A Note on the Legendre Series Solution of the Biharmonic Equation for Cylindrical Problems

The solution of cylindrical problems is addressed. A series solution is considered of the biharmonic equation, in which the series terms of the stress function Φ are expressions based upon Legendre polynomials and logarithmically singular functions. An explicit form of a polynomial supplementing each logarithmically singular part of the series solution is obtained.     

An Incompressible Fluid in a Weakly Deformable Shell. Part I: Analysis of the Model

We consider the flow of a viscous incompressible fluid in a pipe when the boundary is a deformable shell of Naghdi type. We prove that the corresponding system of partial differential equations has a solution when the deformation of the shell is smooth and small enough. We propose an algorithm that uncouples the unknowns and prove its convergence.     

Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos

We apply the recently improved version of the 0–1 test for chaos to real experimental time series of laser droplet generation process. In particular two marginal regimes of dripping are considered: spontaneous and forced dripping. The outcomes of the test reveal that both spontaneous and forced dripping time series can be characterized as chaotic, which coincides with the previous analysis based on nonlinear time series analysis.     

Standard<Emphasis Type="Italic">SU</Emphasis>(5) supergravity grand unification model and predictions

A review is given of the StandardSU(5) supergravity model. This model has passed an important check regarding unification of the electro-weak and the strong couplings using high precision LEP data. It is shown that for a significant domain of the parameter space the model also satisfies constraints on the SUSY spectrum from CDF and LEP, as well as proton stability and cosmological relic density constraints.     

Simulation and design of a bandpass filter on metasubstrates

This work presents an analysis of the microstrip bandpass filter on metamaterial substrates. The filter is composed of two ring resonators with quarter-wavelength side-coupled sections. The filter input is provided, as well as the output port, using a quarter-wavelength side-coupled microstrip line section. Simulations by finite element method have been carried out to verify the effect of the metamaterial substrate properties on the filter performance, and to compare these results to those obtained considering isotropic substrate.     

Analysis of Asymmetric Long-Range Surface-Plasmon Waveguide with High-Confinement Mode

We model and study the asymmetric long-range surface-plasmon waveguides using the finite-element method. We introduce two types of asymmetric structures and discuss their modal properties compared to traditional long-range surface-plasmon waveguides. Although the propagation distance is decreased, the energy-confinement capability is improved for asymmetric long-range waveguiding structures when the geometrical parameters are properly selected. Our simulation result offers guidance for tuning properties of plasmonic waveguides and providing ways for enhancing electromagnetic energy confinement in long-range surface-plasmon waveguides.     

Modeling the deformation behavior of nanocrystalline alloy with hierarchical microstructures

A mechanism-based plasticity model based on dislocation theory is developed to describe the mechanical behavior of the hierarchical nanocrystalline alloys. The stress–strain relationship is derived by invoking the impeding effect of the intra-granular solute clusters and the inter-granular nanostructures on the dislocation movements along the sliding path. We found that the interaction between dislocations and the hierarchical microstructures contributes to the strain hardening property and greatly influence the ductility of nanocrystalline metals. The analysis indicates that the proposed model can successfully describe the enhanced strength of the nanocrystalline hierarchical alloy. Moreover, the strain hardening rate is sensitive to the volume fraction of the hierarchical microstructures. The present model provides a new perspective to design the microstructures for optimizing the mechanical properties in nanostructural metals.     

Synthesis and characterization of nanostructured iron compounds prepared from the decomposition of iron pentacarbonyl dispersed into carbon materials with varying porosities

This work describes the production and characterization of carbon-iron nanocomposites obtained from the decomposition of iron pentacarbonyl (Fe(CO)₅) mixed with different carbon materials: a high surface area activated carbon (AC), powdered graphite (G), milled graphite (MG), and carbon black (CB). The nanocomposites were prepared either under argon or in ambient atmosphere, with a fixed ratio of Fe(CO)₅ (4.0 mL) to carbon precursor (2.0 g). The images of scanning electron microscopy and the analysis of textural properties indicated the presence of nanostructured Fe compounds homogeneously dispersed into the different classes of pores of the carbon matrices. The elemental Fe content was always larger for samples prepared in ambient atmosphere, reaching values in the range of 20–32 wt%. On the other hand, samples prepared under argon showed reduced Fe content, with values in the range 5–10 wt% for samples prepared from precursors with low surface area (G, MG, and CB) and a much higher value (~19 wt%) for samples prepared from the precursor of high surface area (AC). Mössbauer spectroscopy and X-ray diffractometry showed that the nanoparticles were mostly composed of iron oxides in the case of the samples prepared in oxygen-rich ambient atmosphere and also for the AC-derived nanocomposite prepared under argon, which is consistent with the large oxygen content of this precursor. For the other precursors, with reduced or no oxygen content, metallic iron and iron carbides were found to be the dominant phases in samples prepared under oxygen-free atmosphere. The samples prepared in ambient atmosphere and the AC-derived sample prepared under argon exhibited superparamagnetic behavior at room temperature, as revealed by temperature-dependent magnetization curves and Mössbauer spectroscopy.     

Automated determination of size and morphology information from soot transmission electron microscope (TEM)-generated images

The thermophoretic sampling of particulates from hot media, coupled with transmission electron microscope (TEM) imaging, is a combined approach that is widely used to derive morphological information. The identification and the measurement of the particulates, however, can be complex when the TEM images are of low contrast, noisy, and have non-uniform background signal level. The image processing method can also be challenging and time consuming, when the samples collected have large variability in shape and size, or have some degree of overlapping. In this work, a three-stage image processing sequence is presented to facilitate time-efficient automated identification and measurement of particulates from the TEM grids. The proposed processing sequence is first applied to soot samples that were thermophoretically sampled from a laminar non-premixed ethylene-air flame. The parameter values that are required to be set to facilitate the automated process are identified, and sensitivity of the results to these parameters is assessed. The same analysis process is also applied to soot samples that were acquired from an externally irradiated laminar non-premixed ethylene-air flame, which have different geometrical characteristics, to assess the morphological dependence of the proposed image processing sequence. Using the optimized parameter values, statistical assessments of the automated results reveal that the largest discrepancies that are associated with the estimated values of primary particle diameter, fractal dimension, and prefactor values of the aggregates for the tested cases, are approximately 3, 1, and 10 %, respectively, when compared with the manual measurements.