Development of LBGK and incompressible LBGK‐based lattice Boltzmann flux solvers for simulation of incompressible flows

This paper presents lattice Boltzmann Bhatnagar–Gross–Krook (LBGK) model and incompressible LBGK model‐based lattice Boltzmann flux solvers (LBFS) for simulation of incompressible flows. LBFS applies the finite volume method to directly discretize the governing differential equations recovered by lattice Boltzmann equations. The fluxes of LBFS at each cell interface are evaluated by local reconstruction of lattice Boltzmann solution. Because LBFS is applied locally at each cell interface independently, it removes the major drawbacks of conventional lattice Boltzmann method such as lattice uniformity, coupling between mesh spacing, and time interval. With LBGK and incompressible LBGK models, LBFS are examined by simulating decaying vortex flow, polar cavity flow, plane Poiseuille flow, Womersley flow, and double shear flows. The obtained numerical results show that both the LBGK and incompressible LBGK‐based LBFS have the second order of accuracy and high computational efficiency on nonuniform grids. Furthermore, LBFS with both LBGK models are also stable for the double shear flows at a high Reynolds number of 10⁵. However, for the pressure‐driven plane Poiseuille flow, when the pressure gradient is increased, the relative error associated with LBGK model grows faster than that associated with incompressible LBGK model. It seems that the incompressible LBGK‐based LBFS is more suitable for simulating incompressible flows with large pressure gradients. Copyright © 2014 John Wiley & Sons, Ltd.     

南极假丝酵母在纳米聚苯乙烯上的共价固载及其在微波辅助酯化反应中的应用（英文）

Nanopolystyrene was used as a solid support for the covalent immobilization of Candida antarctica lipase B(Cal B) using the photoreactive reagent 1‐fluoro‐2‐nitro‐4‐azido benzene(FNAB) as a cou‐pling reagent. The obtained derivative was then used as a biocatalyst in a microwave assisted ester‐ification experiment. Factors such as contact time, pH, and enzyme concentration were investigated during immobilization. The hydrolytic activity, thermal, and operational stability of immobi‐lized‐Cal B were determined. The maximum immobilized yield(218 μg/mg support) obtained at pH 6.8 exhibited optimum hydrolytic activity(4.42 × 103 mU p‐nitrophenol/min). The thermal stability of Cal B improved significantly when it was immobilized at pH 10, however, the immobilized yield was very low(93.6 μg/mg support). The immobilized‐Cal B prepared at pH 6.8 and pH 10 retained 50% of its initial activity after incubation periods of 14 and 16 h, respectively, at 60 °C. The opera‐tional stability was investigated for the microwave assisted esterification of oleic acid with metha‐nol. Immobilized‐Cal B retained 50% of its initial activity after 15 batch cycles in the micro‐wave‐assisted esterification. The esterification time was notably reduced under microwave irradia‐tion. The combined use of a biocatalyst and microwave heating is thus an alternative total green synthesis process.     

Motion Control of Micro‐/Nanomotors

As we progress towards employing self‐propelled micro‐/nanomotors in envisioned applications such as cargo delivery, environmental remediation, and therapeutic treatments, precise control of the micro‐/nanomotors direction and their speed is essential. In this Review, major emerging approaches utilized for the motion control of micro‐/nanomotors have been discussed, together with the lastest publications describing these approaches. Future studies could incorporate investigations on micro‐/nanomotors motion control in a real‐world environment in which matrix complexity might disrupt successful manipulation of these small‐scale devices.     

A computational method for a class of non-standard time optimal control problems involving multiple time horizons

In this paper, we consider a class of non-standard time optimal control problems involving a dynamical system consisting of multiple subsystems evolving over different time horizons. Different subsystems are required to reach their respective target sets at different termination times. The goal is to minimize the maximum of these termination times. By introducing a discrete variable to represent the system termination ordering, we reformulate this problem as a discrete optimization problem. A discrete filled function method is developed to solve this discrete optimization problem. For illustration, a numerical example is solved.     

N-Heterocyclic carbene catalyzed C-glycosylation: a concise approach from Stetter reaction

Described herein is the first example of an organocatalytic approach for acylanion addition to the anomeric carbon of 2-nitroglucal using an N-heterocyclic carbene catalyst. Control over the reaction conditions gives β-selective and nitro-eliminated C-glycosides, providing opportunities to produce new classes of C-glycoside.     

Subdifferential and optimality conditions for the difference of set-valued mappings

In this paper, an existence theorem of the subgradients for set-valued mappings, which introduced by Borwein (Math Scand 48:189?C204, 1981), and relations between this subdifferential and the subdifferential introduced by Baier and Jahn (J Optim Theory Appl 100:233?C240, 1999), are obtained. By using the concept of this subdifferential, the sufficient optimality conditions for generalized D.C. multiobjective optimization problems are established. And the necessary optimality conditions, which are the generalizations of that in Gadhi (Positivity 9:687?C703, 2005), are also established. Moreover, by using a special scalarization function, a real set-valued optimization problem is introduced and the equivalent relations between the solutions are proved for the real set-valued optimization problem and a generalized D.C. multiobjective optimization problem.     

Structures and Chromaticity of Extremal 3-Colourable Sparse Graphs

 Assume that G is a 3-colourable connected graph with e(G) = 2v(G) −k, where k≥ 4. It has been shown that s ₃(G) ≥ 2 ^{k −3}, where s _r (G) = P(G,r)/r! for any positive integer r and P(G, λ) is the chromatic polynomial of G. In this paper, we prove that if G is 2-connected and s ₃(G) < 2 ^{k −2}, then G contains at most v(G) −k triangles; and the upper bound is attained only if G is a graph obtained by replacing each edge in the k-cycle C _k by a 2-tree. By using this result, we settle the problem of determining if W(n, s) is χ-unique, where W(n, s) is the graph obtained from the wheel W _n by deleting all but s consecutive spokes. Received: January 29, 1999 Final version received: April 8, 2000     

Liouville Action and Weil-Petersson Metric on Deformation Spaces, Global Kleinian Reciprocity and Holography

We rigorously define the Liouville action functional for the finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that classical action – the critical value of the Liouville action functional, considered as a function on the quasi-Fuchsian deformation space, is an antiderivative of a 1-form given by the difference of Fuchsian and quasi-Fuchsian projective connections. This result can be considered as global quasi-Fuchsian reciprocity which implies McMullen's quasi-Fuchsian reciprocity. We prove that the classical action is a Kähler potential of the Weil-Petersson metric. We also prove that the Liouville action functional satisfies holography principle, i.e., it is a regularized limit of the hyperbolic volume of a 3-manifold associated with a quasi-Fuchsian group. We generalize these results to a large class of Kleinian groups including finitely generated, purely loxodromic Schottky and quasi-Fuchsian groups, and their free combinations.