三块弯铁消色散磁聚焦结构最小发射度

通过采用二极铁之间色散函数的相空间匹配所带来的约束条件,从而无需依赖具体的磁聚焦结构,利用Mathematica软件进行计算,得到了在三块二极铁弯转半径相等情况下,两种应用普遍的三块弯铁消色散（TBA）磁聚焦结构的最小发射度所对应的最小结构比例参数。得到了在TBA结构三块二极铁长度及弯转半径任意的情况下,TBA结构能取得的最小结构比例参数,以及TBA结构中三块二极铁长度及弯转半径所要满足的关系。由于计算中无需考虑具体的磁聚焦结构,得到的理论结果及其分析过程具有较强的通用性。     

Lattices and Their Consistent Quantification

The order‐theoretic concept of lattices is introduced along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order‐theoretic structure. Symmetries, such as associativity, constrain consistent quantification, and lead to a constraint equation known as the sum rule. Distributivity in distributive lattices also constrains consistent quantification and leads to a product rule. The sum and product rules, which are familiar from, but not unique to, probability theory, arise from the fact that logical statements form a distributive (Boolean) lattice, which exhibits the requisite symmetries.     

一种基于约束概念格的恒星光谱数据自动分类方法

概念格是数据分析与知识提取的一种有效形式化工具,约束概念格是一种新的概念格结构,具有构造的时空复杂性低,所提取知识的实用性和针对性强等特点。针对海量恒星光谱自动分类任务,依据约束概念格结点外延与训练样本数据集等价划分之间的关系,通过引入外延支持度和划分支持度的概念,提出了一种基于约束概念格的恒星光谱数据分类规则挖掘方法,并采用SDSS恒星光谱数据集,实验验证了由该方法所提取出的分类规则具有较高的分类效率和分类正确率,从而为海量的恒星光谱数据自动分类提供了一种有效方法。     

基于~(87)Rb原子的大失谐光晶格的设计与操控

提出了一种基于~(87)Rb原子的大失谐光学晶格的设计方案,详细介绍了光晶格光束的校准、频率失谐的调整以及光强输出的控制方式.在磁光阱和偏振梯度冷却的基础上,研究了光学晶格的总光强和频率失谐等参数对原子装载的影响,实现了光晶格中冷原子的绝热装载与卸载.通过光强调制的方法,测量了光晶格的振动频率.光晶格的引入,使得温度降低为原有的1/3.涉及的系统设计和结论对其他碱金属原子光晶格的实验设计具有参考价值.     

Diffusion in Lorentz lattice gas cellular automata: The honeycomb and quasi-lattices compared with the square and triangular lattices

We study numerically the nature of the diffusion process on a honeycomb and a quasi-lattice, where a point particle, moving along the bonds of the lattice, scatters from randomly placed scatterers on the lattice sites according to strictly deterministic rules. For the honeycomb lattice fully occupied by fixed rotators two (symmetric) isolated critical points appear to be present, with the same hyperscaling relation as for the square and the triangular lattices. No such points appear to exist for the quasi-lattice. A comprehensive comparison is made with the behavior on the previously studied square and triangular lattices. A great variety of diffusive behavior is found, ranging from propagation, superdiffusion, normal, quasi-normal, and anomalous, to absence of diffusion. The influence of the scattering rules as well as of the lattice structure on the diffusive behavior of a point particle moving on the all lattices studied so far is summarized.     

Diffusion and propagation in triangular Lorentz lattice gas cellular automata

The diffusion process of point particles moving on regular triangular and random lattices, randomly occupied with stationary scatterers (a Lorentz lattice gas cellular automaton), is studied, for strictly deterministic scattering rules, as a function of the concentration of the scatterers. In addition to the normal and various kinds of retarded diffusion found before on the regular square lattice, straight-line propagation through the scatterers is observed.     

PARAMETRIC SIMULTONS IN ONE-DIMENSIONAL NONLINEAR LATTICES

Parametric simultaneous solitary wave (simulton) excitations are shown to be possible in nonlinear lattices. Taking a one-dimensional diatomic lattice with a cubic potential as an example, we consider the nonlinear coupling between the upper cut-off mode of acoustic branch (as a fundamental wave) and the upper cut-off mode of optical branch (as a second harmonic wave). Based on a quasi-discreteness approach the Karamzin－Sukhorukov equations for two slowly varying amplitudes of the fundamental and the second harmonic waves in the lattice are derived when the condition of second harmonic generation is satisfied. The lattice simulton solutions are given explicitly and the results show that these lattice simultons can be nonpropagating when the wave vectors of the fundamental wave and the second harmonic waves are exactly at π/a (where a is the lattice constant) and zero, respectively.     

