Radiative transfer in cylindrical media

A numerical method for the solution of the radiative transfer equation in a circularly symmetric, cylindrical region is developed. The transfer equation is formulated as a second-order differential equation resulting in a set of tridiagonal difference equations. This form is particularly well suited to line formation and energy balance calculations using the complete linearization method. Several numerical examples are presented.     

Radiative transfer in atmospheres with spherical symmetry

A new approximate method to solve the time-independent transfer equation in a system with spherical geometry is presented. No restriction is imposed on the radial variation of the opacity so that the method is applicable even when the opacity is tabulated. The approximation consists in solving the transfer equation only for the outward and inward radial directions and in using the corresponding intensities for the numerical computation of the mean intensity and flux. To obtain the integration weights, we make several hypotheses on the directional dependence of the intensity, taking into account the principal properties of radiation transfer in spherical symmetric systems. We point out the parallelism that exists between this approximation for spherical geometry and a similar one for the plane-parallel case. Results are presented for the conservative and non-conservative cases, and they are compared to those of other authors.     

Radiative transfer in stochastically inhomogeneous media

New radiative transfer theory is developed for stochastically inhomogeneous scattering media. The three-dimensional shapes and large scale (compared to the mean free path) structures of the media are modeled by stochastic interfaces separating regions of different scattering properties. The small scale fluctuations are characterized by a pair-correlation function. The radiative transfer equation is extended to include individual scattering and propagation probabilities of a ray for each subregion as well as the probability for a ray to cross the interface between two subregions. The propagation probability is found to depend on the entire preceding path of the ray; the present formulation accounts for the two previous scatterings. A new adding/doubling algorithm is developed to solve this problem numerically. Transmission through a cloud layer and backward scattering seem to be particularly sensitive to inhomogeneities.     

Heat transfer by radiation and conduction in fibrous media without axial symmetry

Coupled radiative and conductive heat transfer in a fibrous medium formed by silica fibres is investigated in this paper by not taking account of the axial symmetry for the distribution of fibres or the boundary conditions. Radiative properties of the medium are calculated by using the Mie theory. The model obtained depends only on optical parameters (indices of silica) and on morphological parameters (diameter and orientation of the fibres, density of the medium). Simulations make it possible to study the strongly anisotropic behaviour of the scattering of the radiation by a fibre and to study the influence of various parameters on the radiative properties of the medium. The results of the Mie theory make possible the simulation of the heat transfer coupled by radiation and conduction. To do this, we introduce a new numerical scheme able to simulate heat transfer in the lack of axial symmetry. With this model, we can show the effects of distribution of fibres and temperature on the thermal behaviour of the medium as well as showing the importance of the phenomenon of scattering in fibrous media.     

Radiative transfer in finite participating atmospheric aerosol media

The properties of radiation transfer through a plane-parallel atmospheric aerosol medium has been studied. It has been done by employing Mie theory to calculate the radiation transfer scattering parameters of the medium in the form of extinction, scattering, and absorption efficiencies. Then, the equation of radiative transfer through a plane-parallel atmosphere of aerosol has been solved for partial heat fluxes using two different analytical techniques, namely, the Variational Pomraning -Eddington approximation and Galerkin technique. Average efficiencies over log-normal and modified gamma size distributions are calculated. Therefore, the radiative properties of Carbon, Anthracite, Bituminous, Lignite, and Fly ash have been calculated. The obtained numerical results show very good agreement with each other in addition to the previous published work.     

Radiative transfer in finite cylindrical media using transformed integral equations

A modified direct integration method is presented to solve three-dimensional radiative transfer in emitting, absorbing and linear-anisotropic scattering finite cylindrical media. This scheme effectively avoids an integral singularity in the coupled Fredholm type integral equations of radiative transfer. The scheme leads to faster and more accurate results, which are needed in combined mode and non-gray problems. The calculated incident radiation and heat fluxes agree well with published results by discrete ordinates method. Using the transformed integral equations, the effects of boundary emission and reflection can also be easily handled.     

