Multiple waves propagate in random particulate materials

© 2019 Society for Industrial and Applied Mathematics Publications. All rights reserved. For over 70 years it has been assumed that scalar wave propagation in (ensembleaveraged) random particulate materials can be characterized by a single effective wavenumber. Here, however, we show that there exist many effective wavenumbers, each contributing to the effective transmitted wave field. Most of these contributions rapidly attenuate away from boundaries, but they make a significant contribution to the reflected and total transmitted field beyond the low-frequency regime. In some cases at least two effective wavenumbers have the same order of attenuation. In these cases a single effective wavenumber does not accurately describe wave propagation even far away from boundaries. We develop an efficient method to calculate all of the contributions to the wave field for the scalar wave equation in two spatial dimensions, and then compare results with numerical finite-difference calculations. This new method is, to the best of the authors' knowledge, the first of its kind to give such accurate predictions across a broad frequency range and for general particle volume fractions

Deepening subwavelength acoustic resonance via metamaterials with universal broadband elliptical microstructure

Slow sound is a frequently exploited phenomenon that metamaterials can induce in order to permit wave energy compression, redirection, imaging, sound absorption, and other special functionalities. Generally, however, such slow sound structures have a poor impedance match to air, particularly at low frequencies and consequently exhibit strong transmission only in narrow frequency ranges. This therefore strongly restricts their application in wave manipulation devices. In this work, we design a slow sound medium that halves the effective speed of sound in air over a wide range of low frequencies (hence our referral to the microstructure as “broadband”), whilst simultaneously maintaining a near impedance match to air. This is achieved with a rectangular array of acoustically rigid cylinders of elliptical cross section, a microstructure that is motivated by combining transformation acoustics with homogenization. Microstructural parameters are optimized in order to provide the required anisotropic material properties as well as near impedance matching. We then employ this microstructure in order to halve the size of a quarter-wavelength resonator (QWR) or equivalently to halve the resonant frequency of a QWR of a given size. This provides significant space savings in the context of low-frequency tonal noise attenuation in confined environments where the absorbing material is adjacent to the region in which sound propagates, such as in a duct. We employ the term “universal” since we envisage that this microstructure may be employed in a number of diverse applications involving sound manipulation.EPSRC Grant EP/K033208/I and EP/R014604/

An integral equation method for the homogenization of unidirectional fibre-reinforced media; antiplane elasticity and other potential problems

In Parnell & Abrahams (2008 Proc. R. Soc. A 464, 1461–1482. (doi:10.1098/rspa.2007.0254)), a homogenization scheme was developed that gave rise to explicit forms for the effective antiplane shear moduli of a periodic unidirectional fibre-reinforced medium where fibres have non-circular cross section. The explicit expressions are rational functions in the volume fraction. In that scheme, a (non-dilute) approximation was invoked to determine leading-order expressions. Agreement with existing methods was shown to be good except at very high volume fractions. Here, the theory is extended in order to determine higher-order terms in the expansion. Explicit expressions for effective properties can be derived for fibres with non-circular cross section, without recourse to numerical methods. Terms appearing in the expressions are identified as being associated with the lattice geometry of the periodic fibre distribution, fibre cross-sectional shape and host/fibre material properties. Results are derived in the context of antiplane elasticity but the analogy with the potential problem illustrates the broad applicability of the method to, e.g. thermal, electrostatic and magnetostatic problems. The efficacy of the scheme is illustrated by comparison with the well-established method of asymptotic homogenization where for fibres of general cross section, the associated cell problem must be solved by some computational scheme.D.J. is grateful to Thales UK and the Engineering and Physical Sciences Research Council (EPSRC) for funding via a CASE PhD studentship. W.J.P. acknowledges the EPSRC for funding his research fellowship (EP/L018039/1). I.D.A. undertook part of this work whilst in receipt of a Royal Society Wolfson Research Merit Award, and part was supported by the Isaac Newton Institute under EPSRC Grant Number EP/K032208/1. R.C.A. would like to acknowledge support from the EPSRC (EP/N013719/1)

