Packing complete multipartite graphs with 4-cycles

In this paper we completely solve the problem of finding a maximum packing of any complete multipartite graph with edge-disjoint 4-cycles, and the minimum leaves are explicitly given.

Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

Research on the BET surface area and packing of molecules on the activated carbon

Adsorption of different aromatic compounds (two of them are electrolytes) onto an untreated activated carbon (F100) is investigated. The experimental isotherms are fitted into Langmuir homogenous and heterogeneous Model. Theoretical maximum adsorption capacities that are based on the BET surface area of the adsorbent cannot be close to the real value. The affinity and the heterogeneity of the adsorption system observed to be related to the pK(a) of the solutes. The maximum adsorption capacity (Q(max)) of activated carbon for each solute dependent on the molecular area as well as the type of functional group attached on the aromatic compound and also pH of solution. The arrangement of the molecules on the carbon surface is not face down. Furthermore, it is illustrated that the packing arrangement is most likely edge to face (sorbate-sorbent) with various tilt angles. For characterization of the carbon, the N-2 and CO2 adsorption were used. X-ray Photoelectron Spectroscopy (XPS) measurement was used to surface elemental analysis of activated carbon.

Packing lambda-fold complete multipartite graphs with 4-cycles

A maximum packing of any lambda-fold complete multipartite graph (where there are lambda edges between any two vertices in different parts) with edge-disjoint 4- cycles is obtained and the size of each minimum leave is given. Moreover, when lambda =2, maximum 4-cycle packings are found for all possible leaves.

The interlayer swelling and molecular packing in organoclays

Understanding the interlayer swelling and molecular packing in organoclays is important to the formation and design of polymer nanocomposites. This paper presents recent experimental and molecular simulation studies on a variety of organoclays that show a linear relationship between the increase of d-spacing and the mass ratio between organic and clay. A denser molecular packing is observed in organoclays containing surfactants with hydroxyl-ethyl units. Moreover, our simulation results show that the head (nitrogen) groups are essentially tethered to the clay surface while the long hydrocarbon chains tend to adopt a layering structure with disordered conformation, which contrasts with the previous assumptions of either the chains lying parallel to the clay surface or being tilted at rather precise angles. (c) 2005 Elsevier Inc. All rights reserved.

Packing-dependent pore structure in single-walled carbon nanotube arrays

Based on a self-similar array model of single-walled carbon nanotubes (SWNTs), the pore structure of SWNT bundles is analyzed and compared with that obtained from the conventional triangular model and adsorption experimental results. In addition to the well known cylindrical endo-cavities and interstitial pores, two types of newly defined pores with diameters of 2-10 and 8-100 nm are proposed, inter-bundle pores and inter-array pores. In particular, the relationship between the packing configuration of SWNTs and their pore structures is systematically investigated. (c) 2005 American Institute of Physics.

Effect of pore packing defects in 2-D ordered mesoporous carbons on ionic transport

Ordered mesoporous materials show great importance in energy, environmental, and chemical engineering. The diffusion of guest species in mesoporous networks plays an important role in these applications, especially for energy storage, such as supercapacitors based on ordered mesoporous carbons ( OMCs). The ion diffusion behavior in two different 2-D hexagonal OMCs was investigated by using cyclic voltametry and electrochemical impedance spectroscopy. In addition, transmission electron microscopy, small-angle X-ray diffraction, and nitrogen cryosorption methods were used to study the pore structure variations of these two OMCs. It was found that, for the OMC with defective pore channels ( termed as pore packing defects), the gravimetric capacitance was greatly decayed when the voltage scan rate was increased. The experimental results suggest that, for the ion diffusion in 2-D hexagonal OMCs with similar mesopore size distribution, the pore packing defect is a dominant dynamic factor.

Free volume and water uptake in a copolymer hydrogel series

A copolymer of X-hydroxyethyl methacrylate (HEMA) with 2-ethoxy ethyl methacrylate (EEMA) was synthesized and the molecular mobility, free volume, and density properties examined as a function of composition. These properties were correlated with the equilibrium water uptake in order to determine which of the properties were most influential in causing high water sorption, as these materials are suitable candidates for hydrogel systems. It was found that the polar HEMA repeat unit results in a rigid, glassy sample at room temperature due to the high degree of hydrogen bonding between chains whereas high EEMA content leads to rubbery samples with subambient glass transition temperatures. The free volume properties on the molecular scale measured by positron annihilation Lifetime spectroscopy (PALS) showed that higher HEMA content led to smaller, fewer holes and a lower free volume fraction than EEMA. Therefore the high water uptake of HEEMA-containing copolymers is largely related to the high polarity of the HEMA unit compared to EEMA, despite the low content of free volume into which the water can initially diffuse. Trends in density with copolymer composition, as measured on a macroscopic level, differs to that seen by PALS and indicates that the two techniques are measuring different scales of packing. (C) 1998 John Wiley & Sons, Inc.

