Some questions on integral geometry on noncompact symmetric spaces of higher rank

Let be a noncompact symmetric space of higher rank. We consider two types of averages of functions: one, over level sets of the heat kernel on and the other, over geodesic spheres. We prove injectivity results for functions in which extend the results in Pati and Sitaram (Sankya Ser A 62:419-424, 2000).

Constraining complex aquifer geometry with geophysics (2-D ERT and MRS measurements) for stochastic modelling of groundwater flow

Stochastic modelling is a useful way of simulating complex hard-rock aquifers as hydrological properties (permeability, porosity etc.) can be described using random variables with known statistics. However, very few studies have assessed the influence of topological uncertainty (i.e. the variability of thickness of conductive zones in the aquifer), probably because it is not easy to retrieve accurate statistics of the aquifer geometry, especially in hard rock context. In this paper, we assessed the potential of using geophysical surveys to describe the geometry of a hard rock-aquifer in a stochastic modelling framework. The study site was a small experimental watershed in South India, where the aquifer consisted of a clayey to loamy-sandy zone (regolith) underlain by a conductive fissured rock layer (protolith) and the unweathered gneiss (bedrock) at the bottom. The spatial variability of the thickness of the regolith and fissured layers was estimated by electrical resistivity tomography (ERT) profiles, which were performed along a few cross sections in the watershed. For stochastic analysis using Monte Carlo simulation, the generated random layer thickness was made conditional to the available data from the geophysics. In order to simulate steady state flow in the irregular domain with variable geometry, we used an isoparametric finite element method to discretize the flow equation over an unstructured grid with irregular hexahedral elements. The results indicated that the spatial variability of the layer thickness had a significant effect on reducing the simulated effective steady seepage flux and that using the conditional simulations reduced the uncertainty of the simulated seepage flux. As a conclusion, combining information on the aquifer geometry obtained from geophysical surveys with stochastic modelling is a promising methodology to improve the simulation of groundwater flow in complex hard-rock aquifers. (C) 2013 Elsevier B.V. All rights reserved.

Quantum chemical study on influence of intermolecular hydrogen bonding on the geometry, the atomic charges and the vibrational dynamics of 2,6-dichlorobenzonitrile

FT-IR (4000-400 cm(-1)) and FT-Raman (4000-200 cm(-1)) spectral measurements on solid 2,6-dichlorobenzonitrile (2,6-DCBN) have been done. The molecular geometry, harmonic vibrational frequencies and bonding features in the ground state have been calculated by density functional theory at the B3LYP/6-311++G (d,p) level. A comparison between the calculated and the experimental results covering the molecular structure has been made. The assignments of the fundamental vibrational modes have been done on the basis of the potential energy distribution (PED). To investigate the influence of intermolecular hydrogen bonding on the geometry, the charge distribution and the vibrational spectrum of 2,6-DCBN; calculations have been done for the monomer as well as the tetramer. The intermolecular interaction energies corrected for basis set superposition error (BSSE) have been calculated using counterpoise method. Based on these results, the correlations between the vibrational modes and the structure of the tetramer have been discussed. Molecular electrostatic potential (MEP) contour map has been plotted in order to predict how different geometries could interact. The Natural Bond Orbital (NBO) analysis has been done for the chemical interpretation of hyperconjugative interactions and electron density transfer between occupied (bonding or lone pair) orbitals to unoccupied (antibonding or Rydberg) orbitals. UV spectrum was measured in methanol solution. The energies and oscillator strengths were calculated by Time Dependent Density Functional Theory (TD-DFT) and matched to the experimental findings. TD-DFT method has also been used for theoretically studying the hydrogen bonding dynamics by monitoring the spectral shifts of some characteristic vibrational modes involved in the formation of hydrogen bonds in the ground and the first excited state. The C-13 nuclear magnetic resonance (NMR) chemical shifts of the molecule were calculated by the Gauge independent atomic orbital (GIAO) method and compared with experimental results. Standard thermodynamic functions have been obtained and changes in thermodynamic properties on going from monomer to tetramer have been presented. (C) 2013 Elsevier B.V. All rights reserved.

Metallic Nanoparticles Arranged in a Helical Geometry: Route Towards Strong and Broadband Chiro-optical Response

Recent advances in nanotechnology have paved ways to various techniques for designing and fabricating novel nanostructures incorporating noble metal nanoparticles, for a wide range of applications. The interaction of light with metal nanoparticles (NPs) can generate strongly localized electromagnetic fields (Localized Surface Plasmon Resonance, LSPR) at certain wavelengths of the incident beam. In assemblies or structures where the nanoparticles are placed in close proximity, the plasmons of individual metallic NPs can be strongly coupled to each other via Coulomb interactions. By arranging the metallic NPs in a chiral (e.g. helical) geometry, it is possible to induce collective excitations, which lead to differential optical response of the structures to right-and left circularly polarized light (e.g. Circular Dichroism - CD). Earlier reports in this field include novel techniques of synthesizing metallic nanoparticles on biological helical templates made from DNA, proteins etc. In the present work, we have developed new ways of fabricating chiral complexes made of metallic NPs, which demonstrate a very strong chiro-optical response in the visible region of the electromagnetic spectrum. Using DDA (Discrete Dipole Approximation) simulations, we theoretically studied the conditions responsible for large and broadband chiro-optical response. This system may be used for various applications, for example those related to polarization control of visible light, sensing of proteins and other chiral bio-molecules, and many more.

