论文标题
格林的非古典运输功能，具有一般各向异性散射
Green's functions for non-classical transport with general anisotropic scattering
论文作者
论文摘要
在非古典线性运输中，碰撞之间的和弦长度分布是非指数的，而衰减不尊重啤酒的定律。广义辐射转移（GRT）扩展了经典理论，以说明碰撞和忽略所有高阶相关之间的两点相关。对于这种运输形式，我们在无限3D均质介质中带有与一般各向异性散射的无限3D同质介质中的各向同性点源的确切依赖性Green的功能。格林的碰撞速率密度的功能（表征了系统中的吸收和反应速率），以及表征辐射/颗粒位移的辐射/通量，在傅立叶空间中求解。我们使用伽马随机飞行来验证派生，以生成首个各向异性散射基准解决方案，以实现广义线性玻尔兹曼方程。对于具有线性各向异性散射和带有瑞利散射的伽马射线散射的伽马-4航班，碰撞速率密度在实际空间中是一种扩散模式的总和。
In non-classical linear transport the chord length distribution between collisions is non-exponential and attenuation does not respect Beer's law. Generalized radiative transfer (GRT) extends the classical theory to account for such two-point correlation between collisions and neglects all higher order correlations. For this form of transport, we derive the exact time-independent Green's functions for the isotropic point source in infinite 3D homogeneous media with general anisotropic scattering. Green's functions for both collision rate density, which characterizes absorption and reaction rates in the system, and radiance/flux, which characterizes displacement of radiation/particles, are solved in Fourier space. We validate the derivations using gamma random flights to produce the first anisotropic scattering benchmark solutions for the generalized linear Boltzmann equation. For gamma-4 flights with linearly anisotropic scattering and gamma-6 flights with Rayleigh scattering the collision rate density is found explicitly in real space as a sum of diffusion modes.
