Analytical solutions of spherical structures with relativistic corrections

Effective Hamiltonians with Relativistic Corrections

Analytical solutions of the simplified spherical harmonics equations.

We derived analytical solutions of the simplified spherical harmonics equations, an approximation of the radiative transfer equation, for infinitely extended scattering media. The derived equations are simple (sum of exponential functions) and quickly evaluated. We compared the solutions with Monte Carlo simulations in the steady-state and time domains and found much better agreement compared t...

Analytical Solutions of Polymeric Gel Structures under Buckling and Wrinkle

Z. S. LIU∗,¶, S. SWADDIWUDHIPONG†, F. S. CUI∗, W. HONG‡, Z. SUO§ and Y. W. ZHANG∗ ∗Institute of High Performance Computing 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632 †Department of Civil and Environmental Engineering National University of Singapore E1A-07-03, 1 Engineering Drive 2, Singapore 117576 ‡Department of Aerospace Engineering Iowa State University, Ames, IA 50014, USA §Scho...

Relativistic corrections in magnetic systems

We present a weak-relativistic limit comparison between the Kohn-Sham-Dirac equation and its approximate form containing the exchange coupling, which is used in almost all relativistic codes of density-functional theory. For these two descriptions, an exact expression of the Dirac Green’s function in terms of the nonrelativistic Green’s function is first derived and then used to calculate the e...

Radiative transfer in moving spherical atmospheres II. Analytical solution for fully relativistic radial motions

Based on the well known solution of the timeindependent radiative transfer equation along a ray and on suitable point transformations, general quadrature solutions of the monochromatic transfer equation for plane-parallel, spherically-symmetric and arbitrarily shaped 3D configurations with differential motion are derived for the observer’s and the comoving frame. The source function is assumed ...