Efficiency and Stability in a Discrete Model of Country Formation

This paper studies efficient and stable country configurations in a simple model of country formation. Driving force of the model is a trade-off between the benefits of large countries and the costs of heterogeneity of large and diverse populations. We show that efficient configurations as well as stable configurations exist for each value of the model parameter; however, there is no unambiguous relation between them. Moreover, country sizes in efficient configurations may differ by at most two, while in stable configurations the differences in their sizes may be relatively high. Our results contrast with those of Alesina and Spolaore (1997).     

Conformations of polymer chains in voids with an external electric field by Green's function methods

The statistical conformations of a length of polymer chain, such as DNA, trapped in a void within a gel under the influence of an external electric field, have been studied by the method of Green's functions. Based upon a rectangular box approximation for the void shape, the method gives an explicit analytical expression for the end-to-end distance (R_x) as a function of applied field strength, number of chain segments coiled within the void, and size of a chain segment. Results of calculations show that the field compresses the entrained coil into more compact configurations, as would be expected. Such compression is believed to affect the electrophoretic mobility of a long chain molecule like DNA in a dilute gel. © 1995 John Wiley & Sons, Inc.     

Ground States of Lattice Gases with “Almost” Convex Repulsive Interactions

To the best of our knowledge there is only one example of a lattice system with long-range two-body interactions whose ground states have been determined exactly: the one-dimensional lattice gas with purely repulsive and strictly convex interactions. Its ground-state particle configurations do not depend on any other details of the interactions and are known as the generalized Wigner lattices or the most homogeneous particle configurations. The question of the stability of this beautiful and universal result against certain perturbations of the repulsive and convex interactions is interesting in itself. Additional motivations for studying such perturbations come from surface physics (adsorption on crystal surfaces) and theories of correlated fermion systems (recent results on ground-state particle configurations of the one-dimensional spinless Falicov–Kimball model). As a first step, we studied a one-dimensional lattice gas whose two-body interactions are repulsive and strictly convex only from distance 2 on, while its value at distance 1 can be positive or negative, but close to zero. We showed that such a modification makes the ground-state particle configurations sensitive to the tail of the interactions; if the sum of the strengths of the interactions from the distance 3 on is small with respect to the strength of the interaction at distance 2, then particles form two-particle lattice-connected aggregates that are distributed in the most homogeneous way. Consequently, despite breaking of the convexity property, the ground state exhibits the feature known as the complete devil's staircase.     

六方金属在疲劳过程中的位错组态演化──兼论位错理论和协同论在材料强度学中的应用

简述了位错理论发展及在中国传播的历史、位错理论的应用领域、金属中常见的位错组态;介绍了协同论在位错研究中的应用,并据此分析讨论了在钛、锆等六方金属中所获得的某些实验结果。