Recent advances in the LTSNmethod for criticality calculations in slab geometry

The exposure buildup factor formulation in a slab and rectangle geometry by the LTS<SUB align=right>N method

“…This methodology has been applied to a broad class of transport and radiative transfer problems. Some situations in which this methodology appears are the following: a general analytical approach to the one-group, one-dimensional transport equation by Barichello and Vilhena (1993); determination of the criticality parameters in heterogeneous slabs by the LTS N method by Borges and Derivi (2001); the LTS N method: a new analytical approach to solve the neutron transport equation by Vilhena and Barichello (1991); an analytical solution to the multigroup slab geometry discrete ordinates problems by Vilhena and Barichello (1995); extension of the LTS N formulation for discrete ordinates problems without azimuthal symmetry by Segatto and Vilhena (1994); a new iterative method to solve the radiative transfer equation by Vilhena and Segatto (1996); the LTS N solution for radiative transfer problems without azimuthal symmetry with severe anisotropy by Brancher et al (1999); analytical solution of the discrete ordinates problem by the decomposition method by Vargas and Vilhena (1997); a closed-form solution for the one-dimensional radiative conductive problem by the decomposition and LTS N methods by Vargas and Vilhena (1998); a closed-form solution to one-dimensional linear and non-linear radiative transfer problems by Vilhena and Barichello (1999); inverse problems for estimating bottom boundary conditions of natural waters in engineering by Velho et al (2003); determining source term and boundary conditions in hydrological optics by Retamoso et al (2001); estimation of boundary conditions in hydrologic optics by Retamoso et al (2002); determination of the effective multiplication factor in a slab by the LTS N method by Batistela et al (1999); criticality by the LTS N method by Batistela et al (1997); recent advances in the LTS N method for criticality calculations in slab geometry by Orengo et al (2004); the LTS N solution to the neutron transport equation in spherical geometry by Vasques et al (2003); particle transport in the 1-D diffusive atomic mix limit by Larsen et al (2005); and the convergence of the LTS N method was proved by Pazos and Vilhena (1999;2000). On the other hand, recently, the LTS N method has been applied to the solution of the multidimensional S N nodal equations in cartesian geometry by Hauser (2002), …”