基于布里渊区谱的二维光子晶格线性缺陷模式分析

结合均匀光子晶格的衍射关系和晶格中正负缺陷的布里渊区谱特性,探讨了光诱导二维光子晶格中线性缺陷模式的形成条件,对布里渊区中各点的缺陷模式进行了模拟分析,并得到了光子带隙结构中“嵌入点”X₁点的正、负缺陷模式.结果表明：对于二维缺陷,只有当衍射关系曲面中沿两个正交的横向波矢方向同时为正常（反常）衍射的区域才能存在正（负）缺陷模式;而对于一维缺陷,只要在一个横向波矢方向上存在正常（反常）衍射的区域就可以支持正（负）缺陷模式,因此在某些特殊点处,正和负的缺陷模式可以同时存在.X₁点正缺陷模式的存在预示着自聚焦非线性同样可以支持带内孤子.研究结果有助于对光子晶格中晶格孤子（特别是带内孤子）的理解和进一步研究. 关键词： 光诱导光子晶格 光子带隙 线性缺陷态     

Interval order and semiorder lattices

When a set of closed intervals of the reals is partially ordered by decreeing that A<B when A lies strictly to the left of B, the resulting structure is called an interval order. Semiorders may be viewed as interval orders that arise from closed intervals having a fixed length. The paper initiates a careful study of interval orders and semiorders that happen also to be lattices. A structure theory is obtained for a class of interval order lattices that includes all such lattices of finite length. Characterizations are given of when these lattices are modular or distributive, as well as when they are semiorders. The theory is of some interest because the completion by cuts of an interval order is necessarily an interval order lattice. Though it is shown that the completion by cuts of a semiorder need not be a semiorder, necessary and sufficient conditions are given for a lattice of finite length to be isomorphic to the completion by cuts of a semiorder.The author wishes to dedicate this paper to the memory of his late colleague Professor Charles H. Randall.     

Effects of Field Orientation on the Driven Lattice Gas

Steady states of the driven lattice gas (DLG) on triangular, hexagonal and square lattices with the field at several fixed orientations to the principal lattice vectors were studied by Monte Carlo simulation. In most cases a strong field suppressed change to a low-temperature ordered phase. On each lattice, one field orientation that caused nonequilibrium ordering was identified. On triangular and hexagonal lattices, dependence of energy and anisotropy on field strength was studied at those orientations. Anisotropic ordering along the field developed at intermediate temperatures under weak fields. Partial ordering along the field persisted to low temperature under strong fields.     

Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics

Kinetically constrained lattice models of glasses introduced by Kob and Andersen (KA) are analyzed. It is proved that only two behaviors are possible on hypercubic lattices: either ergodicity at all densities or trivial non-ergodicity, depending on the constraint parameter and the dimensionality. But in the ergodic cases, the dynamics is shown to be intrinsically cooperative at high densities giving rise to glassy dynamics as observed in simulations. The cooperativity is characterized by two length scales whose behavior controls finite-size effects: these are essential for interpreting simulations. In contrast to hypercubic lattices, on Bethe lattices KA models undergo a dynamical (jamming) phase transition at a critical density: this is characterized by diverging time and length scales and a discontinuous jump in the long-time limit of the density autocorrelation function. By analyzing generalized Bethe lattices (with loops) that interpolate between hypercubic lattices and standard Bethe lattices, the crossover between the dynamical transition that exists on these lattices and its absence in the hypercubic lattice limit is explored. Contact with earlier results are made via analysis of the related Fredrickson--Andersen models, followed by brief discussions of universality, of other approaches to glass transitions, and of some issues relevant for experiments.     

Replica symmetry breaking in the Ising spin glass model on Bethe-like lattices with loop

The Ising spin glass model on Bethe-like lattices (cactus lattices) is studied using replicas in the presence of a magnetic field. Parisi's order parameter function and the de Almeida–Thouless (AT) line are obtained close to the spin glass transition temperature. The results are compared with those for the Bethe lattice to see the effects of loops. The slope of the order parameter function diminishes considerably for both lattices compared with that for the Sherrington–Kirkpatrick (SK) model. The loci of the AT line for the cactus lattices and the Bethe lattice are above and below that for the SK model, respectively.     

Thermodynamic Transitions of Antiferromagnetic Ising Model on the Fractional Multi-branched Husimi Recursive Lattice

The multi-branched Husimi recursive lattice is extended to a virtual structure with fractional numbers of branches joined on one site. Although the lattice is undrawable in real space, the concept is consistent with regular Husimi lattice. The Ising spins of antiferromagnetic interaction on such a set of lattices are calculated to check the critical temperatures (T_c) and ideal glass transition temperatures (T_k) variation with fractional branch numbers. Besides the similar results of two solutions representing the stable state (crystal) and metastable state (supercooled liquid) and indicating the phase transition temperatures, the phase transitions show a well-defined shift with branch number variation. Therefore the fractional branch number as a parameter can be used as an adjusting tool in constructing a recursive lattice model to describe real systems.     

