T. E. Harris and branching processes

T. E. Harris was a pioneer par excellence in many fields of probability theory. In this paper, we give a brief survey of the many fundamental contributions of Harris to the theory of branching processes, starting with his doctoral work at Princeton in the late forties and culminating in his fundamental book ``The Theory of Branching Processes,'' published in 1963.

Hyperbranched polyurethanes with varying spacer segments between the branching points

Hyperbranched polyurethanes, with varying oligoethyleneoxy spacer segments between the branching points, have been synthesized by a one-pot approach starting from the appropriately designed carbonyl azide that incorporates the different spacer segments. The structures of monomers and polymers were confirmed by IR and H-1-NMR spectroscopy. The solution viscosity of the polymers suggested that they were of reasonably high molecular weight. Reversal of terminal functional groups was achieved by preparing the appropriate monohydroxy dicarbonyl azide monomer. The large number of terminal isocyanate groups at the chain ends of such hyperbranched macromolecules caused them to crosslink prior to its isolation. However, carrying out the polymerization in the presence of 1 equiv of a capping agent, such as an alcohol, resulted in soluble polymers with carbamate chain ends. Using a biphenyl-containing alcohol as a capping agent, we have also prepared novel hyperbranched perbranched polyurethanes with pendant mesogenic segments. These mesogen-containing polyurethanes, however, did not exhibit liquid crystallinity probably due to the wholly aromatic rigid polymer backbone. (C) 1996 John Wiley & Sons, Inc.

On the spurious increase in particle volume fraction during coarsening simulations

The problem of spurious increase in volume fraction of second-phase particles during computer simulations of coarsening is examined. The origin of this problem is traced to the use of too long a time step (used for numerical integration of growth rates with respect to time) which leads to small particles with large negative growth rates shrinking to negative radii at the end of the time step. Such a shrinkage to negative sizes has the effect of pumping solute into the system. It is therefore suggested that the length of the time step be chosen in accordance with the size of the smallest particle present in the system. It is shown that spurious increase in particle Volume has a significant effect on the particle size distributions in the scaling regime (making them broader and more skewed in the Lifshitz-Slyozov-Wagner model). Its effect on coarsening kinetics, however, is found to be small.

SEC-MALDI-TOF mass spectral characterization of a hyperbranched polyether prepared via melt transetherification

An AB(2) monomer, 1-(2-hydroxyethoxy)-3,5-bis-(methoxymethyl)-2,4,6-trimethylbenzene, was synthesized from mesitol and melt-polycondensed in the presence of an acid catalyst via a transetherification process at 145-150 degreesC to yield a soluble, moderately high molecular weight hyperbranched polyether. The degree of branching in the polymer was calculated to be 0.78 by a comparison of its NMR spectrum with that of an appropriately designed model compound. The weight-average molecular weight of the hyperbranched polymer was determined to be 64,600 (weight-average molecular weight/number-average molecular weight = 5.2) by size exclusion chromatography (SEC) in CHCl3, with polystyrene standards. The origin of the broad molecular weight distribution, which could either be intrinsic to such hyperbranched structures or be due to structural heterogeneity, was further probed by the fractionation of the samples by SEC and by the subjection of each fraction to matrix-assisted laser desorption/ionization time-of-flight mass spectral analysis. The mass spectral analysis suggested the presence of two primary types of species: one corresponding to the simple branched structure and the other to macrocyclics. Interestingly, from the relative intensities of the two peaks, it was apparent that cyclization became favorable at higher conversions in the melt transetherification process. (C) 2002 Wiley Periodicals, Inc.