Acoustic scattering from a one-dimensional array; Tail-end asymptotics for efficient evaluation of the quasi-periodic Green's function

© 2019 The Authors Motivated by the problem of acoustic plane wave scattering from an infinite periodic array of cylindrical scatterers, we present a new and easily-implemented way of calculating the quasi-periodic Green's function. This approach is based on an asymptotic expansion of the summand in the quasi-periodic Green's function in order to derive a tail-end correction term, allowing for a rapid and accurate approximation of the function. The tail-end approximation is shown to have much better and faster convergence properties than the usual truncation approach and competes very well with state-of-the-art alternative techniques. This method is then combined with a boundary element scheme to calculate the transmission and reflection coefficients associated with arrays of cylinders of different cross-sections and varying aspect ratios. The results are validated against the existing literature and by independent finite element calculations.EPSRC grant EP/R014604/

Cymatics for the cloaking of flexural vibrations in a structured plate

Based on rigorous theoretical findings, we present a proof-of-concept design for a structured square cloak enclosing a void in an elastic lattice. We implement high-precision fabrication and experimental testing of an elastic invisibility cloak for flexural waves in a mechanical lattice. This is accompanied by verifications and numerical modelling performed through finite element simulations. The primary advantage of our square lattice cloak, over other designs, is the straightforward implementation and the ease of construction. The elastic lattice cloak, implemented experimentally, shows high efficiency

Context Differences Reveal Insulator and Activator Functions of a Su(Hw) Binding Region

Insulators are DNA elements that divide chromosomes into independent transcriptional domains. The Drosophila genome contains hundreds of binding sites for the Suppressor of Hairy-wing [Su(Hw)] insulator protein, corresponding to locations of the retroviral gypsy insulator and non-gypsy binding regions (BRs). The first non-gypsy BR identified, 1A-2, resides in cytological region 1A. Using a quantitative transgene system, we show that 1A-2 is a composite insulator containing enhancer blocking and facilitator elements. We discovered that 1A-2 separates the yellow (y) gene from a previously unannotated, non-coding RNA gene, named yar for y-achaete (ac) intergenic RNA. The role of 1A-2 was elucidated using homologous recombination to excise these sequences from the natural location, representing the first deletion of any Su(Hw) BR in the genome. Loss of 1A-2 reduced yar RNA accumulation, without affecting mRNA levels from the neighboring y and ac genes. These data indicate that within the 1A region, 1A-2 acts an activator of yar transcription. Taken together, these studies reveal that the properties of 1A-2 are context-dependent, as this element has both insulator and enhancer activities. These findings imply that the function of non-gypsy Su(Hw) BRs depends on the genomic environment, predicting that Su(Hw) BRs represent a diverse collection of genomic regulatory elements

Trophic Shifts of a Generalist Consumer in Response to Resource Pulses

Trophic shifts of generalist consumers can have broad food-web and biodiversity consequences through altered trophic flows and vertical diversity. Previous studies have used trophic shifts as indicators of food-web responses to perturbations, such as species invasion, and spatial or temporal subsidies. Resource pulses, as a form of temporal subsidies, have been found to be quite common among various ecosystems, affecting organisms at multiple trophic levels. Although diet switching of generalist consumers in response to resource pulses is well documented, few studies have examined if the switch involves trophic shifts, and if so, the directions and magnitudes of the shifts. In this study, we used stable carbon and nitrogen isotopes with a Bayesian multi-source mixing model to estimate proportional contributions of three trophic groups (i.e. producer, consumer, and fungus-detritivore) to the diets of the White-footed mouse (Peromyscus leucopus) receiving an artificial seed pulse or a naturally-occurring cicadas pulse. Our results demonstrated that resource pulses can drive trophic shifts in the mice. Specifically, the producer contribution to the mouse diets was increased by 32% with the seed pulse at both sites examined. The consumer contribution to the mouse diets was also increased by 29% with the cicadas pulse in one of the two grids examined. However, the pattern was reversed in the second grid, with a 13% decrease in the consumer contribution with the cicadas pulse. These findings suggest that generalist consumers may play different functional roles in food webs under perturbations of resource pulses. This study provides one of the few highly quantitative descriptions on dietary and trophic shifts of a key consumer in forest food webs, which may help future studies to form specific predictions on changes in trophic interactions following resource pulses

