With local thermodynamic equilibrium approximation,radial position-dependent energy flux for diffusive supersonic wave in low density filled cylinder or sphere shell structures with high density walls are given. We obtain arched-type distribution of geometric factor versus radius in cylinder and sphere shell structure. Mean geometric factor is obtained from cross-section average of total radiative energy flux. Effect of spherical shell structure on radiation process is much greaterr than that of cylinder structure. Geometrical free path must be considered in simulation of radiative diffusivity or thermal conductivity for sphere shell structures models. A fitted formula of geometric factor according to numerical solutions is given.

The spin-orbital energy gap in a one-dimensional spin-orbital model deduced from a degenerate Hubbard model with intrasite Hund rule coupling is studied.By using a mean-field method with SU(4) constraint fermion representation of spins and orbitals the valence bond order parameter,quasi-particle excitation gap and the spin and orbital density-density correlation functions are calculated.It is found that,as the Hund's coupling strength increases the excitation spectra show a gap and the magnetic configuration changes from a frustrating disordered state to a spin ferromagnetic and orbital antiferromagnetic ordered state at J₁/J₂=1/3.

With singular quadrature rules,a quadrature method for the second-kind boundary integral equations in linear elasticity problems on polygonal domains is proposed.The discrete matrix can be obtained with no Cauchy singular integral.With the collectively compact convergent theory,we establish a convergence theorem of approximation and get multivariate asymptotic expansions of error.Solving the discrete equations with coarse meshed partitions in paralle,high accurary approximations are obtained by the splitting extrapolation.A posterior error is derived.

An accurate angular quadrature is developed with cylindrical symmetry in transport equations. The most appropriate quadrature for polar angles is the Double-Gauss and for azimuthal angles is the Chebyshev-Gauss in cylindrical geometry. Numerical comparisons of quadratures on two standard problems are shown. They suggest that the new quadrature proves competitive for transport problems both in reducing ray effects and in improving accuracy.

Soliton dynamics is simulated for trans-polyacetylene single-chain systems using the Su-Schrieffer-Heeger (SSH) model with an additional part to include an external electric field. It is shown that the soliton moves along the chain with a constant speed when an external electric field is applied.