APPROXIMATE GAUSS-MARKOV REALISATION OF MULTIVARIATE STOCHASTIC PROCESSES.

Given a spectral density matrix or, equivalently, a real autocovariance sequence, the author seeks to determine a finite-dimensional linear time-invariant system which, when driven by white noise, will produce an output whose spectral density is approximately PHI ( omega ), and an approximate spectral factor of PHI ( omega ). The author employs the Anderson-Faurre theory in his analysis.

A computationally efficient software application for calculating vibration from underground railways

The PiP model is a software application with a user-friendly interface for calculating vibration from underground railways. This paper reports about the software with a focus on its latest version and the plans for future developments. The software calculates the Power Spectral Density of vibration due to a moving train on floating-slab track with track irregularity described by typical values of spectra for tracks with good, average and bad conditions. The latest version accounts for a tunnel embedded in a half space by employing a toolbox developed at K.U. Leuven which calculates Green's functions for a multi-layered half-space. © 2009 IOP Publishing Ltd.

Pipe in Pipe PiP

PiP software is a powerful computational tool for calculating vibration from underground railways and for assessing the performance of vibration countermeasures. The software has a user-friendly interface and it uses the state-of-the-art techniques to perform quick calculations for the problem. The software employs a model of a slab track coupled to a circular tunnel embedded in the ground. The software calculates the Power Spectral Density (PSD) of the vertical displacement at any selected point in the soil. Excitation is assumed to be due to an infinitely-long train moving on a slab-track supported at the tunnel bed. The PSD is calculated for a roughness excitation of a unit value (i.e. "white noise"). The software also calculates the Insertion Gain (IG) which is the ratio between the PSD displacement after and before changing parameters of the track, tunnel or soil. Version 4 of the software accounts for important developments of the numerical model. The tunnel wall is modelled as a thick shell (using the elastic continuum theory) rather than a thin shell. More importantly, the numerical model accounts now for a tunnel embedded in a half space rather than a full space as done in the previous versions. The software can now be used to calculate vibration due to a number of typical PSD roughnesses for rails in good, average and bad conditions.

On bandlimited fading channels at high SNR

This paper provides an overview of results on the capacity of noncoherent, multiple-input multiple-output (MIMO) flat-fading channels with a bandlimited power spectral density. The focus is on results that concern the capacity at high signal-to-noise ratio (SNR). In particular, the capacity pre-log, defined as the limiting ratio of the capacity to the logarithm of the SNR as the SNR tends to infinity, is studied. It is observed that the capacity pre-log is a function of the number of antennas as well as of the bandwidth of the fading channel's power spectral density. It is further observed that the capacity pre-log can be achieved with a simple communication system where the data detection and the channel estimation are performed separately. © 2011 ACM.

Branching toughens fibrous networks.

Fibrous collagenous networks are not only stiff but also tough, due to their complex microstructures. This stiff yet tough behavior is desirable for both medical and military applications but it is difficult to reproduce in engineering materials. While the nonlinear hyperelastic behavior of fibrous networks has been extensively studied, the understanding of toughness is still incomplete. Here, we identify a microstructure mimicking the branched bundles of a natural type I collagen network, in which partially cross-linked long fibers give rise to novel combinations of stiffness and toughness. Finite element analysis shows that the stiffness of fully cross-linked fibrous networks is amplified by increasing the fibril length and cross-link density. However, a trade-off of such stiff networks is reduced toughness. By having partially cross-linked networks with long fibrils, the networks have comparable stiffness and improved toughness as compared to the fully cross-linked networks. Further, the partially cross-linked networks avoid the formation of kinks, which cause fibril rupture during deformation. As a result, the branching allows the networks to have stiff yet tough behavior.

Flow field measurements of a series of turbulent premixed and stratified methane/air flames

This paper presents flow field measurements for the turbulent stratified burner introduced in two previous publications in which high resolution scalar measurements were made by Sweeney et al. [1,2] for model validation. The flow fields of the series of premixed and stratified methane/air flames are investigated under turbulent, globally lean conditions (φg=0.75). Velocity data acquired with laser Doppler anemometry (LDA) and particle image velocimetry (PIV) are presented and discussed. Pairwise 2-component LDA measurements provide profiles of axial velocity, radial velocity, tangential velocity and corresponding fluctuating velocities. The LDA measurements of axial and tangential velocities enable the swirl number to be evaluated and the degree of swirl characterized. Power spectral density and autocorrelation functions derived from the LDA data acquired at 10kHz are optimized to calculate the integral time scales. Flow patterns are obtained using a 2-component PIV system operated at 7Hz. Velocity profiles and spatial correlations derived from the PIV and LDA measurements are shown to be in very good agreement, thus offering 3D mapping of the velocities. A strong correlation was observed between the shape of the recirculation zones above the central bluff body and the effects of heat release, stoichiometry and swirl. Detailed analyses of the LDA data further demonstrate that the flow behavior changes significantly with the levels of swirl and stratification, which combines the contributions of dilatation, recirculation and swirl. Key turbulence parameters are derived from the total velocity components, combining axial, radial and tangential velocities. © 2013 The Combustion Institute.

