Radiative absorption in an infinitely long hollow cylinder with Fresnel surfaces

Radiation absorption in an infinitely long hollow cylinder with Fresnel surfaces is studied using the ray tracing method. It is found that the inner boundary can be modeled as a total reflective surface for the infinitely long hollow cylinder. Radiative absorption of hollow cylinders with Fresnel surfaces is compared to diffusive surfaces predicted by the finite volume method. Effects of refractive index, optical thickness and hole size on radiative absorption are studied. Abrupt changes in radiative absorption near τ_r/τ_Ro=1/n are observed for hollow cylinders with Fresnel surfaces. It is because the Fresnel relation predicts a critical angle at . This trend is not observed in diffusive surfaces. Refractive index and optical thickness are two competing factors that govern the radiative absorption. Higher refractive index drives higher absorption close to the inner surface, while higher optical thickness yields higher absorption near the outer surface. The results of this study can also serve as benchmark solutions for modeling radiative heat transfer in hollow cylinders with Fresnel surfaces. It is also found that the directional or hemispherical emittance can be calculated without solving the radiative transfer equation in the media when the temperature variation in the media is small.     

Monte Carlo simulation of photon transport in a randomly oriented sphere-cylinder scattering medium

A Monte Carlo simulation tool for simulating photon transport in a randomly oriented sphere-cylinder medium has been developed. The simulated medium represents a paper pulp suspension where the constituents are assumed to be mono-disperse micro-spheres, representing dispersed fiber fragments, and infinitely long, straight, randomly oriented cylinders representing fibers. The diameter of the micro-spheres is considered to be about the order of the wavelength and is described by Mie scattering theory. The fiber diameter is considerably larger than the wavelength and the photon scattering is therefore determined by an analytical solution of Maxwell’s equation for scattering at an infinitely long cylinder. By employing a Stokes–Mueller formalism, the software tracks the polarization of the light while propagating through the medium. The effects of varying volume concentrations and sizes of the scattering components on reflection, transmission and polarization of the incident light are investigated. It is shown that not only the size but also the shape of the particles has a big impact on the depolarization.     

Yang-Mills fields due to an infinite charge cylinder

The problem of determining time-independent solutions of the classical Yang-Mills equations for infinitely long charge cylinders is studied. A useful expression for the total energy in the field in terms of just the sources is derived. Numerical solutions have been found in the special cases of a small charge cylinder with a magnetic field B that either lies along the axis of symmetry or encircles the axis. It is as if these two solutions were due to currents encircling the axis or paralleling it, respectively. The condition that the solution behave well at infinity implies an exponential fall off for the fields in the azimuthal B field case and a fall off more rapid than 1/R in the axial B field case, so that in both cases the existence of a B field requires the charge on the axis to be shielded. Consequently, these solutions do not behave at infinity at all like the Maxwell solution for a charge cylinder, and they have a lower energy per unit length. They show that in Yang-Mills theories the source does not determine a unique field. A classical interpretation of this is that the field remembers how the charges were transported during the construction of the cylinder. It also suggests that a quantum mechanical version of this problem would exhibit a “spontaneous symmetry breaking” to a less symmetric, lower energy vacuum.These solutions exhibit a twofold degeneracy, as the magnetic field may be either left- or right-handed in the azimuthal B field case, or point along the +z or ?z axis in the axial B field case.     

Radiation transport and internal reflection in a two region, turbid sphere

We construct an integral equation for the flux intensity in a scattering and absorbing two-region turbid spherical medium using the integro-differential form of the radiative transfer equation. The sphere is uniformly irradiated by an external source of arbitrary angular distribution and contains a distributed volume source. Anisotropic scattering is accounted for by the transport approximation. The Fresnel boundary conditions, which incorporate reflection and refraction, are used at the outer surface and at the interface between the two regions. In this respect, some new interfacial boundary conditions are introduced. For the special case of a non-scattering medium, we obtain exact solutions for specular reflection. Some numerical examples are given which show qualitative agreement with some recent work of other authors. Of particular interest are the emergent angular distribution and the albedo of the surface as a function of the refractive index and the radii of the two regions. We also draw attention to the fact that the boundary conditions at the interface differ according to the relative values of the refractive indices in the two regions. The interfacial boundary conditions for use in diffusion theory are derived and compared with those of Aronson [Boundary conditions for diffusion of light. J opt Soc Am 1995;12:2532]. In appendix B, we show how diffusion theory may be used to include scattering into the problem in a simple way.     

