A Vertex-Aligned Model for Packing 4-Hexagonal Clusters in a Regular Hexagonal Container

This paper deals with a problem the packing polyhex clusters in a regular hexagonal container. It is a common problem in many applications with various cluster shapes used, but symmetric polyhex is the most useful in engineering due to its geometrical properties. Hence, we concentrate on mathematical modeling in such an application, where using the “bee” tetrahex is chosen for the new Compact Muon Solenoid (CMS) design upgrade, which is one of four detectors used in Large Hadron Collider (LHC) experiment at European Laboratory for Particle Physics (CERN). We start from the existing hexagonal containers with hexagonal cells packed inside, and uniform clustering applied. We compare the center-aligned (CA) and vertex-aligned (VA) models, analyzing cluster rotations providing the increased packing efficiency. We formally describe the geometrical properties of clustering approaches and show that cluster sharing is inevitable at the container border with uniform clustering. In addition, we propose a new vertex-aligned model decreasing the number of shared clusters in the uniform scenario, but with a smaller number of clusters contained inside the container. Also, we describe a non-uniform tetrahex cluster packing scheme in the proposed container model. With the proposed cluster packing solution, it is accomplished that all clusters are contained inside the container region. Since cluster-sharing is completely avoided at the container border, the maximal packing efficiency is obtained compared to the existing models.

An Improved Bin-Packing Approach under the Consideration of Fuel Consumption for Delivery Vehicle

With the popularity of e-commerce recently, how to control the operation cost has become an urgent issue need to be solved for all logistics company. This paper proposes an improved bin packing approach under the consideration of fuel consumption for delivery vehicle, to provide logistic company bin packing scheme with the least vehicle numbers and fuel consumption. First, with the consideration of controlling logistics costs, a multi-objective function is built to minimize the number of vehicles and the fuel consumption during delivery. Then a simulated annealing algorithm with improved neighborhood operations is proposed to solve the joint optimization problem. Finally, the effectiveness of the method is evaluated. The results show the proposed approach can effectively reduce logistics costs compared with the conventional bin packing approach and is helpful for reducing fuel consumption by balancing the weight among different vehicles.

A computational study of the molecular and crystal structure and selected physical properties of octahydridosilasequioxane–(Si 2 O 3 H 2 ) 4 . I. Electronic and structural aspects

The free molecule octahydridosilasequioxane, Si 8 O 12 H 8 , was computationally studied, as well as embedded in the unit cell. The point group of the free molecule is indeed O h , and its crystal symmetry is reduced to C 3i , thus confirming the occurrence of two different types of Si−O−Si bond lengths found experimentally. The molecular orbitals of the free molecule show that some electron density occurs in the cubic cavity, thus contributing to the opening of the Si−O−Si angle. A study of the packing in the unit cell identifies a new type of packing scheme in which eight (partial) molecules participate: each apex H atom of one protruding Si−H bond of every molecule points to the corner of an equilateral triangle having 2.631 Å sides. All hydrogen atoms in both the free molecule and in the solid state carry negative partial charges. The reason for this is also explored, as well as its consequences for the unique packing scheme.

3,4:9,10-Perylenetetracarboxylic dianhydride (PTCDA) by electron crystallography

The crystal structures of the α and β modifications of PTCDA were analyzed as projected structures along the a axes by electron crystallography using an imaging plate. The results for the α modification agree well with the sheet-and-stack structure obtained by X-ray diffraction by M. L. Kaplan et al. (private communication, full set of crystal structure data). Projected onto the (102) plane, which is parallel to the molecular sheets, the long molecular axis makes an angle of 42° with the b axis and the hexagonal benzene rings appear slightly elongated, indicating a slight inclination of the molecular plane from the (102) lattice plane. For the β modification, it was concluded that the molecules are aligned in a herringbone packing scheme on the (102) plane similar to that of the α modification, but with a slightly different angle of the long molecular axis with the b axis (38°).

Spezielle Alkylammoniumhexachlorometallate, II [1] Synthese und Kristallstruktur von Bis(1,2-diammoniopropan)hexachlororhodat(III)-chlorid, [H3N-CH(CH3)-CH2-NH3]2[RhCl6]Cl/ Alkylammonium Hexachlorometallates, II [1] Synthesis, and Crystal Structure of Bis(1,2-diammoniopropane) Hexachlororhodate(III) Chloride, (H3N-CH(CH3)-CH2-NH3]-[RhCl6]Cl

Bis(1,2-diammoniopropane) hexachlororhodate(III) chloride, [H3N-CH(CH3)-CH2-NH3]2 [RhCl6]Cl (1) has been obtained by the reaction of rhodium(III) chloride with rac-1,2- diammoniopropane dihydrochloride in hydrochloric acid solution. The quasi-ternary compound, which crystallizes in the orthorhombic space group Pbca (a - 11.0007(13) Å, b = 22.181(2) A, c = 14.638(2) A, V = 3571.7(7) Å3, \ T = -120 °C, Z - 8) contains two crystallographically independent 1,2-diammoniopropane ions beside one hexachlororhodate and one chloride ion. One of the cations shows a R/S-S/R-disorder of enantiomeric pairs in the centrosymmetric crystal lattice. The packing scheme is determined by a complex framework of hydrogen bonds.