Transformation elastodynamics and active exterior acoustic cloaking

This chapter consists of three parts. In the first part we recall the elastodynamic equations under coordinate transformations. The idea is to use coordinate transformations to manipulate waves propagating in an elastic material. Then we study the effect of transformations on a mass-spring network model. The transformed networks can be realized with "torque springs", which are introduced here and are springs with a force proportional to the displacement in a direction other than the direction of the spring terminals. Possible homogenizations of the transformed networks are presented, with potential applications to cloaking. In the second and third parts we present cloaking methods that are based on cancelling an incident field using active devices which are exterior to the cloaked region and that do not generate significant fields far away from the devices. In the second part, the exterior cloaking problem for the Laplace equation is reformulated as the problem of polynomial approximation of analytic functions. An explicit solution is given that allows to cloak larger objects at a fixed distance from the cloaking device, compared to previous explicit solutions. In the third part we consider the active exterior cloaking problem for the Helmholtz equation in 3D. Our method uses the Green's formula and an addition theorem for spherical outgoing waves to design devices that mimic the effect of the single and double layer potentials in Green's formula.Comment: Submitted as a chapter for the volume "Acoustic metamaterials: Negative refraction, imaging, lensing and cloaking", Craster and Guenneau ed., Springe

Detection of abandoned mineshafts using towed-array capacitive resistivity and real-time kinematic GPS navigation

The UK has a long history of mining but it was not until 1875 that the accurate mapping of mine workings and the submission of abandonment plans became a legal requirement. Where mineshafts are indicated on plans, they may be mislocated due to poor or inaccurate surveying. Consequently, the redevelopment of derelict land in the built environment frequently encounters potential geohazards, such as old adits, bell pits and shafts. These mining relics pose a serious risk to health and safety. This paper demonstrates how the combination of modem geophysical survey techniques with state-of-the-art satellite-based positioning may assist in the detection of such features. Recent advances in these fields offer the possibility of using towed-array resistivity instruments in conjunction with highly accurate (sub-decimetre) real-time kinematic global positioning systems (RTKGPS). Here we describe the use of multi-offset towed-array capacitive resistivity (CR) with GPS navigation for mapping resistivity over a known mineshaft in the historic mining area of Bonsall Leys in Derbyshire, UK

Questions of perfect lenses by left handed materials

We consider questions about the much discussed "perfect lenses" made by left handed materials. The transmission and reflection from a slab of left handed materials are investigated and the coefficients are obtained by the standard transfer matrix method. Possible limitations on such superlenses are explored. It is shown that the quality of the lenses can be significantly affected by the absorption that is necessarily present in the materials.Comment: 3 figure

Optimum design and testing of a postbuckled stiffened panel

The efficient, industrially used, linear elastic preliminary design software VICONOPT is employed to design a stiffened panel with a post-buckled reserve of strength. The initial buckling mode is a local skin mode in longitudinal compression with allowance being made for the effects of an initial overall imperfection. The resulting panel has been analyzed using the non-linear FE package ABAQUS and four laboratory specimens have been tested to failure. The similarity of the experimental failure with the VICONOPT and ABAQUS predictions suggests that VICONOPT can give a satisfactory preliminary design. While neither model matches completely the boundary conditions found in a real aircraft compression panel, it is suggested that the VICONOPT model may be a better representation than either the ABAQUS model or the experimental tests

Potential loss of nutrients from different rearing strategies for fattening pigs on pasture

Nutrient load and distribution on pasture were investigated with fattening pigs that: 1) spend a proportion of or their entire life on pasture, 2) were fed either restrictively or ad libitum, and 3) were weaned at different times of the year. The N and P retention in pigs decreased the longer they were kept on pasture. The contents of soil inorganic N and exchangeable K were significantly raised compared to the soil outside the enclosures but with no differences between treatments. Pig grazing did not affect extractable soil P. Regular moving of huts, feeding and water troughs was effective in ensuring that nutrients were more evenly distributed on the paddocks. Grass cover, as determined by spectral reflectance, was not related to the experimental treatments but only to time of year. During spring and summer, grass was present in parts of the paddocks, whereas during autumn and winter the pigs kept grass cover below 10%. Fattening pigs on pasture carries a high risk of nutrient loss and it is concluded that the most environmentally acceptable way of keeping fattening pigs on pasture involves a combination of reduced dietary N intake, reduced stocking rate and seasonal rather than all year production

Amplification of evanescent waves in a lossy left-handed material slab

We carry out finite-difference time-domain (FDTD) simulations, with a specially-designed boundary condition, on pure evanescent waves interacting with a lossy left-handed material (LHM) slab. Our results provide the first full-wave numerical evidence for the amplification of evanescent waves inside a LHM slab of finite absorption. The amplification is due to the interactions between the evanescent waves and the coupled surface polaritons at the two surfaces of the LHM slab and the physical process can be described by a simple model.Comment: 4 pages, 2 figure

Comparisons of Supergranule Characteristics During the Solar Minima of Cycles 22/23 and 23/24

Supergranulation is a component of solar convection that manifests itself on the photosphere as a cellular network of around 35 Mm across, with a turnover lifetime of 1-2 days. It is strongly linked to the structure of the magnetic field. The horizontal, divergent flows within supergranule cells carry local field lines to the cell boundaries, while the rotational properties of supergranule upflows may contribute to the restoration of the poloidal field as part of the dynamo mechanism that controls the solar cycle. The solar minimum at the transition from cycle 23 to 24 was notable for its low level of activity and its extended length. It is of interest to study whether the convective phenomena that influences the solar magnetic field during this time differed in character to periods of previous minima. This study investigates three characteristics (velocity components, sizes and lifetimes) of solar supergranulation. Comparisons of these characteristics are made between the minima of cycles 22/23 and 23/24 using MDI Doppler data from 1996 and 2008, respectively. It is found that whereas the lifetimes are equal during both epochs (around 18 h), the sizes are larger in 1996 (35.9 +/- 0.3 Mm) than in 2008 (35.0 +/- 0.3 Mm), while the dominant horizontal velocity flows are weaker (139 +/- 1 m/s in 1996; 141 +/- 1 m/s in 2008). Although numerical differences are seen, they are not conclusive proof of the most recent minimum being inherently unusual.Comment: 22 pages, 5 figures. Solar Physics, in pres

Unified dark energy models : a phenomenological approach

A phenomenological approach is proposed to the problem of universe accelerated expansion and of the dark energy nature. A general class of models is introduced whose energy density depends on the redshift $z$ in such a way that a smooth transition among the three main phases of the universe evolution (radiation era, matter domination, asymptotical de Sitter state) is naturally achieved. We use the estimated age of the universe, the Hubble diagram of Type Ia Supernovae and the angular size - redshift relation for compact and ultracompact radio structures to test whether the model is in agreement with astrophysical observation and to constrain its main parameters. Although phenomenologically motivated, the model may be straightforwardly interpreted as a two fluids scenario in which the quintessence is generated by a suitably chosen scalar field potential. On the other hand, the same model may also be read in the context of unified dark energy models or in the framework of modified Friedmann equation theories.Comment: 12 pages, 10 figures, accepted for publication on Physical Review

Milagrito: a TeV air-shower array

Milagrito, a large, covered water-Cherenkov detector, was the world's first air-shower-particle detector sensitive to cosmic gamma rays below 1 TeV. It served as a prototype for the Milagro detector and operated from February 1997 to May 1998. This paper gives a description of Milagrito, a summary of the operating experience, and early results that demonstrate the capabilities of this technique.Comment: 38 pages including 24 figure