The Kolkata Paise Restaurant problem and resource utilization

We study the dynamics of the “Kolkata Paise Restaurant problem”. The problem is the following: In each period, N agents have to choose between N restaurants. Agents have a common ranking of the restaurants. Restaurants can only serve one customer. When more than one customer arrives at the same restaurant, one customer is chosen at random and is served; the others do not get the service. We first introduce the one-shot versions of the Kolkata Paise Restaurant problem which we call one-shot KPR games. We then study the dynamics of the Kolkata Paise Restaurant problem (which is a repeated game version of any given one shot KPR game) for large N. For statistical analysis, we explore the long time steady state behavior. In many such models with myopic agents we get under-utilization of resources, that is, we get a lower aggregate payoff compared to the social optimum. We study a number of myopic strategies, focusing on the average occupation fraction of restaurants.     

Arraying of intact liposomes into chemically functionalized microwells

Here, we describe a protocol to bind individual, intact phospholipid bilayer liposomes, which are on the order of 1 microm in diameter, in microwells etched in a regular array on a silicon oxide substrate. The diameter of the wells is on the order of the liposome diameter, so only one liposome is located in each well. The background of the silicon oxide surface is functionalized with a PEG oligomer using the contact printing of a PEG silane to present a surface that resists the adsorption of proteins, lipid material, and liposomes. The interiors of the wells are functionalized with an aminosilane to facilitate the conjugation of biotin, which is then bound to Neutravidin. The avidin-coated well interiors bind the liposomes whose surfaces contain biotinylated lipids. The specific binding of the liposomes to the surface using the biotin-avidin linkage, together with the resistant nature of the background and the physical confinement of the wells, allows the liposomes to remain intact and to not unravel, rupture, and fuse onto the surface. We demonstrate this intact arraying using confocal laser scanning microscopy of fluorophores specifically tagging the microwells, the lipid bilayer, and the aqueous interior of the liposome.     

Natural convection in power-law fluids from two square cylinders in tandem arrangement at moderate Grashof numbers

In this work, free convective flow and heat transfer in power-law fluids from two heated square cylinders in tandem arrangement is studied. The governing differential equations have been solved numerically over wide ranges of Grashof number, 10 ≤ Gr ≤ 1,000, Prandtl number, 0.71 ≤ Pr ≤ 50 and power-law index, 0.4 ≤ n ≤ 1.8. In order to elucidate the extent of inter-cylinder interaction, the non-dimensional inter-cylinder spacing, L/d is varied in the range, 2 ≤ L/d ≤ 6. The results are interpreted in terms of streamline and isotherm contours in the proximity of two cylinders to gain physical insights into the nature of flow. At the next level, the distribution of the local Nusselt number along the surface of the cylinders is presented. At the minimum inter-cylinder spacing due to the intense interference, the downstream cylinder contributes much less to the overall heat transfer whereas it experiences much higher hydrodynamic drag than the upstream cylinder. Broadly, the local and average Nusselt number for both cylinders show a positive dependence on both Grashof and Prandtl numbers. Also, all else being equal, shear-thinning fluid behaviour promotes the rate of heat transfer and shear-thickening fluid behaviour impedes it. Finally, the present numerical results have been correlated by using simple forms of equations thereby enabling the estimation of Nusselt number in a new application.     

Longitudinal and Bending Stresses in a Beam with Saw Cut Edge Cracks∗

Abstract

The Griffith-Irwin theory of brittle fracture of elastic solids predicts the propagation of cracks on the basis of the energy release rate. This depends upon the stress intensity factors for a given crack configuration. The present paper provides these informations for the problem of an infinite number of periodic, non-coplanar, parallel edge cracks in a strip. Two types of crack configurations, namely, periodic cracks of equal length starting from one edge and a set of two coplanar symmetrical edge cracks of equal length are solved for constant and linearly varying pressure distributions. These problems arise naturally in structural mechanics while investigating stresses in extension and bending of cracked strips. Final results are obtained from the numerical solution of certain Fredholm integral equations of the second kind derived from a dual series of Papkovich-Fadle eigenfunctions     

Enhancing the phase stability and ionic conductivity of scandia stabilized zirconia by rare earth co-doping

Effect of co-doping Yb, Gd and Ce in scandia stabilized zirconia (SSZ) on the phase stability, high temperature aging behavior and ionic conductivity was studied. Both binary (10 mol% SSZ) and the ternary (co-doped) compositions were found to be in single cubic phase in the as-processed condition. However, the binary composition exhibited the rhombohedral ‘β’ phase after sintering whereas the ternary compositions remained in the single cubic phase. The sintered pellets were aged at 900 °C for 500 h in air to study the phase stability at high temperature. Transmission electron microscopy revealed that the aged samples of Yb and Gd co-doped compositions contain small amount of the tetragonal phase which resulted in considerable degradation in conductivity (more than 20%). The Ce co-doped sample, on the other hand, was in single cubic phase after aging and this ensured that conductivity reduction was minimal in this composition. The co-doped samples however, showed higher conductivity before and after aging compared to the binary composition. The rhombohedral ‘β’ phase was absent in all the co-doped ternary compositions even after high temperature aging.     

