Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.

The biometeorology of high-altitude insect layers.

Flight at high altitude is part of a migration strategy that maximises insect population displacement. This thesis represents the first substantial analysis of insect migration and layering in Europe. Vertical-looking entomological radar has revealed specific characteristics of high-altitude flight: in particular layering (where a large proportion of the migrating insects are concentrated in a narrow altitude band). The meteorological mechanisms underpinning the formation of these layers are the focus of this thesis. Aerial netting samples and radar data revealed four distinct periods of high-altitude insect migration: dawn, daytime, dusk, and night-time. The most frequently observed nocturnal profiles during the summertime were layers. It is hypothesised that nocturnal layers initiate at a critical altitude (200–500 m above ground level) and time (20:00–22:00 hours UTC). Case study analysis, statistical analysis, and a Lagrangian trajectory model showed that nocturnal insect layers probably result from the insects’ response to meteorological conditions. Temperature was the variable most correlated with nocturnal insect layer presence and intensity because insects are poikilothermic, and temperatures experienced during high-altitude migration in temperate climates are expected to be marginal for many insects’ flight. Hierarchical effects were detected such that other variables—specifically wind speed—were only correlated with insect layer presence and intensity once temperatures were warm. The trajectory model developed comprised: (i) insect flight characteristics; (ii) turbulent winds (which cause vertical spread of the layer); and (iii) mean wind speed, which normally leads to horizontal displacements of hundreds of kilometres in a single migratory flight. This thesis has revealed that there is considerable migratory activity over the UK in the summer months, and a range of fascinating phenomena can be observed (including layers). The UK has moved from one of the least studied to perhaps the best studied environments of aerial insect migration and layering in the world.

Layers of nocturnal insect migrants at high-altitude: the influence of atmospheric conditions on their formation

1 Radar studies of nocturnal insect migration have often found that the migrants tend to form well-defined horizontal layers at a particular altitude. 2 In previous short-term studies, nocturnal layers were usually observed to occur at the same altitude as certain meteorological features, most notably at the altitudes of temperature inversions or nocturnal wind jets. 3 Statistical analyses are presented of four years’ data that compared the presence, sharpness and duration of nocturnal layer profiles (observed using continuously-operating entomological radar) with meteorological variables at typical layer altitudes over the UK. 4 Analysis of these large datasets demonstrated that temperature was the foremost meteorological factor persistently associated with the presence and formation of longer-lasting and sharper layers of migrating insects over southern UK.

The influence of the atmospheric boundary layer on nocturnal layers of noctuids and other moths migrating over southern Britain

Insects migrating at high altitude over southern Britain have been continuously monitored by automatically-operating, vertical-looking radars over a period of several years. During some occasions in the summer months, the migrants were observed to form well-defined layer concentrations, typically at heights of 200-400 m, in the stable night-time atmosphere. Under these conditions, insects are likely to have control over their vertical movements and are selecting flight heights which are favourable for long-range migration. We therefore investigated the factors influencing the formation of these insect layers by comparing radar measurements of the vertical distribution of insect density with meteorological profiles generated by the UK Met. Office’s Unified Model (UM). Radar-derived measurements of mass and displacement speed, along with data from Rothamsted Insect Survey light traps provided information on the identity of the migrants. We present here three case studies where noctuid and pyralid moths contributed substantially to the observed layers. The major meteorological factors influencing the layer concentrations appeared to be: (a) the altitude of the warmest air, (b) heights corresponding to temperature preferences or thresholds for sustained migration and (c), on nights when air temperatures are relatively high, wind-speed maxima associated with the nocturnal jet. Back-trajectories indicated that layer duration may have been determined by the distance to the coast. Overall, the unique combination of meteorological data from the UM and insect data from entomological radar described here show considerable promise for systematic studies of high-altitude insect layering.

Evidence for global circuit current flow through water droplet layers

Abstract Foggy air and clear air have appreciably different electrical conductivities. The conductivity gradient at horizontal droplet boundaries causes droplet charging, as a result of vertical current flow in the global atmospheric electrical circuit. The charging is poorly known, as both the current flow through atmospheric water droplet layers and the air conductivity are poorly characterised experimentally. Surface measurements during three days of continuous fog using new instrument techniques show that a shallow (of order 100 m deep) fog layer still permits the vertical conduction current to pass. Further, the conductivity in the fog is estimated to be approximately 20% lower than in clear air. Assuming a fog transition thickness of one metre, this implies a vertical conductivity gradient of order 10 fS m−2 at the boundary. The actual vertical conductivity gradient at a cloud boundary would probably be greater, due to the presence of larger droplets in clouds compared to fog, and cleaner, more conductive clear air aloft.

Environmental control for layers

Light patterns have less effect on numbers of eggs laid by current stocks than on those of forty years ago, but the principles have not changed. Ovarian activity is stimulated by increasing photoperiods and suppressed by decreasing photoperiods. The light pattern used during rearing can still have large effects on age at 50% lay, even for modern stocks. Early sexual maturity maximises egg numbers but gives smaller eggs. Late maturity maximises egg size at the expense of numbers. The relationship between egg output (g/hen d) and age at first egg is curvilinear, with maximum yield occurring in flocks maturing in about the centre of their potential range. Fancy patterns of increasing daylength after maturity are probably not justified. A flock held on a constant 14h day will lay as many eggs as one given step up lighting. Intermittent lighting saves about 5% of feed consumption with no loss of output, provided that the feed has adequate amino acid content to allow for the reduced feed intake. Producers with light-proof laying houses should be taking advantage of intermittent lighting. The recommended light intensity for laying houses is still 10 lx, although the physiological threshold for response to changes in photoperiod is closer to 2 lx. Very dim (0.05 lx) light filtering into blacked out houses will not stimulate the hypothalamic receptors responsible for photo-sexual responses, but may affect the bird's biological clock, which can alter its response to a constant short photoperiod. Feed intake shows a curvilinear dependence on environmental temperature. At temperatures below the panting threshold, performance can be maintained by adjusting the feed so as to maintain an adequate intake of critical amino acids. Above the panting threshold, the hen is unable to take in enough energy to maintain normal output. There is no dietary modification which can effectively offset this problem. Diurnally cycling temperatures result in feed intake and egg production equivalent to that observed under a constant temperature equal to the mean of the cycle. When the poultry house is cooler at night than by day, it helps to provide light so that the birds can feed during the cooler part of the cycle.

Nutrition of chicks and layers

When formulating least-cost poultry diets, ME concentration should be optimised by an iterative procedure, not entered as a fixed value. This iteration must calculate profit margins by taking into account the way in which feed intake and saleable outputs vary with ME concentration. In the case of broilers, adjustment of critical amino acid contents in direct proportion to ME concentration does not result in birds of equal fatness. To avoid an increase in fat deposition at higher energy levels, it is proposed that amino acid specifications should be adjusted in proportion to changes in the net energy supplied by the feed. A model is available which will both interpret responses to amino acids in laying trials and give economically optimal estimates of amino acid inputs for practical feed formulation. Flocks coming into lay and flocks nearing the end of the pullet year have bimodal distributions of rates of lay, with the result that calculations of requirement based on mean output will underestimate the optimal amino acid input for the flock. Chick diets containing surplus protein can lead to impaired utilisation of the first-limiting amino acid. This difficulty can be avoided by stating amino acid requirements as a proportion of the protein.