Starting from the adiabatic time-dependent Hartree-Fock approximation (ATDHF), we propose an efficient method to calculate the Thouless-Valatin moments of inertia for the nuclear system. The method is based on the rapid convergence of the expansion of the inertia matrix. The accuracy of the proposed method is verified in the rotational case by comparing the results with the exact Thouless-Valatin moments of inertia calculated using the self-consistent cranking model. The proposed method is computationally much more efficient than the full ATDHF calculation, yet it retains a high accuracy of the order of 1%.
We present an elegant method of determining the eigensolutions of the induction and the dynamo equation in a fluid embedded in a vacuum. The magnetic field is expanded in a complete set of functions. The new method is based on the biorthogonality of the adjoint electric current and the vector potential with an inner product defined by a volume integral over the fluid domain. The advantage of this method is that the velocity and the dynamo coefficients of the induction and the dynamo equation do not have to be differentiated and thus even numerically determined tabulated values of the coefficients produce reasonable results. We provide test calculations and compare with published results obtained by the classical treatment based on the biorthogonality of the magnetic field and its adjoint. We especially consider dynamos with mean-field coefficients determined from direct numerical simulations of the geodynamo and compare with initial value calculations and the full MHD simulations.
The energy variance extrapolation method consists in relating the approximate energies in many-body calculations to the corresponding energy variances and inferring eigenvalues by extrapolating to zero variance. The method needs a fast evaluation of the energy variances. For many-body methods that expand the nuclear wave functions in terms of deformed Slater determinants, the best available method for the evaluation of energy variances scales with the sixth power of the number of single-particle states. We propose a new method which depends on the number of single-particle orbits and the number of particles rather than the number of single-particle states. We discuss as an example the case of ${}^4He$ using the chiral N3LO interaction in a basis consisting up to 184 single-particle states.
An efficient method, preconditioned conjugate gradient method with a filtering function (PCG-F), is proposed for solving iteratively the Dirac equation in 3D lattice space for nuclear systems. The filtering function is adopted to avoid the variational collapsed problem and a momentum-dependent preconditioner is introduced to promote the efficiency of the iteration. The PCG-F method is demonstrated in solving the Dirac equation with given spherical and deformed Woods-Saxon potentials. The solutions given by the inverse Hamiltonian method in 3D lattice space and the shooting method in radial coordinate space are reproduced with a high accuracy. In comparison with the existing inverse Hamiltonian method, the present PCG-F method is much faster in the convergence of the iteration, in particular for deformed potentials. It may also provide a promising way to solve the relativistic Hartree-Bogoliubov equation iteratively in the future.
The 12C+12C fusion reaction is famous for its complication of molecular resonances, and plays an important role in both nuclear structure and astrophysics. It is extremely difficult to measure the cross sections of 12C+12C fusions at energies of astrophysical relevance due to very low reaction yields. To measure the complicated resonant structure existing in this important reaction, an efficient thick target method has been developed and applied for the first time at energies Ec.m.<5.3 MeV. A scan of the cross sections over a relatively wide range of energies can be carried out using only a single beam energy. The result of measurement at Ec.m.= 4.1 MeV is compared with other results from previous work. This method would be useful for searching potentially existing resonances of 12C+12C in the energy range 1 MeV<Ec.m.<3 MeV.
An efficient order$-N$ real-space Kubo approach is developed for the calculation of the thermal conductivity of complex disordered materials. The method, which is based on the Chebyshev polynomial expansion of the time evolution operator and the Lanczos tridiagonalization scheme, efficiently treats the propagation of phonon wave-packets in real-space and the phonon diffusion coefficients. The mean free paths and the thermal conductance can be determined from the diffusion coefficients. These quantities can be extracted simultaneously for all frequencies, which is another advantage in comparison with the Greens function based approaches. Additionally, multiple scattering phenomena can be followed through the time dependence of the diffusion coefficient deep into the diffusive regime, and the onset of weak or strong phonon localization could possibly be revealed at low temperatures for thermal insulators. The accuracy of our computational scheme is demonstrated by comparing the calculated phonon mean free paths in isotope-disordered carbon nanotubes with Landauer simulations and analytical results. Then, the upscalibility of the method is illustrated by exploring the phonon mean free paths and the thermal conductance features of edge disordered graphene nanoribbons having widths of $sim$20 nanometers and lengths as long as a micrometer, which are beyond the reach of other numerical techniques. It is shown that, the phonon mean free paths of armchair nanoribbons are smaller than those of zigzag nanoribbons for the frequency range which dominate the thermal conductance at low temperatures. This computational strategy is applicable to higher dimensional systems, as well as to a wide range of materials.