrapping domains were above and below the plane bisecting the long axis. Both a2 M-N and a2 M-TR consist of two dense, oppositely twisted strands with significant interconnections, indicating that the structural change involves a rotation of these strands. In a2 M-HT these strands were partially untwisted with large central openings, revealing the manner in which the proteinase enters the internal cavity of a2 M. ^ In reconstructions of a2 M-N, a2 M-HT and a2 M-TR labeled with a monoclonal Fab, the Fabs were located on distal ends of each constitutive strand, demonstrating an anti-parallel arrangement of the subunits. Separation between the top and bottom pairs of Fabs was nearly the same on all structures, but the pairs were rotated about the long axis. Taken together, these results indicate that upon proteinase cleavage the two strands in a2 M-N separate. The proteinase enters the structure, while the strands re-twist to encage it. In a2 M-TR, which displays receptor-binding arms, more than two subunits are transformed as strands in the transformed half of a2 M-HT were not separated. ^

The role of disulfide bridges in the 3-D structures of the antimicrobial peptides gomesin and protegrin-1: a molecular dynamics study

Some antimicrobial peptides have a broad spectrum of action against many different kinds of microorganisms. Gomesin and protegrin-1 are examples of such antimicrobial peptides, and they were studied by molecular dynamics in this research. Both have a beta-hairpin conformation stabilized by two disulfide bridges and are active against Gram-positive and Gram-negative bacteria, as well as fungi. In this study, the role of the disulfide bridge in the maintenance of the tertiary peptide structure of protegrin-1 and gomesin is analyzed by the structural characteristics of these peptides and two of their respective variants, gomy4 and proty4, in which the four cysteines are replaced by four tyrosine residues. The absence of disulfide bridges in gomy4 and proty4 is compensated by overall reinforcement of the original hydrogen bonds and extra attractive interactions between the aromatic rings of the tyrosine residues. The net effects on the variants with respect to the corresponding natural peptides are: i) maintenance of the original beta-hairpin conformation, with great structural similarities between the mutant and the corresponding natural peptide; ii) combination of positive F and. Ramachandran angles within the hairpin head region with a qualitative change to a combination of positive (F) and negative (.) angles, and iii) significant increase in structural flexibility. Experimental facts about the antimicrobial activity of the gomesin and protegrin-1 variants have also been established here, in the hope that the detailed data provided in the present study may be useful for understanding the mechanism of action of these peptides.

Chrysotile effects on human lung cell carcinoma in culture: 3-D reconstruction and DNA quantification by image analysis

Background: Chrysotile is considered less harmful to human health than other types of asbestos fibers. Its clearance from the lung is faster and, in comparison to amphibole forms of asbestos, chrysotile asbestos fail to accumulate in the lung tissue due to a mechanism involving fibers fragmentation in short pieces. Short exposure to chrysotile has not been associated with any histopathological alteration of lung tissue. Methods: The present work focuses on the association of small chrysotile fibers with interphasic and mitotic human lung cancer cells in culture, using for analyses confocal laser scanning microscopy and 3D reconstructions. The main goal was to perform the analysis of abnormalities in mitosis of fibers-containing cells as well as to quantify nuclear DNA content of treated cells during their recovery in fiber-free culture medium. Results: HK2 cells treated with chrysotile for 48 h and recovered in additional periods of 24, 48 and 72 h in normal medium showed increased frequency of multinucleated and apoptotic cells. DNA ploidy of the cells submitted to the same chrysotile treatment schedules showed enhanced aneuploidy values. The results were consistent with the high frequency of multipolar spindles observed and with the presence of fibers in the intercellular bridge during cytokinesis. Conclusion: The present data show that 48 h chrysotile exposure can cause centrosome amplification, apoptosis and aneuploid cell formation even when long periods of recovery were provided. Internalized fibers seem to interact with the chromatin during mitosis, and they could also interfere in cytokinesis, leading to cytokinesis failure which forms aneuploid or multinucleated cells with centrosome amplification.

A geometrical approach of 3-D FEA for educational purposes applied to electrostatic fields

A geometrical approach of the finite-element analysis applied to electrostatic fields is presented. This approach is particularly well adapted to teaching Finite Elements in Electrical Engineering courses at undergraduate level. The procedure leads to the same system of algebraic equations as that derived by classical approaches, such as variational principle or weighted residuals for nodal elements with plane symmetry. It is shown that the extension of the original procedure to three dimensions is straightforward, provided the domain be meshed in first-order tetrahedral elements. The element matrices are derived by applying Maxwell`s equations in integral form to suitably chosen surfaces in the finite-element mesh.

Multiphase flow in the vascular system of wood: From microscopic exploration to 3-D Lattice Boltzmann experiments

This paper provides insights into liquid free water dynamics in wood vessels based on Lattice Boltzmann experiments. The anatomy of real wood samples was reconstructed from systematic 3-D analyses of the vessel contours derived from successive microscopic images. This virtual vascular system was then used to supply fluid-solid boundary conditions to a two-phase Lattice Boltzmann scheme and investigate capillary invasion of this hydrophilic porous medium. Behavior of the liquid phase was strongly dependent on anatomical features, especially vessel bifurcations and reconnections. Various parameters were examined in numerical experiments with ideal vessel bifurcations, to clarify our interpretation of these features. (c) 2010 Elsevier Ltd. All rights reserved.

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.

A high throughput colorimetric assay of beta-1,3-D-glucans by Congo red dye

Mushroom strains contain complex nutritional biomolecules with a wide spectrum of therapeutic and prophylactic properties. Among these compounds, β-d-glucans play an important role in immuno-modulating and anti-tumor activities. The present work involves a novel colorimetric assay method for β-1,3-d-glucans with a triple helix tertiary structure by using Congo red. The specific interaction that occurs between Congo red and β-1,3-d-glucan was detected by bathochromic shift from 488 to 516 nm (> 20 nm) in UV–Vis spectrophotometer. A micro- and high throughput method based on a 96-well microtiter plate was devised which presents several advantages over the published methods since it requires only 1.51 μg of polysaccharides in samples, greater sensitivity, speed, assay of many samples and very cheap. β-d-Glucans of several mushrooms (i.e., Coriolus versicolor, Ganoderma lucidum, Pleurotus ostreatus, Ganoderma carnosum, Hericium erinaceus, Lentinula edodes, Inonotus obliquus, Auricularia auricular, Polyporus umbellatus, Cordyseps sinensis, Agaricus blazei, Poria cocos) were isolated by using a sequence of several extractions with cold and boiling water, acidic and alkaline conditions and quantified by this microtiter plate method. FTIR spectroscopy was used to study the structural features of β-1,3-d-glucans in these mushroom samples as well as the specific interaction of these polysaccharides with Congo red. The effect of NaOH on triple helix conformation of β-1,3-d-glucans was investigated in several mushroom species.