Precise description of the different far fields encountered in the problem of diffraction of acoustic waves by a quarter-plane

This paper provides a review of important results concerning the Geometrical Theory of Diffraction and Geometrical Optics. It also reviews the properties of the existing solution for the problem of diffraction of a time harmonic plane wave by a half-plane. New mathematical expressions are derived for the wave fields involved in the problem of diffraction of a time harmonic plane wave by a quarter-plane, including the secondary radiated waves. This leads to a precise representation of the diffraction coefficient describing the diffraction occurring at the corner of the quarter-plane. Our results for the secondary radiated waves are an important step towards finding a formula giving the corner diffraction coefficient everywhere. © 2012 The authors.

Stiffness of sands through a laboratory test database

Deformations of sandy soils around geotechnical structures generally involve strains in the range small (0·01%) to medium (0·5%). In this strain range the soil exhibits non-linear stress-strain behaviour, which should be incorporated in any deformation analysis. In order to capture the possible variability in the non-linear behaviour of various sands, a database was constructed including the secant shear modulus degradation curves of 454 tests from the literature. By obtaining a unique S-shaped curve of shear modulus degradation, a modified hyperbolic relationship was fitted. The three curve-fitting parameters are: an elastic threshold strain γe, up to which the elastic shear modulus is effectively constant at G0; a reference strain γr, defined as the shear strain at which the secant modulus has reduced to 0·5G0; and a curvature parameter a, which controls the rate of modulus reduction. The two characteristic strains γe and γr were found to vary with sand type (i.e. uniformity coefficient), soil state (i.e. void ratio, relative density) and mean effective stress. The new empirical expression for shear modulus reduction G/G0 is shown to make predictions that are accurate within a factor of 1·13 for one standard deviation of random error, as determined from 3860 data points. The initial elastic shear modulus, G0, should always be measured if possible, but a new empirical relation is shown to provide estimates within a factor of 1·6 for one standard deviation of random error, as determined from 379 tests. The new expressions for non-linear deformation are easy to apply in practice, and should be useful in the analysis of geotechnical structures under static loading.

New ventilation efficiency measures based on buoyancy removal

New measures for estimating the efficiency of transient ventilation flows are proposed. These measures are developed by considering how effectively a ventilation system removes buoyancy from a space. This approach is distinct from standard efficiency measures which are, in general, based on the removal of a neutrally-buoyant passive tracer. Our new measures, based on (active) buoyancy removal, allow both the instantaneous and time-averaged efficiency of the entire space, or of any region within it, to be determined. In addition, expressions for determining vertical profiles of efficiency are proposed. These new measures enable the effectiveness of different flows to be compared directly and are applicable providing density (temperature) differences exist between the interior environment and the replacement air. Thus, they may be used to contrast the effectiveness of a broad range of building ventilation flows including natural, hybrid and forced ventilation.

Design guidelines for granular particles in a conical centrifugal filter

Essential design criteria for successful drying of granular particles in a conical continuous centrifugal filter are developed in a dimensionless fashion. Four criteria are considered: minimum flow thickness (to ensure sliding bulk flow rather than particulate flow), desaturation position, output dryness and basket failure. The criteria are based on idealised physical models of the machine operation and are written explicitly as functions of the basket size lout, spin velocity Ω and input flow rate of powder Qp. The separation of sucrose crystals from liquid molasses is taken as a case study and the successful regime of potential operating points (lout, Ω) is plotted for a wide range of selected values of flow rate Qp. Analytical expressions are given for minimum and maximum values of the three independent parameters (lout, Ω, Qp) as a function of the slurry and basket properties. The viable operating regime for a conical centrifugal filter is thereby obtained as a function of the slurry and basket properties. © 2012 The Institution of Chemical Engineers.

Reynolds number effects on scalar dissipation rate transport and its modeling in turbulent premixed combustion

The effects of turbulent Reynolds number, Ret, on the transport of scalar dissipation rate of reaction progress variable in the context of Reynolds averaged Navier-Stokes simulations have been analyzed using three-dimensional simplified chemistry-based direct numerical simulation (DNS) data of freely propagating turbulent premixed flames with different values of Ret. Scaling arguments have been used to explain the effects of Ret on the turbulent transport, scalar-turbulence interaction, and the combined reaction and molecular dissipation terms. Suitable modifications to the models for these terms have been proposed to account for Ret effects, and the model parameters include explicit Ret dependence. These expressions approach expected asymptotic limits for large values of Ret. However, turbulent Reynolds number Ret does not seem to have any major effects on the modeling of the term arising from density variation. Copyright © Taylor and Francis Group, LLC.

