Chaotic scattering,transport, and fractals in a simple hydrodynamic flow

Advection of passive tracers in an unsteady hydrodynamic flow consisting of a background stream and a vortex is analyzed as an example of chaotic particle scattering and transport. A numerical analysis reveals a nonattracting chaotic invariant set Λ that determines the scattering and trapping of particles from the incoming flow. The set has a hyperbolic component consisting of unstable periodic and aperiodic orbits and a nonhyperbolic component represented by marginally unstable orbits in the particle-trapping regions in the neighborhoods of the boundaries of outer invariant tori. The geometry and topology of chaotic scattering are examined. It is shown that both the trapping time for particles in the mixing region and the number of times their trajectories wind around the vortex have hierarchical fractal structure as functions of the initial particle coordinates. The hierarchy is found to have certain properties due to an infinite number of intersections of the stable manifold in Λ with a material line consisting of particles from the incoming flow. Scattering functions are singular on a Cantor set of initial conditions, and this property must manifest itself by strong fluctuations of quantities measured in experiments.     

Effect of the “inversion” of a scattering medium in layers of close-packed titanium dioxide nanoparticles

The features of the behavior of the diffuse transmission of layers of close-packed titanium dioxide nanoparticles in the visible and near infrared spectral ranges with an increase in the volume fraction f of the particles in a layer have been analyzed. It has been found that an increase in f for layers of small particles (about 25 nm) with a relatively low volume fraction (0.20–0.25) is accompanied by the expected decrease in diffuse transmission. At the same time, an increase in f for layers of large particles (about 100 nm) with a volume fraction of 0.45–0.50 results in a strong increase in transmission. The described phenomenon has been interpreted in terms of the concepts of inverse scattering systems, where the main scattering centers are air nanocavities in a TiO₂ matrix rather than TiO₂ particles in an air matrix.     

Interference effects in backscattering of light by a layer of a discrete random medium

Multiple backscattering of light by a layer of a discrete random medium is considered. A brief derivation of equations for describing the coherent and incoherent components of scattered light is presented. These equations are solved numerically in the approximation of doubled scattering of light by a semi-infinite medium of spherical scatterers having a size comparable with the wavelength in order to study the effect of the properties of particles on the angular dependence of interference effects. Calculations show that the half-width of the interference peak decreases upon an increase in lateral scattering by particles and that the degree of polarization has a complex angular dependence on the properties of the particles. For an optically thin layer of the medium, the relations defining the interference peak half-width and the scattering angle upon extreme linear polarization as functions of the effective refractive index are given.     

Ultrasonic scattering properties of three random media with implications for tissue characterization

Random media with different structural properties were used to simulate some of the differences in liver morphology that may occur with disease. First, a reference medium consisting of glass spheres in agar was studied to verify the accuracy and precision of the data obtained with our equipment and processing procedures. Then, studies were conducted on a pair of media comprised of graphite particles in gelatin, one of the pair with twice as many particles as the other. Finally, studies were carried out on a set of media composed of Sephadex particles in water. Three samples were employed, each with a different size of Sephadex. The average differential scattering cross section per unit volume sigma sd (v) of each media was obtained as a function of scattering angle v and frequency. The measured sigma sd were compared with predictions based on models of scattering from the media. The agreement between the measured and predicted sigma sd of the glass sphere medium was excellent. The graphite medium with twice the number of particles as the other was observed to scatter twice as much power as the other. The shape of the angular scattering pattern measured from each size of Sephadex followed the prediction reasonably well. The largest size exhibited marked variations in the shape of sigma sd as a function of frequency, while the absolute magnitude of sigma sd of the smallest size grade was extremely sensitive to frequency. Our results suggest that the dependence of sigma sd (v) on scatterer number density and size, both in absolute magnitude and shape, can provide reliable information which may be useful in the diagnosis of some diseases.     

In-situ study of precipitates in Al–Zn–Mg–Cu alloys using anomalous small-angle x-ray scattering

In the present work,the precipitate compositions and precipitate amounts of these elements(including the size distribution,volume fraction,and inter-precipitate distance) on the Cu-containing 7000 series aluminum alloys(7150 and 7085 Al alloys),are investigated by anomalous small-angle x-ray scattering(ASAXS) at various energies.The scattering intensity of 7150 alloy with T6 aging treatment decreases as the incident x-ray energy approaches the Zn absorption edge from the lower energy side,while scattering intensity does not show a noticeable energy dependence near the Cu absorption edge.Similar results are observed in the 7085 alloy in an aging process(120℃) by employing in-situ ASAXS measurements,indicating that the precipitate compositions should include Zn element and should not be strongly related to Cu element at the early stage after 10 min.In the aging process,the precipitate particles with an initial average size of ~ 8 ?A increase with aging time at an energy of 9.60 ke V,while the increase with a slower rate is observed at an energy of 9.65 ke V as near the Zn absorption edge.     

