Radiative Transfer Theory

Relying upon the values of the geometric albedo of Saturn obtained in the methane absorption bands at λ = 887, 864, 842, 727, and 619 nm in 1993, how the aerosol and gaseous scattering components of the effective optical depth change with depth in the atmosphere of the planet are analyzed. The model of homogeneous spherical aerosol particles is used. For the altitude levels in the pressure range from 0.18 to 1.5 bar, that the parameters of aerosol particles used in the analysis are close to their actual values is confirmed. Above the level of 0.054 bar, the presence of stratospheric aerosol was detected. At least seven peculiarities were found in the vertical structure of the cloud cover of the upper atmosphere of Saturn. The altitude position of the maximum relative concentration of aerosol was estimated at approximately a level of 0.3 or 0.12 bar given the relative concentration of methane as 0.0021 or 0.0533, respectively. In the atmospheric layers of Saturn, where the pressure is larger than 0.44 bar, the cloud extended in altitude and containing no distinguishable aerosol layers was found. In the layers deeper than 1.5 bar, indications of probable changes in the parameters of aerosol particles were detected.

The processes that lead to formation of spatial distribution of polarization parameters in the Earth's atmosphere are studied. Among the modern development of devices for atmospheric polarimetric measurements, the prospects for creating equipment for on-ground measurements are highlighted. A method is described for determining polarization parameters at the celestial hemisphere with use of data on the on-ground polarimetric measurements. A spatial diagram of the mutual location of the main components in the light-scattering process is provided. Formulas for calculating the angle (AoLP) and degree (DoLP) of the celestial linear polarization in the case of light scattering by a purely gaseous component of the atmosphere are given. The effect of changes in the characteristics of the atmospheric aerosol on the specified celestial polarization parameters is considered. The key idea of the proposed method for controlling the reliability of on-ground polarimetric measurements consists in using the stability of the spatial distribution of the AoLP parameter in the celestial hemisphere. The algorithm for such control is described and recommendations for its practical application are provided. The use of the DoLP parameter is indicated as an opportunity only for qualitative evaluation of the data of on-ground polarimetric measurements. Examples of visualization of the spatial distribution of celestial polarization parameters in the model environment for a selected position, date, and time of observation are given.

This study considers the design and control of a radiant furnace by the use of an inverse formulation. The furnace considered is one that is used to heat an object from an initial temperature to a final steady state while the temperature across the heated object is kept spatially uniform. The design problem considered is a transient boundary condition estimation problem. The necessary heater distributions can be calculated by inverse design but when such a system is built, some discrepancies will result between the design based on the numerical model and what the physical system achieves. There are many reasons for differences, and the design and control engineer should correct for the discrepancies at some level. A control algorithm is developed in this study that makes use of the information provided by the inverse design and data from the physical system to train a neural net, which is then used to control the system to overcome the errors in the predicted operation.

Inverse methods provide a good alternative to traditional trial-and-error methods for design of thermal systems. The inverse boundary condition estimation problem in radiating enclosures involves the solution of an ill-posed system that requires regularization to obtain a reasonable physical solution. This study compares three different regularized solution techniques that can be used in the inverse boundary condition estimation problems in a three-dimensional radiating enclosure. The regularized solution techniques covered in this study are the conjugate gradient method, bi-conjugate gradient method and truncated singular value decomposition.

The validation of the multiresolution model of sea surface infrared optical properties developed at ON-ERA is investigated in the one-dimensional case by comparison with a reference model, using a submillimeter discretization of the surface. Having expressed the optical properties, we detail the characteristics of each model. A set of numerical tests is made for various wind speeds, resolutions, and realizations of the sea surface. The tests show a good agreement between the results except for grazing angles, where the impact of multiple reflections and the effects of adjacent rough surfaces on shadow have to be investigated.

In this work, we systematically calculate transition magnetic moments, radiative decay widths, and axialvector coupling constants of octet hidden-charm molecular pentaquark states with different flavor representations in constituent quark model. We discuss the relations between transition magnetic moments and decay widths for pentaquark states. For octet pentaquark states with the 8 1f and 8 2f flavor representations, decay widths of the processes P ψ j 3

In this chapter we discuss the application of spectro-polarimetry diagnostics to the investigation of astrophysical plasmas. We first present an overview of why polarization must be expected in the spectral-line radiation that we receive from a large variety of cosmic objects, and then treat in some detail specific atomic models (e.g., the 0–1 and 1–0 two-level atoms), which illustrate how physical and electro-dynamical properties of the emitting plasma can be inferred by studying the polarized radiation in the corresponding spectral lines. The practical applications described in this chapter are taken exclusively from the realm of solar physics, mainly for two reasons: a) From a historical point of view, the Sun was the first cosmic object to which polarization analysis of radiation was successfully applied, proving the existence of solar magnetic fields, and demonstrating the diagnostic potential of radiation phenomena involving resonance polarization. b) Because spectro-polarimet...

One of the greatest future challenges in cosmic physics is the empirical investigation of the magnetic field vector in a variety of astrophysical plasmas, including the solar corona. The chances of attaining this goal would be dramatically increased if we could carry out spectropolarimetric observations from space in order to measure the polarization signals that scattering processes induce in permitted UV/EUV spectral lines, such as those of the Lyman series of hydrogen. The physical interpretation of this type of observations would allow us to infer the magnetic field vector via the Hanle effect, which consists in the modification of scattering polarization signals due to the presence of a magnetic field. In particular, the Hanle effect either in forward scattering or at 90 • scattering is a unique and powerful tool for the "measurement" of magnetic fields in the solar transition region and corona. Here we highlight the great diagnostic potential of spectropolarimetry and argue that ESA should take advantage of the present European leadership in this field to open this new diagnostic window on the Universe.

