In this paper we introduce the concept of geometrically quasiconvex functions on the co-ordinates and establish some Hermite-Hadamard type integral inequalities for functions defined on rectangles in the plane. Some  inequalities for product of two geometrically quasiconvex functions on the co-ordinates are considered.

To solve the neutron Boltzmann equation in anisotropic or void regions, one may use deterministic methods such as the discrete ordinates method or the even-parity approach. Both methods have shown numerous applications and developments in the last 30 years. Nevertheless both exhibit drawbacks in three-dimensions void regions that require special treatments, such as using characteristics method ...

The algorithm of the method of mean ordinates involves the following steps: • It is assumed that atmospheric aerosol consists of three components, each described by a lognormal distribution; • The ranges of size distribution parameter intervals are specified so as to accommodate all conceivable types of aerosol. The distribution parameters are quantized within their intervals; • All possible co...

We apply high-order mixed finite element discretization techniques and their associated preconditioned iterative solvers to the Variable Eddington Factor (VEF) equations in two spatial dimensions. The VEF discretizations are coupled a Discontinuous Galerkin (DG) of discrete ordinates transport equation form effective linear algorithms that compatible with (curved) meshes. This combination is mo...

High-fidelity nuclear reactor core simulations require a precise knowledge of the neutron flux inside the reactor core. This flux is modeled by the linear Boltzmann equation also called neutron transport equation. In this thesis, we focus on solving this equation using the discrete ordinates method (SN) on Cartesian mesh. This method involves a source iteration scheme including a sweep over the...

A second-order “Time-Dependent Multiple Balance” (TDMB) method for solving neutron transport problems is introduced and investigated. TDMB consists of two coupled equations: (i) the original balance equation (the integrated over a time step) (ii) “balance-like” auxiliary (an approximate equation). Simple analysis shows that accurate robust (unconditionally free from spurious oscillation). sourc...

In this paper experimental and numerical studies of shortpulsed lasers propagation through scattering and absorbing media are investigated. Experimental results of a 60 ps pulse laser transmission in tissue phantoms are presented and compared with Monte Carlo simulation. Good agreement between the Monte Carlo simulation and experimental measurement is found. Three models are developed for the s...