Effect of Interchain Coupling on Quantum Lattice Fluctuation and Fluctuation Induced Interchain Order Transition in Trans-polyacetylene

Based on the modified Su-Schrieffer-Heeger Harniltonian and by adding the interchain hopping term,we consider the effect of interchain coupling on quantum lattice fluctuation in trans-polyacetylene.It has been found that the interchain coupling does not always weaken quantum lattice fluctuation.After overcoming a barrier of 1 eV or so,the quantum lattice fluctuation can induce a transition of interchain order.The physical meaning of these features is discussed.

Tunneling dynamics of Bose-Einstein condensates with higher-order interactions in optical lattice

The nonlinear Landau Zener tunneling and nonlinear Rabi oscillations of Bose-Einstein condensate （BEC） with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters （i.e., the modulation amplitude and frequency） and the strength of periodic potential.

A study on distributive and modular lattice ordered fuzzy soft group and its duality

Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft group is the generalization of soft group. Abdulkadir Aygunoglu and Halis Aygun introduced the notion of fuzzy soft groups in 2009[1]. In this paper, the concept of lattice ordered fuzzy soft groups and its duality has been introduced. Then distributive and modular lattice ordered fuzzy soft groups are analysed. The objective of this paper is to study the lattice theory over the collection of fuzzy soft group in a parametric manner. Some pertinent properties have been analysed and hence established duality principle.

Effects of anharmonic lattice distortion on orbital and magnetic orderings in KCuF_3

Lattice, magnetic and orbital structures in KCuF3 are self-consistently determined by our cluster self-consistent field approach based on a spin-orbital-lattice Hamiltonian. Two stable structures are obtained and found to be degenerate, which confirms the presence of the coexistent phases observed experimentally. We clearly show that due to the inherent frustration, the ground state of the system only with the superexchange interaction is degenerate; while the Jahn-Teller distortion, especially the anharmonic effect, stabilizes the orbital ordered phase at about 23% in the x2-y2 orbit and at 77% in the 3z2-r2 orbit. Meanwhile the magnetic moment of Cu is considerably reduced to 0.56μB, and magnetic coupling strengths are highly anisotropic, Jx/Jxy ≈ 18. These results are in good agreement with the experiments, implying that the anharmonic Jahn-Teller effect plays an essential role in stabilising the orbital ordered ground state of KCuF3.

A mass-conserved multiphase lattice Boltzmann method based on high-order difference

The Z–S–C multiphase lattice Boltzmann model [Zheng, Shu, and Chew(ZSC), J. Comput. Phys. 218, 353(2006)]is favored due to its good stability, high efficiency, and large density ratio. However, in terms of mass conservation, this model is not satisfactory during the simulation computations. In this paper, a mass correction is introduced into the ZSC model to make up the mass leakage, while a high-order difference is used to calculate the gradient of the order parameter to improve the accuracy. To verify the improved model, several three-dimensional multiphase flow simulations are carried out,including a bubble in a stationary flow, the merging of two bubbles, and the bubble rising under buoyancy. The numerical simulations show that the results from the present model are in good agreement with those from previous experiments and simulations. The present model not only retains the good properties of the original ZSC model, but also achieves the mass conservation and higher accuracy.

Lattice Boltzmann simulations of high-order statistics in isotropic turbulent flows

The lattice Boltzmann method （LBM） is coupled with the multiple-relaxation- time （MRT） collision model and the three-dimensional 19-discrete-velocity （D3Q19） model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high- order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investi- gated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity （ESS） method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This valida~ tion provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.

Orientational Order of C_(60) Molecules in Low-dimensional Lattices

The orientational order is an important concept of the materials composed of large molecules or clusters. Using high-resolution scanning tunneling microscopy, we have studied the orientational order of two kinds of typical low-dimensional C60 lattices: two-dimensional molecules array and C60(111) multi-layer film surface. Due to the change of the crystal field, their orientational orders are distinctly different from those in bulk system, and some unique phenomena appear.

Logical Properties of Lattice Filter of Lattice Implication Algebra

Some new properties of lattice filters are presented based on the order-preserving mapping and lattice homomorphism, and two necessary and sufficient conditions for lattice filters under the chain type are given. Then, the relations between lattice filter and lattice implication algebras （LIAs）, i. e., the relations between lattice filter and LIA-filters, and the related properties are investigated. In addition, three necessary and sufficient conditions for LIA-filters are discussed. The obtained results may serve as some theoretical supports to lattice-valued logical system.

DNA extraction method selection for agricultural soil using TOPSIS multiple criteria decision-making model

There is an increased interest in the extraction of nucleic acids from various environmental samples since culture-independent molecular techniques contribute to deepen and broaden the understanding of a greater portion of uncultivable microorganisms. Due to difficulties to select the optimum DNA extraction method in view of downstream molecular analyses, this article presents a straightforward mathematical framework for comparing some of the most commonly used methods. Four commercial DNA extraction kits and two physical-chemical methods (bead-beating and freeze-thaw) were compared for the extraction of DNA under several quantitative DNA analysis criteria: yield of extraction, purity of extracted DNA (A260/280 and A260/230 ratios), degradation degree of DNA, easiness of PCR amplification, duration of extraction, and cost per extraction. From a practical point of view, it is unlikely that a single DNA extraction strategy can be optimum for all selected criteria. Hence, a systematic Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was employed to compare the methods. The PowerSoil? DNA Isolation Kit was systematically defined as the best performing method for extracting DNA from soil samples. More specifically, for soil:manure and soil:manure:biochar mixtures, the PowerSoil?DNA Isolation Kit method performed best, while for neat soil samples its alternative version gained the first rank.

