Asymptotics of the meta-atom: plane wave scattering by a single Helmholtz resonator.

Using a combination of multipole methods and the method of matched asymptotic expansions, we present a solution procedure for acoustic plane wave scattering by a single Helmholtz resonator in two dimensions. Closed-form representations for the multipole scattering coefficients of the resonator are derived, valid at low frequencies, with three fundamental configurations examined in detail: the thin-walled, moderately thick-walled and extremely thick-walled limits. Additionally, we examine the impact of dissipation for extremely thick-walled resonators, and also numerically evaluate the scattering, absorption and extinction cross-sections (efficiencies) for representative resonators in all three wall thickness regimes. In general, we observe strong enhancement in both the scattered fields and cross-sections at the Helmholtz resonance frequencies. As expected, dissipation is shown to shift the resonance frequency, reduce the amplitude of the field, and reduce the extinction efficiency at the fundamental Helmholtz resonance. Finally, we confirm results in the literature on Willis-like coupling effects for this resonator design, and connect these findings to earlier works by several of the authors on two-dimensional arrays of resonators, deducing that depolarizability effects (off-diagonal terms) for a single resonator do not ensure the existence of Willis coupling effects (bianisotropy) in bulk. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

On the Wiener-Hopf solution of water-wave interaction with a submerged elastic or poroelastic plate.

A solution to the problem of water-wave scattering by a semi-infinite submerged thin elastic plate, which is either porous or non-porous, is presented using the Wiener-Hopf technique. The derivation of the Wiener-Hopf equation is rather different from that which is used traditionally in water-waves problems, and it leads to the required equations directly. It is also shown how the solution can be computed straightforwardly using Cauchy-type integrals, which avoids the need to find the roots of the highly non-trivial dispersion equations. We illustrate the method with some numerical computations, focusing on the evolution of an incident wave pulse which illustrates the existence of two transmitted waves in the submerged plate system. The effect of the porosity is studied, and it is shown to influence the shorter-wavelength pulse much more strongly than the longer-wavelength pulse.

A potential hidden layer of meteorites below the ice surface of Antarctica.

Antarctica contains some of the most productive regions on Earth for collecting meteorites. These small areas of glacial ice are known as meteorite stranding zones, where upward-flowing ice combines with high ablation rates to concentrate large numbers of englacially transported meteorites onto their surface. However, meteorite collection data shows that iron and stony-iron meteorites are significantly under-represented from these regions as compared with all other sites on Earth. Here we explain how this discrepancy may be due to englacial solar warming, whereby meteorites a few tens of centimetres below the ice surface can be warmed up enough to cause melting of their surrounding ice and sink downwards. We show that meteorites with a high-enough thermal conductivity (for example, iron meteorites) can sink at a rate sufficient to offset the total annual upward ice transport, which may therefore permanently trap them below the ice surface and explain their absence from collection data.

Mean residence time for drugs subject to enterohepatic cycling.

A physiologically realistic model of enterohepatic cycling (EHC) which includes separate liver and gallbladder compartments, discontinuous gallbladder emptying and first-order absorption from both an oral formulation and secreted bile (kapo and kab, respectively) has been developed. The effect of EHC on area under the first-moment curve (AUMC) of drug concentration in plasma and on parameters derived from the AUMC was investigated. Unlike AUC, AUMC is dependent on the time and time-course of gallbladder emptying, increasing as the interval between gallbladder emptying increases. Consequently, mean residence time (MRT) is also a time-dependent parameter. Analytical solutions for MRTiv and MRTpo were derived. Mean absorption time (MAT = MRTpo - MRTiv) is also time-dependent, contrary to findings previously published for a model of EHC with a continuous time lag. MAT is also dependent on kapo, kba and the hepatic extraction ratio. The difference between MRTpos for two formulations with unequal kapo values may deviate from the difference in the inverse of their absorption rate constants. Implications for design and interpretation of pharmacokinetic studies include (i) MAT values may be dominated by the time-course of recycling rather than the time-course of the initial absorption, depending on the extent of EHC and (ii) the unpredictable nature of the time of gallbladder emptying will contribute to intrasubject variability in derived parameters during crossover studies. Knowledge of the extent of EHC is invaluable in deciding whether modification of the in vitro release characteristics of an oral formulation will have any effect on the overall time-course of absorption in vivo. Techniques to monitor or control gallbladder emptying may be helpful for reducing variability in pharmacokinetic studies for compounds which are extensively cycled in bile.