Discrete breathers — Advances in theory and applications

Nonlinear classical Hamiltonian lattices exhibit generic solutions — discrete breathers. They are time-periodic and (typically exponentially) localized in space. The lattices have discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. We will introduce the concept of these localized excitations and review their basic properties including dynamical and structural stability. We then focus on advances in the theory of discrete breathers in three directions — scattering of waves by these excitations, persistence of discrete breathers in long transient processes and thermal equilibrium, and their quantization. The second part of this review is devoted to a detailed discussion of recent experimental observations and studies of discrete breathers, including theoretical modelling of these experimental situations on the basis of the general theory of discrete breathers. In particular we will focus on their detection in Josephson junction networks, arrays of coupled nonlinear optical waveguides, Bose–Einstein condensates loaded on optical lattices, antiferromagnetic layered structures, PtCl based single crystals and driven micromechanical cantilever arrays.     

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the triangular,honeycomb and kagome lattices

In order to analyse the lattice dependence of ferromagnetism in the two-dimensional Hubbard model we investigate the instability of the fully polarised ferromagnetic ground state (Nagaoka state) on the triangular, honeycomb and kagome lattices. We mainly focus on the local instability, applying single spin flip variational wave functions which include majority spin correlation effects. The question of global instability and phase separation is addressed in the framework of Hartree-Fock theory. We find a strong tendency towards Nagaoka ferromagnetism on the non-bipartite lattices (triangular, kagome) for more than half filling. For the triangular lattice we find the Nagaoka state to be unstable above a critical density of n = 1.887 at U = ∞, thereby significantly improving former variational results. For the kagome lattice the region where ferromagnetism prevails in the phase diagram widely exceeds the flat band regime. Our results even allow the stability of the Nagaoka state in a small region below half filling. In the case of the bipartite honeycomb lattice several disconnected regions are left for a possible Nagaoka ground state.     

Hamiltonian walks and polymer configurations

Kasteleyn's treatment of the hamiltonian walk problem on lattice graphs is briefly reviewed. The asymptotic behaviour of the number of hamiltonian walks on the kth covering of a closed oriented lattice graph is expressed in terms of the asymptotic behaviour of the number of oriented trees on the lattice graph. Asymptotic results on the enumeration of hamiltonian walks are presented for the covering and underlying lattices of the Manhattan oriented square lattice, and the covering lattices of certain orientations of the diamond and cubic lattices. The effect of boundary conditions is examined.Relations are established between hamiltonian walks and close-packed polymer configurations. An analysis of the assumptions in lattice models of the melting and glass transitions in polymers shows that the Flory-Huggins approximation underestimates the total number of polymer configurations, but that corrections can be made without altering the principal features of the models thus permitting better agreement with the experimental data.     

Magnetic dipolar ordering on geometrically frustrated brick-shaped lattices

The magnetic ordering of frustrated arrays of nanoscale islands can be strongly influenced by the array patterns. We theoretically present three kinds of artificial geometrically frustrated systems with different brick-shaped geometries, defined as brick-shaped lattices, and investigate their magnetic dipolar ordering at the ground state using the Monte Carlo method. The simulated results show that the magnetic ordering of three brick-shaped frustrated lattices depends strongly on the strength of dipolar interactions, depending on the lattice spacing. It is found that the long-range dipolar interactions tend to suppress the long-range ordered state and induce the short-range quasi-ice state at each vertex of the lattices. In addition, the correlations for neighboring spin pairs are closely related to not only the dipolar coupling strength but also the geometry of the lattices.     

Lattices of Quantum Automata

We defined and studied three different types of lattice-valued finite state quantum automata (LQA) and four different kinds of LQA operations, discussed their advantages, disadvantages, and various properties. There are four major results obtained in this paper. First, no one of the above mentioned LQA follows the law of lattice value conservation. Second, the theorem of classical automata theory, that each nondeterministic finite state automaton has an equivalent deterministic one, is not necessarily valid for finite state quantum automata. Third, we proved the existence of semilattices and also lattices formed by different types of LQA. Fourth, there are tight relations between properties of the original lattice l and those of the l-valued lattice formed by LQA.     

Noncommutative Symmetric Differences in Orthomodular Lattices

We deal with the following question: What is the proper way to introduce symmetric difference in orthomodular lattices? Imposing two natural conditions on this operation, six possibilities remain: the two (commutative) normal forms of the symmetric difference in Boolean algebras and four noncommutative terms. It turns out that in many respects the noncommutative forms, though more complex with respect to the lattice operations, in their properties are much nearer to the symmetric difference in Boolean algebras than the commutative terms. As application we demonstrate the usefulness of noncommutative symmetric differences in the context of congruence relations.