First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

An efficient finite difference scheme for three-dimensional, non-equilibrium flows using operator splitting

An efficient finite difference scheme is presented for the inviscid terms of the three-dimensional, compressible flow equations for chemical non-equilibrium gases. This scheme represents an extension and an improvement of one proposed by the author, and includes operator splitting.

Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

Mobile-to-mobile MIMO transmit-receive diversity systems: analysis and performance in three-dimensional double-correlated channels

Mobile-to-mobile (M-to-M) communications are expected to play a crucial role in future wireless systems and networks. In this paper, we consider M-to-M multiple-input multiple-output (MIMO) maximal ratio combining system and assess its performance in spatially correlated channels. The analysis assumes double-correlated Rayleigh-and-Lognormal fading channels and is performed in terms of average symbol error probability, outage probability, and ergodic capacity. To obtain the receive and transmit spatial correlation functions needed for the performance analysis, we used a three-dimensional (3D) M-to-M MIMO channel model, which takes into account the effects of fast fading and shadowing. The expressions for the considered metrics are derived as a function of the average signal-to-noise ratio per receive antenna in closed-form and are further approximated using the recursive adaptive Simpson quadrature method. Numerical results are provided to show the effects of system parameters, such as distance between antenna elements, maximum elevation angle of scatterers, orientation angle of antenna array in the x–y plane, angle between the x–y plane and the antenna array orientation, and degree of scattering in the x–y plane, on the system performance. Copyright © 2011 John Wiley & Sons, Ltd.

Three dimensional analysis of cardiovascular development in mouse embryos using X-ray microcomputed tomography

Micro-computed tomography (μCT) has been successfully used to study the cardiovascular system of mouse embryos in situ. With the use of barium as a suitable contrast agent, blood vessels have been imaged and analysed quantitatively such as blood volume and vessel sizes on embryos of ages 14.5 to 16.5 days old. The advantage of using this imaging modality is that it has provided three dimensional information whilst leaving samples intact for further study.

A three-dimensional magnetometer for motion sensing of a balloon-carried atmospheric measurement package

An instrument is described which carries three orthogonal geomagnetic field sensors on a standard meteorological balloon package, to sense rapid motion and position changes during ascent through the atmosphere. Because of the finite data bandwidth available over the UHF radio link, a burst sampling strategy is adopted. Bursts of 9s of measurements at 3.6Hz are interleaved with periods of slow data telemetry lasting 25s. Calculation of the variability in each channel is used to determine position changes, a method robust to periods of poor radio signals. During three balloon ascents, variability was found repeatedly at similar altitudes, simultaneously in each of three orthogonal sensors carried. This variability is attributed to atmospheric motions. It is found that the vertical sensor is least prone to stray motions, and that the use of two horizontal sensors provides no additional information over a single horizontal sensor

Monitoring and modelling the three-dimensional flow of water under drip irrigation

The interpretation of soil water dynamics under drip irrigation systems is relevant for crop production as well as on water use and management. In this study a three-dimensional representation of the flow of water under drip irrigation is presented. The work includes analysis of the water balance at point scale as well as area-average, exploring uncertainties in water balance estimations depending on the number of locations sampled. The water flow was monitored by detailed profile water content measurements before irrigation, after irrigation and 24 h later with a dense array of soil moisture access tubes radially distributed around selected drippers. The objective was to develop a methodology that could be used on selected occasions to obtain 'snap shots' of the detailed three-dimensional patterns of soil moisture. Such patterns are likely to be very complex, as spatial variability will be induced for a number of reasons, such as strong horizontal gradients in soil moisture, variations between individual sources in the amount of water applied and spatial variability is soil hydraulic properties. Results are compared with a widely used numerical model, Hydrus-2D. The observed dynamic of the water content distribution is in good agreement with model simulations, although some discrepancies concerning the horizontal distribution of the irrigation bulb are noted due to soil heterogeneity. (c) 2006 Elsevier B.V. All rights reserved.

An adaptive finite element water column model using the Mellor-Yamada level 2.5 turbulence closure scheme

A one-dimensional water column model using the Mellor and Yamada level 2.5 parameterization of vertical turbulent fluxes is presented. The model equations are discretized with a mixed finite element scheme. Details of the finite element discrete equations are given and adaptive mesh refinement strategies are presented. The refinement criterion is an "a posteriori" error estimator based on stratification, shear and distance to surface. The model performances are assessed by studying the stress driven penetration of a turbulent layer into a stratified fluid. This example illustrates the ability of the presented model to follow some internal structures of the flow and paves the way for truly generalized vertical coordinates. (c) 2005 Elsevier Ltd. All rights reserved.

