Photon path length analysis of radiative heat transfer in planar layers with arbitrary temperature distributions

The internal source analytical technique is extended to predict the radiative heat transfer for a layer having an arbitrary temperature distribution. By combining a number of internal sources distributed at various optical depths in the layer and weighting them appropriately, a nonisothermal layer is modeled. Heat flux and intensity distributions within layers having a single internal source are presented. The distributions are found to present trends unique to the internal source problem. Isothermal layers are modeled and compare very well with published results. Increased accuracy is attained for all cases and particularly for larger optical depths and smaller albedos by increasing the number of internal sources. The technique is applied to a nonisothermal layer having a temperature distribution similar to that for a hot medium with a cold boundary region. The effect of the boundary region on the normalized heat flux leaving the layer is seen to collapse to a single line for small layer optical thicknesses and large albedos, the slope of which is governed by the temperature ratio T_max/T_min.     

Photon path length distributions for an isotropically scattering planar medium

The optical path length concept is employed to determine path length distributions by an approximate numerical inversion of the Laplace transform. Six-term or 13-term closed-form representations of the hemispherical reflectance and transmittance optical path length distributions are presented. The mean path lengths and the distributions integrated over path length are found to be in excellent agreement with known results for a scattering optical depth range of 0.001 to 50.0. Any absorption feature of a medium is easily included in a scattering calculation using the results presented. Internal directional heat flux optical path length distributions are shown to exhibit the effects of higher orders of scattering.     

Two-dimensional radiative transfer in a finite scattering planar medium

The source function, radiative flux, and intensity at the boundaries are calculated for a two-dimensional, scattering, finite medium subjected to collimated radiation. The scattering phase function is composed of a spike in the forward direction super-imposed on an isotropic background. Exact radiative transfer theory is used to formulate the problem and Ambarzumian's method is used to obtain results. Using the principle of superposition, the results for any step variation in incident radiation are expressed in terms of universal functions for the semi-infinite step case. Two-dimensional effects are most pronounced at large optical thicknesses and albedos.     

Photon conservation in scattering by large ice crystals with the SASKTRAN radiative transfer model

The scattering of visible light by ice crystals and dust in radiative transfer models is challenging in part due to the large amount of scattering in the forward direction. We introduce a technique that ensures numerical conservation of photons in any radiative transfer model and that quantifies the integration error associated with highly asymmetric phase functions. When applied to a successive-orders of scatter model, the technique illustrates the high accuracy obtained in numerical integration of molecular and aerosol scattering. As well, a phase function truncation and renormalization technique is applied to scattering by ice crystals with very large size parameters, between 100 and 1000, and the scaled radiative transfer equation is solved with the spherical successive-orders model, SASKTRAN. Since computations shown this work are performed in a fully spherical model atmosphere, the computed radiances are not subject to the discontinuity at the horizon that is inherent in models using a plane–parallel assumption. The methods introduced in this work are of particular interest in modeling limb radiances in the presence of thin cirrus clouds.     

Differential approximations for transient radiative transfer in refractive planar media with pulse irradiation

Transient radiative transfer in an anisotropically scattering refractive planar medium with pulse irradiation is solved by various approximation methods, such as P?1, P?1 parabolic, P_1/3 and two-flux. The time-resolved transmittance and reflectance are calculated for various radiative parameters, and are compared with those obtained by the discrete ordinate method (DOM). Among the approximation methods considered, the P_1/3 approximation is the better one, because its results are in overall good agreement with those obtained by the more rigorous DOM, except the transmittance around the peak for neither thin nor very thick slabs. It is found that the curved paths of radiation and the internal reflection of the back scattered radiation enhance the effect of scattering.     

Transient conductive and radiative transfer in a planar layer with Arrhenius heat generation

Transient conductive and radiative energy transfer in a gray absorbing-emitting planar medium bounded by black walls is studied. The temperature distribution is uniform when the medium starts releasing energy according to the Arrhenius equation. The Crank-Nicolson method is used in the radiative-dominant case with good accuracy. Time-dependent temperature and heat flux distributions are calculated until steady-state is reached. Confirmation of the solution technique is made by comparison with previous investigations. The dimensionless activation energy required for ignition varies from 4.1 for pure conduction to 7.5 for pure radiation.     

