A globally convergent numerical method for an inverse elliptic problem of optical tomography

A new globally convergent numerical method is developed for an inverse problem for the elliptic equation with the unknown potential. The boundary data simulating measurements in optical tomography are generated by the running source. Global convergence analysis is presented along with numerical experiments.     

An improvement in the flory corresponding-states theory of polymer solutions

The original Flory corresponding-states theory of polymer solutions requires an entropic correction parameter Q₁₂, the sign and value of which seem to be arbitrary, and the physical meaning of which is obscure. Moreover, calculated excess volumes of mixing for many polymer solutions are often in significant disagreement with experimental data. In order to eliminate these problems, we have modified the kinetic part of the partition function, introduced an effective mass for the mixture segment, and adopted the nonlinearity of the number of degrees of freedom with respect to the composition for the mixture segment. In addition, the effect of nonrandom configurations of the segments in the mixture has been included. In the improved equations, derived in this work, the Flory interaction parameter χ can be considered to comprise three parts: (a) a kinetic part due to the contribution of the average number of degrees of freedom and the effective mass of the mixture; (b) a free volume part; and (c) an interaction part including the contributions due to the contact interaction and the nonrandom configuration of the segments in the mixture, caused by the interaction. The improved theory is in good agreement with literature data on polystyrene solutions and poly (dimethyl siloxane) solutions.