SIMPLE LATTICE BOLTZMANN MODEL FOR TRAFFIC FLOWS

A lattice Boltzmann model with 5-bit lattice for traffic flows is proposed. Using the Chapman-Enskog expansion and multi-scale technique, we obtain the higher-order moments of equilibrium distribution function. A simple traffic light problem is simulated by using the present lattice Boltzmann model, and the result agrees well with analytical solution.

New Decision-Making Technique Based on Hurwicz Criteria for Fuzzy Ranking

Efficient decision-making remains an open challenge in the research community,and many researchers are working to improve accuracy through the use of various computational techniques.In this case,the fuzzification and defuzzification processes can be very useful.Defuzzification is an effective process to get a single number from the output of a fuzzy set.Considering defuzzification as a center point of this research paper,to analyze and understand the effect of different types of vehicles according to their performance.In this paper,the multi-criteria decision-making(MCDM)process under uncertainty and defuzzification is discussed by using the center of the area(COA)or centroidmethod.Further,to find the best solution,Hurwicz criteria are used on the defuzzified data.Anewdecision-making technique is proposed using Hurwicz criteria for triangular and trapezoidal fuzzy numbers.The proposed technique considers all types of decision makers’perspectives such as optimistic,neutral,and pessimistic which is crucial in solving decisionmaking problems.A simple case study is used to demonstrate and discuss the Centroid Method and Hurwicz Criteria for measuring risk attitudes among decision-makers.The significance of the proposed defuzzification method is demonstrated by comparing it to previous defuzzification procedures with its application.

Recent Results on Weakly Compact Operators on Banach Lattices

There have been many really positive results co ncerning the weakly compact operators on Banach lattices in terms of their order structure as well as in many respects. This paper will survey some known recent results in this area.

Generalized Topological Molecular Lattices

The aim of this paper is to introduce the concept of generalized topological molecular lattices briefly GTMLs as a generalization of Wang’s topological molecular lattices TMLs, Császár’s setpoint generalized topological spaces and lattice valued generalized topological spaces. Some notions such as continuous GOHs, convergence theory and separation axioms are introduced. Moreover, the relations among them are investigated.

Lattice of Finite Group Actions on Prism Manifolds

The set of finite group actions (up to equivalence) which operate on a prism manifold M, preserve a Heegaard Klein bottle and have a fixed orbifold quotient type, form a partially ordered set. We describe the partial ordering of these actions by relating them to certain sets of ordered pairs of integers. There are seven possible orbifold quotient types, and for any fixed quotient type we show that the partially ordered set is isomorphic to a union of distributive lattices of a certain type. We give necessary and sufficent conditions, for these partially ordered sets to be isomorphic and to be a union of Boolean algebras.

Lattice Theory for Finite Dimensional Hilbert Space with Variables in Z_d

In this work, join and meet algebraic structure which exists in non-near-linear finite geometry are discussed. Lines in non-near-linear finite geometry ?were expressed as products of lines in near-linear finite geometry ?(where?p?is a prime). An existence of lattice between any pair of near-linear finite geometry ?of ?is confirmed. For q|d, a one-to-one correspondence between the set of subgeometry ?of ?and finite geometry ?from the subsets of the set {D(d)}?of divisors of d?(where each divisor represents a finite geometry) and set of subsystems {∏(q)}?(with variables in Zq) of a finite quantum system ∏(d)?with variables in Zd?and a finite system from the subsets of the set of divisors of d?is established.

Lattice Implication Algebrasand MV-algebras

Lattice implication algebras is an algebraic structure which is established by combining lattice and implication algebras. In this paper,the relationship between lattice implication algebras and MV algebra was discussed,and then proved that both of the categorys of the two algebras are categorical equivalence. Finally,the infinitely distributivity in lattice implication algebras were proved.

船舶住舱辐射空调送回风方式格序优选研究

[目的]旨在研究住舱内部环境对人员生活舒适度和工作效率的影响,提高和改善船舶空调系统的热舒适性。[方法]对典型船舶单人住舱的异侧上送下回、同侧上送下回、异侧下送上回以及同侧下送上回4种送回风方式,使用Airpak软件对住舱内的温度场、湿度、PMV-PPD和空气龄等参数进行仿真模拟分析。[结果]结果表明:采用异侧上送下回送风的室温可恒定于24℃,湿度保持在50%左右且湿度场分布更为均匀,PMV分布更均匀且其值趋于0,空气龄PPD在舱内的分布更为均匀且数值很小。[结论]运用格序理论优选原理,在船舶单人住舱中,异侧上送下回的送回风方式为优选方案。

向量格中关于拉格朗日乘子存在性的证明

通过研究向量格中的Hahn-Banach定理,利用线性算子扩张的一般结果,进一步给出向量格中拉格朗日乘子存在性的证明.

分数阶Navier-Stokes方程的格子Boltzmann方法

对于分数阶Navier-Stokes方程的数值求解问题,首先将该方程进行离散化处理,然后构造D1Q3格子Boltzmann模型,并采用Taylor展开和Chapman-Enskog多尺度展开等技术恢复宏观方程,同时推导出该模型平衡态分布函数的表达式。最后根据一维的两个数值算例对方程进行数值模拟以及误差分析,并将得到的数值解与精确解进行比较,从而验证格子Boltzmann方法的准确性与有效性。