Enhanced backscattering and blazing effect from gratings, quasi-gratings and randomly rough surfaces

The blazing effect is probably the most important property of diffraction gratings used for spectroscopic purposes. On the other hand, the enhanced backscattering phenomenon has been generally studied in the framework of scattering from randomly rough surfaces. Using numerical results from rigorous theories, it will be shown that these phenomena, which have very different origins, should have more precise definitions. In a special case of a randomly rough surface formed by random corners, it will be shown that the effects of these phenomena are sometimes very difficult to distinguish.     

Detection of a scatter target over a randomly rough surface by using the angular correlation function in a finite-element approach

Abstract

It is known that the angular correlation function of scattered fields from a randomly rough surface has a conspicuous enhancement on the memory line, and becomes much smaller away from the line. The finite-element method is employed to solve the problem of scattering from a scatter target situated over a randomly rough surface. Numerical results show that the width of the angular correlation function becomes broadened owing to the presence of the target. It can be used to detect the presence of a target placed over the rough surface.     

Effects of magnetic atoms on the properties of ternary superconductors

Conclusion It is noteworthy that while only two classes of systems (the Chevrel phases and the rare-earth rhodium borides) have so far received extensive study, nonetheless a great many new phenomena have been encountered. This, however, should only be considered the beginning of a new and potentially very rich field, especially if one considers the vast number of possibilities of ternary compounds that can be produced. To take only one other example, recent work has shown that the compound Sc₂Fe₃Si₅ is superconducting with a superconducting transition of 4.5 K (29). This at first may appear surprising since ever in the Chevrel phase materials, the addition of Fe atoms is detrimental to superconductivity. However, recent Mossbauer effect experiments (29) have shown that the Fe in this material is not magnetic, having a magnetic moment of less than 0.03 µ_B. These silicides have also been made with rare-earth ions in place of the Sc(²⁸). The compounds show magnetic transitions and are currently under investigation. Several other interesting systems have been synthesized, and it appears that many more will be coming in the near future. The results reported above have shown the utility of hyperfine data in clarifying many of the new phenomena that occur, and it should be expected that as this new field grouws, these kinds of measurements will continue to play an active role (30).     

Time-local gaussian processes,path integrals and nonequilibrium nonlinear diffusion

In this paper we discuss the concept of time-local gaussian processes. These are processes for which the state variable at time t + τ is gaussian distributed around its most probable value at that time, for a specified realization a small time interval τ earlier. On one hand it will be shown that these processes are related to a very simple path sum. On the other hand the associated stochastic differential equation is derived by means of the Kramers-Moyal method, and will be seen to be the most general nonlinear Fokker-Planck equation. The significance of the present formulation for nonequilibrium processes and the comprehension of critical phenomena will be evaluated.     

A numerical evaluation of Rayleigh's theory applied to scattering by randomly rough dielectric surfaces

Abstract

We present a numerical simulation of scattering by one-dimensional randomly rough surfaces. It is based on the use of plane-wave expansions to describe the Melds on the surface (i.e. Rayleigh hypothesis). Accuracy and convergence properties of two different numerical implementations are studied. Some examples of results for a dielectric and a metallic Gaussian rough surface are shown to be in good agreement with calculations by a rigorous numerical method. The Rayleigh method appears to be a fast computation tool for dielectric surfaces with slopes of less than 0.2.     

Scattering and diffraction of a plane wave by a randomly rough half-plane*

Abstract

The scattering and diffraction of a TE (transverse electric) plane wave by a randomly rough half-plane are studied by a combination of three techniques: the Wiener-Hopf technique, the small perturbation method and a probabilistic method based on the shift-invariance of a homogeneous random function. By use of the D^a-Fourier transformation based on the shift-invariance, it is shown that the scattered wave is written by an inverse Fourier transformation of a homogeneous random function with a complex parameter. For a small rough case, such a random function with a complex parameter is expanded in a perturbation series and then the first-order solution is obtained exactly in an integral form. The first-order solution involves two physical processes such that the edge-diffracted wave is scattered by the randomly rough plane and the scattered wave, due to roughness, is diffracted by the half-plane. The solution is transformed into a sum of the Fresnel integrals with complex arguments, an integral along the steepest descent path and a branch-cut integral, which are evaluated numerically. Then, intensities of the coherently scattered wave and incoherent wave are calculated in the region near the edge and illustrated in figures.     