Scattering properties of aqueous suspensions with absorbing dispersed phase

Scattering matrices of aqueous suspensions of copper oxide and graphite the particles of which are characterized by strong absorption at a wavelength of 0.63 μm have been measured in the scattering angle range of 10°–155°. The results of the measurements are compared with calculation data for axially symmetric scatterers (ellipsoids of revolution and cylinders). It is shown that, if the size parameter equals 4–6, even under conditions of strong radiation absorption by particles of the dispersive medium, deviation of their shape from axial symmetry has an effect on the scattering properties of the medium.     

Selection of optical radiation in scattering in partially ordered disperse media

Results of theoretical studies of the interaction between optical radiation and partially ordered disperse media are reported. In terms of the amplitude-phase screen model consideration is given to the concentration effects of whitening and darkening in random close-packed systems of optically soft particles. The concentration dependence of transmission of close-packed systems of coarse particles is described with the use of a small-angle solution of the stochastic finite-difference transfer equation. The effects of coherent reirradiation occurring in close-packed monolayers of highly refracting particles are analyzed using a quasicrystalline approximation of the theory of multiple wave scattering and the radial particle distribution function obtained from a solution of the Percus-Yevick equation. This approach extended to multilayer systems is used to describe formation of forbidden photon zones in transmission spectra of one- and three-dimensional disperse systems with a high degree of ordering. Results of quantitative calculations are shown to agree well with experimental data. The possibility of using established regularities for optimization of spectral characteristics of selective elements based on spatially ordered disperse systems with different structural organization is discussed. Institute of Molecular and Atomic Physics of the National Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 5, pp. 721–733, September–October, 1998.     

随机分布黑碳-硅酸盐混合凝聚粒子的消光特性研究

基于分形理论,采用蒙特卡罗方法对随机分布的混合凝聚粒子的空间结构进行了仿真模拟。利用Bruggeman有效介质理论得到了占有不同体积份额黑碳的内混合凝聚粒子的等效复折射率。采用离散偶极子近似方法对随机分布混合凝聚粒子在内外混合状态下的吸收、散射和消光效率因子等消光特性参量进行了数值计算,深入探讨了混合方式、容积含量、入射波长以及基本粒子粒径和数量对混合凝聚粒子消光特性的影响规律。通过将所得数值结果与T矩阵方法的数值结果进行比较发现,两种数值方法计算的结果非常相近。结果表明,随机分布混合凝聚粒子的散射效率因子对混合方式非常敏感,消光效率因子对混合方式较敏感,而吸收效率因子对混合方式不敏感。随着凝聚粒子尺度参数的增大,混合方式对散射和消光效率因子的影响逐渐显著。内外混合方式下,随着黑碳体积比的增大随机分布混合凝聚粒子的吸收、散射和消光效率因子均近似线性增大,并且增大的幅度随着粒子尺度参数的增大而增大。     

Light absorption by island metal films in the infrared range

This study reports on theoretical investigations of the electric and magnetic absorption of small metallic particles as functions of their shape, with the wavelength of incident e/m radiation assumed to be much greater than the size of the particles. A general expression for the absorption cross-section is derived for the cases when both the bulk and surface electron scattering are dominant. In the IR-region the absorption cross-section is shown to be extremely sensitive to the shape of particles; for particles of a constant volume, yet different in shape, it can change by several orders of magnitude. It is also shown that under dominant surface scattering the optical conductivity of an asymmetric particle is described by a tensor whose principal values are calculated for the ellipsoidal shape. The expression obtained for the electric and magnetic absorption renders ground to infer that the ratio of the contributions due to these absorption mechanisms greatly depends on the shape of particles and polarization of light.     

On the Renormalization of the One–Pion Exchange Potential and the Consistency of Weinberg’s Power Counting

Nogga, Timmermans and van Kolck recently argued that Weinberg’s power counting in the few–nucleon sector is inconsistent and requires modifications. Their argument is based on the observed cutoff dependence of the nucleon–nucleon scattering amplitude calculated by solving the Lippmann–Schwinger equation with the regularized one–pion exchange potential and the cutoff Λ varied in the range Λ = 2 . . . 20 fm^?1. In this paper we discuss the role the cutoff plays in the application of chiral effective field theory to the two–nucleon system and study carefully the cutoff–dependence of phase shifts and observables based on the one–pion exchange potential. We show that (i) there is no need to use the momentum–space cutoff larger than Λ ~ 3 fm^?1; (ii) the neutron–proton low–energy data show no evidence for an inconsistency of Weinberg’s power counting if one uses Λ ~ 3 fm^?1.     

