Numerical simulation of multiple light scattering in layers consisting of opaque particles with a dull surface (geometrical optics approximation)

A numerical model is presented which allows one, in the geometrical optics approximation, to calculate scattering contributions of specified multiplicity in layers comprised of opaque particles with dull surfaces. For definiteness, the particles are assumed to be spherical with the Lambertian law of light scattering by the particle surface. The greatest scattering multiplicity is restricted, in this model, only by computer capacity. In this paper, the scattering multiplicities up to the sixth order inclusively are studied. Layers of moderate optical thickness, as well as the case of a semi-infinite medium with different particle packing densities, are analyzed for different geometries of illumination and observation. It is shown that for conservative scattering by the particle surface, the contribution of higher-order scattering decreases with increasing order number, which is related to the shadow-hiding effect. The scattering indicatrices of higher orders approach the isotropic case. The even and odd scattering orders show a systematic difference between themselves.     

Maximum coefficient of light extinction in a nonabsorbing dispersive medium

The maximum value of the light extinction coefficient μ, which can be observed in a dispersive medium with a relative refractive index n of the scattering particles, is studied within the framework of a quasi-crystalline approximation for nonabsorbing dispersive media consisting of monodisperse spherical scatterers. A change in the diffraction parameter x of the scattering particles and their volume concentration c _v is accompanied by nonmonotonic variations of the extinction coefficient, and the function μ(x, c _v ) exhibits several maxima. The dimensions and concentrations of particles are determined, for which the extinction coefficient reaches the absolute maximum μ^max. The μ^max value exhibits a monotonic growth with increasing relative refractive index n of the scattering particles. The conditions of validity of the Ioffe-Regel criterion of radiation localization have been studied. It is established that the localization in nonabsorbing dispersive media can be observed only for n ? 2.7. The intervals of x and c _v in which the criterion of radiation localization is satisfied in dispersive media consisting of particles with n = 3.0 and 3.5 are determined.     

火灾烟颗粒分形模型和球形模型光散射的比较研究

对烟颗粒的光散射进行模拟计算是研究火灾烟颗粒光散射特性的重要手段,目前对于火灾烟颗粒光散射的数值计算多采用球形或椭球模型.实际上,火灾烟颗粒的形貌与球形和椭球均存在着显著差异.扫描电子显微镜图像表明,烟颗粒具有近似分形的结构.本文利用离散偶极近似方法计算了随机取向的火灾烟颗粒分形凝团以及同体积的球形颗粒的光散射Muller矩阵,并对两者的归一化Muller矩阵元素随散射角的分布进行了比较.研究表明:火灾烟颗粒分形模型和球形模型的归一化矩阵元素F₁₁(θ)/     

Light scattering by an inhomogeneous spherical particle with intermediate layers

A model of a radially inhomogeneous multilayer spherical particle with a continuously varying refractive index in the intermediate layers between the shells of the particle and between the particle and the surroundings is proposed. Such a particle scatters light much like a dust particle with a rough and ragged surface of the layers, which is simulated with the help of the discrete dipole approximation method. For dust particles whose surface shape deviates from the spherical one, the refractive index profile and the behavior of the extinction Q _ext(x) and absorption Q _abs(x) efficiency factors with increasing thickness of the intermediate layers are studied. Properties of such particles in dependence on the number of layers are also studied. It is revealed that, as the number of shells increases, the order of the relative position of substances ceases to play a role, as is also the case for a multilayer spherical particle without intermediate layers. It is shown that, upon an increase in the number of shells at the same percentages of substances in the intermediate layers, the difference of the values of Q _ext(x) and Q _abs(x) from the corresponding values calculated with the model without intermediate layers decreases.     