4,4 '-Dipyridyl-N,N '-dioxide complexes of metal-thiocyanate/selenocyanate: pi-stacked molecular rods as three-dimensional support for two-dimensional polymeric sheets and intra/interchain S center dot center dot center dot S interaction dependent architecture of the R-2(2)(8) synthon driven assembly of one-dimensional polymeric chains

Three supramolecular complexes of Co(II) using SCN-/SeCN- in combination with 4,4'-dipyridyl-N,N'-dioxide (dpyo), i.e., {[Co(SCN)(2)(dpyo)(2)].(dpyo)}(n) ( 1), {[Co(SCN)(2)(dpyo)(H2O)(2)].(H2O)}(n) ( 2), {[Co(SeCN)(2)(dpyo)(H2O)(2)]center dot(H2O)}(n) ( 3), have been synthesized and characterized by single-crystal X-ray analysis. Complex 1 is a rare example of a dpyo bridged two-dimensional (2D) coordination polymer, and pi-stacked dpyo supramolecular rods are generated by the lattice dpyo, passing through the rhombic grid of stacked layers, resulting in a three-dimensional (3D) superstructure. Complexes 2 and 3 are isomorphous one-dimensional (1D) coordination polymers [-Co-dpyo-Co-] that undergo self-assembly leading to a bilayer architecture derived through an R-2(2)(8) H-bonding synthon between coordinated water and dpyo oxygen. A reinvestigation of coordination polymers [Mn(SCN)(2)(dpyo)( H2O)(MeOH)](n) ( 4) and {[Fe(SCN)(2)(dpyo)(H2O)(2)]center dot(H2O)}(n) ( 5) reported recently by our group [ Manna et al. Indian J. Chem. 2006, 45A, 1813] reveals brick wall topology rather than bilayer architecture is due to the decisive role of S center dot center dot center dot S/Se center dot center dot center dot Se interactions in determining the helical nature in 4 and 5 as compared to zigzag polymeric chains in 2 and 3, although the same R-2(2)(8) synthon is responsible for supramolecular assembly in these complexes.

Macrocyclic amines as structure-directing agents for the synthesis of three-dimensional antimony-sulfide frameworks

A new family of antimony sulfides, incorporating the macrocyclic tetramine 1,4,8,11-tetraazacyclotetradecane ( cyclam), has been prepared by a hydrothermal method. [C10N4H26][Sb4S7] (1), [Ni(C10N4H24)][Sb4S7] (2), and [Co(C10N4H24)](x)[C10N4H26](1-x)[Sb4S7] (0.08 <= x <= 0.74) (3) have been characterized by single-crystal X-ray diffraction, elemental analysis, thermogravimetry, and analytical electron microscopy. All three materials possess the same novel three-dimensional Sb4S72- framework, constructed from layers of parallel arrays of Sb4S84- chains stacked at 90 to one another. In 1, doubly protonated macrocyclic cations reside in the channel structure of the antimonysulfide framework. In 2 and 3, the cyclam acts as a ligand, chelating the divalent transition- metal cation. Analytical and X-ray diffraction data indicate that the level of metal incorporation in 2 is effectively complete, whereas in 3, both metalated and nonmetalated forms of the macrocycle coexist within the structure.

Finite element aided design evolution of composite leaf spring

This paper shows the process of the virtual production development of the mechanical connection between the top leaf of a dual composite leaf spring system to a shackle using finite element methods. The commercial FEA package MSC/MARC has been used for the analysis. In the original design the joint was based on a closed eye-end. Full scale testing results showed that this configuration achieved the vertical proof load of 150 kN and 1 million cycles of fatigue load. However, a problem with delamination occurred at the interface between the fibres going around the eye and the main leaf body. To overcome this problem, a second design was tried using transverse bandages of woven glass fibre reinforced tape to wrap the section that is prone to delaminate. In this case, the maximum interlaminar shear stress was reduced by a certain amount but it was still higher than the material’s shear strength. Based on the fact that, even with delamination, the top leaf spring still sustained the maximum static and fatigue loads required, the third design was proposed with an open eye-end, eliminating altogether the interface where the maximum shear stress occurs. The maximum shear stress predicted by FEA is reduced significantly and a safety factor of around 2 has been obtained. Thus, a successful and safe design has been achieved.