Radiative transfer in atmospheres with spherical symmetry—IV. the non-conservative problem

Non-conservative transfer problems are conceptually more complicated than the conservative ones because the source function introduces a new scale height. This problem is specially important in spherical geometry, where, due to the curvature of the layers, one must also take into account the scale height of the opacity. With the introduction of the auxiliary variables μ_c and μ_r, it has been possible to obtain very simple linear closure relations for the μ moment system; μ_c is the cosine of the critical zenithal angle ?_c from which the intensity peak appears; μ_r is an intermediate value of μ between μ_c and 1 which permits an explanation of the geometrical dilution and leads easily to a peaking linear relation. With these closure relations, we have solved the moment system for different opacity laws and source functions which represent many cases of astrophysical interest. Likewise, we have compared the quality of our results for different orders of approximation.     

Radiative transfer in atmospheres with spherical symmetry—III. The Eddington approximation

A new generalization of the Eddington approximation for systems with spherical geometry is presented. For this kind of geometry, we have deduced an analytical expression for the Eddington factor, where the opacity law, which we assume to be a known function of the radial distance r, is an explicit variable. This expression, which is easily computable, together with the two first moment equations, gives better results for spherical systems than the corresponding $\text{? =}\text{1}\text{3}$ relation in plane ones.     

Radiative transfer in spatially heterogeneous,two-dimensional,anisotropically scattering media

A method is presented for solving the radiative transfer equation for a general anisotropically scattering and emitting medium exposed to arbitrary boundary radiation conditions. The method allows, in principle, for quite arbitrary spatial variability in the scattering and extinction properties of the medium. We formulate the method in the context of 2-dimensional radiative transfer and describe general solution procedures, based on the principles of invariant imbedding, which are applied in the form of doubling algorithms to obtain solutions for optically thick media. Some selected results are shown to demonstrate the versatility of the approach.     

Radiative symmetry breaking in supersymmetric models

We propose a scheme where the three relevant physics scales related to the supersymmetry, electroweak, and baryon minus lepton (B−L) breakings are linked together and occur at the TeV scale. The phenomenological implications in the Higgs and leptonic sectors are discussed.     

Radiative electroweak symmetry breaking revisited

In the absence of a tree-level scalar-field mass, renormalization-group methods permit the explicit summation of leading-logarithm contributions to all orders of the perturbative series within the effective potential for SU(2)xU(1) electroweak symmetry. This improvement of the effective potential function is seen to reduce residual dependence on the renormalization mass scale. The all-orders summation of leading-logarithm terms involving the dominant three couplings contributing to radiative corrections is suggestive of a potential characterized by a plausible Higgs boson mass of 216 GeV. However, the tree potential's local minimum at phi=0 is restored if QCD is sufficiently strong.     

Radiative transfer in atmospheres with spherical symmetry—II. The conservative Milne problem

A new method of successive approximations is developed to solve transfer problems in spherical coordinates. It is equivalent to methods involving the introduction of a closure relation for the μm-moment system. From a practical point of view, it is a two-direction method with variable quadrature weights which are easily computable for any depth variation of the opacity. These quadrature weights are taken as new variables; this allows us, even in the lowest orders, to dispose of closure relations that take into account the principal properties of the radiation field in spherical systems: quasi-isotropic radiation at great optical depths and unidirectional beam “peaking effect” at large values of the radial distance.In the first approximation, we find simple properties like those of the first order in the discretization method for plane-parallel systems. Therefore, it is formally possible to identify these two methods which have a similar practical application. We find for the mean intensity J(r), in the Milne problem, an analytical expression which corresponds to J = 3H(τ + cte) in the plane-parallel geometry.This work is a generalization of several important aspects of another study published in 1976 from which we have only kept the formalism. The new closure relation for the moment system is physically more complete and permits the development of new important results and allows the possibility of an easy solution in every order. From the first results obtained here, we show and analyze the differences between this study and the preceding one.     