Predicting the acoustics of squeak and rattle

This paper discusses the development of a computationally efficient numerical method for predicting the acoustics of rattle events upfront in the design cycle. The method combines Finite Elements, Boundary Elements and SEA and enables the loudness of a large number of rattle events to be efficiently predicted across a broad frequency range. A low frequency random vibro-acoustic model is used in conjunction with various closed form analytical expressions in order to quickly predict impact probabilities and locations. An existing method has been extended to estimate the statistics of the contact forces across a broad frequency range. Finally, broadband acoustic radiation is predicted using standard low, mid and high frequency vibro-acoustic methods and used to estimate impact loudness. The approach is discussed and a number of validation examples are presented.

Modeling nonlinearities in MEMS oscillators

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude¿frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier-based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases. © 1986-2012 IEEE.

Stiffness of clays and silts: Normalizing shear modulus and shear strain

An analysis is presented of a database of 67 tests on 21 clays and silts of undrained shear stress-strain data of fine-grained soils. Normalizations of secant G in terms of initial mean effective stress p9 (i.e., G=p9 versus log g) or undrained shear strength cu (i.e., G=cu versus log g) are shown to be much less successful in reducing the scatter between different clays than the approach that uses the maximum shear modulus,Gmax, a technique still not universally adopted by geotechnical researchers and constitutive modelers. Analysis of semiempirical expressions forGmax is presented and a simple expression that uses only a void-ratio function and a confining-stress function is proposed. This is shown to be superior to a Hardin-style equation, and the void ratio function is demonstrated as an alternative to an overconsolidation ratio (OCR) function. To derive correlations that offer reliable estimates of secant stiffness at any required magnitude of working strain, secant shear modulus G is normalized with respect to its small-strain value Gmax, and shear strain g is normalized with respect to a reference strain gref at which this stiffness has halved. The data are corrected to two standard strain rates to reduce the discrepancy between data obtained from static and cyclic testing. The reference strain gref is approximated as a function of the plasticity index.Aunique normalized shear modulus reduction curve in the shape of a modified hyperbola is fitted to all the available data up to shear strains of the order of 1%. As a result, good estimates can be made of the modulus reduction G/Gmax ±30% across all strain levels in approximately 90% of the cases studied. New design charts are proposed to update the commonly used design curves. © 2013 American Society of Civil Engineers.

Stack ventilation in multi-storey atrium buildings: A dimensionless design approach

Using a simplified mathematical model, a preliminary design strategy for steady stack ventilation in multi-storey atrium buildings is developed. By non-dimensionalising the governing equations of flow, two key dimensionless parameters are identified - a ventilation performance indicator, λ, and atrium enhancement parameter, E - which quantify the performance of the ventilation system and the effectiveness of the atrium in assisting flows. Analytical expressions are determined to inform the vent sizes needed to provide the desired balance between indoor air temperature, ventilation flow rate and heat inputs for any distribution of occupants within the building, and also to ensure unidirectional flow. Dimensionless charts for determining the required combination of design variables are presented with a view to informing first-order design guidance for naturally ventilated buildings. © 2013 Elsevier Ltd.

Shock amplification, curve veering and the role of damping

The circumstances are investigated under which high peak acceleration can occur in the internal parts of a system when subjected to impulsive driving on the outside. Previous work using a coupled beam model has highlighted the importance of veering pairs of modes. Such a veering pair can be approximated by a lumped system with two degrees of freedom. The worst case of acceleration amplification is shown to occur when the two oscillators are tuned to the same frequency, and for this case closed-form expressions are derived to show the parameter dependence of the acceleration ratio on the mass ratio and coupling strength. Sensitivity analysis of the eigenvalues and eigenvectors indicates that mass ratio is the most sensitive parameter for altering the veering behaviour in an undamped system. Non-proportional damping is also shown to have a strong influence on the veering behaviour. The study gives design guidelines to allow permissible acceleration levels to be achieved by the choice of the effective mass and damping of the indirectly driven subsystem relative to the directly driven subsystem. © 2013 Elsevier Ltd.

Symmetry-extended counting rules for periodic frameworks.

A symmetry-adapted version of the Maxwell rule appropriate to periodic bar-and-joint frameworks is obtained, and is further extended to body-and-joint systems. The treatment deals with bodies and forces that are replicated in every unit cell, and uses the point group isomorphic to the factor group of the space group of the framework. Explicit expressions are found for the numbers and symmetries of detectable mechanisms and states of self-stress in terms of the numbers and symmetries of framework components. This approach allows detection and characterization of mechanisms and states of self-stress in microscopic and macroscopic materials and meta-materials. Illustrative examples are described. The notion of local isostaticity of periodic frameworks is extended to include point-group symmetry.

