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Based on an extensively study of the Dyson-Schwinger equations for a fully dressed quark propagator in the "rainbow" approximation, a parametrized fully dressed quark propagator is proposed in this paper. The parametrized propagator describes a confining quark propagator in hadron since it is analytic everywhere in complex p(2)-plane and has no Lemmann representation. The validity of the new propagator is discussed by comparing its predictions on self-energy functions A(f) (p(2)), B-f (p(2)) and effective mass M-f (p(2)) of quark with flavor f to their corresponding theoretical results produced by Dyson-Schwinger equations. Our comparison shows that the parametrized quark propagator is a good approximation to the fully dressed quark propagator given by the solutions of Dyson-Schwinger equations in the rainbow approximation and is convenient to use in any theoretical calculations.

Based on an extensive study of the Dyson-Schwinger equations for a fully dressed quark propagator in the "rainbow" approximation, a parametrized form of the quark propagator is suggested. The corresponding quark self-energy Sigma(f) and the structure of non-local quark vacuum condensate are investigated. The algebraic form of the quark propagator proposed in this work describes a confining quark propagation, and is quite convenient to be used in any numerical calculations.

Based on Dyson-Schwinger equations in "rainbow" approximation, fully. dressed confining quark propagator is obtained, and then the masses of light quarks (m(u), m(d), and m(s)) are derived from the fully dressed confining quark propagator. At the same time, the local and non-local quark vacuum condensates as well as the quark-gluon mixed condensate are also predicted. Furthermore, the quark masses are also deduced from the Gell-Mann-Oakes-Renner relation and chiral perturbative theory. The results from different methods are consistent with each other.

Based on Glauber Multiple Scattering Theory, high-energy proton elastic scattering on halo-like nucleus 13C is studied in a single nucleon wave function with low angular momentum configurations. A great agreement with experimental data is obtained and the theoretical prediction clearly shows that 13 C has a neutron halo-like structure.Then, the origin and nature of nuclear halo phenomena are explained in terms of nuclear short-range correlations. Our conclusion shows that the origin of nuclear halo-like phenomena originates from short range nuclear correlation.

In this study, the consensus problem for a class of second-order multi-agent systems with nonuniform time delays is investigated. A linear consensus protocol is used to make all agents reach consensus and move with a constant velocity. By a frequency-domain analysis, a simplified sufficient condition is given to guarantee the consensus stability of the dynamic system. Finally, the effectiveness of the obtained theoretical results is illustrated through numerical simulations.

Using the first-principles methods, we study the formation energetics properties of intrinsic defects, and the charge doping properties of extrinsic defects in transparent conducting oxides CuCrO2. Intrinsic defects, some typical acceptor-type, and donor-type extrinsic defects in their relevant charge state are considered. By systematically calculating the formation energies and transition energy, the results of calculation show that, VCu, Oi, and OCu are the relevant intrinsic defects in CuCrO2; among these intrinsic defects, VCu is the most efficient acceptor in CuCrO2. It is found that all the donor-type extrinsic defects have difficulty in inducing n-conductivity in CuCrO2 because of their deep transition energy level. For all the acceptor-type extrinsic defects, substituting Mg for Cr is the most prominent doping acceptor with relative shallow transition energy levels in CuCrO2. Our calculation results are expected to be a guide for preparing promising n-type and p-type materials in CuCrO2.

The Kurganov scheme is a third-order semi-discrete central numerical algorithm. The high solution of the scheme is ensured by a piecewise quadratic non-oscillatory reconstruction which consists of the cell-average data. We employ a modification of the smooth limiter of reconstruction in a simple way. The modified limiter possesses rigorous positivity and the reformulation does not change the non-oscillatory property of reconstruction. In order to explore the potential capability of application of the modified Kurganov scheme to magnetohydrodynamics (MHD) and resistive magnetohydrodynamics (RMHD) equations, two numerical problems are simulated in two dimensions (2D). These numerical simulations demonstrate that the modified Kurganov scheme keeps high precision and has stable reliable results for MHD and RMHD applications.

The space-time conservation element and solution element (CESE) scheme is a new second order numerical scheme based on the concept of space-time conservation integration. In order to further overcome excessive numerical damping due to small Courant–Friedrichs–Lewy (CFL) number and to obtain a high quality solution, a Courant number insensitive (CNIS) scheme and a high-order scheme have been proposed by Chang et al. for fluid mechanics problems recently. In this study, to explore the potential capability of applications of the CNIS CESE scheme and the high-order CESE scheme to magnetohydrodynamics (MHD) equations, several benchmark MHD problems are calculated in one and two dimensions: (i) Brio and Wu's shock tube, (ii) Dai and Woodward's case, (iii) the Orszag–Tang vortex problem, (iv) the Riemann problem. The numerical results just prove that the CNIS scheme is more accurate and can keep the divergence free condition of the magnetic field, even if the CFL number is < 1. Meanwhile, the tests show that the high order CESE scheme possesses the ability to solve MHD problems but is sensitive to the Courant number.