Solar coronal polarization observations are an underused data product because of the difficulties in interpreting the data and in calculating an inversion.The physics of the polarization is well understood and documented in the literature. The purpose of this paper is to present a general overview on how to interpret polarization signals without calculating an inversion. This is intended to introduce the data to those who are unfamiliar to polarization, and in so doing, make the data more accessible.

Recent determinations of the mean free path of ionising photons (mfp) in the intergalactic medium (IGM) at z = 6 are lower than many theoretical predictions. In order to gain insight, we investigate the evolution of the mfp in our new massive fully coupled radiation hydrodynamics cosmological simulation of reionization: Cosmic Dawn III (CoDa III). CoDa III's scale (94 3 cMpc 3) and resolution (8192 3 grid) make it particularly suitable to study the IGM during reionization. The simulation was performed with RAMSES-CUDATON on Summit, and used 131072 processors coupled to 24576 GPUs, making it the largest reionization simulation, and largest ever RAMSES simulation. A superior agreement with global constraints on reionization is obtained in CoDa III over CoDa II, especially for the evolution of the neutral hydrogen fraction and the cosmic photo-ionization rate, thanks to an improved calibration, later end of reionization (z = 5.6), and higher spatial resolution. Analyzing the mfp, we find that CoDa III reproduces the most recent observations very well, from z = 6 to z = 4.6. We show that the distribution of the mfp in CoDa III is bimodal, with short (neutral) and long (ionized) mfp modes, due to the patchiness of reionization and the coexistence of neutral versus ionized regions during reionization. The neutral mode peaks at sub-kpc to kpc scales of mfp, while the ionized mode peak evolves from 0.1Mpc/h at z = 7 to ∼ 10 Mpc/h at z = 5.2. Computing the mfp as the average of the ionized mode provides the best match to the recent observational determinations. The distribution reduces to a single neutral (ionized) mode at z > 13 (z < 5).

Recent determinations of the mean free path of ionizing photons (mfp) in the intergalactic medium (IGM) at z = 6 are lower than many theoretical predictions. In order to gain insight, we investigate the evolution of the mfp in our new massive fully coupled radiation-hydrodynamics cosmological simulation of reionization: Cosmic Dawn III (CoDa III). CoDa III’s scale ($\rm 94^3 \, cMpc^3$) and resolution ($\rm 8192^3$ grid) make it particularly suitable to study the IGM during reionization. The simulation was performed with ramses-cudaton on Summit, and used 13 1072 processors coupled to 24 576 GPUs, making it the largest reionization simulation, and largest ever ramses simulation. A superior agreement with global constraints on reionization is obtained in CoDa III over Cosmic Dawn II (CoDa II), especially for the evolution of the neutral hydrogen fraction and the cosmic photoionization rate, thanks to an improved calibration, later end of reionization (z = 5.6), and higher spatial res...

Abstract. Dozens of natural forces and cycles dominate the Earth’s weather, climate, and climate change, some acting independently and others in complex interactions among and between these forces and cycles. Climate and climate change science is highly complex, involving dozens of scientific disciplines, and is poorly understood. The science of climate and climate change is far from settled.

Here, we discuss some significant drivers of climate change, provide an overview of overlooked ones, and challenge some popularly accepted ones. We start by analyzing the science, examining the historical record and geologic evidence, and discussing intriguing possibilities and their possible roles and contributions.  Here is a grouping of the significant drivers of climate change:

Recent determinations of the mean free path of ionising photons (mfp) in the intergalactic medium (IGM) at z = 6 are lower than many theoretical predictions. In order to gain insight into this issue, we investigate the evolution of the mfp in our new massive fully coupled radiation hydrodynamics cosmological simulation of reionization: Cosmic Dawn III (CoDa III). CoDa III's scale (94 3 cMpc 3) and resolution (8192 3 grid) make it particularly suitable to study the evolution of the IGM during the Epoch of Reionization (EoR). The simulation was performed with RAMSES-CUDATON on Summit, and used 131072 processors coupled to 24576 GPUs, making it the largest EoR simulation, and largest RAMSES simulation ever performed. A superior agreement with global constraints on reionization is obtained in CoDa III over CoDa II, especially for the evolution of the neutral hydrogen fraction and the cosmic photo-ionization rate, thanks to an improved calibration, later end of reionization (z = 5.6), and higher spatial resolution. Analyzing the mfp, we find that CoDa III reproduces the most recent observations very well, from z = 6 to z = 4.6. We show that the distribution of the mfp in CoDa III is bimodal, with short (neutral) and long (ionized) mfp modes, respectively, due to the patchiness of reionization and the coexistence of neutral versus ionized regions during the EoR. The neutral mode peaks at sub-kpc to kpc scales of mfp, while the ionized mode peak evolves from 0.1Mpc/h at z = 7 to ∼ 10 Mpc/h at z = 5.2. Computing the mfp as the average of the ionized mode provides the best match to the recent observational determinations. The distribution reduces to a single neutral (ionized) mode at z > 13 (z < 5).