Determination of azimuthal features of jets without measuring the angle of the reaction plane

A new method is proposed for determining the coefficient of elliptic anisotropy of jets in ultrarelativistic heavy-ion collisions. This method, which does not involve directly reconstructing the reaction plane, is a generalization of the method used in current experiments to measure the coefficient of elliptic anisotropy of particle fluxes. It is shown that, for the spectrum of hadronic jets, the method makes it possible to explore the azimuthal asymmetry caused by the rescattering of hard partons and by their energy losses in dense quark-gluon matter formed in the region of the initial overlap of nuclei in collisions at a nonzero value of the impact parameter—in particular, under the conditions of the CMS experiment at LHC.     

Radiative transfer in three-dimensional rectangular enclosures containing inhomogeneous,anisotropically scattering media

Radiative transfer in a three-dimensional rectangular enclosure containing radiatively participating gases and particles is studied using the first- and third-order spherical harmonics approximations. Inhomogeneities in the radiative properties of the medium, as well as in the radiation characteristics of the boundaries, are allowed for. The scattering phase function is represented by the delta-Eddington approximation, and it is assumed to be a function of the location in order to account for density variation of the particles in the medium. Numerical solutions of the model equations are obtained using a finite difference scheme. For the purpose of validating the P₃-approximation, the results are compared with those based on Hottel's zonal method.     

Transverse zeeman effect for ions in uniaxial crystals with and without mirror plane symmetry

Intra-configuration electric dipole transitions may occur for an ion in a crystal at a site that is not a center of inversion. When an external magnetic field is directed perpendicularly to the principal crystal symmetry axis c, intensity variations in the optical spectrum due to transitions between Zeeman states may appear as the crystal is rotated about c or as the direction of polarization of the incident light is changed with respect to the Zeeman field direction. The electric dipole selection rules giving rise to these intensity fluctuations are derived by consideration of Earney's mirror plane symmetry, and are shown to be identical to those obtained by other means.     

Radiative transfer in plant leaves

A two-layer model of light scattering and absorption in plant phytoelements is considered, which takes into account absorption of light by pigments and water and light scattering by particles of two types: chloroplasts and air cavities. An elementary light scattering event is described using the Mie theory. Multiple light scattering in a leaf is described within the framework of the theory of radiative transfer. The equation of radiative transfer with a strongly anisotropic phase function is solved using the method of addition of layers and the method of reduction to a medium with effective parameters depending on the propagation direction of light. The spectral dependences of reflection and transmission coefficients are calculated in the visible range as functions of the leaf structure.     

Radiative electroweak symmetry breaking in the extra dimensions scenarios

We study radiative spontaneous electroweak symmetry breaking in the non-supersymmetric extra dimension scenarios of the standard model extension proposed by Antoniadis et al., Dienes et al. and Pomarol et al. In the framework of the multi-scale effective theory, by using the renormalization group method with an up-to-down viewpoint, we find that the effects of Kaluza-Klein excitations of bosons of the standard model can change the sign of the Higgs mass term of the standard model from positive to negative and break the electroweak symmetry. The critical scale for the electroweak phase transition to occur depends on the compactification scale (say 1.6 (2.0) TeV if the compactification scale is assumed to be 0.8 (1.5) TeV or so), and is insensitive to the mass of the Higgs particle. This radiative spontaneous symmetry breaking mechanism can work naturally in the extra dimension scenarios, and neither new particle contents beyond the standard model from the supersymmetry nor technicolor are necessary. Received: 7 January 2002 / Revised version: 2 March 2002 / Published online: 7 June 2002     

Radiative breaking scenario for the GUT gauge symmetry

The origin of the grand unified theory (GUT) scale from the top-down perspective is explored. The GUT gauge symmetry is broken by the renormalization group effects, which is an extension of the radiative electroweak symmetry breaking scenario to the GUT models. That is, in the same way as the origin of the electroweak scale, the GUT scale is generated from the Planck scale through the radiative corrections to the soft supersymmetry breaking mass parameters. This mechanism is applied to a perturbative SO(10) GUT model, recently proposed by us. In the SO(10) model, the relation between the GUT scale and the Planck scale can naturally be realized by using order-one coupling constants. PACS 12.10.-g, 12.10.Dm, 12.10.Kt     

Radiative transfer in statistically heterogeneous mixtures

We solve three radiative-transfer problems in a two-phase medium for a Markov process.