Packing into the smallest square: Worst-case analysis of lower bounds

We address the problem of packing a given set of rectangles into the minimum size square. We consider three versions of the problem, arising when the rectangles (i) are squares; (ii) have a fixed orientation; (iii) can be rotated by 90. For each case we study lower bounds, and analyze their worst-case performance ratio. In addition, we evaluate through computational experiments their average performance on instances from the literature.     

精品课程教材《高分子物理实验》建设的体会——三个及时融入

中国科学技术大学"高分子物理实验"课程是2006年安徽省精品课程,作者结合教学研究和精品课程建设经验,总结出了"三个及时融入"的教材建设理念,本文结合实例对该理念的具体含义进行了阐述.     

Excess volumes of ternary mixtures of N,N-dimethylformamide-diethyl ketone-1-alkanols at 303.15K

Volume changes on mixing of ternary liquid mixtures of N,N-dimethylformamide and diethyl ketone with 1-alkanols have been measured as a function of composition at 303.15 K. The alkanols include 1-propanol, 1-butanol, 1-pentanol and 1-hexanol. The measured V^E values are negative in the mixtures of N,N-dimethylformamide, diethyl ketone and 1-propanol, or 1-butanol. The V^E data exhibits an inversion in sign in the mixture containing 1-pentanol and positive excess volumes are observed in the mixture containing 1-hexanol. The measured data are compared with predicted values based upon empirical relations. The excess volume for the binary mixture of N,N-dimethylformamide with diethyl ketone has been measured over the entire range of composition at 303.15 K. The V^E values are negative for the binary mixture.     

基于创新能力培养的化学专业本科实验教学新体系的构建与实践

课程体系是人才培养的载体。为了更好地培养拔尖创新人才,南京大学化学国家级实验教学示范中心依据化学学科的特点和发展趋势,以科学内容的内在联系和研究规律为主线构建了“化学实验基础?化学合成与表征+化学原理与测量?化学功能分子实验+化学生物学综合实验+基于项目的研究实验”实验课程新体系,按照一流课程建设要求(高阶性、创新性和挑战度)对实验教学内容进行了优化,并建立起与之相适应的实验教学平台。新课程体系综合考虑了化学一级学科的整体性和关联学科的交叉性,在南京大学化学化工学院“拔尖计划”和“强基计划”学生中实施,教学效果显著。     

Molar excess free energy of mixing of 1-propanol or 2-propanol with cyclohexane at 298.15 and 308.15 K in terms of association model with a Flory contribution term

Excess molar Gibbs free energies of mixing for 1-propanol or 2-propanol + cyclohexane over the whole composition range at 298.15 and 308.15 K have been calculated from vapour pressure data measured by static method. The data have been analysed in terms of a Mecke-Kempter association model with a Flory contribution term.     

超声复合振动系统中的“局部共振”现象实验研究

本从实验的角度出发,对超声复合振动系统中细长杆的“局部共振”现象进行了较为精确的测量,主要研究了细杆长度与谐振频率之间的关系,超声振子对“局部共振”的影响,以及“局部共振”中细杆长度对振幅的影响,从而为深入研究“局部共振”现象产生的机理提供了更多的依据。     

Quadratic convex reformulations for quadratic 0–1 programming

This is a summary of the author’s PhD thesis supervised by A. Billionnet and S. Elloumi and defended on November 2006 at the CNAM, Paris (Conservatoire National des Arts et Métiers). The thesis is written in French and is available from http://www.cedric.cnam.fr/PUBLIS/RC1115. This work deals with exact solution methods based on reformulations for quadratic 0–1 programs under linear constraints. These problems are generally not convex; more precisely, the associated continuous relaxation is not a convex problem. We developed approaches with the aim of making the initial problem convex and of obtaining a good lower bound by continuous relaxation. The main contribution is a general method (called QCR) that we implemented and applied to classical combinatorial optimization problems.      

Experiment and modelling of birefringent flows using commercial CFD code

It is well-known that certain fluids are birefringent and when flows are viewed in polarised light interference fringes are observed. The fringes are caused by a phase shift in the light passing through the fluid and are proportional to the integral of the maximum shear strains in the fluid. In order to understand what is happening within the three dimensional flow and overcome the difficulties due to this integration, additional computational or experimental information is needed.

In this work, a commercially available computer code (Fluent) is used for the first time to model the flows. The flow data are then exported to a spreadsheet where the shear rates are integrated across the field and then banded for graphical output. The results from this are then compared to results generated from birefringent flow experiments and the agreement is found to be good since the modelled fringes show the same patterns as those in the experiment. This novel use of computational and experimental techniques together will allow quantitative analysis of three-dimensional flows in the future.

Currently, there are still a lot of empirical variables involved in fitting the computational fringes to the experiment, but the results of this preliminary study show that this is a promising approach to this type of problem.     

Flow in a symmetric channel with an expanded section

We consider the flow in a symmetric two-dimensional channel with an expanded section. By examining the effect of varying the ratio of the inlet and outlet channel widths, we are able to place the earlier results of Mizushima et al. (Phys. Fluids 8 (1996) 2933) within an entire spectrum of nonlinear phenomena. Laboratory experiments support predicted behaviour in two regions of parameter space and highlight the importance of imperfections in the experimental apparatus.     

Cavitation onset caused by a dynamic pressure wave in liquid pipelines

When liquids flow in the pipelines, the onset of cavitation can be characterized by a variant of the Euler number known as the cavitation number (CN), which is based on the velocity and denoted by C in this paper. Conventionally, cavitation is considered to be induced when C ~ 1. However, experimental observations and several pipe bursts indicate that the CN may incorrectly predict the onset of cavitation. For example, when leakage occurs in the pipeline or a valve in the pipeline is opened, the resultant pressure loss generates a dynamic pressure wave with a small amplitude, which may lead to bubble formation, even though C ~ 1 is not satisfied. Hence, this paper proposes another CN based on the amplitude of the generated dynamic pressure wave, rather than the velocity, for ascertaining the onset of cavitation. The validity of the proposed CN was verified through experiments and a case study. The results indicated that the proposed CN can be effectively used for cavitation prediction induced by pressure fluctuations and for investigating phenomena such as pressure fluctuation, leakage, and corrosion in liquid pipelines, tanks, and pressure vessels, as well as the safety design of liquefied natural gas tanks and tankers.