This paper presents some numerical results relative to a solution, based on the density matrix formalism, of the non-LTE, polarized radiative transfer problem for a twolevel atom. The results concern the atomic upper level population and alignment, and the emergent radiation Stokes profiles, for a plane-parallel, static, isothermal atmosphere embedded in a magnetic field of intermediate strength, such that the Zeeman splitting has to be taken into account in the line profile. Zeeman coherences are neglected, whereas magnetooptical effects are taken into account, resulting in a full 4 x 4 absorption matrix. Induced emission is neglected and complete frequency redistribution, in the rest and laboratory frames, is assumed. Pure Doppler absorption profile (gaussian shape) has also been assumed. The presentation of the results is preceded by a brief discussion of their accuracy and of the numerical difficulties that were met in the solution of the problem.

Depolarizing collisions are elastic or quasielastic collisions that equalize the populations and destroy the coherence between the magnetic sublevels of atomic levels. In astrophysical plasmas, the main depolarizing collider is neutral hydrogen. We consider depolarizing rates on the lowest levels of neutral and singly ionized alkali earths Mg i, Sr i, Ba i, Mg ii, Ca ii, and Ba ii, due to collisions with H •. We compute ab initio potential curves of the atom-H • system and solve the quantum mechanical dynamics. From the scattering amplitudes, we calculate the depolarizing rates for Maxwellian distributions of colliders at temperatures T 10,000 K. A comparative analysis of our results and previous calculations in the literature is completed. We discuss the effect of these rates on the formation of scattering polarization patterns of resonant lines of alkali earths in the solar atmosphere, and their effect on Hanle effect diagnostics of solar magnetic fields.

The present study deals with an estimation of the optimum powers of the panel heaters that produces uniform thermal conditions over a 3-D design object placed inside a 3-D radiant enclosure. Radiation element method by ray emission model (REM 2) has been used to calculate the radiative information. The objective function has been minimized using the micro-genetic algorithm (MGA). To investigate the effect of the enclosure height on the optimal heater power setting, the problem has been investigated for four different aspect ratios. For the given heat flux or temperature distribution on the design object, the user has the choice to select heaters of varying power ranges, and in the present work, the validity of this formulation has been exemplified by selecting different power ranges of the heaters. The effect of specular reflections from the refractory walls and heater surfaces has also been accounted. For the desired uniform thermal conditions on the 3-D design object, the powers of the panel heaters have been accurately estimated using the REM 2 and the MGA.

For uniform thermal conditions on 3-D irregular shaped design objects, this paper reports estimation of optimal power of the panel heaters placed along the walls of a 3-D radiant furnace. Hemispherical, cylindrical, conical, and a combination of cylindrical and conical, and finally a case study of a car body model are considered as the design objects (DOs). The entire surface areas of the furnace walls and that of the DO are divided into surface elements. The surface elements of the furnace walls are made of the panel heaters. In this boundary design problem, the objective function is developed as an error function of estimated and the desired heat fluxes on the surfaces of DO. The radiative exchange among the surface elements is computed using the radiation element method by ray emission model (REM 2), and the objective function is minimized using the micro-genetic algorithm (MGA). Power of the panel heaters are estimated for different sizes of the DOs. Although the panel heaters have been placed along the furnace walls, for uniform thermal conditions, for a given DO, not all are required. Having known that not all are required, to ease the control, estimations have also been shown by grouping the heaters along the furnace walls. This study provides a guideline for a priori knowing the heater setting and their corresponding power requirement in heating of 3-D irregular shaped objects.

The present study deals with an estimation of the optimum powers of the panel heaters that produces uniform thermal conditions over a 3-D design object placed inside a 3-D radiant enclosure. Radiation element method by ray emission model (REM 2) has been used to calculate the radiative information. The objective function has been minimized using the micro-genetic algorithm (MGA). To investigate the effect of the enclosure height on the optimal heater power setting, the problem has been investigated for four different aspect ratios. For the given heat flux or temperature distribution on the design object, the user has the choice to select heaters of varying power ranges, and in the present work, the validity of this formulation has been exemplified by selecting different power ranges of the heaters. The effect of specular reflections from the refractory walls and heater surfaces has also been accounted. For the desired uniform thermal conditions on the 3-D design object, the powers of the panel heaters have been accurately estimated using the REM 2 and the MGA.

For uniform thermal conditions on 3-D irregular shaped design objects, this paper reports estimation of optimal power of the panel heaters placed along the walls of a 3-D radiant furnace. Hemispherical, cylindrical, conical, and a combination of cylindrical and conical, and finally a case study of a car body model are considered as the design objects (DOs). The entire surface areas of the furnace walls and that of the DO are divided into surface elements. The surface elements of the furnace walls are made of the panel heaters. In this boundary design problem, the objective function is developed as an error function of estimated and the desired heat fluxes on the surfaces of DO. The radiative exchange among the surface elements is computed using the radiation element method by ray emission model (REM 2), and the objective function is minimized using the micro-genetic algorithm (MGA). Power of the panel heaters are estimated for different sizes of the DOs. Although the panel heaters have been placed along the furnace walls, for uniform thermal conditions, for a given DO, not all are required. Having known that not all are required, to ease the control, estimations have also been shown by grouping the heaters along the furnace walls. This study provides a guideline for a priori knowing the heater setting and their corresponding power requirement in heating of 3-D irregular shaped objects.

