A maple® package for the calculus of variations based on jet manifolds

This contribution presents a computer algebra package for Lagrangian systems with p???1 independent and q???1 dependent variables. The Lagrangian may depend on the partial derivatives up to the order n???0 of the dependent variables with respect to the independent ones. In the case of one independent variable, p?=?1, the package derives the equations of motion in the form of a system of q ordinary differential equations of order 2n, for p?>?1 the result is a system of q partial differential equation up to the order 2n. In addition the package determines all the required boundary conditions in the case of p???3 and n???2. Since the presented method uses the concept of jet manifolds, a short introduction to the notation of jet theory is provided. Two examples — the Timoshenko beam and the Kirchhoff plate — demonstrate the main features of the presented computer algebra based approach.     

Rapid and simultaneous determination of salvianolic acid A and salvianolic acid B by complex chromatography and study on related mechanism of coordination

Salvianolic acid A (Sal A) and salvianolic acid B (Sal B) are water-soluble phenolic acids in Danshen extract and they have high medicinal value. A rapid and novel complex high-performance liquid chromatography (HPLC) method has been developed and validated for the simultaneous determination of Sal A and Sal B within 10 min. The determination of Sal A and Sal B was carried out on a Waters Symmetry Shield RP18 column (5 μm, 3.9 mm × 150 mm), using methanol-deionized water (55:45, v/v, with 5 mmol L⁻¹ CaCl₂ and 1% acetic acid) as the mobile phase at the flow rate of 0.8 mL min⁻¹ within 10 min. The wavelength was set at 280 nm. It changed the peak sequence of Sal A and Sal B and improved their effect of determination by adding CaCl₂ in the mobile phase because Sal A and Sal B coordinated with Ca²⁺. The mechanism of coordination between Sal A, Sal B and Ca²⁺ has been studied by way of Fourier transform infrared spectroscopy (FTIR), electrospray ionization mass spectrometry (ESI-MS) and computer model. The possible structures of the complex and complex ratio are provided in this article. The experiments have facilitated the study of Sal A-Ca²⁺ complex, Sal B-Ca²⁺ complex and provide a theoretical basis for industrialized extraction of Sal A and Sal B in the future.     

Communication performance of d -meshes in molecular dynamics simulation

Communication algorithms, tailored for molecular dynamics simulation on d-meshes, are evaluated in terms of communication efficiency. It has been shown elsewhere that d-meshes are better than other regular topologies, e.g., hypercubes and standard toroidal 4-meshes, when compared in their diameter and average distance among nodes. Collective communication is needed in molecular dynamics simulation for the distribution of coordinates and calculation and distribution of new energies. We show that both collective communication patterns used in molecular dynamics can be efficiently solved with congestion-free algorithms for all-to-all communication based on store-and-forward routing and routing tables. Our results indicate that d-meshes compete with hypercubes in parallel computers. Therefore d-meshes can also be used as a communication upgrade of existing molecular dynamics simulation platforms and can be successfully applied to perform fast molecular dynamics simulation.     

FirmNet: the scope of firms and the allocation of task in a knowledge-based economy

The increasing knowledge intensity of jobs, typical of a knowledge economy, highlights the role of firms as integrators of know how and skills. As economic activity becomes mainly intellectual and requires the integration of specific and idiosyncratic skills, firms need to allocate skills to tasks and traditional hierarchical control may result increasingly ineffective. In this work, we explore under what circumstances networks of agents, which bear specific skills, may self-organize in order to complete tasks. We use a computer simulation approach and investigate how local interaction of agents, endowed with skills and individual decision-making rules, may produce aggregate network structure able to perform tasks. To design algorithms that mimic individual decision-making, we borrow from computer science literature and, in particular, from studies addressing protocols that produce cooperation in P2P networks. We found that self-organization depends on imitation of successful peers, competition among agents holding specific skills, and the structural features of, formal or informal, organizational networks embedding both professionals, holding skills, and project managers, holding access to jobs.

Behaviour approximated on subgroups

The recovery of behaviour from its approximation over substructures is fraught with pathology. Here the extent is considered to which the behaviour of a continuous function on a locally compact Abelian group can be approximated by its behaviour on proper closed subgroups. Known results are summarised when the behaviour concerns integrability and the group is the circle; then boundedness and other limiting behaviour ‘at infinity’ are considered for more general groups. It is shown that if a continuous function is bounded on each proper closed subgroup of a connected locally compact Abelian group then it is bounded on the whole group. As befits this Festschrift, the techniques are predominantly topological. In passing we reflect on criteria for the difficult problem of identifying ‘substructures’ in Computer Science.     

一类时滞分数阶计算机病毒模型的稳定性研究

本文研究一类改进的时滞分数阶计算机病毒模型正平衡点的稳定性问题.利用线性化方法和拉普拉斯变换获得模型对应的线性化系统的特征方程,通过讨论特征方程的根以及横截条件研究时滞和正平衡点稳定性之间的关系,推导了Hopf分支出现时时滞临界值的计算公式,并选择恰当的系统参数进行数值模拟以验证理论分析的合理性.     

线型缩聚反应的计算机模拟

缩聚反应是一类重要的高分子合成方法。其中最简单的反应为线型缩聚体系,它可分为两类,分别是含有两个可缩合的官能团的单体或单体对进行的相互缩合的体系。Flory在上世纪四十年代采用统计方法对该缩聚体系做过系统的理论研究,并在官能团等活性的假定下提出了著名的Flory分布函数,由此揭示了反应体系中数均聚合度xn、重均聚合度xw、不同聚合度分子的分布情况与反应程度p的关系。本文利用计算机模拟的方法,同样在官能团等活性的假定下模拟了线性缩聚反应的全反应过程,所得到的结果与用统计方法所得到的结果完全一致。本方法是对整个真实反应过程的直观模拟,对研究相似的以逐步聚合反应机理进行的反应具有普适性,并具有可拓展到模拟更真实的粘性聚合体系以及研究反应动力学的潜力。     

Analysis of SiC crystal sublimation growth by fully coupled compressible multi-phase flow simulation

A fully coupled compressible multi-phase flow solver was developed to effectively design a large furnace for producing large-size SiC crystals. Compressible effect, convection and buoyancy effects, flow coupling between argon gas and species, and the Stefan effect are included. A small and experimental furnace is used to validate the solver. First, the essentiality of 2D flow calculation and the significance of incorporating buoyancy effect and gas convection, the Stefan effect, and flow interaction between argon gas and species were investigated by numerical results. Then the effects of argon gas on deposition rate, growth rate, graphitization on the powder source, and supersaturation and stoichiometry on the seed were analyzed. Finally, the advantages of an extra chamber design were explained, and improvement of growth rate was validated by the present solver.