Anthropogenic aerosol fraction over Afro-Asian regions inferred using Kalpana-I and MISR data

Mineral dust constitutes the single largest contributor of natural aerosols over continents. The first step towards separating natural aerosol radiative impact from its anthropogenic counterparts over continents is to gather information on dust aerosols. The infrared (IR) radiance (10.5-12.5 mu m) acquired from the Kalpana-I satellite (similar to 8-km resolution) was used to retrieve regional characteristics of dust aerosols over the Afro-Asian region during the winter of 2004, coinciding with a national aerosol campaign. Here, we used aerosol-induced IR radiance depression as an index of dust load. The regional distribution of dust over various arid and semi-arid regions of India and adjacent continents has been estimated, and these data in conjunction with regional maps of column aerosol optical depth (AOD) are used to infer anthropogenic aerosol fraction. Surprisingly, even over desert locations in India and Saudi Arabia, the anthropogenic fraction was relatively high (similar to 0.3 to 0.4) and the regionally averaged anthropogenic fraction over India was 0.62 +/- 0.06.

Influence of matrix characteristics on fracture toughness of high volume fraction Al2O3/Al–AlN composites

The role of matrix microstructure on the fracture of Al-alloy composites with 60 vol% alumina particulates was studied. The matrix composition and microstructure were systematically varied by changing the infiltration temperature and heat treatment. Characterization was carried out by a combination of metallography, hardness measurements, and fracture studies conducted on compact tension specimens to study the fracture toughness and crack growth in the composites. The composites showed a rise in crack resistance with crack extension (R curves) due to bridges of intact matrix ligaments formed in the crack wake. The steady-state or plateau toughness reached upon stable crack growth was observed to be more sensitive to the process temperature rather than to the heat treatment. Fracture in the composites was predominantly by particle fracture, extensive deformation, and void nucleation in the matrix. Void nucleation occurred in the matrix in the as-solutionized and peak-aged conditions and preferentially near the interface in the underaged and overaged conditions. Micromechanical models based on crack bridging by intact ductile ligaments were modified by a plastic constraint factor from estimates of the plastic zone formed under indentations, and are shown to be adequate in predicting the steady-state toughness of the composite.

Fracture and R-curves in high volume fraction Al2O3/Al composites

Fracture toughness and fracture mechanisms in Al2O3/Al composites are described. The unique flexibility offered by pressureless infiltration of molten Al alloys into porous alumina preforms was utilized to investigate the effect of microstructural scale and matrix properties on the fracture toughness and the shape of the crack resistance curves (R-curves). The results indicate that the observed increment in toughness is due to crack bridging by intact matrix ligaments behind the crack tip. The deformation behavior of the matrix, which is shown to be dependent on the microstructural constraints, is the key parameter that influences both the steady-state toughness and the shape of the R-curves. Previously proposed models based on crack bridging by intact ductile particles in a ceramic matrix have been modified by the inclusion of an experimentally determined plastic constraint factor (P) that determines the deformation of the ductile phase and are shown to be adequate in predicting the toughness increment in the composites. Micromechanical models to predict the crack tip profile and the bridge lengths (L) correlate well with the observed behavior and indicate that the composites can be classified as (i) short-range toughened and (ii) long-range toughened on the basis of their microstructural characteristics.

Determination of solid fraction evolution during solidification of aluminum alloy in presence of linear electromagnetic stirring

In many industrial casting processes, knowledge of the solid fraction evolution during the solidification process is a key factor in determining the process parameters such as cooling rate, stirring intensity and in estimating the total solidification time. In the present work, a new method of estimating solid fraction is presented, which is based on calorimetric principles. In this method, the cooling curve data at each point in the melt, along with the thermal boundary conditions, are used to perform energy balance in the mould, from which solid fraction generation during any time interval can be estimated. This method is applied to the case of a rheocasting process, in which Al-Si alloy (A356 alloy) is solidified by stirring in a cylindrical mould placed in the annulus of a linear electromagnetic stirrer. The metal in the mould is simultaneously cooled and stirred to produce a cylindrical billet with non-dendritic globular microstructure. Temperature is measured at key locations in the mould to assess the various heat exchange processes prevalent in the mould and to monitor the solidification rate. The results obtained by energy balance method are compared with those by the conventional procedure of calculating solid fraction using the Schiel equation.

