Electromagnetic Wave Scattering by Small Impedance Particles of an Arbitrary Shape

Scattering of electromagnetic (EM) waves by one and many small ($ka\ll 1$) impedance particles $D_m$ of an arbitrary shape, embedded in a homogeneous medium, is studied. Analytic formula for the field, scattered by one particle, is derived. The scattered field is of the order $O(a^{2-\kappa})$, where $\kappa \in [0,1)$ is a number. This field is much larger than in the Rayleigh-type scattering. An equation is derived for the effective EM field scattered by many small impedance particles distributed in a bounded domain. Novel physical effects in this domain are described and discussed

Wave scattering by small bodies and creating materials with a desired refraction coefficient

Asymptotic solution to many-body wave scattering problem is given in the case of many small scatterers. The small scatterers can be particles whose physical properties are described by the boundary impedances, or they can be small inhomogeneities, whose physical properties are described by their refraction coefficients. Equations for the effective field in the limiting medium are derived. The limit is considered as the size $a$ of the particles or inhomogeneities tends to zero while their number $M(a)$ tends to infinity. These results are applied to the problem of creating materials with a desired refraction coefficient. For example, the refraction coefficient may have wave-focusing property, or it may have negative refraction, i.e., the group velocity may be directed opposite to the phase velocity. This paper is a review of the author's results presented in MR2442305 (2009g:78016), MR2354140 (2008g:82123), MR2317263 (2008a:35040), MR2362884 (2008j:78010), and contains new results.Comment: In this paper the author's invited plenary talk at the 7-th PACOM (PanAfrican Congress of Mathematicians), is presente

Electromagnetic wave scattering by many conducting small particles

A rigorous theory of electromagnetic (EM) wave scattering by small perfectly conducting particles is developed. The limiting case when the number of particles tends to infinity is discussed

Chemoconvection patterns in the methylene-blue–glucose system: weakly nonlinear analysis

The oxidation of solutions of glucose with methylene-blue as a catalyst in basic media can induce hydrodynamic overturning instabilities, termed chemoconvection in recognition of their similarity to convective instabilities. The phenomenon is due to gluconic acid, the marginally dense product of the reaction, which gradually builds an unstable density profile. Experiments indicate that dominant pattern wavenumbers initially increase before gradually decreasing or can even oscillate for long times. Here, we perform a weakly nonlinear analysis for an established model of the system with simple kinetics, and show that the resulting amplitude equation is analogous to that obtained in convection with insulating walls. We show that the amplitude description predicts that dominant pattern wavenumbers should decrease in the long term, but does not reproduce the aforementioned increasing wavenumber behavior in the initial stages of pattern development. We hypothesize that this is due to horizontally homogeneous steady states not being attained before pattern onset. We show that the behavior can be explained using a combination of pseudo-steady-state linear and steady-state weakly nonlinear theories. The results obtained are in qualitative agreement with the analysis of experiments

Inversion of low-frequency subsurface data in a finite-depth ocean

AbstractLet:[▿2+k2+k2v(x)]u=−δ(x−y) in L=R2 × [0,h],u= 0 at x3 = 0, ux3 = 0 at x3 = h, u(x,y,k) satisfies the limiting absorption principle. Letu(x,y,k) be known for all x,y∈ P ≔ {x:x3 = d}, where 0< d<h is a small fixed number (subsurface data), and allk∈ (0,k0),k0 > 0 is a small number. These data determine v(x) uniquely and an analytical procedure is given for finding v(x) given the above data. It is assumed that v(x), the inhomogeneity in the refraction coefficient (of the ocean of depth h), is an arbitrary compactly supported square integrable function

Phase Steering and Focusing Behavior of Ultrasound in Cementitious Materials

Deterioration of civil infrastructure system (CIS) raises not only safety issues but also socio-economic concerns. In order to meet the high demand of structural condition assessment and health monitoring, development of quick, reliable and accurate NDE methods became critical issues recently. Compared to metal structures, NDE for cement-based materials is still premature and requires further development

Transverse oscillations of systems of coronal loops

We study the collective kinklike normal modes of a system of several cylindrical loops using the T-matrix theory. Loops that have similar kink frequencies oscillate collectively with a frequency which is slightly different from that of the individual kink mode. On the other hand, if the kink frequency of a loop is different from that of the others, it oscillates individually with its own frequency. Since the individual kink frequency depends on the loop density but not on its radius for typical 1 MK coronal loops, a coupling between kink oscillations of neighboring loops take place when they have similar densities. The relevance of these results in the interpretation of the oscillations studied by \citet{schrijver2000} and \citet{verwichte2004}, in which transverse collective loop oscillations seem to be detected, is discussed. In the first case, two loops oscillating in antiphase are observed; interpreting this motion as a collective kink mode suggests that their densities are roughly equal. In the second case, there are almost three groups of tubes that oscillate with similar periods and therefore their dynamics can be collective, which again seems to indicate that the loops of each group share a similar density. All the other loops seem to oscillate individually and their densities can be different from the rest

High frequency limit of the Transport Cross Section and boundedness of the Total Cross Section in scattering by an obstacle with impedance boundary conditions

The scalar scattering of the plane wave by a strictly convex obstacle with impedance boundary conditions is considered. The uniform boundedness of the Total Cross Section for all values of frequencies is proved. The high frequency limit of the Transport Cross Section is founded and presented as a classical functional of the variational theory

Sperm competition-induced plasticity in the speed of spermatogenesis

Background: Sperm competition between rival ejaculates over the fertilization of ova typically selects for the production of large numbers of sperm. An obvious way to increase sperm production is to increase testis size, and most empirical work has focussed on this parameter. Adaptive plasticity in sperm production rate could also arise due to variation in the speed with which each spermatozoon is produced, but whether animals can respond to relevant environmental conditions by modulating the kinetics of spermatogenesis in this way has not been experimentally investigated. Results: Here we demonstrate that the simultaneously hermaphroditic flatworm Macrostomum lignano exhibits substantial plasticity in the speed of spermatogenesis, depending on the social context: worms raised under higher levels of sperm competition produce sperm faster. Conclusions: Our findings overturn the prevailing view that the speed of spermatogenesis is a static property of a genotype, and demonstrate the profound impact that social environmental conditions can exert upon a key developmental process. We thus identify, to our knowledge, a novel mechanism through which sperm production rate is maximised under sperm competition