Notes on number density fluctuations and the scattering cross section for electromagnetic waves scattered from a thermal nonequilibrium plasma

The scattering cross section and the Doppler spectrum for electromagnetic waves scattered by the electron density fluctuations of a plasma, where the mean kinetic temperature of the electronsT _e may differ from that of the ionsT _i , has been obtained among others byFejer, Buneman, Renau, Camnitz andFlood, andSalpeter. These authors use different methods of approach to calculate the autocovariance of the electron number-density fluctuations (from the mean) and then obtain the scattering cross section. Because of the differing results, the methods, concepts, and derivations of the scattering cross section are carefully examined in this paper. It is shown that the short-time dynamical considerations incorporated in the formulation of the statistical theory of the electron number-density fluctuations of the plasma as used by several authors (for instanceFejer, Buneman, Salpeter,) leads to results of limited validity. In addition, a fundamental error in calculating the electron density fluctuations leads these latter authors to an incorrect scattering cross section. The theory of scattering of electromagnetic waves from a plasma, where the electrons arenot in thermal equilibrium with the ions but statistical equilibrium exists, is developed in a general way. The covariance of the number-density fluctuations from the mean of the charged species of the plasma and the scattering cross sectionσ(q) are obtained. In particular it is shown that for a wavelength λ much greater than the effective Debye lengthd, the backscattering cross section increases and approaches complete incoherent scattering asT _e /T _i increases. This result is explained by noting that in the case of thermal equilibrium, the predicted value of the back-scattering cross section is smaller than that of the backscattering cross section from completely uncorrelated electron density fluctuations because the electrostatic interaction between the charged particles of the plasma, which is a function ofT _e andT _i , introduces a certain amount of organization in otherwise completely uncorrelated electron density fluctuations. When the mean temperature of the electrons increases relative to that of the ions, the organization introduced in the fluctuations diminishes because of the increasing thermal agitation of the electrons relative to that of the ions, and the backscattering process approaches that of incoherent backscattering (Thomson-type scattering). The spectrum function of incoherent scattering of electromagnetic waves from a nonequilibrium plasma is obtained and some cases of current interest are plotted.     

Thermodynamics of the rupture in a Morse lattice

The rupture of a Morse lattice is considered in the presentpaper. The critical rupture force F _cr is found todecrease with the number of particles N as F _cr ~ 1/\(\sqrt{N}\). The partition function is obtained for two states ofthe lattice – with all equal bond lengths and one broken bond.In the first case an accurate expressions for thermodynamicparameters are obtained, and thermodynamic expressions arederived in the harmonic approximation in the latter case. Theanalytical predictions are confirmed by extensive MD simulations.Cis-trans isomerization is considered as an example. Volumefractions of trans- and cis-isomers versus number ofmonomer units N are found depending on the torsion stiffnesses.     

Self-referencing measurement of an ultrashort pulse by the standard shear interferometry method

A new method for the self-referencing measurement of the amplitude-phase shape of an ultrashort pulse is proposed. The method uses a two-frequency characteristic of the pulse, which is defined as S(F ₁)S(F ₂), where F is the frequency, S(F) is the complex Fourier spectrum of the pulse, and F ₁ and F ₂ are two independent variables. It is shown that this characteristic can be generated as a two-dimensional polychromatic light wave upon generation of the sum frequency of two crossed spectral decompositions of one and the same pulse, as well as upon space-time Fourier transform of radiation of the noncollinearly generated second harmonic of the pulse. In an orthogonal system of transverse coordinates F ₁ + F ₂ and F ₁ ? F ₂, at any given value of F ₁ + F ₂, the radiation frequency of this wave in the direction of the second coordinate F ₁ ? F ₂ does not change. Therefore, the phase structure of the two-frequency characteristic can be reconstructed by the standard method of lateral shear interferometry in the direction of this coordinate. In the reconstructed two-dimensional phase structure of the two-frequency characteristic, any section by the plane F ₁ = const or F ₂ = const yields the phase structure of the spectrum of the pulse under study. This makes it possible to reconstruct the amplitude-phase shape of the pulse.     

Geometrical optics approximation for light scattering by absorbing spherical particles

By means of geometrical optics, an approximation method is presented to compute the light scattering intensity of absorbing spherical particles illuminated by a plane wave. For absorbing particles, the effective refractive index and the effective refractive angle are related to the complex refractive index and incident angle. The formulas for calculation of the break of phases of reflection and refraction, which are different from the case of transparent particles, are exactly derived. Verification of the geometrical optics approximation (GOA) was performed by case studies and comparison of the present results with the Mie scattering. It is found that agreement between the GOA and the Mie theory is excellent in forward directions for weakly/moderately absorbing particles. Differently, for strongly absorbing particles, good agreement between the calculation methods is in the forward directions and large scattering angles. The agreement between the GOA and the Mie theory is better for larger particles.     