In this study, an analysis for solving inverse radiative boundary design problem with discrete design variables is developed and presented when radiation is the dominant mode of heat transfer. An absorbing, emitting, and participating medium is considered in radiative equilibrium. The discrete ordinate method (DOM) is implemented to solve the radiative transfer equation (RTE). The goal of the design problem is to find the optimum power of heaters from a discrete set of powers in such a way that they produce the desired temperature and heat flux profile over the design surface. Therefore, several metaheuristic optimization methods including the genetic algorithm (GA), particle swarm optimization (PSO), and its modified forms such as PSO with Constriction Factor (PSO-CF), PSO with repulsion factor (PSO-RF) and PSO with adaptive inertia weight (PSO-W) are explored to solve the inverse problem. The accuracy of the direct solution of radiative heat transfer is examined by comparison of the present results with findings from the literature. Then the efficiency and accuracy of the optimization methods are assessed by their ability of finding and reconstructing of the results from the direct solution. Finally, the effects of some thermos-physical properties including the absorption coefficient, emissivity of the heater surface and design surface, on the optimum solutions are examined. The comparison of the results revealed that the genetic optimization algorithm converged faster and with fewer calculations of the objective function compared to other optimization techniques.

Pattern recognition and time-series analyses will enable one to evaluate and generate predictions of specific phenomena. The albedo pattern and time-series analyses are very much useful especially in relation to climate condition monitoring. This study is conducted to seek for Malaysia albedo pattern changes. The pattern recognition and changes will be useful for variety of environmental and climate monitoring researches such as carbon budgeting and aerosol mapping. The 10 years (2000-2009) MODIS satellite images were used for the analyses and interpretation. These images were being processed using ERDAS Imagine remote sensing software, ArcGIS 9.3, the 6S code for atmospherical calibration and several MODIS tools (MRT, HDF2GIS, Albedo tools). There are several methods for time-series analyses were explored, this paper demonstrates trends and seasonal time-series analyses using converted HDF format MODIS MCD43A3 albedo land product. The results revealed significance changes of albedo percentages over the past 10 years and the pattern with regards to Malaysia's nebulosity index (NI) and aerosol optical depth (AOD). There is noticeable trend can be identified with regards to its maximum and minimum value of the albedo. The rise and fall of the line graph show a similar trend with regards to its daily observation. The different can be identified in term of the value or percentage of rises and falls of albedo. Thus, it can be concludes that the temporal behavior of land surface albedo in Malaysia have a uniform behaviours and effects with regards to the local monsoons. However, although the average albedo shows linear trend with nebulosity index, the pattern changes of albedo with respects to the nebulosity index indicates that there are external factors that implicates the albedo values, as the sky conditions and its diffusion plotted does not have uniform trend over the years, especially when the trend of 5 years interval is examined, 2000 shows high negative linear trend relationship (R 2 = 0.8017), while in 2005 the R 2 is 0.4428 of positive linear trend relationship and in 2009 its negative relationship has remarkably change when the R 2 is 0.9663 according to the second order polynomial trend line.

This study proposes new matrix relationships of the radiative interactions in enclosures along with their corresponding applications. By means of several transformations one establishes matrix formulae based on equations of radiative exchanges containing variables defined in a discrete analog form, and further on, by means of a multidisciplinary approach, the solutions are organized in algorithms that use the theory of networks, graphs and electric circuits. The theoretical advancements consist in two different paths: the matrix formalism method (MFM) and the network analogy method (NAM). As a result of the advancements, a high degree of parameterization of the problem of radiative transfer in an enclosure is achieved and it facilitates superior physical interpretations at the level of the ensemble. It will be simple to use the developed methodologies in designs, balances and simulations. The conceived analytical methods are valuable, compact instruments for performing accurate radiative design for various technical systems: buildings, furnaces, solar collectors, etc. A mathematical formula det(F-I)=0 that is a consequence of the closed shape property of the enclosures is put forth for the first time. The inverse problem that may rise from the proposed boundary conditions is considered and solved. A validation of the analytical instruments provided by MFM and NAM is performed by using the Ansys Fluent tool that confirmed the results in margins less than 5%. The importance of the study resides in its applicability in diverse disciplines. In addition to the theoretical advancements, a comprehensive example is provided.

We present a Bayesian inference on the neutral hydrogen fraction of the intergalactic medium (IGM), , at ∼ 6-8 using the properties of Lyman break galaxies during the Epoch of Reionization. We use large samples of LBG candidates at 5.5 ≤ ≤ 8.2 with spectroscopy from Keck/DEIMOS and Keck/MOSFIRE. For each galaxy, we incorporate either the Lyman-equivalent width (EW) for detections or the EW limit spectrum for nondetections to parameterize the EW distribution at various ultraviolet brightnesses for a given redshift. Using our reference sample of galaxy candidates from the ionized universe at ∼ 6.0, we are able to infer at two redshifts: ∼ 6.7 and ∼ 7.6. This work includes intrinsically faint, gravitationally lensed galaxies at ∼ 6.0 in order to constrain the intrinsic faint-end Ly EW distribution and provide a comparable population of galaxies to counterparts in our sample that are at higher redshift. The inclusion of faint galaxy candidates, in addition to a more sophisticated modelling framework, allows us to better isolate effects of the interstellar medium and circumgalactic medium on the observed Lyman-distribution from those of the IGM. We infer an upper limit of ≤ 0.25 at = 6.7 ± 0.2 and a neutral fraction of = 0.83 +0.08 −0.11 at = 7.6± 0.6, both within 1 uncertainty, results which favor a moderately late and rapid reionization.