Analytic solutions to Maxwell–London equations and levitation force for a general magnetic source in the presence of a long type-II superconducting cylinder

The interaction between a general magnetic source and a long type-II superconducting cylinder in the Meissner or mixed state is studied within the London theory. We first study the Meissner state and solve the Maxwell–London equations when the source is a magnetic monopole located at an arbitrary position. Then the field and supercurrent for a more complicated magnetic charge distribution can be obtained by superposition. A magnetic point dipole with arbitrary direction is studied in detail. It turns out that the levitation force on the dipole contains in general an angular as well as a radial component. By integration we obtain the field and supercurrent when the source is a two-dimensional monopole (a magnetically charged long thread along the axial direction), from which the results for a two-dimensional point dipole easily follow. In the latter case the levitation force points in the radial direction regardless of the orientation of the dipole. The case for a current carrying long straight wire parallel to the cylindrical axis is solved separately. The limit of ideal Meissner state is discussed in most cases. The case of mixed state is discussed briefly. It turns out that vortex lines along the axial direction and vortex rings concentric with the cylinder have no effect outside the cylinder and the levitation forces remain the same as in the case of the Meissner state.     

Scattering cross-section of an inhomogeneous plasma cylinder

Scattering of em waves by the plasma cylinder is of significance in radar target detection, plasma diagnosis, etc. This paper discusses the general method tocalculate the scattering cross-section of em waves from a plasma cylinder which is radially inhomogeneous and infinitely long. Numerical results are also provided for several plasma density profiles. The effect of the electron density distribution on the scattering cross-section is investigated.     

Beamforming with a circular array of microphones mounted on a rigid sphere (L)

Beamforming with uniform circular microphone arrays can be used for localizing sound sources over 360°. Typically, the array microphones are suspended in free space or they are mounted on a solid cylinder. However, the cylinder is often considered to be infinitely long because the scattering problem has no exact solution for a finite cylinder. Alternatively one can use a solid sphere. This investigation compares the performance of a circular array mounded on a rigid sphere with that of such an array in free space and mounted on an infinite cylinder, using computer simulations. The examined techniques are delay-and-sum and circular harmonics beamforming, and the results are validated experimentally.     

长柱状气溶胶粒子的光散射特性

以中纬度卷云中常见的长柱状冰晶为例,利用长柱状粒子光散射理论,探讨了入射光为线偏振时,电矢量平行和垂直于入射面情况下,单个长柱状粒子的散射光强度分布和偏振特性随入射角、尺度参数与偏振态的转化关系:随着入射角的增大,散射强度、偏振总体趋于对称且数值振荡频率降低,散射强度总体减小,偏振的改变程度总体增大;随着尺度参数的增大,散射强度、偏振的数值振荡频率增大,散射强度数值振荡峰的幅度整体减小,电矢量平行于粒子长轴时主偏振的数量、强度和位置皆有变迁,电矢量垂直于粒子长轴时前后主偏振位置相对固定;随着偏振度的减小,散射强度、偏振趋向于一致,两者的数值改变程度减小,当偏振度减小到0时,散射强度、偏振变得完全相同。选取火山尘埃和烟灰与冰晶对比,阐述了粒子散射光的强度分布和偏振特性随折射率的变化规律:折射率虚部不改变散射强度的整体趋势,但使散射强度和偏振的振荡峰幅度增大,当其数值较大时,使得偏振的数值振荡峰覆盖范围拓宽。     

FDTD investigation on the electromagnetic scattering from a target above a randomly rough sea surface

A finite-difference time-domain approach for electromagnetic scattering characteristic from a two-dimensional (2-D) infinitely long target with arbitrary cross-section above the one-dimensional (1-D) randomly rough sea surface is presented. Taking the composite scattering of rough sea surface and infinitely long cylinder as an example, the angular distribution of the scattering cross-section with different incident angles is calculated and it shows good agreement with the numerical result by the conventional Method of Moments (MOM). Finally, the influence of the windspeed on the sea surface, the incident angle, as well as the size and location of the target on the composite radar cross-section (RCS) with different polarisations is investigated in detail.     

Dual Variational Form of the Model of Thermal Explosion in a Quiescent Medium with Temperature-Dependent Thermal Conductivity

Based on the dual variational formulation of the nonlinear stationary heat conduction problem, a mathematical model is constructed that describes the temperature state of a stationary medium in a volume of an arbitrary shape. The thermal conductivity of the medium and the volumetric energy release depend on the temperature. This model is applied to analyzing the conditions of thermal explosion in an infinitely long circular cylinder for exponential temperature dependences of the above parameters. In the particular case of constant thermal conductivity of this cylinder, a comparison with the published results is carried out.     

Rainbow Scattering by an Inhomogeneous Cylinder with an Off-Axis Gaussian Beam Incidence at Normal

The problem of an off-axis Gaussian beam incident perpendicular on an infinitely long multi-layered cylinder is investigated. The efficient and accurate recursive algorithm for computing the scattering field is discussed. The stability of the numerical scheme allows us to extend the feasible range of computations, both in size parameter and in number of layers for a given size. Particular attention is paid to rainbow scattering of homogeneous and inhomogeneous fibers.     