Model of X-Ray Polycapillary Lens in the Geometrical Optics Approximation

Optical properties of the focusing full polycapillary X-ray lens are calculated. The numerical calculation model is constructed in the geometrical optics approximation using theMonte Carlo method for generating focal spot sizes of the X-ray source. The results of calculations of lens transport characteristics are compared for the point source and the finite focus size source.     

Mechanism for the bidirectional shape memory effect in titanium nickelide crystals

A mechanism for the bidirectional and all-round shape memory effects observed in titanium nickelide crystals is discussed quantitatively by using the theory of diffuse martensitic transformations (DMTs). These effects are associated with an anisotropic distribution of Ti₃Ni₄ particles, which arises in bent crystals subjected to annealing followed by relaxation of coherent microstresses produced by the particles. Using the DMT theory, the influence of the stepwise B2 → R → B19′ phase transition on the magnitude and sign of the radius of curvature of a thin strip of titanium nick-elide is calculated and the conditions are determined under which the bidirectional and all-round shape memory effects occur depending on structural factors and the geometrical parameters of the strip.     

Influence of two-dimensional bragg diffraction on the competition of the waveguide TE<Subscript>0</Subscript> and TM<Subscript>0</Subscript> modes during formation of spontaneous gratings in AgCl-Ag thin films

An intricate space-time instability of patterns of small-angle scattering and diffraction of a laser beam on the structures appearing in AgCl-Ag films under exposure to the same beam is investigated. The instability is related to the formation of spontaneous gratings in the film resulting from the interference of the incident beam with the waveguide modes scattered in the film. The existence of a two-dimensional Bragg diffraction on the TE₀ and TM₀ modes with subsequent formation of secondary spontaneous gratings is revealed and is theoretically substantiated. It is established that the difference in the indicatrices of the radiation scattered into the TE₀ and TM₀ modes for the s-and p-polarizations manifests itself in different kinds of diffraction and small-angle scattering patterns at the output of illuminated samples.     

Bound states of three and four resonantly interacting particles

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonance bound state of two fermions in a spin-singlet state, with corresponding scattering length a _F . Applying this approach to the calculation of the dimmer-dimer scattering length a _B , we recover exactly the already known result a _B = 0.6 a _F . We use the developed approach to obtain new results in 2D for fermions and bosons. Namely, we calculate bound state energies for three bbb and four bbbb resonantly interacting bosons in 2D. For the case of resonance interaction between fermions and bosons, we exactly calculate bound state energies of the following complexes: two bosons plus one fermion bbf, two bosons plus two fermions bf↑bf↓, and three bosons plus one fermion bbbf.     

Computer simulations for multiple scattering of light rays in systems of opaque particles

A new computer model for multiple light scattering in arbitrary systems of opaque diffusely scattering particles is considered. For ray tracing and scattering in such systems, the geometric optics approximation is used. Semi-infinite media and clusters with spherical and irregular shaped particles are investigated. The irregular particles are approximated with a discrete set of small triangular facets attached to each other. The particle surface is supposed to scatter by the Lambertian indicatrix. Scattering of the first six orders is considered, but the model can be effectively used for calculations of higher orders too. Phase-angle curves of scattering for media and clusters with different packing density are calculated. It is shown that the contributions of scattering orders rapidly diminish as the order grows even for non-absorbing particulate surfaces. Only the first scattering order shows the opposition effect and is rather sensitive to packing density. Higher orders do not show any features near zero phase angle. The contributions of high orders increase slightly, when the packing density increases. The form of particles is important mostly for the second scattering order. For clusters of particles both packing density and number of particles are important for phase function behavior. Clusters consisting of 100 particles show weak phase-angle dependences of high orders of scattering. These dependences become more prominent with increase of number of particles. Phase curves for spherical and cubic clusters are compared. It turns out that the influence of cluster shape is only a minor factor.     