Fracture of brittle lattice materials: A review

The mechanics of failure for elastic-brittle lattice materials is reviewed. Closed-form expressions are summarized for fracture toughness as a function of relative density for a wide range of periodic lattices. A variety of theoretical and numerical approaches has been developed in the literature and in the main the predictions coincide for any given topology. However, there are discrepancies and the underlying reasons for these are highlighted. The role of imperfections at the cell wall level can be accounted for by Weibull analysis. Nevertheless, defects can also arise on the meso-scale in the form of misplaced joints, wavy cell walls and randomly distributed missing cell walls. These degrade the macroscopic fracture toughness of the lattice. © 2010 Springer Science+Business Media B.V.

Toll-like receptor 4 signaling pathway can be triggered by grass carp reovirus and Aeromonas hydrophila infection in rare minnow Gobiocypris rarus

Toll-like receptor 4 (TLR4) is critical for LPS recognition and cellular responses. It also recognizes some viral envelope proteins. Detection mostly results in the inflammation rather than specific antiviral responses. However, it's unclear in fish. In this report, a TLR4 gene (named as GrTLR4b) was cloned and characterized from rare minnow Gobiocypris rarus. The full length of GrTLR4b cDNA consists of 2766 nucleotides and encodes a polypeptide of 818 amino acids with an estimated molecular mass of 94,518 Da and a predicted isoelectric point of 8.41. The predicted amino acid sequence comprises a signal peptide, six leucine-rich repeat (LRR) motifs, one leucine-rich repeat C-terminal (LRRCT) motif, followed by a transmembrane segment of 23 amino acids, and a cytoplasmic region of 167 amino acids containing one Toll - interleukin 1 - receptor (TIR) motif. It's closely similar to the zebrafish (Danio rerio) TLR4b amino acid sequence with an identity of 77%. Quantitative RT-PCR analysis showed GrTLR4b mRNA was constitutive expression in gill, heart, intestine, kidney, liver, muscle and spleen tissues in healthy animals and up-regulated by viruses and bacteria. After being infected by grass carp reovirus or Aeromonas hydrophila, GrTLR4b expressions were up-regulated from 24 h post-injection and lasted until the fish became moribund (P < 0.05). These data implied that TLR4 signaling pathway could be activated by both viral and bacterial infection in rare minnow. (C) 2009 Elsevier Ltd. All rights reserved.

Allelopathic mechanism of pyrogallol to Microcystis aeruginosa PCC7806 (Cyanobacteria): From views of gene expression and antioxidant system

Pyrogallol is a potent allelochemical on Microcystis aeruginosa, but its allelopathic mechanism is not fully known. In order to explore this mechanism, gene expressions for prx, mcyB, psbA, recA, grpE, fabZ under pyrogallol stress were studied, and activities of the main antioxidant enzymes were also measured. The results showed that expression of grpE and recA showed no significant change under pyrogallol stress, while psbA and mcyB were up-regulated at 4 mg L-1. Both prx and fabZ were up-regulated even under exposure to 1 mg L-1 pyrogallol concentration. The activities of superoxide dismutase (SOD) and catalase (CAT) were enhanced under pyrogallol stress. Levels of malodialdehyde (MDA) at 2 and 4 mg L-1 pyrogallol were significantly higher than those of the controls. It was concluded that oxidant damage is an important mechanism for the allelopathic effect of pyrogallol on M. aeruginosa. (c) 2009 Elsevier Ltd. All rights reserved.

Reactive Many-Body Expansion for a Protonated Water Cluster.

We generalize the standard many-body expansion technique that is used to approximate the total energy of a molecular system to enable the treatment of chemical reactions by quantum chemical techniques. By considering all possible assignments of atoms to monomer units of the many-body expansion and associating suitable weights with each, we construct a potential energy surface that is a smooth function of the nuclear positions. We derive expressions for this reactive many-body expansion energy and describe an algorithm for its evaluation, which scales polynomially with system size, and therefore will make the method feasible for future condensed phase simulations. We demonstrate the accuracy and smoothness of the resulting potential energy surface on a molecular dynamics trajectory of the protonated water hexamer, using the Hartree-Fock method for the many-body term and Møller-Plesset theory for the low order terms of the many-body expansion.