Application of Nitrogen and Carbon Stable Isotopes (δ15Ν and δ13C) to Quantify Food Chain Length and Trophic Structure

Increasingly, stable isotope ratios of nitrogen (delta N-15) and carbon (delta C-13) are used to quantify trophic structure, though relatively few studies have tested accuracy of isotopic structural measures. For laboratory-raised and wild-collected plant-invertebrate food chains spanning four trophic levels we estimated nitrogen range (NR) using delta N-15, and carbon range (CR) using delta C-13, which are used to quantify food chain length and breadth of trophic resources respectively. Across a range of known food chain lengths we examined how NR and CR changed within and between food chains. Our isotopic estimates of structure are robust because they were calculated using resampling procedures that propagate variance in sample means through to quantified uncertainty in final estimates. To identify origins of uncertainty in estimates of NR and CR, we additionally examined variation in discrimination (which is change in delta N-15 ordelta C-13 from source to consumer) between trophic levels and among food chains. delta N-15 discrimination showed significant enrichment, while variation in enrichment was species and system specific, ranged broadly (1.4‰ to 3.3‰), and importantly, propagated variation to subsequent estimates of NR. However, NR proved robust to such variation and distinguished food chain length well, though some overlap between longer food chains infers a need for awareness of such limitations. delta C-13 discrimination was inconsistent; generally no change or small significant enrichment was observed. Consequently, estimates of CR changed little with increasing food chain length, showing the potential utility of delta C-13 as a tracer of energy pathways. This study serves as a robust test of isotopic quantification of food chain structure, and given global estimates of aquatic food chains approximate four trophic levels while many food chains include invertebrates, our use of four trophic level plant-invertebrate food chains makes our findings relevant for a majority of ecological systems

A high quality assembly of the Nile Tilapia (Oreochromis niloticus) genome reveals the structure of two sex determination regions

Background  Tilapias are the second most farmed fishes in the world and a sustainable source of food. Like many other fish, tilapias are sexually dimorphic and sex is a commercially important trait in these fish. In this study, we developed a significantly improved assembly of the tilapia genome using the latest genome sequencing methods and show how it improves the characterization of two sex determination regions in two tilapia species.  Results  A homozygous clonal XX female Nile tilapia (Oreochromis niloticus) was sequenced to 44X coverage using Pacific Biosciences (PacBio) SMRT sequencing. Dozens of candidate de novo assemblies were generated and an optimal assembly (contig NG50 of 3.3Mbp) was selected using principal component analysis of likelihood scores calculated from several paired-end sequencing libraries. Comparison of the new assembly to the previous O. niloticus genome assembly reveals that recently duplicated portions of the genome are now well represented. The overall number of genes in the new assembly increased by 27.3%, including a 67% increase in pseudogenes. The new tilapia genome assembly correctly represents two recentvasagene duplication events that have been verified with BAC sequencing. At total of 146Mbp of additional transposable element sequence are now assembled, a large proportion of which are recent insertions. Large centromeric satellite repeats are assembled and annotated in cichlid fish for the first time. Finally, the new assembly identifies the long-range structure of both a ~9Mbp XY sex determination region on LG1 in O. niloticus, and a ~50Mbp WZ sex determination region on LG3 in the related species O. aureus.  Conclusions  This study highlights the use of long read sequencing to correctly assemble recent duplications and to characterize repeat-filled regions of the genome. The study serves as an example of the need for high quality genome assemblies and provides a framework for identifying sex determining genes in tilapia and related fish species