Light scattering by a sphere with variable optical properties of the intermediate layer

A two-parameter model of a scattering spherical particle with a layer of a variable thickness (the first parameter), inside which the refractive index is specified by an arbitrary continuous function (the second parameter), is proposed. An algorithm for calculating the extinction and backscattering efficiency factors with the help of a developed piecewise-hyperbolic approximation of the scattering coefficients is presented. A correct choice of the parameters allowed us to obtain good agreement between the experimental and calculated data on the extinction and backscattering efficiency for typical polydisperse systems of particles of irregular shape.     

Structural Transitions in Elemental Tin at Ultra High Pressures up to 230 GPa

The quantum heat generation, interaction force, and friction torque for two rotating spherical nanoparticles with the radius R are calculated. In contrast to a static case where an upper bound in the radiative heat transfer between two particles exists, the quantum heat generation for two rotating particles diverges at distances between particles d < d ₀ = R(3/ε″(ω₀))^1/3 (where ε″(ω₀) is the imaginary part of the dielectric function for the material of a particle at the resonance frequency ω₀), when the rotation frequency coincides with poles in the excitation generation rate at Ω = 2ω₀. These poles are due to the anomalous Doppler effect and the mutual polarization of particles and exist even in the presence of dissipation in particles. The anomalous heat generation is associated with the conversion of mechanical rotation energy into heat mediated by quantum friction. Similar singularities also exist for the interaction force and friction torque. The results can be of significant importance for biomedical applications.     

Light scattering properties of sea-salt aerosol particles inferred from modeling studies and ground-based measurements

Direct climate radiative forcing depends on the aerosol optical depth τ, the single scattering albedo ?, and the up-scatter fraction β; these quantities are functions of the refractive index of the particles, their size relative to the incident wavelength, and their shape. Sea-salt aerosols crystallize into cubic shapes or in agglomerates of cubic particles under low relative humidity conditions. The present study investigates the effects of the shape of dried sea-salt particles on the detection of light scattering from the particles. Ground-based measurements of scattering and backscattering coefficients have been performed with an integrating nephelometer instrument for a wavelength . The measurements are compared to two models: the Mie theory assuming a spherical shape for the particles and the Discrete Dipole Approximation (DDA) model for the hypothesis of cubic shape of the sea-salt aerosols. The comparison is made accurately by taking into account the actual range of the scattering angles measured by the nephelometer in both models that is from 7° to 170° for the scattering coefficient and from 90° to 170° for the backscattering coefficient. Modeled scattering and backscattering coefficients increase for nonspherical particles compared to spherical shape of particles with diameter larger than about 1 μm. However, the comparison of the modeling results with the measurements gives best agreement for particles diameter less than about 1 μm. The size distribution of the particles is measured with two instruments with different size bins: an electrical low-pressure impactor (ELPI) and an aerodynamic particle sizer (APS). It is found that the size of the bins of the instruments to determine the number concentration of the particles in accordance with their diameter is critical in the comparison of measurements with modeling.     

Calculation of the diffusion coefficient in acoustic turbulence

The first (Born) approximation commonly used to calculate the diffusion coefficient D_T of a passive scalar in acoustic turbulence is shown to be insufficient. Even for a small main parameter—the Mach number, M?1—the next approximation gives a larger contribution to D_T than does the first approximation, but negative in sign. We present a procedure for correctly calculating D_T based on the solution of a nonlinear DIA (direct interaction approximation) equation for the mean Green’s function of the problem. We include an additional term in the general formula for D_T that directly describes the compressibility of acoustic turbulence. This term has not been known previously and has been disregarded even in the Born approximation. A positive value was obtained for D_T=CM³u₀/p₀. The spectrum E(x) was assumed to be smooth at distances Δ x～M²?1.     

Nucleus shape at the scission point at different kinetic energies of fission fragments

Deformations of fission fragments at fixed kinetic energies of a light fragment have been calculated within the droplet model. The calculations performed demonstrate the existence of a spherical shape with A ₁ = 76 and A _h = 134 (β₁, β_h ≈ 0). Fragments with A ₁ < 76 and A _h < 130 pass from the spherical to flattened shape. Fragments with A _h < 126 again acquire an elongated shape.