A note on the equivalence of shock manifold equations

Summary The shock manifold equation is a first order nonlinear partial differential equation, which describes the kinematics of a shockfront in an ideal gas with constant specific heats. However, it was found that there was more than one of these shock manifold equations, and the shock surface could be embedded in a one parameter family of surfaces, obtained as a solution of any of these shock manifold equations. Associated with each shock manifold equation is a set of characteristic curves called shock rays. This paper investigates the nature of various associated shock ray equations.On leave from Beloit College, Beloit, WI, 535111 U.S.A.     

Fractional Order PI‐PD Control of Liquid Level in Coupled Two Tank System and its Experimental Validation

This paper presents a level control problem of a coupled two tank single input single output (SISO) system. A cascade control strategy is adopted having a fractional order proportional integral (FOPI) controller and fractional order proportional derivative (FOPD) controller in the outer and the inner loops, respectively. Cascaded integer order proportional integral (IOPI) and integer order proportional derivative (IOPD) controllers are also designed to compare the performances. A frequency domain approach is followed to design all the controllers. It is mathematically shown that the FOPI and FOPD controllers can achieve less steady state error and consume less energy than that of the IOPI and IOPD controllers while meeting the same phase margin and gain crossover frequency. All propositions are validated on an experimental setup.     

Wavelet Packet Entropy and RBFNN Based Fault Detection,Classification and Localization on HVAC Transmission Line

The article presents a technique for fast and accurate detection, classification and localization of faults on the high voltage transmission systems considering the alternator's dynamics and the effect of transformers. The systems have been simulated by ATP/EMTP software and three phase fault currents at one end of the transmission line are recorded with a sampling frequency of 50 kHz. The fault signals are decomposed by wavelet packet decomposition (WPD) up to 3^rd level with mother wavelet db6 to calculate wavelet packet entropy (WPE) which has the ability to measure the uncertainty of fault signals during feature extraction. A properly designed radial basis function neural network (RBFNN) trained with these features can recognize, classify and locate faults faster as it utilizes only half cycle data after fault initiation. This technique has been verified for different fault categories, fault impedances and fault inception angles (FIA) at different locations for two different transmission systems. The investigated results demonstrate that the wavelet packet entropy is very powerful for extracting the features from the fault signals and RBFNN is very accurate for classification and localization of faults on the transmission line including locations close to the generator's end.     

A thermal investigation on coals from Assam (India)

A thermal characterization of two coal samples from Ledo and Tikak collieries of Makum coalfield, Assam, India using XRD, FT-IR, and TGA was reported in this paper. The coal samples were heated for 20, 40 and 60 min in a 1000-watt heater (temperature ∼ 250 °C) in presence of air and characterized by XRD and FT-IR spectroscopy. Both the coals contain amorphous and crystalline phases. The raw coals also contain very small peaks due to quartz, calcite, gypsum, pyrite, and chlorite. The XRD patterns were found to change upon heating. In the coals heated for 20 and 40 min, it was observed that both amorphous and crystalline parts are common in them; crystalline part being the major one in the 40 min heated samples. The XRD patterns of the samples heated for 60 min indicate the presence of major quantities of α-quartz, hematite, and chlorite in them. They also show some new peaks, which are assigned to be kaolinite, illite, magnetite and very small in comparison to the amorphous portion in raw coals. α-quartz was found to be most stable crystalline phase of silica in the coals. The crystallinity % (X-ray) of the coals heat-treated for different times was determined and found to be increasing with time of heating. The FT-IR spectra of raw and heat-treated coal samples at 250 °C were also recorded and compared. The spectra were observed to be almost similar and it was observed that few functional groups disappear on heating at 250 °C. The same coal samples were also characterized by thermogravimetric analysis (TGA) and differential thermal analysis (DTA) techniques. On heat treatment in air atmosphere up to 800 °C, 20–27% weight loss occurs due to removal of various volatile materials. DTA results indicate the chemical reactivity of the coal sample initially at 80–110 °C due to loss of water, and two other major reactions at around 420 and 530 °C due to primary and secondary volatization.     

Removal of toxic uranium from synthetic nuclear power reactor effluents using uranyl ion imprinted polymer particles