DEFINING alpha-HELIX GEOMETRY BY C-alpha ATOM TRACE vs (phi-psi) TORSION ANGLES: A COMPARATIVE ANALYSIS

A regular secondary structure is described by a well defined set of values for the backbone dihedral angles (phi,psi and omega) in a polypeptide chain. However in real protein structures small local variations give rise to distortions from the ideal structures, which can lead to considerable variation in higher order organization. Protein structure analysis and accurate assignment of various structural elements, especially their terminii, are important first step in protein structure prediction and design. Various algorithms are available for assigning secondary structure elements in proteins but some lacunae still exist. In this study, results of a recently developed in-house program ASSP have been compared with those from STRIDE, in identification of alpha-helical regions in both globular and membrane proteins. It is found that, while a combination of hydrogen bond patterns and backbone torsional angles (phi-psi) are generally used to define secondary structure elements, the geometry of the C-alpha atom trace by itself is sufficient to define the parameters of helical structures in proteins. It is also possible to differentiate the various helical structures by their C-alpha trace and identify the deviations occurring both at mid-positions as well as at the terminii of alpha-helices, which often lead to occurrence of 3(10) and pi-helical fragments in both globular and membrane proteins.

Optimization of clamped beam geometry for fracture toughness testing of micron-scale samples

Fracture toughness measurements at the small scale have gained prominence over the years due to the continuing miniaturization of structural systems. Measurements carried out on bulk materials cannot be extrapolated to smaller length scales either due to the complexity of the microstructure or due to the size and geometric effect. Many new geometries have been proposed for fracture property measurements at small-length scales depending on the material behaviour and the type of device used in service. In situ testing provides the necessary environment to observe fracture at these length scales so as to determine the actual failure mechanism in these systems. In this paper, several improvements are incorporated to a previously proposed geometry of bending a doubly clamped beam for fracture toughness measurements. Both monotonic and cyclic loading conditions have been imposed on the beam to study R-curve and fatigue effects. In addition to the advantages that in situ SEM-based testing offers in such tests, FEM has been used as a simulation tool to replace cumbersome and expensive experiments to optimize the geometry. A description of all the improvements made to this specific geometry of clamped beam bending to make a variety of fracture property measurements is given in this paper.

Geomorphology reveals active decollement geometry in the central Himalayan seismic gap

The similar to 700-km-long ``central seismic gap'' is the most prominent segment of the Himalayan front not to have ruptured in a major earthquake during the last 200-500 yr. This prolonged seismic quiescence has led to the proposition that this region, with a population >10 million, is overdue for a great earthquake. Despite the region's recognized seismic risk, the geometry of faults likely to host large earthquakes remains poorly understood. Here, we place new constraints on the spatial distribution of rock uplift within the western similar to 400 km of the central seismic gap using topographic and river profile analyses together with basinwide erosion rate estimates from cosmogenic Be-10. The data sets show a distinctive physiographic transition at the base of the high Himalaya in the state of Uttarakhand, India, characterized by abrupt strike-normal increases in channel steepness and a tenfold increase in erosion rates. When combined with previously published geophysical imaging and seismicity data sets, we interpret the observed spatial distribution of erosion rates and channel steepness to reflect the landscape response to spatially variable rock uplift due to a structurally coherent ramp-flat system of the Main Himalayan Thrust. Although it remains unresolved whether the kinematics of the Main Himalayan Thrust ramp involve an emergent fault or duplex, the landscape and erosion rate patterns suggest that the decollement beneath the state of Uttarakhand provides a sufficiently large and coherent fault segment capable of hosting a great earthquake.

Three-dimensional numerical analysis of geocell-reinforced soft clay beds by considering the actual geometry of geocell pockets

Due to its complex honeycomb structure, the numerical modeling of the geocell has always been a big challenge. Generally, the equivalent composite approach is used to model the geocells. In the equivalent composite approach, the geocellsoil composite is treated as the soil layer with improved strength and stiffness values. Though this approach is very simple, it is unrealistic to model the geocells as the soil layer. This paper presents a more realistic approach of modeling the geocells in three-dimensional (3D) framework by considering the actual curvature of the geocell pocket. A square footing resting on geocell reinforced soft clay bed was modeled using the ``fast Lagrangian analysis of continua in 3D'' (FLAC(3D)) finite difference package. Three different material models, namely modified Cam-clay, Mohr-Coulomb, and linear elastic were used to simulate the behaviour of foundation soil, infill soil and the geocell, respectively. It was found that the geocells distribute the load laterally to the wider area below the footing as compared to the unreinforced case. More than 50% reduction in the stress was observed in the clay bed in the presence of geocells. In addition to geocells, two other cases, namely, only geogrid and geocell with additional basal geogrid cases were also simulated. The numerical model was systematically validated with the results of the physical model tests. Using the validated numerical model, parametric studies were conducted to evaluate the influence of various geocell properties on the performance of reinforced clay beds.