Branching Particle Systems and Superprocess

In this paper, we describe a system of particles that perform independent random motions in space and at the end of their lifetimes give birth to a random number of offspring. We show that the system in the large density, small mass, rapid branching or long time scale limit converges to a measure-valued diffusion called the superprocess.

Branching out at C-2 of septanosides. Synthesis of 2-deoxy-2-C-alkyl/aryl septanosides from a bromo-oxepine

This paper deals with the synthesis of 2-deoxy-2-C-alkyl/aryl septanosides. A range of such septanoside derivatives was synthesized by using a common bromo-oxepine intermediate, involving C-C bond forming organometallic reactions. Unsaturated, seven-membered septanoside vinyl bromides or bromo-oxepines, obtained through a ring expansion methodology of the cyclopropane derivatives of oxyglycals, displayed a good reactivity towards several acceptor moieties in C-C bond forming Heck, Suzuki and Sonogashira coupling reactions, thus affording 2-deoxy-2-C-alkyl/aryl septanosides. Whereas Heck and Sonogashira coupling reactions afforded 2-deoxy-2-C-alkenyl and -alkynyl derivatives, respectively, the Suzuki reaction afforded 2-deoxy-2-C-aryl septanosides. Deprotection and reduction of the 2-deoxy-2-alkenyl derivative afforded the corresponding 2-deoxy-2-C-alkyl septanoside free of protecting groups. The present study illustrates the reactivity of bromo-oxepine in the synthesis of hitherto unknown septanosides, branching out at C-2, through C-C bond formation with alkyl and aryl substituents.

A method for measurement of planar liquid volume fraction in dense sprays

A methodology for measurement of planar liquid volume fraction in dense sprays using a combination of Planar Laser-Induced Fluorescence (PLIF) and Particle/Droplet Imaging Analysis (PDIA) is presented in this work. The PLIF images are corrected for loss of signal intensity due to laser sheet scattering, absorption and auto-absorption. The key aspect of this work pertains to simultaneously solving the equations involving the corrected PLIF signal and liquid volume fraction. From this, a quantitative estimate of the planar liquid volume fraction is obtained. The corrected PLIF signal and the corrected planar Mie scattering can be also used together to obtain the Sauter Mean Diameter (SMD) distribution by using data from the PDIA technique at a particular location for calibration. This methodology is applied to non-evaporating sprays of diesel and a more viscous pure plant oil at an injection pressure of 1000 bar and a gas pressure of 30 bar in a high pressure chamber. These two fuels are selected since their viscosity values are very different with a consequently very different spray structure. The spatial distribution of liquid volume fraction and SMD is obtained for two fuels. The proposed method is validated by comparing liquid volume fraction obtained by the current method with data from PDIA technique. (C) 2012 Elsevier Inc. All rights reserved.

Detailed investigation of contact deformation in ZrN/Zr multiplayer-understanding the role of volume fraction, bilayer spacing, and morphology of interfaces

A systematic study was done to understand the influence of volume fractions and bilayer spacings for metal/nitride multilayer coating using finite element method (FEM). An axisymmetric model was chosen to model the real situation by incorporating metal and substrate plasticity. Combinations of volume fractions and bilayer spacings were chosen for FEM analysis consistent with experimental results. The model was able to predict trends in cracking with respect to layer spacing and volume fraction. Metal layer plasticity is seen to greatly influence the stress field inside nitride. It is seen that the thicker metal induces higher tensile stresses inside nitride and hence leads to lower cracking loads. Thin metal layers < 10 nm were seen to have curved interfaces, and hence, the deformation mode was interfacial delamination in combination with edge cracking. There is an optimum seen with respect to volume fraction similar to 13% and metal layer thickness similar to 30 nm, which give maximum crack resistance.