Scattering response of a bianisotropic cylinder with electrically small cross-section

EM scattering response of an infinitely long bianisotropic cylinder with electrically small cross-section suspended in free space is presented. Formulation of this problem is based on the coupled integral equation method with the long wavelength approximation. Reduced expressions for the scattering of plane waves, both E-wave and H-wave types, are obtained. It is revealed that for certain polarization matrices determined by the constitutive parameters of the scatterer, cross-polarization and/or co-polarization phenomena may occur, respectively.     

Scattering of light by multiple dielectric cylinders: comparison of radiative transfer and Maxwell theory

We have compared radiative transfer theory with analytical solutions of the Maxwell equations for light scattering by multiple infinitely long parallel cylinders at perpendicular incidence. The calculated scattering cross sections for both methods show large differences, but the angle-dependent differential scattering cross-section results are very similar for small cylinder densities, except close to the forward direction. In contrast to recently published results, it is shown that the radiative transfer equation is a useful approximation for small cylinder concentrations.     

Anisotropy of light propagation in biological tissue

We investigated the propagation of light in biological tissues that have aligned cylindrical microstructures (e.g., muscle, skin, bone, tooth). Because of pronounced anisotropic light scattering by cylindrical structures (e.g., myofibrils and collagen fibers) the spatially resolved reflectance exhibits a directional dependence that is different close to and far from the incident source. We applied Monte Carlo simulations, using the phase function of an infinitely long cylinder, to explain quantitatively the experimental results. These observations have consequences for noninvasive determination of the optical properties of tissue as well as for the diagnosis of early tissue alterations.     

Investigation of composite electromagnetic scattering from ship-like target on the randomly rough sea surface using FDTD method

Composite electromagnetic scattering from a two-dimensional (2D) ship-like target on a one-dimensional sea surface is investigated by using the finite-difference time-domain (FDTD) method. A uniaxial perfectly matched layer is adopted for truncation of FDTD lattices. The FDTD updated equations can be used for the total computation domain by choosing the uniaxial parameters properly. To validate the proposed numerical technique, a 2D infinitely long cylinder over the sea surface is taken into account first. The variation of angular distribution of the scattering changing with incident angle is calculated. The results show good agreement with the conventional moment method. Finally, the influence of the incident angle, the polarization, and the size of the ship-like target on the composite scattering coefficient is discussed in detail.     

Interaction of directive electromagnetic radiation with isotropic plasma-coated PEMC cylinder

ABSTRACT

In this study, we analyzed the influence of isotropic plasma on far field scattering radiation of perfect electromagnetic conductor (PEMC) cylinder in the presence of directive electromagnetic radiation excited from an electric line source. Two cases regarding electric line source have been considered to gain more graphical variation corresponding to plasma parameters. In the first case, electric line source is placed outside the coating layer while in second case electric line source placed inside the coating. It has been demonstrated that the far field scattering patterns of PEMC, PEC, and PMC are strongly dependent on plasma parameters; however, their importance to control scattering pattern slightly changed/reversed corresponding to electric line source placement (inside the coating and outside the coating).     

基于成像法的气溶胶粒形和散射分析仪

粒形是影响气溶胶粒子光散射特性的基本参量,其定量信息的研究受到越来越多的关注。气溶胶粒形的常规测量手段为散射法和显微成像法。将散射法与显微成像法有机结合,提出了基于成像法设计气溶胶粒形和散射分析仪的新方案,实现了仪器测量的自身完善。利用自编的无限长圆柱理论的仿真程序,分析了线偏振光入射下,已知形状的单个棉絮纤维粒子的散射强度和偏振。实验数据和程序运算结果的比较表明,用该方法设计的分析仪的检测是可靠的。     

On the theory of phase transformations with a nonuniform nucleation rate

An expression for the phase volume fraction in a system with a nonuniform nucleation rate is derived by using the geometrical-probabilistic approach. Examples of such systems considered here are (1) a plane layer (with nucleation in the midplane) and random planes in space, (2) an infinitely long cylinder (with nucleation on the axis) and random lines in space, and (3) a sphere (with nucleation at the center) and nucleation at random points. In each case, an expression for the phase volume fraction is derived for the time-dependent rates of nucleation and growth. The equivalence of homogeneous nucleation and nucleation at points is established.     

粗糙海面及其上方导体目标复合电磁散射的混合算法研究

利用基于电流计算的矩量法结合高频算法基尔霍夫近似的混合算法,分析了一维PM谱粗糙海面及其上方二维无限长任意截面导体目标的双站复合电磁散射特性.混合算法将粗糙面和目标分别划分到KA区域和MOM区域,由于无需数值求解粗糙海面区域的表面极化电流,该算法的运算时间和对计算机内存的需求主要取决于粗糙面上方目标的网格划分情况.数值结果以无限长导体圆柱为例计算了其与一维下垫PM谱粗糙海面的复合双站散射截面,并将计算结果与经典MOM结果进行了比对和验证,结果表明混合方法具有较高的计算效率.最后应用混合方法讨论了不同极化状态、海上不同风速以及目标不同尺寸和位置对复合散射截面的影响. 关键词： 粗糙海面 电磁散射 混合算法 矩量法