We study the propagation of high-frequency electromagnetic waves in randomly heterogeneous bianisotropic media with dissipative properties. For that purpose we consider randomly fluctuating optical responses of such media with correlation lengths comparable to the typical wavelength of the waves. Although the fluctuations are weak, they induce multiple scattering over long propagation times and/or distances such that the waves end up travelling in many different directions with mixed polarizations. We derive the dispersion and evolution properties of the Wigner measure of the electromagnetic fields, which describes their angularly-resolved energy density in this propagation regime. The analysis starts from Maxwell's equations with general constitutive equations. We first ignore the random fluctuations of the optical response and obtain uncoupled transport equations for the components of the Wigner measure on the different propagation modes (polarizations). Then we use a multi-scale expansion of the Wigner mesure to obtain the radiative transfer equations satisfied by these components when the fluctuations are no longer ignored. The radiative transfer equations are coupled through their collisional parts, which account for the scattering of waves by the random fluctuations and their possible changes in polarization. The collisional kernels describing these processes depend on the power and cross-power spectral densities of the fluctuations at the wavelength scale. The overall derivation is based on the interpretation of Wigner transforms and Wigner measures in terms of semiclassical pseudo-differential operators in their standard quantization.

Abstract—Monte Carlo (MC) simulation is extensively used for solving thermal radiation problems in high-temperature environments, such as combustion chambers and furnaces, and irregular-geometry enclosures containing participative media such as combustive gases. ...

Future Square Kilometre Array (SKA) surveys are expected to generate huge data sets of 21 cm maps on cosmological scales from the Epoch of Reionization. We assess the viability of exploiting machine learning techniques, namely, convolutional neural networks (CNNs), to simultaneously estimate the astrophysical and cosmological parameters from 21 cm maps from seminumerical simulations. We further convert the simulated 21 cm maps into SKA-like mock maps using the detailed SKA antennae distribution, thermal noise, and a recipe for foreground cleaning. We successfully design two CNN architectures (VGGNet-like and ResNet-like) that are both efficiently able to extract simultaneously three astrophysical parameters, namely the photon escape fraction (fesc), the ionizing emissivity power dependence on halo mass (Cion), and the ionizing emissivity redshift evolution index (Dion), and three cosmological parameters, namely the matter density parameter (Ωm), the dimensionless Hubble constant (h)...

The validation of the multiresolution model of sea surface infrared optical properties developed at ON-ERA is investigated in the one-dimensional case by comparison with a reference model, using a submillimeter discretization of the surface. Having expressed the optical properties, we detail the characteristics of each model. A set of numerical tests is made for various wind speeds, resolutions, and realizations of the sea surface. The tests show a good agreement between the results except for grazing angles, where the impact of multiple reflections and the effects of adjacent rough surfaces on shadow have to be investigated.

In this paper, we describe several linearized radiative transfer models which can be used for the retrieval of cloud parameters from EPIC (Earth Polychromatic Imaging Camera) measurements. The approaches under examination are (1) the linearized forward approach, represented in this paper by the linearized discrete ordinate and matrix operator methods with matrix exponential, and (2) the forward-adjoint approach based on the discrete ordinate method with matrix exponential. To enhance the performance of the radiative transfer computations, the correlated k-distribution method and the Principal Component Analysis (PCA) technique are used. We provide a compact description of the proposed methods, as well as a numerical analysis of their accuracy and efficiency when simulating EPIC measurements in the oxygen A-band channel at 764 nm. We found that the computation time of the forwardadjoint approach using the correlated k-distribution method in conjunction with PCA is approximately 13 s for simultaneously computing the derivatives with respect to cloud optical thickness and cloud top height.

In this work we report an analytical representation for the solution of the radiative-conductive SN equation in a plane-parallel atmosphere in a heterogeneous domain considering an arbitrary continuous functions for the albedo. The basic idea consists in the application of the decomposition procedure to the non-linear radiative-conductive SN problem that are easily solved by the well know LTSN method. The length of the recursive system is properly chose in order to get a prescribed accuracy for the results. We also present numerical simulations for the results.

In this study, an analysis for solving inverse radiative boundary design problem with discrete design variables is developed and presented when radiation is the dominant mode of heat transfer. An absorbing, emitting, and participating medium is considered in radiative equilibrium. The discrete ordinate method (DOM) is implemented to solve the radiative transfer equation (RTE). The goal of the design problem is to find the optimum power of heaters from a discrete set of powers in such a way that they produce the desired temperature and heat flux profile over the design surface. Therefore, several metaheuristic optimization methods including the genetic algorithm (GA), particle swarm optimization (PSO), and its modified forms such as PSO with Constriction Factor (PSO-CF), PSO with repulsion factor (PSO-RF) and PSO with adaptive inertia weight (PSO-W) are explored to solve the inverse problem. The accuracy of the direct solution of radiative heat transfer is examined by comparison of the present results with findings from the literature. Then the efficiency and accuracy of the optimization methods are assessed by their ability of finding and reconstructing of the results from the direct solution. Finally, the effects of some thermos-physical properties including the absorption coefficient, emissivity of the heater surface and design surface, on the optimum solutions are examined. The comparison of the results revealed that the genetic optimization algorithm converged faster and with fewer calculations of the objective function compared to other optimization techniques.

