Finite Intervals in the Lattice of Topologies

We discuss the question whether every finite interval in the lattice of all topologies on some set is isomorphic to an interval in the lattice of all topologies on a finite set – or, equivalently, whether the finite intervals in lattices of topologies are, up to isomorphism, exactly the duals of finite intervals in lattices of quasiorders. The answer to this question is in the affirmative at least for finite atomistic lattices. Applying recent results about intervals in lattices of quasiorders, we see that, for example, the five-element modular but non-distributive lattice cannot be an interval in the lattice of topologies. We show that a finite lattice whose greatest element is the join of two atoms is an interval of T ₀-topologies iff it is the four-element Boolean lattice or the five-element non-modular lattice. But only the first of these two selfdual lattices is an interval of orders because order intervals are known to be dually locally distributive.     

非正则算子的一个刻画

文中给出了Banach格之间非正则算子的一个刻画,它是Abramovich提出的一个问题之部分肯定回答。     

Lattice Boltzmann simulation for the spiral waves in the excitable medium

We propose lattice Boltzmann method for the spiral waves. Using Chapman-Enskog expansion and multiscales technique, we obtain equilibrium distribution functions of the model. As an example, we simulate the Selkov reactions with scratching mark, i. e. using a scratching mark pacemaker, obtained one classical spiral waves.     

分配伪补格的主理想

本文给出了分配伪补格 ( L;∧ ,∨ ,* ,0 ,1 )中的主理想 I=( d]成为同余理想的充分必要条件 .当 L是局部有限时 (即 d∈ S( L) ,Fd={x|x* * =d}有限 ) ,对骨架 S( L)中的每个元素 d,我们找到了以 I=( d]为核心的最小同余关系 ,利用以上结果我们得到一个 Stone代数是布尔代数的一些等价条件 .     

Thermal behavior of biogenic apatite crystals in bone: An X‐ray diffraction study

The thermal behavior of the bovine bone mineral and synthetic stoichiometric hydroxyapatite was investigated by X‐ray diffraction. The bone samples in solid (planar oriented pieces) and in powder form were examined to elucidate how the microstructural and textural properties of bone mineral are modified under heating. As could be expected, the thermal behavior of the bone mineral depends not only on the structural distortions, but also on the crystal habit, texture and ordering of biocrystals in tissue. The temperature growth of biogenic apatite crystals, unlike synthetic hydroxyapatite, is seen to be nonmonotonic and multi‐staged. At 600 to 700°C the biomineral crystallites grow rapidly due to disappearance of the mosaic structure as the lattice imperfections are annealed. After heating between 700°C and 900°C the bone mineral appears to be composed of roughly equidimensional ≥200 nm crystals. The further growth of the crystals in the range from 900 to 1300°C occurs by the mass transport mechanism, supporting the idea that the bone mineral is not a discrete aggregation of crystals, but rather a continuous mineral phase with direct crystal‐crystal bonding. Estimates are presented to show the important role of the surface mass transport mechanism in the growth of apatite crystals. The material obtained by heating a cortical bone fragment between 900°C and 1300°C turns out to be composed of two crystal types: crystals oriented along the bone axis (major morphology) and those of differing shape and orientation (minor morphology). The heating‐induced variations in the longitudinal and transverse dimensions of differing‐morphology crystals are found to be coherent. Small amounts of CaO, MgO and other crystalline phases are seen to be formed in the bone mineral under heating. © 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Kondo effect for electron transport through an artificial quantum dot

We have calculated the transport properties of electron through an artificial quantum dot by using the numerical renormalization group technique in this paper. We obtain the conductance for the system of a quantum dot which is embedded in a one-dimensional chain in zero and finite temperature cases. The external magnetic field gives rise to a negative magnetoconductance in the zero temperature case. It increases as the external magnetic field increases. We obtain the relation between the coupling coefficient and conductance. If the interaction is big enough to prevent conduction electrons from tunnelling through the dot, the dispersion effect is dominant in this case. In the Kondo temperature regime, we obtain the conductivity of a quantum dot system with Kondo correlation.     

Dislocation energy and calculation from Peierls stress： a rigorous the lattice theory

In the classical Peierls--Nabarro (P-N) theory of dislocation, there is a long-standing contradiction that the stable configuration of dislocation has maximum energy rather than minimum energy. In this paper, the dislocation energy is calculated rigorously in the context of the full lattice theory. It is found that besides the misfit energy considered in the classical P-N theory, there is an extra elastic strain energy that is also associated with the discreteness of lattice. The contradiction can be automatically removed provided that the elastic strain energy associated with the discreteness is taken into account. This elastic strain energy is very important because its magnitude is larger than the misfit energy, its sign is opposite to the misfit energy. Since the elastic strain energy and misfit energy associated with discreteness cancel each other, and the width of dislocation becomes wide in the lattice theory, the Peierls energy, which measures the height of the effective potential barrier, becomes much smaller than that given in the classical P-N theory. The results calculated here agree with experimental data. Furthermore, based on the results obtained, a useful formula of the Peierls stress is proposed to fully include the discreteness effects.     

Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number (Re) flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50,000 in the literature; however, this paper can readily extend the maximum to 1000,000 with the above combination.     

Solitary Excitations of Dipolar Bosons in Optical Lattice under Magnetic Fields

We obtain the multisolitary solutions of the extended Bose-Hubbard model which describes dipolar Bose- Einstein condensates in optical lattices under time-dependent magnetic fields, and indicate that the nonlinearity is due to both on-site short-range interactions and also （long-range） dipole-dipole interactions which can act between neighboring sites. The discrete breathers as nonlinear excitations are always oscillatory in time and can also be spatially localized, while the oscillatory frequencies are determined by an external field. We show that these excitations will be observable and discuss how the parameters can be tuned in future experiments.     

格子Boltzmann方法中的曲边界处理

研究了格子Boltzmann方法中实现曲边界条件的3种格式,对它们的精度和稳定性进行了分析和比较.通过二维Poiseuille流和等边三角域上空腔流的模拟,讨论了这3种格式的数值精度和稳定性.