Demixing in binary systems at high pressure

Abstract

It is a well-recognized fact that the application of pressure has a large influence on the properties of pure substances. It will be shown here that this is even more true in the case of mixtures. Under high pressure, several new and interesting phenomena are observed. Some recent results will be presented and discussed.     

Thermo-and photostimulated depolarization in self-compensated CdF2:Ga and CdF2:In crystals

A study is reported of the conductivity of CdF₂ semiconductor crystals doped by indium and gallium donor impurities and residing in a semi-isolated state. The latter results from self-compensation of the impurities, in the course of which one half of them creates two-electron DX centers, and the second is ionized. Photo-and thermostimulated depolarization of these crystals has been studied. It was shown that the observed polarization/depolarization phenomena have a nonlocal nature and are due to the charges present in these crystals changing their positions. These changes may be formally considered as charge displacement to macroscopic distances considerably in excess of the interatomic ones. The mechanisms responsible for these phenomena are discussed. Fiz. Tverd. Tela (St. Petersburg) 41, 1575–1581 (September 1999)     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

Abstract

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

Dispersion and damping of a surface plasmon polariton on a one-dimensional randomly rough metal surface

Abstract

By the use of the reduced Rayleigh equation for the amplitude of a surface plasmon polariton on a one-dimensional randomly rough metal surface that is in contact with vacuum, we calculate the dispersion and damping of the surface electromagnetic wave to the lowest nonzero order in the rms height of the surface. It is found that the frequency of the surface plasmon polariton is depressed by the surface roughness. The attenuation of the surface plasmon polariton in the long wavelength limit is due primarily to its scattering into other surface plasmon polaritons, while in the short wavelength limit it is due primarily to its roughness-induced scattering into volume electromagnetic waves in the vacuum. The energy mean free path of the surface plasmon polariton is shorter on a randomly rough metal surface than it is on a lossy planar metal surface, and the surface plasmon polariton is more tightly bound to a rough surface than to a planar one.     

Magnetic field effects in proteins

ABSTRACT

Many animals can sense the geomagnetic field, which appears to aid in behaviours such as migration. The influence of man-made magnetic fields on biology, however, is potentially more sinister, with adverse health effects being claimed from exposure to fields from mobile phones or high voltage power lines. Do these phenomena have a common, biophysical origin, and is it even plausible that such weak fields can profoundly impact noisy biological systems? Radical pair intermediates are widespread in protein reaction mechanisms, and the radical pair mechanism has risen to prominence as perhaps the most plausible means by which even very weak fields might impact biology. In this New Views article, I will discuss the literature over the past 40 years that has investigated the topic of magnetic field effects in proteins. The lack of reproducible results has cast a shadow over the area. However, magnetic field and spin effects have proven to be useful mechanistic tools for radical mechanism in biology. Moreover, if a magnetic effect on a radical pair mechanism in a protein were to influence a biological system, the conditions necessary for it to do so appear increasing unlikely to have come about by chance.     

The Rhodes-Wohlfarth parameter as assessment of the displacive degree in ferroelectrics: The case of the Ф4> model

The Rhodes-Wohlfarth parameter extended to ferroelectrics by Tokunaga [J. Phys. Soc. Jap. 57, 4275 (1988)] is here analyzed within the model. It is shown that it can be directly related with the displacive degree of the transition as described by the ratio C / E ₀ , between the non-local coupling, C, driving the transition and the depth of the energy well, E₀, associated with the distorted structure. However, the Rhodes-Wohlfarth parameter becomes asymptotically constant as C / E ₀ decreases, i.e. for systems closer to the order disorder limit. Under this viewpoint, the very limited range of values observed for this experimental parameter is explained and is shown that, in general, it can only assess quantitatively the character of the transition in rather displacive cases. The argument can be generalized to more complex systems, and when applied to well known materials, a rough estimation of the displacive degree and the relevant microscopic energetic parameters in rather displacive ferroelectrics is possible. Received 23 December 1998 and Received in final form 4 May 1999     

Gaussian beam scattering from arbitrarily shaped objects with rough surfaces

Abstract

The scattered field of Gaussian beam scattering from arbitrarily shaped dielectric objects with rough surfaces is investigated for optical and infrared frequencies by using the plane wave spectrum method and the Kirchhoff approximation, and the formulae for the coherent and incoherent scattering cross sections are obtained theoretically based on geometrical optics and tangent plane approximations. The infrared laser scattering cross sections of a rough sphere are calculated at 1.06 μm, and the influence of the beam size is analysed numerically. It is shown that when the beam size is much larger than the size of the object, the results in this paper will be close to those of an incident plane wave.     

