Scattering of electromagnetic waves by many small perfectly conducting or impedance bodies

A theory of electromagnetic (EM) wave scattering by many small particles of an arbitrary shape is developed. The particles are perfectly conducting or impedance. For a small impedance particle of an arbitrary shape, an explicit analytical formula is derived for the scattering amplitude. The formula holds as a → 0, where a is a characteristic size of the small particle and the wavelength is arbitrary but fixed. The scattering amplitude for a small impedance particle is shown to be proportional to a2−κ, where κ ∈ [0,1) is a parameter which can be chosen by an experimenter as he/she wants. The boundary impedance of a small particle is assumed to be of the form ζ = ha−κ, where h = const, Reh ≥ 0. The scattering amplitude for a small perfectly conducting particle is proportional to a3, and it is much smaller than that for the small impedance particle. The many-body scattering problem is solved under the physical assumptions a ≪ d ≪ λ, where d is the minimal distance between neighboring particles and λ is the wavelength. The distribution law for the small impedance particles is N(∆) ∼ 1/a2−κ∆ N(x)dx as a → 0. Here, N(x) ≥ 0 is an arbitrary continuous function that can be chosen by the experimenter and N(∆) is the number of particles in an arbitrary sub-domain ∆. It is proved that the EM field in the medium where many small particles, impedance or perfectly conducting, are distributed, has a limit, as a → 0 and a differential equation is derived for the limiting field. On this basis, a recipe is given for creating materials with a desired refraction coefficient by embedding many small impedance particles into a given material. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4929965

Specific "scientific" data structures, and their processing

Programming physicists use, as all programmers, arrays, lists, tuples, records, etc., and this requires some change in their thought patterns while converting their formulae into some code, since the "data structures" operated upon, while elaborating some theory and its consequences, are rather: power series and Pad\'e approximants, differential forms and other instances of differential algebras, functionals (for the variational calculus), trajectories (solutions of differential equations), Young diagrams and Feynman graphs, etc. Such data is often used in a [semi-]numerical setting, not necessarily "symbolic", appropriate for the computer algebra packages. Modules adapted to such data may be "just libraries", but often they become specific, embedded sub-languages, typically mapped into object-oriented frameworks, with overloaded mathematical operations. Here we present a functional approach to this philosophy. We show how the usage of Haskell datatypes and - fundamental for our tutorial - the application of lazy evaluation makes it possible to operate upon such data (in particular: the "infinite" sequences) in a natural and comfortable manner.Comment: In Proceedings DSL 2011, arXiv:1109.032

Charge Fluctuation Forces Between Stiff Polyelectrolytes in Salt Solution: Pairwise Summability Re-examined

We formulate low-frequency charge-fluctuation forces between charged cylinders - parallel or skewed - in salt solution: forces from dipolar van der Waals fluctuations and those from the correlated monopolar fluctuations of mobile ions. At high salt concentrations forces are exponentially screened. In low-salt solutions dipolar energies go as $R^{-5}$ or $R^{-4}$; monopolar energies vary as $R^{-1}$ or $\ln{R}$, where $R$ is the minimal separation between cylinders. However, pairwise summability of rod-rod forces is easily violated in low-salt conditions. Perhaps the most important result is not the derivation of pair potentials but rather the demonstration that some of these expressions may not be used for the very problems that originally motivated their derivation.Comment: 8 pages and 1 fig in ps forma

Observer weighting of interaural cues in positive and negative envelope slopes of amplitude-modulated waveforms

The auditory system can encode interaural delays in highpass-filtered complex sounds by phase locking to their slowly modulating envelopes. Spectrotemporal analysis of interaurally time-delayed highpass waveforms reveals the presence of a concomitant interaural level cue. The current study systematically investigated the contribution of time and concomitant level cues carried by positive and negative envelope slopes of a modified sinusoidally amplitude-modulated (SAM) high-frequency carrier. The waveforms were generated from concatenation of individual modulation cycles whose envelope peaks were extended by the desired interaural delay, allowing independent control of delays in the positive and negative modulation slopes. In experiment 1, thresholds were measured using a 2-interval forced-choice adaptive task for interaural delays in either the positive or negative modulation slopes. In a control condition, thresholds were measured for a standard SAM tone. In experiment 2, decision weights were estimated using a multiple-observation correlational method in a single-interval forced-choice task for interaural delays carried simultaneously by the positive, and independently, negative slopes of the modulation envelope. In experiment 3, decision weights were measured for groups of 3 modulation cycles at the start, middle, and end of the waveform to determine the influence of onset dominance or recency effects. Results were consistent across experiments: thresholds were equal for the positive and negative modulation slopes. Decision weights were positive and equal for the time cue in the positive and negative envelope slopes. Weights were also larger for modulations cycles near the waveform onset. Weights estimated for the concomitant interaural level cue were positive for the positive envelope slope and negative for the negative slope, consistent with exclusive use of time cues.We thank Virginia M. Richards and Bruce G. Berg for helpful discussions. We also thank Brian C. J. Moore and an anonymous reviewer for their insightful comments on an earlier draft of the manuscript. Work supported by grants from the National Science Council, Taiwan NSC 98-2410-H-008-081-MY3 and NIH R01DC009659

Specialized ommatidia of the polarization-sensitive dorsal rim area in the eye of monarch butterflies have non-functional reflecting tapeta

Many insects exploit sky light polarization for navigation or cruising-course control. The detection of polarized sky light is mediated by the ommatidia of a small specialized part of the compound eye: the dorsal rim area (DRA). We describe the morphology and fine structure of the DRA in monarch butterflies (Danaus plexippus). The DRA consists of approximately 100 ommatidia forming a narrow ribbon along the dorsal eye margin. Each ommatidium contains two types of photoreceptor with mutually orthogonal microvilli orientations occurring in a 2:6 ratio. Within each rhabdomere, the microvilli are well aligned. Rhabdom structure and orientation remain constant at all retinal levels, but the rhabdom profiles, as seen in tangential sections through the DRA, change their orientations in a fan-like fashion from the frontal to the caudal end of the DRA. Whereas these properties (two microvillar orientations per rhabdom, microvillar alignment along rhabdomeres, ommatidial fan array) are typical for insect DRAs in general, we also report and discuss here a novel feature. The ommatidia of monarch butterflies are equipped with reflecting tapeta, which are directly connected to the proximal ends of the rhabdoms. Although tapeta are also present in the DRA, they are separated from the rhabdoms by a space of approximately 55 μm effectively inactivating them. This reduces self-screening effects, keeping polarization sensitivity of all photoreceptors of the DRA ommatidia both high and approximately equal

Audio-Motor Integration for Robot Audition

International audienceIn the context of robotics, audio signal processing in the wild amounts to dealing with sounds recorded by a system that moves and whose actuators produce noise. This creates additional challenges in sound source localization, signal enhancement and recognition. But the speci-ficity of such platforms also brings interesting opportunities: can information about the robot actuators' states be meaningfully integrated in the audio processing pipeline to improve performance and efficiency? While robot audition grew to become an established field, methods that explicitly use motor-state information as a complementary modality to audio are scarcer. This chapter proposes a unified view of this endeavour, referred to as audio-motor integration. A literature review and two learning-based methods for audio-motor integration in robot audition are presented, with application to single-microphone sound source localization and ego-noise reduction on real data

The Becquerel rays and the properties of radium,

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