Investigating landing gear noise using fly-over data: The case of a Boeing 747-400

Modeling the noise originating from a landing gear has proven to be a challenging task, because of its complicated structure. In full-scale, landing gear noise can only be investigated experimentally by source localization techniques and fly-over measurements with microphone arrays. In the present work, measurements of a Boeing B747-400 were used to determine the contribution of the landing gear to the overall noise emitted during a fly-over and how the broadband noise from the landing gear scales with the flight velocity. A tonal source from the nose landing gear was identified at 380 Hz with a harmonic at 760 Hz and it most likely originates from a cavity. It was also found that the Power Spectral Density (PSD) of the high frequency broadband component varies linearly with frequency and there is some scaling with the ow velocity. Finally, the nose landing gear was shown to be a significant contributor to the overall airframe noise as expected.

A general mass law for broadband energy harvesting

It is well known that the power absorbed by a linear oscillator when excited by white noise base acceleration depends only on the mass of the oscillator and the spectral density of the base motion. This places an upper bound on the energy that can be harvested from a linear oscillator under broadband excitation, regardless of the stiffness of the system or the damping factor. It is shown here that the same result applies to any multi-degree-of-freedom nonlinear system that is subjected to white noise base acceleration: for a given spectral density of base motion the total power absorbed is proportional to the total mass of the system. The only restriction to this result is that the internal forces are assumed to be a function of the instantaneous value of the state vector. The result is derived analytically by several different approaches, and numerical results are presented for an example two-degree-of-freedom-system with various combinations of linear and nonlinear damping and stiffness. © 2013 The Author.

The dynamic effect of a piled-foundation building on an incident vibration field from an underground railway tunnel

This paper presents a three-dimensional comprehensive model for the calculation of vibration in a building based on pile-foundation due to moving trains in a nearby underground tunnel. The model calculates the Power Spectral Density (PSD) of the building's responses due to trains moving on floating-slab tracks with random roughness. The tunnel and its surrounding soil are modelled as a cylindrical shell embedded in half-space using the well-known PiP model. The building and its piles are modelled as a 2D frame using the dynamic stiffness matrix. Coupling between the foundation and the ground is performed using the theory of joining subsystems in the frequency domain. The latter requires calculations of transfer functions of a half-space model. A convenient choice based on the thin-layer method is selected in this work for the calculations of responses in a half-space due to circular strip loadings. The coupling considers the influence of the building's dynamics on the incident wave field from the tunnel, but ignores any reflections of building's waves from the tunnel. The derivation made in the paper shows that the incident vibration field at the building's foundation gets modified by a term reflecting the coupling and the dynamics of the building and its foundation. The comparisons presented in the paper show that the dynamics of the building and its foundation significantly change the incident vibration field from the tunnel and they can lead to loss of accuracy of predictions if not considered in the calculation.

Cross-sectional structure of tetrahedral amorphous carbon thin films

A cross-sectional transmission electron microscope study of the low density layers at the surface and at the substrate-film interface of tetrahedral amorphous carbon (ta-C) films grown on (001) silicon substrates is presented. Spatially resolved electron energy loss spectroscopy is used to determine the bonding and composition of a tetrahedral amorphous carbon film with nanometre spatial resolution. For a ta-C film grown with a substrate bias of -300 V, an interfacial region approximately 5 nm wide is present in which the carbon is sp2 bonded and is mixed with silicon and oxygen from the substrate. An sp2 bonded layer observed at the surface of the film is 1.3 ± 0.3 nm thick and contains no detectable impurities. It is argued that the sp2 bonded surface layer is intrinsic to the growth process, but that the sp2 bonding in the interfacial layer at the substrate may be related to the presence of oxygen from the substrate.

Density stratified environments: The double-tank method

We present an alternative method of producing density stratifications in the laboratory based on the 'double-tank' method proposed by Oster (Sci Am 213:70-76, 1965). We refer to Oster's method as the 'forced-drain' approach, as the volume flow rates between connecting tanks are controlled by mechanical pumps. We first determine the range of density profiles that may be established with the forced-drain approach other than the linear stratification predicted by Oster. The dimensionless density stratification is expressed analytically as a function of three ratios: the volume flow rate ratio n, the ratio of the initial liquid volumes λ and the ratio of the initial densities ψ. We then propose a method which does not require pumps to control the volume flow rates but instead allows the connecting tanks to drain freely under gravity. This is referred to as the 'free-drain' approach. We derive an expression for the density stratification produced and compare our predictions with saline stratifications established in the laboratory using the 'free-drain' extension of Oster's method. To assist in the practical application of our results we plot the region of parameter space that yield concave/convex or linear density profiles for both forced-drain and free-drain approaches. The free-drain approach allows the experimentalist to produce a broad range of density profiles by varying the initial liquid depths, cross-sectional and drain opening areas of the tanks. One advantage over the original Oster approach is that density profiles with an inflexion point can now be established. © 2008 Springer-Verlag.