Universal behaviour of scattering amplitudes for scattering from a plane in an average rough surface for small grazing angles

Abstract

It is shown that for scattering from a plane in an average rough surface, the scattering cross section of the range of small grazing angles of the scattered wave demonstrates a universal behaviour. If the angle of incidence is fixed (in general it should not be small), the diffusive component of the scattering cross section for the Dirichlet problem is proportional to θ² where θ is the (small) angle of elevation, and for the Neumann problem it does not depend on θ. For the backscattering case these dependences correspondingly become θ⁴ and θ°. The result is obtained from the structure of the equations that determine the scattering problem rather than by use of an approximation.     

Instability of a flame front propagating through a fuel-rich droplet–vapour–air cloud

A simple model of a flame front propagating through a fuel-rich droplet–vapour–air mixture is presented in which the fuel droplets are assumed to evaporate in a sharp front ahead of the reaction front. By performing a linear stability analysis neutral stability boundaries are determined. It is shown that the presence of the spray of droplets in the fresh mixture can have a profound effect by causing cellularization of the flame front. Specifically, we demonstrate that under certain circumstances a spray flame can be cellular when its equivalent non-spray flame is completely stable. Furthermore, it is shown that even when the non-spray flame is itself cellular the equivalent spray flame will have a finer cellular structure. These theoretical predictions verify qualitatively for the first time independent experimental observations from the literature. It is thus shown that the primary effect of the spray on the stability of these flames is due to heat loss from the absorption of heat by the droplets for vaporization. The influence of the initial liquid fuel loading and the latent heat of vaporization on the critical wavenumber associated with cellularity provide further evidence of the responsibility of the heat loss mechanism for these spray-related phenomena. Finally, the cellularity of the spray flames with their attendant increase in flame front area suggest a plausible rationale for the experimentally observed burning velocity enhancement induced by the use of a spray of fuel droplets.     

Calculation of the scattering of electromagnetic waves from a two-dimensional perfectly conducting surface using the method of ordered multiple interaction

Abstract

Calculations, using the method of ordered multiple interaction (MOMI), of the scattering of electromagnetic waves from a two-dimensional, randomly rough, perfectly conducting surface with a ratio of RMS height [sgrave] to correlation length a of 1.0 or smaller are presented which demonstrate the robustness of the method. Convergence is achieved in six iterations or less. Some surfaces with [sgrave] = a = 1.0λ and certain topological features exhibited slow convergence. The MOMI inherently will show slow convergence when there are multiple back and forth scatterings. Since resonant scattering is characterized by this type of scattering, this suggests the presence of surface resonances on these surfaces.     

Angular correlation function of wave scattering by a random rough surface and discrete scatterers and its application in the detection of a buried object

Abstract

The scattering of waves by a buried object is often obscured by the clutter around it. Such clutter can be attributed to the scattering by random rough surfaces and random discrete scatterers. Recent studies show that, because of the memory effect, the angular correlation function can suppress the effects of clutter and make the scattering by the buried object more conspicuous. In this paper, we study the angular correlation function of wave scattering by a buried object underneath a layer of random discrete scatterers and a non-Gaussian random rough surface. Such problems are common when the target is buried below a rough surface that is underneath a layer of vegetation. Numerical results are illustrated for various parameters of rough surfaces and discrete scatterers. The angular correlation function is calculated by frequency and angular averaging. It is shown that the use of the angular correlation function can enhance target detection in the presence of clutter.     

Onset of turbulence in open liquid flows as a nonequilibrium noise-induced secondorder phase transition

It is shown that there is a profound analogy between the transition to turbulence in open liquid flows and the noise-induced excitation of oscillations of a pendulum with a randomly oscillating pivot. It is significant that this analogy is based not on the similarity of the equations describing these processes, but on the generality of the laws of the theory of oscillations. The existence of this analogy makes it possible to understand and account for numerous phenomena observed in both numerical simulations and real experiments. Moreover, this analogy suggests several recommendations to experimenters for achieving a more thorough suppression of undesirable turbulent pulsations in subsonic jets. Zh. Tekh. Fiz. 68, 31–39 (January 1998)