This study proposes new matrix relationships of the radiative interactions in enclosures along with their corresponding applications. By means of several transformations one establishes matrix formulae based on equations of radiative exchanges containing variables defined in a discrete analog form, and further on, by means of a multidisciplinary approach, the solutions are organized in algorithms that use the theory of networks, graphs and electric circuits. The theoretical advancements consist in two different paths: the matrix formalism method (MFM) and the network analogy method (NAM). As a result of the advancements, a high degree of parameterization of the problem of radiative transfer in an enclosure is achieved and it facilitates superior physical interpretations at the level of the ensemble. It will be simple to use the developed methodologies in designs, balances and simulations. The conceived analytical methods are valuable, compact instruments for performing accurate radiative design for various technical systems: buildings, furnaces, solar collectors, etc. A mathematical formula det(F-I)=0 that is a consequence of the closed shape property of the enclosures is put forth for the first time. The inverse problem that may rise from the proposed boundary conditions is considered and solved. A validation of the analytical instruments provided by MFM and NAM is performed by using the Ansys Fluent tool that confirmed the results in margins less than 5%. The importance of the study resides in its applicability in diverse disciplines. In addition to the theoretical advancements, a comprehensive example is provided.

Remote sensing from satellite or airborne platforms of land or sea surfaces in the visible and near infrared is strongly affected by the presence of the atmosphere along the path from Sun to Target (surface) to Sensor. This paper presents 6S (Second Simulation of the Satellite Signal in the Solar Spectrum), a computer code which can accurately simulate the above problems. The 6S code is an improved version of 5S (Simulation of the Satellite Signal in the Solar Spectrum), developed by the Laboratoire d'Optique Atmospherique ten years ago. The new version now permits calculations of near-nadir (down-looking) aircraft observations, accounting for target elevation, non lambertian surface conditions, and new absorbing species (CH4, N2O, CO). The computational accuracy for Rayleigh and aerosol scattering effects has been improved by the use of state-of-theart approximations and implementation of the successive order of scattering (SOS) algorithm. The step size (resolution) used for spectral integration has been improved to 2.5 nm. The goal of this paper is not to provide a complete description of the methods used as that information is detailed in the 6S manual, but rather to illustrate the impact of the improvements between 5S and 6S by examining some typical remote sensing situations. Nevertheless, the 6S code has still limitations. It cannot handle spherical atmosphere and as a result, it cannot be used for limb observations. In addition, the decoupling we are using for absorption and scattering effects does not allow to use the code in presence of strong absorption bands.

It is well known that including the delta-scaling in the radiative transfer calculation improves the accuracy of radiative transfer in a cloud layer. An improved scheme is proposed to handle the delta-scaling in the radiative transfer calculation. The improved scheme is able to calculate irradiance of a vertical inhomogeneous cloud layer. The inherent optical properties (IOPs) in a cloud layer vary with height. Linear functions are used to represent the variation of IOPs. Compared to the exponential expression, the linear functions simplified the representation of IOPs. A perturbation method based on Eddington approximation is applied to solve the radiative transfer equation. The accuracy of the proposed scheme is evaluated by comparing reflectance and absorptance to the benchmark Discrete Ordinates Radiative Transfer (DIS-ORT) simulation for two ideal layers and two water cloud cases. Results show that the error limited to 3.4% for reflectance calculation and 7% for absorptance in using the proposed scheme, while the error of the conventional Eddington approximation is > 20% for both reflectance and absorptance. The proposed scheme also improved the accuracy of calculation by considering the vertical inhomogeneity of the IOPs in water cloud cases.

We have constructed an instrument to measure the polarization of light emitted by the solar corona in order to constrain the strength and orientation of coronal magnetic fields. We call this instrument the Coronal Multichannel Polarimeter (CoMP). The CoMP is integrated into the Coronal One Shot coronagraph at Sacramento Peak Observatory and employs a combination birefringent filter and polarimeter to form images in two wavelengths simultaneously over a 2.8R field of view. The CoMP measures the complete polarization state at the 1074.7 and 1079.8 Fe XIII coronal emission lines, and the 1083.0 nm He I chromospheric line. In this paper we present design drivers for the instrument, provide a detailed description of the instrument, describe the calibration methodology, and present some sample data along with estimates of the uncertainty of the measured magnetic field.

The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric conductors and dielectric bodies. Furthermore, these representations, and resulting integral equations, are fully stable in the static limit as ω → 0 in multiply connected geometries. In this paper, we present the first high-order accurate solver based on this representation for bodies of revolution. The resulting solver uses a Nyström discretization of a onedimensional generating curve and high-order integral equation methods for applying and inverting surface differentials. The accuracy and speed of the solvers are demonstrated in several numerical examples.

The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric conductors and dielectric bodies. Furthermore, these representations, and resulting integral equations, are fully stable in the static limit as ω → 0 in multiply connected geometries. In this paper, we present the first high-order accurate solver based on this representation for bodies of revolution. The resulting solver uses a Nyström discretization of a onedimensional generating curve and high-order integral equation methods for applying and inverting surface differentials. The accuracy and speed of the solvers are demonstrated in several numerical examples.