Photon path length distribution in random media from spectral speckle intensity correlations

We show that the spectral speckle intensity correlation (SSIC) technique can be profitably exploited to recover the path length distribution of photons scattered in a random turbid medium. We applied SSIC to the study of Teflon slabs of different thicknesses and were able to recover, via the use of the photon diffusion approximation theory, the characteristic transport mean free path ℓ^∗ and absorption length s _a of the medium. These results were compared and validated by means of complementary measurements performed on the same samples with standard pulsed laser time of flight techniques.     

Derivation and application of the reciprocity relations for radiative transfer with internal illumination

A Green's function formulation is used to derive basic reciprocity relations for planar radiative transfer in a general medium with internal illumination. Reciprocity (or functional symmetry) allows an explicit and generalized development of the equivalence between source and probability functions. Assuming similar symmetry in three-dimensional space, a general relationship is derived between planar-source intensity and point-source total directional energy. These quantities are expressed in terms of standard (universal) functions associated with the planar medium, while all results are derived from the differential equation of radiative transfer.     

Comparison of radiative transfer approximations for a highly forward scattering planar medium

We examine critically the accuracy of the two-flux, spherical harmonics and discrete ordinates methods for predicting radiative transfer in a planar, highly-forward scattering and absorbing medium. Numerical results for the radiative fluxes show that the two-flux and P₃-approximations yield accurate results compared to solutions based on the F_N-method. Indeed, these approximate methods are relatively simple and have potential for generalization to predict radiative transfer in multidimensional systems, as long as an appropriate simplification of the phase function is utilized.     

Multi-coupled single scattering method of solving vector radiative transfer equations

<正>A new method of multi-coupled single scattering(MCSS) for solving a vector radiative transfer equation is developed and made public on Internet.Recent solutions from Chandrasekhar’s X-Y method is used to validate the MCSS’s result,which shows high precision.The MCSS method is theoretically simple and clear,so it can be easily and credibly extended to the simulation of aerosol/cloud atmosphere’s radiative properties,which provides effective support for research into polarized remote sensing.     

Laser pulse length dependence of internal energy transfer in UV-MALDI-MS

Recent internal energy (IE) measurements for various analytes in matrix-assisted laser desorption ionization (MALDI) have indicated that the amount of IE transferred to analytes not only depends on the matrix but also on the nature of the analyte. Common matrixes, such as -cyano-4-hydroxycinnamic acid (CHCA), 3,5-dimethoxy-4-hydroxycinnamic acid (sinapinic acid, SA), and 2,5-dihydroxy-benzoic acid (DHB), had been characterized as cold or hot according to the IEs of analyte ions produced in the corresponding MALDI plume. In this contribution, we present evidence that IE transfer in MALDI depends on the matrix, analyte, as well as on the laser pulse properties. A substituted benzylpyridinium salt as a thermometer molecule (TM) was investigated in CHCA, SA, and DHB matrixes. A nitrogen laser (4 ns pulse length) and a mode locked frequency tripled Nd:YAG laser (22 ps pulse length) were used as excitation sources at various fluences. Survival yields (SYs) of the analyte molecular ions were extracted from the spectra and the corresponding IEs were obtained from Rice–Ramsperger–Kassel–Marcus (RRKM) theory. The SYs indicate that the IEs of analyte ions in MALDI are analyte, matrix, and laser source dependent. The ion generation threshold fluences follow the same order for both lasers: CHCA<SA<DHB, but for the analyte the mode locked 3× Nd:YAG laser source requires a higher threshold fluence than the nitrogen laser. Despite the higher fluence, the SYs are generally higher (the corresponding IEs are lower) for the 3× Nd:YAG laser than for the nitrogen laser. The SYs of the TM molecular ions decrease with an increase of fluence for both the ns laser and the ps laser. PACS 82.80.Ms; 82.20.Nk; 81.15.Fg     

Bandlimiting in conflict with spatial bounding of radiative sources

The curl of the Poynting vector for the bandlimited electromagnetic field of a timeharmonic point-source dipole is expanded asymptotically for large axial and off-axial distances of a halfspace. Truncating the plane-wave spectrum of the dipole field at any finite value of spatial frequency produces whirls in the time-averaged energy flux which are at variance with the expansion theorem for the field of a bounded source; due to bandlimiting, the angular and radial coordinates of the Poynting vector are not for all directions separable and the curl of the Poynting vector has the wrong orderr ^−5/2, at least for some directions, when the radial distancer approaches infinity.     