Numerical study of laminar, standing hydraulic jumps in a planar geometry

We solve the two-dimensional, planar Navier-Stokes equations to simulate a laminar, standing hydraulic jump using a Volume-of-Fluid method. The geometry downstream of the jump has been designed to be similar to experimental conditions by including a pit at the edge of the platform over which liquid film flows. We obtain jumps with and without separation. Increasing the inlet Froude number pushes the jump downstream and makes the slope of the jump weaker, consistent with experimental observations of circular jumps, and decreasing the Reynolds number brings the jump upstream while making it steeper. We study the effect of the length of the domain and that of a downstream obstacle on the structure and location of the jump. The transient flow which leads to a final steady jump is described for the first time to our knowledge. In the moderate Reynolds number regime, we obtain steady undular jumps with a separated bubble underneath the first few undulations. Interestingly, surface tension leads to shortening of wavelength of these undulations. We show that the undulations can be explained using the inviscid theory of Benjamin and Lighthill (Proc. R. Soc. London, Ser. A, 1954). We hope this new finding will motivate experimental verification.

High-throughput miniaturized microfluidic microscopy with radially parallelized channel geometry

In this article, we present a novel approach to throughput enhancement in miniaturized microfluidic microscopy systems. Using the presented approach, we demonstrate an inexpensive yet high-throughput analytical instrument. Using the high-throughput analytical instrument, we have been able to achieve about 125,880 cells per minute (more than one hundred and twenty five thousand cells per minute), even while employing cost-effective low frame rate cameras (120 fps). The throughput achieved here is a notable progression in the field of diagnostics as it enables rapid quantitative testing and analysis. We demonstrate the applicability of the instrument to point-of-care diagnostics, by performing blood cell counting. We report a comparative analysis between the counts (in cells per mu l) obtained from our instrument, with that of a commercially available hematology analyzer.

Advancing Edge Speeds of Epithelial Monolayers Depend on Their Initial Confining Geometry

Collective cell migrations are essential in several physiological processes and are driven by both chemical and mechanical cues. The roles of substrate stiffness and confinement on collective migrations have been investigated in recent years, however few studies have addressed how geometric shapes influence collective cell migrations. Here, we address the hypothesis that the relative position of a cell within the confinement influences its motility. Monolayers of two types of epithelial cells-MCF7, a breast epithelial cancer cell line, and MDCK, a control epithelial cell line-were confined within circular, square, and cross-shaped stencils and their migration velocities were quantified upon release of the constraint using particle image velocimetry. The choice of stencil geometry allowed us to investigate individual cell motility within convex, straight and concave boundaries. Cells located in sharp, convex boundaries migrated at slower rates than those in concave or straight edges in both cell types. The overall cluster migration occurred in three phases: an initial linear increase with time, followed by a plateau region and a subsequent decrease in cluster speeds. An acto-myosin contractile ring, present in the MDCK but absent in MCF7 monolayer, was a prominent feature in the emergence of leader cells from the MDCK clusters which occurred every similar to 125 mu m from the vertex of the cross. Further, coordinated cell movements displayed vorticity patterns in MDCK which were absent in MCF7 clusters. We also used cytoskeletal inhibitors to show the importance of acto-myosin bounding cables in collective migrations through translation of local movements to create long range coordinated movements and the creation of leader cells within ensembles. To our knowledge, this is the first demonstration of how bounding shapes influence long-term migratory behaviours of epithelial cell monolayers. These results are important for tissue engineering and may also enhance our understanding of cell movements during developmental patterning and cancer metastasis.

Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration-free, boundary-type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non-singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection-diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed.

A Numerical Study of Indentation Using Indenters of Different Geometry

Finite element simulation of the Berkovich, Vickers, Knoop, and cone indenters was carried out for the indentation of elastic-plastic material. To fix the semiapex angle of the cone, several rules of equivalence were used and examined. Despite the asymmetry and differences in the stress and strain fields, it was established that for the Berkovich and Vickers indenters, the load-displacement relation can closely be simulated by a single cone indenter having a semiapex angle equal to 70.3degrees in accordance with the rule of the volume equivalence. On the other hand, none of the rules is applicable to the Knoop indenter owing to its great asymmetry. The finite element method developed here is also applicable to layered or gradient materials with slight modifications.

Using internal fibre geometry to improve the performance of pin-loaded holes in composite materials

The anisotropic nature of fibre reinforced composites leads to large stress concentrations around pin-loaded holes through standard weave cloths. Proper understanding of how this anisotropic nature affects the load distribution around holes can be utilised to reduce these con-centrations if sufficient thought is given to the internal fibre geometry near to the hole. Such local reinforcements need not be highly complex and can be readily produced without excessive effort, producing significant improvements in performance. © 1996 Kluwer Academic Publishers.