Fabrication of stable, transparent and superhydrophobic nanocomposite films with polystyrene functionalized carbon nanotubes

Stable, transparent and superhydrophobic carbon nanotube (CNT) nanocomposite films were fabricated by one-step spray casting process using the polystyrene functionalized CNTs, which were prepared by “living” free-radical polymerization and analyzed by means of infrared spectroscopy and thermal gravimetric analysis. The CNT film has a high water contact angle of 160° and a sliding angle of less than 3°. The surface topography of the fabricated film was characterized by field emission scanning electron microscopy. The transparency of the CNT film was investigated by UV–vis spectroscopy. The result shows that the CNT film has light transmittance of about 78% in the visible light region.     

The constructal unification of biological and geophysical design

Here we show that the emergence of scaling laws in inanimate (geophysical) flow systems is analogous to the emergence of allometric laws in animate (biological) flow systems, and that features of evolutionary “design” in nature can be predicted based on a principle of physics (the constructal law): “For a finite-size flow system to persist in time (to live) it must evolve in such a way that it provides easier and easier access to its currents”, meaning that the configuration and function of flow systems change over time in a predictable way that improves function, distributes imperfection, and creates geometries that best arrange high and low resistance areas or volumes. This theoretical unification of the phenomena of animate and inanimate flow design generation is illustrated with examples from biology (lung design, animal locomotion) and the physics of fluid flow (river basins, turbulent flow structure, self-lubrication). The place of this design-generation principle as a self-standing law in thermodynamics is discussed. Natural flow systems evolve by acquiring flow configuration in a definite direction in time: existing configurations are replaced by easier flowing configurations.     

自适应间断有限元方法求解双曲守恒律方程

研究自适应Runge-Kutta间断Galerkin (RKDG)方法求解双曲守恒律方程组,并提出两种生成相容三角形网格的自适应算法.第一种算法适用于规则网格,实现简单、计算速度快.第二种算法基于非结构网格,设计一类基于间断界面的自适应网格加密策略,方法灵活高效.两种方法都具有令人满意的计算效果,而且降低了RKDG的计算量.     

Elasticity transition and loop formation in vibrated bead chains: A simulation of polymer chains

By measuring the distribution function of the end-to-end distance, we find that strongly shaken bead chains exhibit many properties, such as the rigid-rod-to-Gaussian chain transition, scaling, fast drop of loop formation probability in the short-chain regime, and enhancement of loop formation probability for kinked chains, of long-chain polymers. Though there is difference in local details between our chains and the worm-like chains, our results are consistent with recent calculations based on the worm-like chain model in many respects.     

Incompatibility networks as models of scale-free small-world graphs

We make a mapping from Sierpinski fractals to a new class of networks, the incompatibility networks, which are scale-free, small-world, disassortative, and maximal planar graphs. Some relevant characteristics of the networks such as degree distribution, clustering coefficient, average path length, and degree correlations are computed analytically and found to be peculiarly rich. The method of network representation can be applied to some real-life systems making it possible to study the complexity of real networked systems within the framework of complex network theory.     

Symmetry Analysis and Conservation Laws to the(2+1)-Dimensional Coupled Nonlinear Extension of the Reaction-Diffusion Equation

In this paper, a detailed Lie symmetry analysis of the(2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple direct method,which is equivalent to Lie point symmetry group actually. Similarity reduction and some exact solutions of the original equation are obtained based on the optimal system of one-dimensional subalgebras. In addition, conservation laws are constructed by employing the new conservation theorem.     

On the existence of stable bundles with prescribed Chern classes on Calabi–Yau threefolds

We prove a case of the conjecture of Douglas, Reinbacher and Yau about the existence of stable vector bundles with prescribed Chern classes on a Calabi–Yau threefold. For this purpose we prove the existence of certain stable vector bundle extensions over elliptically fibered Calabi–Yau threefolds.     

Continuous Correspondence of Conservation Laws of the Semi-discrete AKNS System

In this paper we investigate the semi-discrete Ablowitz–Kaup–Newell–Segur (sdAKNS) hierarchy, and specifically their Lax pairs and infinitely many conservation laws, as well as the corresponding continuum limits. The infinitely many conserved densities derived from the Ablowitz-Ladik spectral problem are trivial, in the sense that all of them are shown to reduce to the first conserved density of the AKNS hierarchy in the continuum limit. We derive new and nontrivial infinitely many conservation laws for the sdAKNS hierarchy, and also the explicit combinatorial relations between the known conservation laws and our new ones. By performing a uniform continuum limit, the new conservation laws of the sdAKNS system are then matched with their counterparts of the continuous AKNS system.     

CONSERVATION LAWS FOR HEATED LAMINAR RADIAL LIQUID AND FREE JETS

The conserved quantities for the heated radial liquid jet and the heated radial free jet are established by using conservation laws. The flow in a heated radial jet is described by Prandtl's momentum boundary layer equation, the continuity equation and the energy equation. Viscous dissipation is neglected. The multiplier approach is used to derive the conservation laws for the system of three equations for the velocity components and the temperature and three conserved vectors are obtained. The conservation laws for the system of two partial differential equations for the stream function formulation are also computed by the multiplier approach and three conserved vectors are obtained. One of these is a non-local conserved vector for the system. The conserved quantities for the heated radial liquid jet and the heated radial free jet, emitted into a stationary fluid of uniform temperature θ_∞, are derived by integrating the conservation laws across the jet.