Light scattering in a layer of correlatively arranged optically soft particles

The light scattering by an ensemble of monodisperse spatially correlated optically soft spherical particles is studied in the interference approximation. A model of the interaction of particles is proposed in which the spatial correlation between particles is determined by a radius R _c exceeding the particle radius R _p. The radial distribution function is calculated in the Percus-Yevick approximation for hard spheres of the radius R _c. To simulate the radiation scattering from an individual particle of the radius R _p, the Mie equations are used. It is shown that, in a medium of correlated small nonabsorbing particles of the radius R _c > R _p, an abnormal wavelength dependence of the refractive index is possible at a low volume concentration of particles. The results obtained explain some experimentally observed features of the scattering in sodium borosilicate glasses with a small concentration of scattering centers.     

Analysis of Gain Volume in Random Laser in a Spherical Multiple Scattering Medium

We performed numerical simulation of a random laser in a spherical multiple scattering medium in order to examine the saturation absorption in the excitation process and the resultant increasing process of the gain volume under the random laser action. The size of the gain volume increases with 1/3 power of the excitation pulse energy in the weak excitation region, and then approaches a critical value L_th when the excitation pulse energy is increased above the threshold. The dependence of L_th, as well as the dependence of the threshold excitation pulse energy on the dye concentration, transport mean free path, stimulated emission cross section and excited state lifetime were also examined. These results of the simulation well correspond to the experimental results by a two-beam spatial-correlation method.     

Aerosol light absorption and its measurement: A review

Light absorption by aerosols contributes to solar radiative forcing through absorption of solar radiation and heating of the absorbing aerosol layer. Besides the direct radiative effect, the heating can evaporate clouds and change the atmospheric dynamics. Aerosol light absorption in the atmosphere is dominated by black carbon (BC) with additional, significant contributions from the still poorly understood brown carbon and from mineral dust. Sources of these absorbing aerosols include biomass burning and other combustion processes and dust entrainment.For particles much smaller than the wavelength of incident light, absorption is proportional to the particle volume and mass. Absorption can be calculated with Mie theory for spherical particles and with more complicated numerical methods for other particle shapes.The quantitative measurement of aerosol light absorption is still a challenge. Simple, commonly used filter measurements are prone to measurement artifacts due to particle concentration and modification of particle and filter morphology upon particle deposition, optical interaction of deposited particles and filter medium, and poor angular integration of light scattered by deposited particles. In situ methods measure particle absorption with the particles in their natural suspended state and therefore are not prone to effects related to particle deposition and concentration on filters. Photoacoustic and refractive index-based measurements rely on the heating of particles during light absorption, which, for power-modulated light sources, causes an acoustic signal and modulation of the refractive index in the air surrounding the particles that can be quantified with a microphone and an interferometer, respectively. These methods may suffer from some interference due to light-induced particle evaporation. Laser-induced incandescence also monitors particle heating upon absorption, but heats absorbing particles to much higher temperatures to quantify BC mass from the thermal radiation emitted by the heated particles. Extinction-minus-scattering techniques have limited sensitivity for measuring aerosol light absorption unless the very long absorption paths of cavity ring-down techniques are used. Systematic errors can be dominated by truncation errors in the scattering measurement for large particles or by subtraction errors for high single scattering albedo particles. Remote sensing techniques are essential for global monitoring of aerosol light absorption. While local column-integrated measurements of aerosol light absorption with sun and sky radiometers are routinely done, global satellite measurements are so far largely limited to determining a semi-quantitative UV absorption index.     

Stimulated Raman scattering in light and heavy water under picosecond laser excitation

The spectra of stimulated Raman scattering in ordinary and heavy water under excitation by second harmonic of a picosecond Nd:YAG laser were compared. It was shown that when stimulated Raman scattering is excited in water in cavities of a photonic crystal (synthetic opal matrix constructed of silica nanoglobules) or a photonic glass in the form of close-packed monodimensional millimeter-size amorphous-quartz balls, the efficiency of stimulated Raman scattering increases significantly compared to a uniform liquid medium.     

Radiative properties of densely packed spheres in semitransparent media: A new geometric optics approach

This contribution presents a new Ray-tracing method for calculating effective radiative properties of densely packed spheres in non-absorbing or semitransparent host medium. The method is restricted to the geometric optic objects and neglects the wave effects. The effective radiative properties such as the absorption and scattering coefficients, and phase function are retrieved from the calculation of mean-free paths of scattering and absorption, and the angular scattering probability of radiation propagating in the dispersed medium. The model accounts for the two geometric effects called here as non-point scattering and ray transportation effects. The successful comparison of the current model with data of radiative properties and transmittances of particle beds in a non-absorbing medium reported in the literature confirm its suitability. It is shown that: (i) for opaque or absorbing particles (not systematically opaque), the non-point scattering is the dominant geometric effects whereas both non-point scattering and ray transportation effects occur for weakly absorbing and transparent particles. In the later cases, these two geometric effects oppose and may cancel out. This may explain why the Independent scattering theory works well for packed of quasi-transparent particles; (ii) the non-point scattering and ray transportation effects can be captured through the scattering and absorption coefficients while using the classical form of phase function. This enables using the standard radiative transfer equation (RTE); (iii) the surrounding medium absorption can be accounted for without any homogenization rule. It contributes to increasing the effective absorption coefficient of the composite medium as expected but, at the same time, it reduces the particle extinction; and (iv) the current transfer calculation predicts remarkably the results of direct Monte Carlo (MC) simulation. This study tends therefore to confirm that the RTE can be applied to densely packed media by using effective radiative properties.     