Rheological behaviour of the mushy zone and its effect on the formation of casting defects during solidification

A new conceptual framework has been developed which explains the formation of shear-related casting defects such as porosity, segregation and tears. The theory relates defect formation to the mechanical behaviour of the partially solidified microstructure when shear stresses are developed during the filling of a casting and by the subsequent feeding processes during solidification. Two transition points, the dendrite coherency point and the maximum packing solid fraction, divide the mushy zone into three regions of different mechanical and feeding behaviours. The response of the mush to shear is related to the presence of these zones during solidification of a casting. The resulting defects are rationalized by considering the governing local shear stress and shear rate, local strength and time available for fluid flow. The design of the casting, the casting process used and the alloy composition all influence the relative importance of shearing on defect formation. (C) 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.

Role of compaction versus aggregate disruption on slumping and shrinking of repacked hardsetting seedbeds

Slumping of hardsetting seedbeds upon wetting is likely to determine the shrinking and development of strength on drying. Different processes have been invoked, including aggregate disruption, material relocation, and compaction. To gain a better understanding of the role played by compaction compared with aggregate disruption in seedbed slumping and shrinking, mechanical analysis was combined with previous morphogenetical description. The global structural behavior of repacked seedbeds of a hardsetting sandy loam soil was studied after wetting and again after subsequent drying. Bulk density was measured in 5-mm-depth increments using gamma attenuation, and water content was determined at 10-mm-depth increments. Various wetting conditions were used to simulate a range of climatic and management conditions, including flood irrigation, furrow irrigation of a formed seedbed, drip irrigation, and rainfall. Aggregate coalescence under overburden pressure played the main role in slumping, even though microcracking enhanced coalescence. Most of the slumping occurred at calculated effective stress > 1.1 kPa. Intense aggregate breakdown at the top of seedbeds under fast wetting led to slight slumping because the resulting clogging of the initial interaggregate packing voids was balanced, in part, by the increase in microporosity resulting from aggregate disruption. However, aggregate coalescence induced by overburden pressure developing at the seedbed bottom often resulted in a strong decrease in total porosity. The effect of rainfall kinetic energy on crust bulk density was strong compared with the effect of fast wetting (bulk density increase of about 0.07 Mg m(-3) and 0.03 Mg m(-3), respectively) and could be ascribed to compaction rather than to aggregate breakdown. Shrinking on drying was related to the continuity of the microstructure resulting from wetting rather than to the intensity of slumping. Aggregate breakdown led to more shrinking than did aggregate coalescence.

Machining of micro aspherical mould inserts

This paper reports a parametric investigation and development of grinding technologies for micro aspherical mould inserts using parallel grinding method. The parametric investigation revealed that at nanometric scale the undeformed chip thickness has little influence on the surface finish of ground inserts. The grinding trace spacing has a slightly larger influence on the surface finish. A new technique was developed to true and dress the resin bonded micro wheels with mesh size of #3000, which produced a satisfactory wheel form accuracy and relatively high grain packing density. A form error compensation technique was also developed, with which mould inserts of submicron form accuracy were consistently produced. Using the developed technologies, micro aspherical inserts of diameters ranging from 200 mu m to 1000 mu m with surface finish of around 10 nm and form error of similar to 0.2-0.4 mu m were successfully fabricated. (c) 2005 Elsevier Inc. All rights reserved.

Axial Young's modulus prediction of single-walled carbon nanotube arrays with diameters from nanometer to meter scales

Based on a self-similar array model, we systematically investigated the axial Young's modulus (Y-axis) of single-walled carbon nanotube (SWNT) arrays with diameters from nanometer to meter scales by an analytical approach. The results show that the Y-axis of SWNT arrays decreases dramatically with the increases of their hierarchy number (s) and is not sensitive to the specific size and constitution when s is the same, and the specific Young's modulus Y-axis(s) is independent of the packing configuration of SWNTs. Our calculations also show that the Y-axis of SWNT arrays with diameters of several micrometers is close to that of commercial high performance carbon fibers (CFs), but the Y-axis(s) of SWNT arrays is much better than that of high performance CFs. (C) 2005 American Institute of Physics.