Average-weight-controlled bin-oriented heuristics for the one-dimensional bin-packing problem

Bin-oriented heuristics for one-dimensional bin-packing problem construct solutions by packing one bin at a time. Several such heuristics consider two or more subsets for each bin and pack the one with the largest total weight. These heuristics sometimes generate poor solutions, due to a tendency to use many small items early in the process. To address this problem, we propose a method of controlling the average weight of items packed by bin-oriented heuristics. Constructive heuristics and an improvement heuristic based on this approach are introduced. Additionally, reduction methods for bin-oriented heuristics are presented. The results of an extensive computational study show that: (1) controlling average weight significantly improves solutions and reduces computation time of bin-oriented heuristics; (2) reduction methods improve solutions and processing times of some bin-oriented heuristics; and (3) the new improvement heuristic outperforms all other known complex heuristics, in terms of both average solution quality and computation time.     

N-d维广义Brownian单的像集一致Packing测度和一致Packing维数

我们获得了Ｎ－ｄ维广义Ｂｒｏｗｎｉａｎ单的像集的一致Ｐａｃｋｉｎｇ测度和一致Ｐａｃｋｉｎｇ维数。     

A first principles explanation for the experimentally observed increase in A-term band broadening in small domain silica monoliths and other chromatographic supports

The present computational study illustrates how the existence of a residual lower limit on the variance of the skeleton and through-pore size of monolithic columns can be expected to severely compromise the possibility to prepare well-performing small domain monolithic columns. Adopting rather conservative estimates for the minimal standard deviation on the pore and the skeleton size (0.2 and 0.04 microm, respectively), the presented calculations show that, if such a fixed lower limit on the size variance exists, it will be impossible to decrease the A-term band broadening below a given critical value, no matter how small the domain size is made. From a given critical domain size value on, any attempt to further decrease the domain size without being able to co-reduce the size variance can be expected to be counterproductive and leads to an increase instead of to a further decrease of the plate heights.     

化工原理填料吸收塔与板式精馏塔计算问题类比教学的探讨

Analogy teaching of calculation of packing absorption column and plate tower of distillation was studied in this paper. Firstly, a detailed analogy of the above calculation problems was studied according to the frame of calculation type, calculation basis, quantitative calculation and qualitative analysis. Secondly, the qualitative analysis of the above calculations was used as examples to illustrate the analysis methodology. Students could master very well the sameness and difference of the calculation of absorption and distillation through analogy teaching.     

Statistical analysis of packed beds,the origin of short-range disorder,and its impact on eddy dispersion

We quantified the microstructural disorder of packed beds and correlated it with the resulting eddy dispersion. For this purpose we designed a set of bulk (unconfined) monodisperse random sphere packings with a systematic, protocol-dependent degree of microstructural heterogeneity, covering a porosity range from the random-close to the random-loose packing limit (? = 0.366–0.46). With the precise knowledge of particle positions, size, and shape we conducted a Voronoï tessellation of all packings and correlated the statistical moments of the Voronoï volume distributions (standard deviation and skewness) with the porosity and the protocol-dependent microstructural disorder. The deviation of the Voronoï volume distributions from the delta function of a crystalline packing describes the origin of short-range disorder of the investigated random packings. Eddy dispersion was simulated over a wide range of reduced velocities (0.5 ≤  ν ≤ 750) and analyzed with the comprehensive Giddings equation. Transient dispersion was found to correlate with the spatial scales of heterogeneity in the packings. The analysis of short-range disorder based on the Voronoï volume distributions revealed a strong correlation with the short-range interchannel contribution to eddy dispersion, whereas transchannel dispersion was relatively little affected. The presented approach defines a strictly scientific route to the key morphology–transport relationships of current and future chromatographic supports, including their morphological reconstruction, statistical analysis, and the correlation with relevant transport phenomena. It also guides us in our understanding, comparison, and optimization of the diverse packing algorithms and protocols used in simulations and experimental studies.     

119Sn electric field gradients in model clusters of chalcogenide glasses

Calculations of ¹¹⁹Sn electric field gradients (EFG) have been performed using the Extended Hückel approximation on characteristic molecular clusters simulating possible types of sites in chalcogenide glasses. The motivation for these calculations derives from theoretical concepts on varying near neighbor relationships in these types of glasses, and from recent ¹¹⁹Sn Mössbauer experiments on Sn-doped Ge_x(Se or S)_1–x bulk glasses which reveal three types (A, B and C) of chemically inequivalent sites, with distinct values and composition dependences for their isomer shifts and quadrupole splittings. The model clusters chosen for the calculations were the ethane-like (Ge₂Se₃)_n quasi-one-dimensional chains of varying lengths which have been proposed as possible sources of the B site. In addition, calculations were also carried out on several additional types of clusters, in order to help in interpreting the results for the chains. We find that the magnitude of the quadrupole splitting in isolated linear ethane-like chains is very small, and almost independent of the particular site along the chain at which Sn replaces Ge. It therefore seems unlikely that such isolated linear clusters would be the source of the B sites. These sites are more likely to be related to distortions of the ethane-like clusters into non-linear configurations, as well as interactions with neighboring clusters, as forced by the constraints of the packing in the structure of the glass.     

Densest translational lattice packing of non-convex polygons

A translational lattice packing of k polygons P₁,P₂,P₃,…,P_k is a (non-overlapping) packing of the k polygons which is replicated without overlap at each point of a lattice i₀v₀+i₁v₁, where v₀ and v₁ are vectors generating the lattice and i₀ and i₁ range over all integers. A densest translational lattice packing is one which minimizes the area |v₀×v₁| of the fundamental parallelogram. An algorithm and implementation is given for densest translational lattice packing. This algorithm has useful applications in industry, particularly clothing manufacture.     

Disjoint congruence classes and a timetabling application

We consider a combinatorial problem motivated by a special simplified timetabling problem for subway networks. Mathematically the problem is to find (pairwise) disjoint congruence classes modulo certain given integers; each such class corresponds to the arrival times of a subway line of a given frequency. For a large class of instances we characterize when such disjoint congruence classes exist and how they may be determined. We also study a generalization involving a minimum distance requirement between congruence classes, and a comparison of different frequency families in terms of their “efficiency”. Finally, a general method based on integer programming is also discussed.