代数系列课程习题讨论课的改革与实践

通过作者多年教学实践和总结 ,提出代数习题讨论课对培养学生分析解决问题的能力 ,初步的研究创新意识和提高代数课的教学质量是一个很有益的教学环节 .     

Rapid evaluation of oscillating lattice sums

We have generalized a method for the rapid evaluation of oscillating lattice sums for layered geometries, based on the Ewald's summation technique. Different types of long range interactions as well as different lattice symmetries can be considered, in particular modulated magnetic structures, periodic domain patterns, or periodic lattice distortions. As examples the demagnetizing energies for different thin films systems and magnetic excitations in a single atomic layer are calculated.     

Lattice gas with “interaction potential”

We present an extension of a simple automaton model to incorporate nonlocal interactions extending over a spatial range in lattice gases. From the viewpoint of statistical mechanics, the lattice gas with interaction range may serve as a prototype for non-ideal-gas behavior. From the density fluctuations correlation function, we obtain a quantity which is identified as a potential of mean force. Equilibrium and transport properties are computed theoretically and by numerical simulations to establish the validity of the model at macroscropic scale.     

Micro-Raman mapping on an anatase TiO2 single crystal with a large percentage of reactive (0 0 1) facets

After it has been successfully synthesized in 2008, so far, no Raman investigations on the micro-sized anatase TiO₂ single crystal which has a large percentage of the reactive (0 0 1) facets have been conducted to the best of our knowledge. In the present work, this unique anatase TiO₂ single crystal was investigated by noninvasive and nondestructive Raman mapping technique. Raman images of both non-polarized and polarized measurements showed that the Raman features of the crystal varied with measurement position. The differences among the Raman spectra measured on different crystal facets were believed to result from the orientations and the symmetry rules. Whereas the differences among those measured at different points of the same crystal facet under the same measurement condition were supposed to indicate the defects of the crystal structure, such as oxygen vacancies, local lattice disorder etc. Furthermore, the appearance of the two second order Raman peaks of 803 and 918 cm⁻¹ as well as the blue-shift of 395 cm⁻¹ peak implies the anharmonicity of the crystal structure, which is also probably caused by the crystal defects. Our results provide useful information about the structure of this unique anatase TiO₂ material, and could be complementary to those that acquired by other characterization techniques.     

A study of wide moving jams in a new lattice model of traffic flow with the consideration of the driver anticipation effect and numerical simulation

In this paper, a new lattice model of traffic flow is proposed to investigate wide moving jams in traffic flow with the consideration of the driver anticipation information about two preceding sites. The linear stability condition is obtained by using linear stability analysis. The mKdV equation is derived through nonlinear analysis, which can be conceivably taken as an approximation to a wide moving jam. Numerical simulation also confirms that the congested traffic patterns about wide moving jam propagation in accordance with empirical results can be suppressed efficiently by taking the driver anticipation effect of two preceding sites into account in a new lattice model.     

Unconventional superconductivity originating from disconnected Fermi surfaces in correlated superconductors : A case study for iron pnictides

We first generally summarize the effect of disconnected Fermi surfaces in spin fluctuation mediated superconductivity. We argue that disconnected Fermi surfaces are favorable in that the sign of the superconducting gap can be changed without nodal lines intersecting the Fermi surface. Then, as an example of actual materials that have disconnected Fermi surfaces, we focus on the iron-based high T_c superconductors. We construct a model that contains all of the five Fe d bands, and apply random-phase approximation. We find that multiple spin fluctuation modes develop due to the nesting between disconnected Fermi surfaces, and the superconductivity originating from the cooperation or competition between these multiple spin fluctuation modes depends on the lattice structure. In particular, the appearance of the Fermi surface around (π, π) in the unfolded Brillouin zone is sensitive to the pnictogen height h_Pn measured from the Fe plane, and the height can act as a switch between high T_c nodeless and low T_c nodal pairings. In the high T_c case, the superconducting gap is fully open on all of the five Fermi surfaces, but changes sign across the nesting vectors that bridge the disconnected Fermi surfaces.     

Multiscale simulation of flow and heat transfer of nanofluid with lattice Boltzmann method

Based on the lattice Boltzmann (LB) approach, a novel hybrid method has been proposed for getting insight into the microscale characteristics of the multicomponent flow of nanofluid. In this method, the whole computational domain is divided into two regions in which different-sized meshes are involved for simulation (fine mesh and coarse mesh). The multicomponent LB method is adopted in the fine mesh region, and the single-component LB approach is applied to the coarse mesh region where the nanofluid is treated as a mixed single-component fluid. The conservation principles of mass, momentum and energy are used to derive a hybrid scheme across the different scaled regions. Numerical simulation is carried out for the Couette flow and convective heat transfer in a parallel plate channel to validate the hybrid method. The computational results indicate that by means of the present method, not only the microscopic characteristics of the nanofluid flow can be simulated, but also the computational efficiency can be remarkably improved compared with the pure multicomponent LB method.     

K_3Dy(PO_4)_2晶体的生长

二磷酸钕钾作为新型的化学计量比激光材料已有报导.由于二磷酸稀土钾盐具有独特的结构性质,即PO_4四面体与LnO_7十面体的相互隔离,使Ln~(3+)-Ln~(3+)之间的相互作用减少,荧光猝灭较小,以及在磷酸盐晶体中有较高的热稳定性,因而引起人们的关注.对K_3Ln(PO_4)_2(Ln:Pr,Nd,Sm,Gd)晶体的生长、结构和光谱已进行了深入的研究,但是Tb-Lu的稀土二磷酸钾盐晶体由于难以生长,至今未见报导.本文参照K_3Nd(PO_4)_2晶体的生长方法,用助熔剂缓冷法从KCl-KF熔体中生长出K_3Dy(PO_4)_2晶体.工艺过程如     

A combined electrochemical and DFT study of the lattice strain effect on the surface reactivity of Pd

We report a combined study of electrochemical experiments and ab initio calculations on tuning the surface reactivity of Pd via a compressive lattice strain achieved by employing nanoparticles of Pd-Cu alloys with a Pd-rich surface.Surface oxygen-containing species were used as the probing molecule for revealing the surface reactivity.Both density functional theory (DFT) calculations and experiments showed linear relationships,with very close slopes,between the adsorption strength of OH_(ads) and the Pd lattice constant.Not only is this work a successful realization of controllable modulation in the surface reactivity,but it also provides valuable information for the rational design of Pd-based catalysts for fuel cell applications.