Multiple dot-in-rod PbS/CdS heterostructures with high photoluminescence quantum yield in the near-infrared

Pb cations in PbS quantum rods made from CdS quantum rods by successive complete cationic exchange reactions are partially re-exchanged for Cd cations. Using STEM-HAADF, we show that this leads to the formation of unique multiple dot-in-rod PbS/CdS heteronanostructures, with a photoluminescence quantum yield of 45-55%. We argue that the formation of multiple dot-in-rods is related to the initial polycrystallinity of the PbS quantum rods, where each PbS crystallite transforms in a separate PbS/CdS dot-in-dot. Effective mass modeling indicates that electronic coupling between the different PbS conduction band states is feasible for the multiple dot-in-rod geometries obtained, while the hole states remain largely uncoupled.     

Preclusion of nano scale self-assembly in block-selective non-aqueous solvents for rod–coil and coil–rod–coil macromolecular surfactants based on perylene tetracarboxylic diimide

Self-assembly of amphiphilic molecules ranging from simple surfactants to block copolymers in a solvent depends on one part of the molecule (one block in block copolymers) being soluble, and the other not. The aggregation of the insoluble segment in the block-selective solvent leads to the self assembly. In this paper, we describe a system of amphiphilic rod–coil and coil–rod–coil molecules, which do not show self assembly in block-selective non-aqueous solvents. We prepared rod–coil molecules based on hydrophilic propylene oxide/ethylene oxide copolymer (PO–EO copolymer) (Jeffamine®) as the flexible segment and photo-conducting large aromatic perylenediimide (PTCDI) as the rod. PO–EO copolymer was attached either to one side of PTCDI (MJ–PTCDI) or both sides (DJ–PTCDI). The former can be considered an inverse macromolecular surfactant, since the tail is hydrophilic and the head is hydrophobic. The DJ–PTCDI is a pseudo Gemini surfactant. Because of the presence of the chromophore, UV–Vis and fluorescent spectra could be used to study the self assembly of these amphiphilic rod coil polymers in solution. PTCDI forms π-interaction mediated aggregates in aqueous solution and these are H-stacked in MJ–PTCDI and J-stacked in DJ–PTCDI. Variable temperature UV and NMR spectra show that the assembly is stable over a large temperature range in water. The aggregates are also stable up to a pH of 12. However, when a non-aqueous solvent is used, no aggregation occurs. This is attributed to the “solvation” of the π-system of the PTCDI. With the addition of water, such solvation seems to be interrupted and aggregation occurs when water becomes a major component. We find that the mole percentage of the aggregates in acetone/water mixtures increases almost linearly with the concentration of water, providing a route to control the extent of aggregation of the chromophores. Due to the long, waxy PO–EO copolymer, MJ–PTCDI and DJ–PTCDI do not show liquid crystalline behavior or nanorod morphology, which were seen with short side chains. The optical microscopy of the bulk material shows aggregated crystals of PTCDI in the waxy matrix, showing that even in the presence of PO–EO copolymer, the molecular assembly of PTCDI takes place in the bulk. Secondary assembly was seen, in that upon ageing of the aqueous solutions, the drop cast films show that the spherical aggregates one-dimensionally coalesced into long fibers. Although UV–Vis spectra indicated no aggregation in non-aqueous solvents, drop-cast films of these solutions show needle-like aggregates and Lego-like assemblies.     

Efficient simultaneous reverse Monte Carlo modeling of pair-distribution functions and extended x-ray-absorption fine structure spectra of crystalline disordered materials

An efficient implementation of simultaneous reverse Monte Carlo (RMC) modeling of pair distribution function (PDF) and EXAFS spectra is reported. This implementation is an extension of the technique established by Krayzman et al. [J. Appl. Cryst. 42, 867 (2009)] in the sense that it enables simultaneous real-space fitting of x-ray PDF with accurate treatment of Q-dependence of the scattering cross-sections and EXAFS with multiple photoelectron scattering included. The extension also allows for atom swaps during EXAFS fits thereby enabling modeling the effects of chemical disorder, such as migrating atoms and vacancies. Significant acceleration of EXAFS computation is achieved via discretization of effective path lengths and subsequent reduction of operation counts. The validity and accuracy of the approach is illustrated on small atomic clusters and on 5500-9000 atom models of bcc-Fe and α-Fe(2)O(3). The accuracy gains of combined simultaneous EXAFS and PDF fits are pointed out against PDF-only and EXAFS-only RMC fits. Our modeling approach may be widely used in PDF and EXAFS based investigations of disordered materials.     

An unexpected formation of benzoyl benzoin from benzil during the attempted Knoevenagel type condensation with dimethylmalonate (or malononitrile)

An unexpected product, 2-oxo-1,2-diphenylethyl benzoate (benzoyl benzoin), was isolated during the attempted Knoevenagel reaction of benzil and dimethylmalonate (or malononitrile) in the presence of potassium carbonate. The product was confirmed by spectral analysis as well as by single crystal studies and a mechanism is proposed to explain its formation.