Angular smoothing and spatial diffusion from the Feynman path integral representation of radiative transfer

The propagation kernel for time dependent radiative transfer is represented by a Feynman path integral (FPI). The FPI is approximately evaluated in the spatial-Fourier domain. Spatial diffusion is exhibited in the kernel when the approximations lead to a Gaussian dependence on the Fourier domain wave vector. The approximations provide an explicit expression for the diffusion matrix. They also provide an asymptotic criterion for the self-consistency of the diffusion approximation. The criterion is weakly violated in the limit of large numbers of scattering lengths. Additional expansion of higher-order terms may resolve whether this weak violation is significant.     

The optical path length approach to radiation heat transfer with isotropic scattering and gaseous absorption

The hemispherical total reflectance and transmittance for banded gaseous absorption and isotropic scattering are determined by the optical path length approach. The optical path length approach decouples the scattering and absorption so that any absorption can be evaluated once the path length distributions have been evaluated. The path length distributions are determined by numerical inversion of the Laplace transform and the exponential wide band model is employed to evaluate the absorption. The effects of scattering total optical depth, scattering albedo, pressure broadening parameter and gaseous optical depth on the scattering total band absorption properties are presented and discussed.     

Photon statistics in single molecule fluorescence with Rabi oscillations

An expression for the distribution function of photons detected in non-resonant single molecule fluorescence excited by CW-laser light is derived. Numerical calculations of the photon distribution for fluorescence whose autocorrelation function exhibits Rabi oscillations are carried out. It is found that phase memory does not influence noticeably on the photon distribution function in non-resonant fluorescence.     

Pure-triplet scattering for radiative transfer in binary discrete random finite media with reflective boundaries and internal source of radiation

The stochastic solution of the monoenergetic radiative transfer equation in a finite slab random medium with pure-triplet anisotropic scattering is considered. The random medium is assumed to consist of two randomly mixed immiscible fluids labelled by 1 and 2. The extinction function, the scattering kernel, and the internal source of radiation are treated as discrete random variables, which obey the same statistics. The theoretical model used here for stochastic media transport assumes Markovian processes and exponential chord length statistics. The boundaries of the medium under consideration are considered to have specular and diffuse reflectivities with an internal source of radiation inside the medium. The ensemble-average partial heat fluxes are obtained in terms of the average albedos of the corresponding source-free problem, whose solution is obtained by using the Pomraning–Eddington approximation. Numerical results are calculated for the average forward and backward partial heat fluxes for different values of the single scattering albedo with variation of the parameters that characterize the random medium. Compared to the results obtained by Adams et al. in the case of isotropic scattering based on the Monte Carlo technique, it can be demonstrated that we have good comparable data.     

Pure-triplet scattering for radiative transfer in binary discrete random finite media with reflective boundaries and internal source of radiation

The stochastic solution of the monoenergetic radiative transfer equation in a finite slab random medium with pure-triplet anisotropic scattering is considered. The random medium is assumed to consist of two randomly mixed immiscible fluids labelled by 1 and 2. The extinction function, the scattering kernel, and the internal source of radiation are treated as discrete random variables, which obey the same statistics. The theoretical model used here for stochastic media transport assumes Markovian processes and exponential chord length statistics. The boundaries of the medium under consideration are considered to have specular and diffuse reflectivities with an internal source of radiation inside the medium. The ensemble-average partial heat fluxes are obtained in terms of the average albedos of the corresponding source-free problem, whose solution is obtained by using the Pomraning-Eddington approximation. Numerical results are calculated for the average forward and backward partial heat fluxes for different values of the single scattering albedo with variation of the parameters that characterize the random medium. Compared to the results obtained by Adams et al. in the case of isotropic scattering based on the Monte Carlo technique, it can be demonstrated that we have good comparable data.     

Non-gray radiative transfer in plane-parallel media with reflecting boundaries

A generalized equation of radiative transfer in the two-group picket-fence model is analyzed for a plane parallel, emitting, absorbing and isotropically scattering medium containing uniform heat sources and having boundary surfaces which are diffuse emitters and diffuse reflectors and are maintained at uniform but arbitrary temperatures. The solution of the general problem is expressed by the superposition of simpler problems which are solved by the application of the normal-mode-expansion technique. Highly accurate numerical results are presented for the temperature distribution and the radiative heat flux in the medium.