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We discuss a fluid dynamic variant of the classical Bernoulli’s brachistochrone problem. The classical brachistochrone for a non-dissipative particle is governed by maximization of the particle’s kinetic energy, resulting in a cycloid. We consider a variant where the particle is replaced by a cylinder (bottle) filled with a viscous fluid and attempt to identify the shape of the curve connecting two points along which the bottle would move in the shortest time. We derive the system of integro-differential equations governing system dynamics for a given shape of the curve. Using these equations, we pose the brachistochrone problem by invoking an optimal control formalism and show that (in general) the curve deviates from a cycloid. This is due to the fact that increasing the rate of change of the bottle’s kinetic energy is accompanied by increased viscous dissipation. We show that the bottle motion is governed by a balance between the desire to minimize travel time and the need to reach the end point in the face of increased dissipation. The trade-off between these two physical forces plays a vital role in determining the brachistochrone of a fluid-filled cylinder. We show that in the two limits of either vanishing or high viscosity, the brachistochrone for this problem reduces to a cycloid. An intermediate viscosity range is identified where the fluid brachistochrone is non-cycloidal. Finally, we show the relevance of these results to the dynamics of a rolling liquid marble.
One of the major barriers to the adoption of solid oxide fuel cells (SOFCs) is the short lifetime of the fuel cell stacks. A stack consists of a number of cells in series separated by an interconnect. Due to the high temperatures necessary for SOFCs, typical commercial interconnects are ceramic. Great attention has been paid to decreasing the operating temperature of SOFCs in order to extend the life and decrease the cost of the stack. As operating temperatures decrease below 1000°C, alternative interconnect materials become viable. Stainless steel interconnects are more cost effective than ceramic interconnects but the high temperatures and the oxidizing environment of the cathode leads to the formation of a chromium oxide scale that increases the stack resistance. Chromium from the stainless steel can also enter the vapor phase and redeposit on the cathode thereby blocking the electrochemically active sites. One method to neutralize these effects is to coat the metallic interconnect in a ceramic such as La.8Sr.2MnO3 (LSM). The coating acts as a diffusion barrier both against chromium diffusing into the cathode and oxygen diffusing into the interconnect. In this study LSM has been deposited using plasma spray and tested in a dual atmosphere setup using impedance spectroscopy to analyze the performance of the coatings at various temperatures. The area specific resistance and chemical composition of the scale was examined in order to determine the affect of the LSM coating.
Cultivated pigeonpea has a narrow genetic base. Wild relatives play an important role in the efforts to broaden its genetic base. In this report, we present a successful wide-cross between the cultivated pigeonpea and Cajanus lanceolatus, a wild relative from the secondary gene pool, native to Australia, with desirable traits such as frost and drought resistance. A range of F1 progeny were obtained and the resultant F1 hybrid plants set mature pods and seeds. The hybrids had intermediate morphology, sharing the traits of both the parents. All the F1 hybrids flowered profusely. Some of the hybrids were completely male sterile and some were partially fertile with pollen fertility ranging from 35 to 50 %. Meiotic analysis of the fertile F1 hybrids revealed a high degree of meiotic chromosome pairing between the two parental genomes. Meiotic analysis of the sterile F1 hybrids revealed that the breakdown of microsporogenesis occurred at the post-meiotic stage after the formation of tetrads. Fertile plants formed regular bivalents with normal disjunction, except for occasional asynchrony at meiotic II division.
Sintered Si3N4 (with 2 w/o A12O3 and 6 w/o Y2O3) was studied by acoustic emission method during indentation testing and during heating to and cooling from 920ºC in air. The acoustic emission activity was discontinous and its magnitude and duration increased with load applied during indentation testing. Intense acoustic emission signals were detected on cooling Si3N4 ceramics to temperatures below 590ºC, particularly below 450ºC. X-ray diffraction studies showed the presence of SiO2 (Quartz) after heating the sample to 920ºC during acoustic emission study, compared to single phase β Si3N4 before the heat treatment.
We study the complexity of supergranular cells using the intensity patterns obtained at the Kodaikanal solar observatory during the solar maximum. Our data consists of visually identified supergranular cells, from which a fractal dimension D is obtained according to the relation P ∝ AD/2 where A is the area and P is the perimeter of the cells. We find a difference in the fractal dimension between the active and the quiet region cells which is conjectured to be due to the magnetic activity level.
The molten salt method has in the past been employed to synthesize a large number of compounds at low temperatures. In this work we report the formation of solid solutions of BaTiO3–SrTiO3 and BaZrO3–SrZrO3 using a molten salt eutectic of NaOH–KOH as a solvent. Alkaline earth carbonates and titanium oxide were used as precursors for the titanate system, and alkaline earth carbonates and zirconium oxide were used as precursors for the zirconate system. It was found that both systems form solid solutions throughout the composition range. The implications of these results with regards to the applicability of the molten salt method as a tool to investigate low temperature phase equilibria are discussed.
Acoustic energy has been primarily used in materials research to disaggregate solids and/or disperse them in fluids. It has also been used in a few studies to influence or cause new reactions in organic and organometallic systems. However, the potential of acoustic energy in the area of inorganic reactions and materials science has been virtually unexploited. We report herein new effects of acoustic waves in catalyzing reactions in the systems Al2O3 + H2O and Al2O3 + P2O5 + H2O. In this study the effect of different alumina precursors and their particle size on their reactivity with water and H3PO4 was investigated when exposed to 20 kHz waves.
A relaxor ferroelectric of composition 0.93Pb(Mg1/3Nb2/3)O3-0.07PbTiO3 was sintered with 3 wt.% commercial sealing glass at 750 °C for 30 min to achieve ≥95% of theoretical density and a nearly pure perovskite phase. At higher glass additions (up to 20 wt.%), higher sintering temperatures (up to 800 °C), and longer sintering times (up to 4 h), the amount of perovskite (PMN type) decreases and that of pyrochlore (6PbO · MgO · 3Nb2O5 or 3PbO · 2Nb2O5) increases. On sintering at 800 °C for 4 h no perovskite phase is present in compositions with even 1% glass addition. The reaction of glass with the PMN phase was found to lead to the disappearance of the perovskite. Addition of 0.1 to 0.6 wt.% MgO to compositions containing 1 and 3 wt.% glass (and balance PMN-PT) results in essentially pure PMN perovskite phase on sintering at 700–800 °C for 30–240 min, confirming that the reaction of glass with PMN and depletion of MgO from PMN can be arrested. The sintered ceramics exhibit relaxor behavior and possess dielectric properties essentially commensurate with the phase composition.
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