Scattering by a plane-parallel layer with high concentration of optically soft particles

A method describing light propagation in a plane-parallel light-scattering layer with large concentration of homogeneous particles is developed. It is based on the radiative transfer equation and the doubling method. The interference approximation is used to take into account collective scattering effects. Spectral dependence of transmitted light for a layer of nonabsorbing optically soft particles with subwavelength-sized particles is investigated. At small volume concentration of the particles the weak spectral dependences of wave exponents for coherently transmitted and diffuse light are observed. It is shown that in a layer with large volume concentration of the subwavelength-sized particles the wave exponent can exceed considerably the value of four, which takes place for the Rayleigh particles. The dependence of wave exponents for coherently transmitted and diffuse light on the refractive index and concentration of particles is investigated in detail. Multiple scattering of light results in the reduction of the exponent. The quantitative results are presented and discussed. It is shown that there is a range of wavelengths where the negative values of the wave exponent at the regime of multiple scattering are implemented.     

Effects of soot absorption and scattering on LII intensities in laminar coflow diffusion flames

Absorption and scattering of laser-induced incandescence (LII) intensities by soot particles present between the measurement volume and the detector were numerically investigated at detection wavelengths of 400 and 780 nm in a laminar coflow ethylene/air flame. The radiative properties of aggregated soot particles were calculated using the Rayleigh-Debye-Gans polydisperse fractal aggregate theory. The radiative transfer equation in emitting, absorbing, and scattering media was solved using the discrete-ordinates method. The radiation intensity along an arbitrary direction was obtained using the infinitely small weight technique. The effects of absorption and scattering on LII intensities are found to be significant under the conditions of this study, especially at the shorter detection wavelength and when the soot volume fraction is higher. Such a wavelength-dependent signal-trapping effect leads to a lower soot particle temperature estimated from the ratio of uncorrected LII intensities at the two detection wavelengths. The corresponding soot volume fraction derived from the absolute LII intensity technique is overestimated. The Beer-Lambert relationship can be used to describe radiation attenuation in absorbing and scattering media with good accuracy provided the effective extinction coefficient is adequately.     

Measurement of the absorption coefficient of scattering liquid media by the calorimetric method

Using the example of a number of hydrosols (gold nanorods and nanoshells, silver nanoshells, zinc phthalocyanine nanoparticles), we show that the absorption coefficient of a scattering liquid medium can be measured from its heating by a short-time laser irradiation. The degree of heating was determined from expansion of the liquid in an ampoule with a capillary (the principle of liquid thermometer). Irradiation was performed at a wavelength of 671 or 1069 nm. From the transmission of samples of hydrosols at these wave-lengths, the sum of the absorption and scattering coefficients has been determined. To measure the absorption spectra of scattering liquids by this method, a laser with a tunable radiation wavelength is required. In the case of monodisperse colloidal solutions, the method ensures the measurement of the absorption and scattering cross-section ratio of particles.     

Reconstruction of the characteristics of a light-scattering layer from its reflectance and transmittance: The neural network method

The problem of reconstructing the probability of photon survival, the optical layer thickness, and the parameter of asymmetry of the scattering indicatrix of an elementary volume from the dependence of the reflectance and the transmittance on the angle of incidence of radiation onto a layer of a medium with Fresnel reflection from the boundaries is considered. To solve this problem, a method based on the use of correlation neural networks is proposed. For training and control of the operation of neural networks, the reflectance and the transmittance of the layer calculated within the framework of the radiation transfer theory were used. For the simulation of the scattering characteristics of an elementary volume, the Mie theory was used. Estimates of errors in the reconstruction of the characteristics of the medium were performed.     

Transmittance of a gaseous medium with allowance for the molecular absorption and aerosol scattering

The transparency of a molecular gaseous medium comprising spherical aerosol particles is calculated. The characteristics of the transformed radiant energy that has passed through particles with different microphysical properties are analyzed. It is established that the joint effect of the molecular absorption and aerosol scattering in the IR range must be considered. Based on the characteristics of scattering particles, the boundary conditions are written that allow the molecular absorption and scattering to be considered separately. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 18–25, June, 2007.