Major quantities of uranium find use as nuclear fuel in nuclear power reactors. In view of the extreme toxicity of uranium and consequent stringent limits fixed by WHO and various national governments, it is essential to remove uranium from nuclear power reactor effluents before discharge into environment. Ion imprinted polymer (IIP) materials have traditionally been used for the recovery of uranium from dilute aqueous solutions prior to detection or from seawater. We now describe the use of IIP materials for selective removal of uranium from a typical synthetic nuclear power reactor effluent. The IIP materials were prepared for uranyl ion (imprint ion) by forming binary salicylaldoxime (SALO) or 4-vinylpyridine (VP) or ternary SALO-VP complexes in 2-methoxyethanol (porogen) and copolymerizing in the presence of styrene (monomer), divinylbenzene (cross-linking monomer), and 2,2'-azobisisobutyronitrile (initiator). The resulting materials were then ground and sieved to obtain unleached polymer particles. Leached IIP particles were obtained by leaching the imprint ions with 6.0 M HCl. Control polymer particles were also prepared analogously without the imprint ion. The IIP particles obtained with ternary complex alone gave quantitative removal of uranyl ion in the pH range 3.5-5.0 with as low as 0.08 g. The retention capacity of uranyl IIP particles was found to be 98.50 mg/g of polymer. The present study successfully demonstrates the feasibility of removing uranyl ions selectively in the range 5 microg - 300 mg present in 500 mL of synthetic nuclear power reactor effluent containing a host of other inorganic species.     

Determining the Mechanism of In-Service Cylinder Distortion in Aluminum Engine Blocks with Cast-In Gray Iron Liners

In recent years, stringent government legislation on vehicle fuel efficiency has pushed the automotive industry to replace steel and cast iron power train components with light weight Al alloys. However, unlike their ferrous-based equivalents, Al-Si alloy engine blocks are prone to permanent dimensional distortion in critical locations such as the cylinder bore regions. Understanding the mechanisms that cause distortion will promote the use of Al alloys over ferrous alloys for power train applications and enable automotive manufacturers to meet emission standards and reduce fuel consumption. In this study, neutron diffraction was used to evaluate residual stress along the Al cylinder bridge and the gray cast iron liners of distorted and undistorted engine blocks. Microstructural analysis was carried out using OM, SEM, and TEM, while mechanical testing was accomplished via ambient and elevated temperature [~453 K (180 °C)] tensile testing. The results suggest that the distorted engine block had high tensile residual stress in the Al cylinder bridge, reaching a maximum of 170 MPa in the hoop direction, which triggered permanent dimensional distortion in the cylinders when exposed to service conditions. In addition, the middle of the cylinder had the highest magnitude of distortion since this region had a combination of high tensile residual stress (hoop stress of 150 MPa) and reduced strength compared with the bottom of the cylinder.     

Solving subclasses of multi-player stochastic games via linear complementarity problem formulations—a survey and some new results

We briefly survey some results on the orderfield property of 2-player and multi-player stochastic games and their mixtures. Some of these classes of stochastic games can be solved by formulating them as a Linear Complementarity Problem (LCP) or (Generalized) Vertical Linear Complementarity Problem (VLCP). We discuss some of these results and prove that certain new subclasses and mixtures of multi-player (or n-person) stochastic games can be solved via LCP formulations. Mohan, Neogy and Parthasarathy (in Proceedings of the International Conference on Complementarity Problems, 1997) proposed an LCP formulation of ??-discounted (multi-player) polystochastic games where the transitions are controlled by one player, and proved that this LCP is processible by Lemke??s algorithm. Using this formulation repeatedly, we prove that we can solve a subclass of ??-discounted switching control polystochastic games. As our proof is constructive, we have an algorithm for solving this subclass. This algorithm only involves iteratively solving different LCPs and hence, it follows that this subclass has the orderfield property, a?question left open in the paper on orderfield property of mixtures of stochastic games by Krishnamurthy et al., (Indian J. Stat. 72:246?C275, 2010). Furthermore, we use results from Krishnamurthy et al., Indian J. Stat. 72:246?C275, (2010) to solve some mixture classes using LCP (or VLCP) formulations. We also propose two different VLCP formulations for ??-discounted zero-sum perfect information stochastic games, the underlying matrices of both formulations being R ₀. As a result, we also have an alternative proof of the orderfield property of such games.     

Single-step growth dynamics of core–shell GaN on Ga<Subscript>2</Subscript>O<Subscript>3</Subscript> freestanding nanoprotruded microbelts

Freestanding wurtzite GaN nanoprotruded microbelts with Ga₂O₃ core, with typical thickness 1–10 μm, and length of few millimeters are synthesized by thermal annealing of Ga metal and subsequent reaction with ammonia at a low flow rate. They are of distinctive rectangular shape with a typical width of 10–100 μm. Thickness of the belt is about 1/10th of the width and length up to a few millimeters. The GaN, Ga₂O₃ layers and the GaN–Ga₂O₃ interface are characterized by high-resolution transmission electron microscopy after focused ion beam sectioning of the belt. Initially, Ga₂O₃ nucleates after reaction with the O₂ available in the environment, and subsequent reaction with NH₃ results in the formation of core–shell structure in the catalyst-free vapor–solid growth process. Having a low-symmetry phase, Ga₂O₃ can grow only in certain preferred directions thus controlling the final morphology of the belt. Nanoscale protrusions ~50–100 nm found on the surface of the belts could be an ideal system for building functional devices.