Context. Progress in the solution to some of the most outstanding open problems of solar physics, such as coronal heating, solar wind acceleration, the generation and triggering of explosive events like flares and CMEs, hinges on the provision of a more stringent estimate of the solar magnetic field coordinates. Aims. We seek a way to infer the magnetic field of the solar atmosphere. A very promising way of doing this is by using the Hanle effect in resonance scattering in the Lα line of the solar atmosphere. Methods. By forward modelling the known scattering effects in the presence of magnetic fields, i.e. rotation of the plane of polarisation and depolarisation of the linear polarisation parameters, and by comparing them to observations, one could potentially uncover the magnetic morphology and restrict its intensity range. We simulate the effects of simple dipole configurations along the coordinate axes and analyse the outcome through two kinds of graphs (i.e. the difference in angle of the plane of linear polarisation with respect to the field-free case, and the relative depolarisation). Results. The graphs are either symmetric, anti-symmetric or asymmetric with respect to the (y, z) plane. This is explained by invoking two symmetry operations and taking into account that the magnetic field is a pseudovector. We also show the polarimetric effects of active regions and use them pairwise with the magnetic field due to dipoles to analyse the polarimetric signatures of magnetic field line loops. Inspired by the famous TRACE image, we finally show what one could expect from polarimetry performed on the region of the solar atmosphere displayed in the image. Conclusions. By combining the two complementary remote sensing techniques, i.e. the Zeeman and the Hanle effect, in all thinkable ways with tracers such as the images revealed by TRACE, SOHO, STEREO, etc., we hope one day to be able to infer the solar magnetic field coordinates. Much theoretical and instrumental work still lies ahead, however.

In the light of the recent Planck downward revision of the electron scattering optical depth, and of the discovery of a faint active galactic nuclei (AGN) population at z > 4, we reassess the actual contribution of quasars to cosmic reionization. To this aim, we extend our previous Markov Chain Monte Carlo based data-constrained semi-analytic reionization model and study the role of quasars on global reionization history. We find that the quasars can alone reionize the Universe only for models with very high AGN emissivities at high redshift. These models are still allowed by the recent cosmic microwave background data and most of the observations related to H I reionization. However, they predict an extended and early He II reionization ending at z 4 and a much slower evolution in the mean He II Ly-α forest opacity than what the actual observation suggests. Thus, when we further constrain our model against the He II Ly-α forest data, this AGN-dominated scenario is found to be clearly ruled out at 2σ limits. The data seems to favour a standard two-component picture where quasar contributions become negligible at z 6 and a non-zero escape fraction of ∼10 per cent is needed from early-epoch galaxies. For such models, mean neutral hydrogen fraction decreases to ∼10 −4 at z = 6.2 from ∼0.8 at z = 10.0 and helium becomes doubly ionized at much later time, z ∼ 3. We find that these models are as well in good agreement with the observed thermal evolution of IGM as opposed to models with very high AGN emissivities.

Recently, the Hydrogen Epoch of Reionization Array (HERA) has produced the experiment’s first upper limits on the power spectrum of 21 cm fluctuations at z ∼ 8 and 10. Here, we use several independent theoretical models to infer constraints on the intergalactic medium (IGM) and galaxies during the epoch of reionization from these limits. We find that the IGM must have been heated above the adiabatic-cooling threshold by z ∼ 8, independent of uncertainties about IGM ionization and the radio background. Combining HERA limits with complementary observations constrains the spin temperature of the z ∼ 8 neutral IGM to 27 K 〈 T ¯ S 〉 630 K (2.3 K 〈 T ¯ S 〉 640 K) at 68% (95%) confidence. They therefore also place a lower bound on X-ray heating, a previously unconstrained aspects of early galaxies. For example, if the cosmic microwave background dominates the z ∼ 8 radio background, the new HERA limits imply that the first galaxies produced X-rays more efficiently than local ones. The z ∼ ...

The scattering of radiation in the presence of weak magnetic fields can give rise to coherence or interference phenomena that will profoundly affect the frequency, geometric, and polarization properties of the scattering event. In this paper we discuss and illustrate some of the features of the coherence phenomena associated with the scattering redistribution for the normal Zeeman triplet. The frequency dependent as well as the frequency independent scattering function is considered in a linear polarization basis. In addition we illustrate some properties of this redistribution function in the Stokes representation. Since the primary purpose of this paper is to demonstrate the nature of some of the properties of the coherence problems, that might be important in the inter pretation of magnetic fields from polarization measurements of scattered radiation, it has been necessary in this initial work to neglect several features of the problem which are noted in the paper and are currently under investigation.

The problem of resonance scattering in a finite medium which is permeated by a uniform magnetic field is described. A parallel beam of unpolarized photons is assumed incident upon the lower surface of the scattering medium, the direction of propagation being perpendicular to the magnetic field Through inclusion of the Hanle effect which influences the phase coherency of the scattering process, it has been possible to treat the case of weak fields for the normal Zeeman triplet. This is in contrast to most studies of the transport of polarized radiation in which a strong field is assumed, giving rise to well-separated Zeeman components. By the Monte Carlo process "photons" are traced through the scattering medium by using the probabilistic laws of interaction, and, by counting the "photons" as they exit, line profiles and the degree of polarization are determined. Results are given for viewing the medium both along and perpendicular to the magnetic field. When the medium is optically thin and viewed along the magnetic field, the linear polarization may change from 100 to 0 per cent because of the Hanle effect. As the optical depth increases, additional depolarization occurs because of multiple scattering, and it is found that an average of only five to ten scatterings are required to completely depolarize the radiation essentially independent of the magnetic field strength. Future application of this type of calculation is discussed in relation to quiescent prominences in the solar atmosphere.

