Melting of microinclusions close packed in an elastic matrix

A novel representation is proposed of the liquid state in a microcavity, the collective nature of that state being taken into account. In this case a microinclusion undergoing melting is described as a single two-level system. The phase transition of melting in a close-packed system of such inclusions embedded in an elastic medium is described rigorously within the framework of the self-consistent approach. When an additional intermediate premelting state is taken into account, the curve of the steady-state phase transition with a critical point that happens on the phase diagram can be transformed in different ways, depending on the values of the specific parameters. In the simplest case shortening of the straight line takes place; bending is also possible. There is a region of the parameters where the critical line is split. In the latter case the existence of the triple point is also possible. The results obtained are in agreement with the experimental data.     

Minimizing the cycle time of multiple-product processing networks with a fixed operation sequence,setups, and time-window constraints

We solve a special case of the single-robot cyclic scheduling problem with a fixed robot operation sequence and time window constraints on processing times. It generalizes the known single-part fixed-sequence problems into the one to cover a processing network with multiple part types and setup time requirements between the processing steps for different parts at the shared stations. The objective is to minimize the cycle time. We prove that this problem is equivalent to the parametric critical path problem, and propose a strongly polynomial time solution algorithm which uses a new labeling procedure to identify all feasible parameter values. The proposed algorithm is based on an extension to the known Bellman–Ford algorithm.     

Size-selected Ni catalyst islands for single-walled carbon nanotube arrays

Many properties of single-walled carbon nanotube (SWCNT) arrays are determined by the size and surface coverage of the metal catalyst islands from which they are nucleated. Methods using thermal fragmentation of continuous metal films frequently fail to produce size-uniform islands. Hybrid numerical simulations are used to propose a new approach to controlled self-assembly of Ni islands of the required size and surface coverage using tailored gas-phase generated nanocluster fluxes and adjusted surface temperatures. It is shown that a maximum surface coverage of 0.359 by 0.96–1.02 nm Ni catalyst islands can be achieved at a low surface temperature of 500 K. Optimized growth of Ni catalyst islands can lead to fabrication of size-uniform SWCNT arrays, suitable for numerous nanoelectronic applications. This approach is deterministic and is applicable to a range of nanoassemblies where high surface coverage and island size uniformity are required.

     

Invariant manifolds and the stability of traveling waves in scalar viscous conservation laws

The stability of traveling wave solutions of scalar viscous conservation laws is investigated by decomposing perturbations into three components: two far-field components and one near-field component. The linear operators associated to the far-field components are the constant coefficient operators determined by the asymptotic spatial limits of the original operator. Scaling variables can be applied to study the evolution of these components, allowing for the construction of invariant manifolds and the determination of their temporal decay rate. The large time evolution of the near-field component is shown to be governed by that of the far-field components, thus giving it the same temporal decay rate. We also give a discussion of the relationship between this geometric approach and previous results, which demonstrate that the decay rate of perturbations can be increased by requiring that initial data lie in appropriate algebraically weighted spaces.     

Efficient one-pot synthesis of substituted 2-amino-1,3,4-oxadiazoles

A convenient one-pot method for the preparation of substituted 2-amino-1,3,4-oxadiazoles has been developed. The method is a significant improvement over previously reported syntheses. Reaction of carboxylic acids with thiosemicarbazides afforded the corresponding oxadiazoles in moderate to good yields. In general, the products precipitated from the reaction mixture, and were collected by filtration. In most of the cases, no chromatographic separations were required. To explore the scope and limitations of this reaction, various aliphatic, aromatic, and heteroaromatic carboxylic acids were reacted with different substituted thiosemicarbazides. The influence of R¹ and R² substituents on the reaction yield and additional results demonstrating the versatility of this method are presented.     

Strong Lefschetz property under reduction

Let n > 1 and G be the group SU(n) or Sp(n). This paper constructs compact symplectic manifolds whose symplectic quotient under a Hamiltonian G-action does not inherit the strong Lefschetz property.     

Conformational analysis of bridgehead-substituted bicyclo[m.m.m]alkanes and bicyclo[8.8.n]alkanes

Conformational analyses of bicyclo[m.m.m]alkanes where m=1-10 and of bicyclo[8.8.n]alkanes where n=1-7 bearing methyl groups on the bridgeheads were carried out using a Monte Carlo search strategy. In the bicyclo[m.m.m]alkane series, greater variability was observed for the inter-bridgehead distance for larger values of m. This suggests that properly substituted bicyclo[8.8.8]hexacosanes or larger ring systems might serve as molecular springs.     

Hydrolytic Methods for the Quantification of Fructose Equivalents in Herbaceous Biomass

A low, but significant, fraction of the carbohydrate portion of herbaceous biomass may be composed of fructose/fructosyl-containing components (“fructose equivalents”); such carbohydrates include sucrose, fructooligosaccharides, and fructans. Standard methods used for the quantification of structural-carbohydrate-derived neutral monosaccharide equivalents in biomass are not particularly well suited for the quantification of fructose equivalents due to the inherent instability of fructose in conditions commonly used for hemicellulose/cellulose hydrolysis (>80% degradation of fructose standards treated at 4% sulfuric acid, 121°C, 1 h). Alternative time, temperature, and acid concentration combinations for fructan hydrolysis were considered using model fructans (inulin, β-2,1, and levan, β-2,6) and a grass seed straw (tall fescue, Festuca arundinacea) as representative feedstocks. The instability of fructose, relative to glucose and xylose, at higher acid/temperature combinations is demonstrated, all rates of fructose degradation being acid and temperature dependent. Fructans are shown to be completely hydrolyzed at acid concentrations well below that used for the structural carbohydrates, as low as 0.2%, at 121°C for 1 h. Lower temperatures are also shown to be effective, with corresponding adjustments in acid concentration and time. Thus, fructans can be effectively hydrolyzed under conditions where fructose degradation is maintained below 10%. Hydrolysis of the β-2,1 fructans at temperatures ≥50°C, at all conditions consistent with complete hydrolysis, appears to generate difructose dianhydrides. These same compounds were not detected upon hydrolysis of levan, sucrose, or straw components. It is suggested that fructan hydrolysis conditions be chosen such that hydrolysis goes to completion; fructose degradation is minimized, and difructose dianhydride production is accounted for.