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Accident scenarios implying the failure of the active and passive reactor protection system are the most severe in their consequences since they are accompanied by the melting of fuel elements, fuel assemblies, and the entire core and, as a consequence, the release of fission products (FP) from the fuel melt and structural materials. The location of reactor facilities near populated areas requires an understanding of the consequences of hypothetical accidents with the destruction of the core. The most important is information on the amount of FP released into the environment. To assess the possible dose load on personnel and the environment in a hypothetical accident, data on the release of radioactive nuclides from the damaged, including molten, core are required. This work presents approaches that can be used to calculate the amount of fission products released from the fuel melt. The proposed approaches are based on general patterns of behavior and release of impurities from liquid solutions. To simulate this process, a system of differential equations is solved. The proposed approaches were implemented in the form of a software module for calculating the release of FP from the melt. Using the developed module, a test problem for the release of FP from a molten oxide fuel was solved, and an analysis of the results of real experiments carried out at the National Laboratory in Oak Ridge was carried out. Satisfactory convergence of the calculated data on the yield of both nonvolatile (Ce, Sr) and volatile (Xe, Kr) fission products is shown.

In the article presented are the results modeling the behavior of mixed uranium-plutonium nitride fuel with an admixture of oxygen and carbon during irradiation in fast reactor. It was shown that accumulation of fission products and formation of secondary phases lead to formation of heterogeneous multicomponent solid solution including, in particular, metal, telluride, oxide, intermetal and sesquialteral nitride secondary phases. Influence of the secondary phases formed during irradiation on the effective thermal conductivity of the fuel is assessed in the framework of a generalized theory by Odelevskii developed for heterogeneous systems with isolated inclusions. It was found that in the irradiated nitride fuel, the main correction of the thermal conductivity is related to formation of the U2N3 phase. As it is shown, that with increase of fuel burnup and growth of secondary condensed phases, the effective thermal conductivity decreases up to about 3% for burnup of 5.5%.

Diffuse reflection of a narrow collimated light beam from a slab of a dense random medium is considered theoretically and experimentally for the case of the source and the detector fibres dipped into the random medium, as is the case for an endoscopic catheter. By use of the diffusion approximation, a simple and physically clear analytical expression is derived for the distribution of the diffuse reflectance of the light beam along the surface of the random medium slab. We include the effects of reflections from the top and bottom surfaces of the slab. The analytical expression derived predicts that, in the case of small absorption, the relative reflectance is a universal function defined by the geometrical parameters and is independent of specific properties of the random medium. The theoretical prediction is found to show good agreement with the results of measurements.

A model for describing uranium-plutonium mixed nitride fuel pellet burning was developed. Except fission products generating, the model includes impurities of oxygen and carbon. Nitrogen behaviour in nitride fuel was analysed and the nitrogen chemical potential in solid solution with uranium-plutonium nitride was constructed. The chemical program module was tested with the help of thermodynamic equilibrium phase distribution calculation. Results were compared with analogous data in literature, quite good agreement was achieved, especially for uranium sesquinitride, metallic species and some oxides. Calculation of a process of nitride fuel burning was also conducted. Used mechanistic approaches for fission product evolution give the opportunity to find fission gas release fractions and also volumes of intergranular secondary phases. Calculations present that the most massive secondary phases are the oxide and metallic phases. Oxide phase contain approximately 1 % wt of substance over all time of burning with slightly increasing of content. Metallic phase has considerable rising of mass and by the last stage of burning it contains about 0.6 % wt of substance. Intermetallic phase has less increasing rate than metallic phase and include from 0.1 to 0.2 % wt over all time of burning. The highest element fractions of released gaseous fission products correspond to caesium and iodide.

We present an exact expression for the diffusion constant of vector electromagnetic waves in a random medium of dielectric scatterers in the form of the Green-Kubo relation. The derivation is based on a proper version of the Ward-Takahashi identity for classical waves. The relation between the density of states of the electromagnetic field and the absorption length in the model of weakly absorbing scatterers is discussed.

We discuss a rigorous vectorial theory as a model to represent the enhanced backscattering of polarized light from a random medium. The theory is based on the well known relation between the contributions of the ladder and cyclical diagrams to the intensity which allows to express these contributions in terms of radiative transfer theory. The tensor transfer equation for the electromagnetic field in a half-space occupied by point-like scatterers is explicitly solved with the aid of the Wiener–Hopf method. For the case of normal incidence the angular distribution of the backscattered intensity and the enhancement factor are found for arbitrary angles between the incident and detected linear polarizations and the scanning plane. To describe spatial anisotropy of the backscattering cone the half width at half maximum of the intensity is calculated as a function of these angles. Coherent backscattering of circularly polarized light is also considered.

Coherent backscattering of scalar waves from a semi-infinite discrete nonabsorbing random medium of nonisotropic scatterers is considered. The dependence of the line shape of the backscattering peak of the scattering nonisotropy is studied in the frameworks of the diffusion approximation. Various versions of this approximation are applied in which, in particular, the gradiental terms are taken into account, and various forms of boundary conditions are used. It is shown that the peak line shape is almost independent of the form of boundary conditions only in the vicinity of the backscattering direction. The validity of the diffusion approximation is discussed.

The Bethe-Salpeter equation for scalar waves in a random dielectric medium is considered. An eigenfunction expansion and the Ward identity, generalized for the case of an energy dependent potential, are used to find the asymptotic solution. An exact expression for the diffusion constant is obtained in the form of the generalized Green-Kubo formula. Also the accepted point of view on the absence of diffusion in two-dimensional random systems is argued.

Recently, in connection with the problem of Anderson localization of light, a new physical mechanism was considered for the decrease of the diffusion coefficient, in which it is supposed that the velocity of energy transport, which appears in the diffusion constant D= @23E l tr /3, may be much smaller than the phase velocity. Using an exact definition of the diffusion coefficient and generalized Ward identity, we, however, show that in the low-density approximation υ E coincides with the phase velocity

Recently Nieh et al. [Phys. Rev. E 57, 1145 (1998)] have considered a version of derivation of the Ward identities for scalar and vector classical wave field propagation in random media and noted that their results are in contradiction with those obtained by Barabanenkov and Ozrin [Phys. Lett. A 154, 38 (1991)]. In this Comment we show that the derivation given by Nieh et al. is based on an incorrect equation for the energy-vertex function where the term that takes into account the contributions of the scatterer polarization to the field energy is lost. Restoring this term removes the above-noted contradiction.

Publisher Summary This chapter describes enhanced backscattering in optics. The chapter considers backscatter enhancement in light scattered from a body embedded in a random medium. A similar phenomenon occurs in multiple scattering of light in a randomly inhomogeneous medium where there are no clear-cut scatterers that stand out against a background. The effects of backscatter enhancement and weak localization are phenomena, in which coherent paths of the Watson-Ruffine type are essential. The chapter describes multiple new manifestations of coherent effects in backscattering. These include the effects of long-distance correlations, the partial reversal of the phase front in a random medium, the magic cap effect, antispecular scattering by very rough random surfaces, and backscattering involving surface waves. The chapter also discusses the opposite case of a small number of scatterers, in which summation cannot be replaced with integration.