A brief review, presented in simplified terms, is given for the theory of the origin of coronal emission-line polarization. A classical view of the scattering problem in terms of harmonic oscillators is first presented where the influence of the magnetic field is demonstrated. The Van Vleck depolarization phenomena is described in these terms. Next, a more precise physical picture of the emission-line polarization is established through a discussion of the Zeeman effect in scattering. Sample results are discussed for three-dimensional coronal emission-line models based upon the solution of the statistical equilibrium equations for magnetic sublevels of the Fexiv ion. Finally, comments are directed toward the determination of magnetic fields based upon emission-line polarization observations where both modeling and deconvolution procedures are mentioned.

This paper describes a data archaeology and rescue of temperature-dependent thermal infrared (IR) optical constants for liquid water from previously published works. The data rescue is based upon digitization of a figure published by Pinkley et al. [J. Opt. Soc. Am. 67, 494 (1977)], which showed ratios of laboratory measured spectral reflectances taken at 4 different temperatures (1, 16, 39, and 50°C) with those measured previously at 27°C. Using our digitization of these data, we perform Kramers-Kronig analyses to derive temperature-dependent optical constants for existing standard datasets taken at room temperatures for the entire thermal IR spectrum. These datasets are of interest for the accurate modeling of thermal IR surface emissivity and reflectance over the range of global surface temperatures.

We review methods to measure magnetic fields within the corona using the polarized light in magnetic-dipole (M1) lines. We are particularly interested in both the global magnetic-field evolution over a solar cycle, and the local storage of magnetic free energy within coronal plasmas. We address commonly held skepticisms concerning angular ambiguities and line-of-sight confusion. We argue that ambiguities are, in principle, no worse than more familiar remotely sensed photospheric vector fields, and that the diagnosis of M1 line data would benefit from simultaneous observations of EUV lines. Based on calculations and data from eclipses, we discuss the most promising lines and different approaches that might be used. We point to the S-like [Fe XI] line (J = 2 to J = 1) at 789.2 nm as a prime target line (for the Advanced Technology Solar Telescope (ATST) for example) to augment the hotter 1074.7 and 1079.8 nm Si-like lines of [Fe XIII] currently observed by the Coronal Multi-channel Polarimeter (CoMP). Significant breakthroughs will be made possible with the new generation of coronagraphs, in three distinct ways: i) through single-point inversions (which encompasses also the analysis of MHD wave modes), ii) using direct comparisons of synthetic MHD or force-free models with polarization data, and iii) using tomographic techniques.

Depolarizing collisions are elastic or quasielastic collisions that equalize the populations and destroy the coherence between the magnetic sublevels of atomic levels. In astrophysical plasmas, the main depolarizing collider is neutral hydrogen. We consider depolarizing rates on the lowest levels of neutral and singly ionized alkali earths Mg i, Sr i, Ba i, Mg ii, Ca ii, and Ba ii, due to collisions with H •. We compute ab initio potential curves of the atom-H • system and solve the quantum mechanical dynamics. From the scattering amplitudes, we calculate the depolarizing rates for Maxwellian distributions of colliders at temperatures T 10,000 K. A comparative analysis of our results and previous calculations in the literature is completed. We discuss the effect of these rates on the formation of scattering polarization patterns of resonant lines of alkali earths in the solar atmosphere, and their effect on Hanle effect diagnostics of solar magnetic fields.

Theoretical study is made of the transfer between orientation and alignment of excited-state atoms by anisotropic collisions with ground-state atoms. The anisotropy considered is due to the anisotropic velocity distribution of atoms excited by a single-mode laser beam. The transfer rate and relaxation rates for each multipole moment are calculated for the excited state with J = 1 as a function of detuning of the laser frequency from the center of an absorption line and mass of perturbing ground-state atoms. Experiments to observe the transfer from alignment to orientation and from orientation to alignment in a weak magnetic field are considered, and corresponding signals are analyzed in terms of the transfer and relaxation rates.

We report on spectropolarimetric observations of Ha in prominences made with the Télescope Héliographique pour l'Etude du Magnétisme et des Instabilités Solaires and the High Altitude Observatory/Advanced Stokes Polarimeter. Stokes Q and U show the expected profile shape from resonance scattering polarization and the Hanle effect. In contrast, most of the time, Stokes V does not show the antisymmetric profile shape typical of the Zeeman effect but a profile that indicates the presence of strong atomic orientation in the hydrogen levels, to an extent that cannot be explained by invoking the alignment-to-orientation transfer mechanism induced by the prominence magnetic field. We found that the largest signal amplitudes of Stokes V (comparable to that of Stokes Q and U) could be produced by a process of selective absorption of circularly polarized radiation from the photosphere, which requires that the prominence be in the vicinity of an active region. Although recent observations of active region filaments indicate such a selective absorption mechanism as a plausible explanation of the anomalous signals observed, the particular set of conditions that must be met suggest that a different explanation may be required to explain the almost ubiquitous symmetric V signal observed in Ha prominences. Therefore, we speculate that an alternative mechanism inducing strong atomic orientation at the observed level could be due to the presence of electric fields inducing an electric Hanle effect on Ha. Although we are still working toward a careful modeling of this effect, including both electric and magnetic fields, we present some preliminary considerations that seem to support this possibility.