A Review of Neutron Transport Approximations

Critical parameters and decay constants for one-speed neutrons in slabs and spheres with anisotropic scattering

Time-dependent, one-speed neutron transport equations with strong forward and backward scattering together with isotropic scattering are studied in homogeneous slabs and spheres. First, a simple formal equivalence between the transport equations for a critical and for a time-decaying system is established. Then, the transport equation is converted into a more conventional one. The FN method of solving the resulting transport equation is applied to the calculation of the critical parameters and decay constants for the fundamental mode of the flux distribution and one-speed neutrons in spheres and infinite slabs. Numerical results are given for a number of significant figures and compared with those already available in the literature.

Calculation of the higher order eigenvalues for a homogeneous sphere using the FN method

The transport of monoenergetic neutrons in spherical geometry with forward scattering and vacuum boundary conditions is considered. The scaled transport equation is solved using the Fn method by considering the pseudo-slab problem. Numerical results for the fundamental and higher order eigenvalues are presented for several significant figures. Some selected results are compared with those obtained using various methods in the literature. Finally, a few remarks about the behavior of the criticality eigenvalue of the neutron transport equation with forward scattering is given.

Broadband Time Domain Diffuse Optical Reflectance Spectroscopy: A Review of Systems, Methods, and Applications

This review presents recent developments and a wide overview of broadband time domain diffuse optical spectroscopy (TD-DOS). Various topics including physics of photon migration, advanced instrumentation, methods of analysis, applications covering multiple domains (tissue chromophore, in vivo studies, food, wood, pharmaceutical industry) are elaborated. The key role of standardization and recent studies in that direction are discussed. Towards the end, a brief outlook is presented on the current status and future trends in broadband TD-DOS.

Chebyshev polynomial (TN ) approximation to neutron transport theory and application to the critical slab problem

The critical slab problem has been studied in the one-speed neutron transport equation with isotropic scattering by using the first kind of Chebyshev Polynomials. The moment criticality solutions were obtained for the uniform finite slab using Mark and Marshak type vacuum boundary conditions. The results obtained by this approximation are presented in tables which also include the results obtained by the PN method for comparison.

Grundlagen optischer und fluoreszenzgestützter Tomographie in diffusen Medien

Three-dimensional, tomographic imaging of biological tissues by means of visible light is becoming increasingly important. Current progress in the mathematical-physical modelling of photon propagation in scattering media allows spatially-resolved reconstructions of optical parameters with common computing hardware. Especially in the field of molecular imaging, optical tomography promises a transfer of knowledge from successful in vitro assays (as evaluated by fluorescence microscopy) to in vivo imaging of living animals. In the latter case, spatial resolution is not as critical as the ability to quantify the concentration of fluorescence-labelled probes, a task not solvable by the use of common planar imaging techniques. In this article, the theoretical foundations of optical tomography are introduced along with some examples of applications.