Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Micro-treatment options for components of organic fraction of MSW in residential areas

There is a growing interest in management of MSW through micro-treatment of organic fraction of municipal solid wastes (OFMSW) in many cities of India. The OFMSW fraction is high (> 80%) in many pockets within South Indian cities like Bangalore, Chikkamagalur, etc. and is largely represented by vegetable, fruit, packing and garden wastes. Among these, the last three have shown problems for easy decomposition. Fruit wastes are characterized by a large pectin supported fraction that decomposes quickly to organic acids (becomes pulpy) that eventually slow down anaerobic and aerobic decomposition processes. Paper fraction (newsprint and photocopying paper) as well as paddy straw (packing), bagasse (from cane juice stalls) and tree leaf litter (typical garden waste and street sweepings) are found in reasonably large proportions in MSW. These decompose slowly due to poor nutrients or physical state. We have examined the suitability of these substrates for micro-composting in plastic bins by tracking decomposition pattern and physical changes. It was found that fruit wastes decompose rapidly to produce organic acids and large leachate fraction such that it may need to be mixed with leachate absorbing materials (dry wastes) for good composting. Leaf litter, paddy straw and bagasse decompose to the tune of 90, 68 and 60% VS and are suitable for composting micro-treatment. Paper fractions even when augmented with 10% leaf compost failed to show appreciable decomposition in 50 days. All these feedstocks were found to have good biological methane potential (BMP) and showed promise for conversion to biogas under a mixed feed operation. Suitability of this approach was verified by operating a plug-flow type anaerobic digester where only leaf litter gathered nearby (as street sweepings) was used as feedstock. Here only a third of the BMP was realized at this scale (0.18 m(3) biogas/kg VS 0.55 m(3)/kg in BMP). We conclude that anaerobic digestion in plug-flow like digesters appear a more suitable micro-treatment option (2-10 kg VS/day) because in addition to compost it also produces biogas for domestic use nearby.

Robust flight stability and control for micro air vehicles.

This chapter presents the real time validation of fixed order robust 112 controller designed for the lateral stabilisation of a micro air vehicle named Sarika2. Digital signal processor (DSP) based onboard computer named flight instrumentation controller (FIC) is designed to operate under automatic or manual mode. FIC gathers data from multitude of sensors and is capable of closed loop control to enable autonomous flight. Fixed order lateral H-2 controller designed with the features such as incorporation of level I flying qualities, gust alleviation and noise rejection is coded on to the FIC. Challenging real time hardware in loop simulation (HILS) is done with dSPACE1104 RTI/RTW. Responses obtained from the HILS are compared with those obtained from the offline simulation. Finally, flight trials are conducted to demonstrate the satisfactory performance of the closed loop system. The generic design methodology developed is applicable to all classes of Mini and Micro air vehicles.

Interrelations of micro-organisms and mulberry III. The beneficial influence of certain heterotrophs on the nitrifiers in rhizosphere

Evidence has been presented to show that the autotrophic nitrifying organisms get stimulated in the mulberry rhizosphere. Three species of Pseudomonas, one each of Achromobacter and Bacillus capable of degrading methionine were shown to be stimulated in the rhizosphere. These bacteria were capable of reversing the inhibitory effect of methionine on soil nitrification. Two of them were able to form nitrite from methionine. The possibility that the increased nitrifying activity in the mulberry rhizosphere in the presence of methionine found in mulberry root exudations was the result of the activity of these organisms was suggested.

Interrelations of micro-organisms and mulberry II. Phyllosphere microflora and nitrogen fixation in leaf and root surfaces

The mulberry leaves were shown to harbour substantial populations of bacteria, streptomycetes, yeasts, and moulds. Azotobacter and Beijerinckia were observed to contribute to nearly 5 to 10 per cent of the bacterial population. When grown in water culture under sterile conditions, Azotobacter inoculation on the leaf or root surface was found to increase plant growth, dry wt, and nitrogen content of the mulberry. The beneficial effect of Azotobacter was largely influenced by the presence of a carbon source in the plant nutrient solution. The root inoculation in comparison to leaf application was found to confer greater benefits to the growing plant. The presence of carbohydrates and amino acids in the leaf leachates of mulberry was shown. The mutual beneficial nature of the association of the plant and Azotobacter has been brought to light.

Interrelations of soil micro-orgamisms and mulberry I.Phytohormone production by soil and rhizosphere bacteria and their effect on plant growth

Bacteria isolated from the rhizosphere of mulberry (Morus indica) as well as from control soil were tested for their effects on the growth of mulberry seedlings and for phytohormone production. About 12.8 per cent of the rhizosphere and 9.7 per cent of the soil isolates produced phytohormones in cultures. Rhizosphere isolates were more active in hormone synthesis than their soil counterparts. Soaking mulberry stem cuttings in culture filtrates of phytohormone synthesisers hastened their rooting. Culture filtrates of many isolates — hormone producers or not — stimulated or inhibited the growth of shoot and/or root of plants. Many cultures could also inhibit the germination of mulberry seeds.

Robust fixed order lateral H-2 controller for micro air vehicle

This paper presents a robust fixed order H-2 controller design using Strengthened discrete optimal projection equations, which approximate the first order necessary optimality condition. The novelty of this work is the application of the robust H-2 controller to a micro aerial vehicle named Sarika2 developed in house. The controller is designed in discrete domain for the lateral dynamics of Sarika2 in the presence of low frequency atmospheric turbulence (gust) and high frequency sensor noise. The design specification includes simultaneous stabilization, disturbance rejection and noise attenuation over the entire flight envelope of the vehicle. The resulting controller performance is comprehensively analyzed by means of simulation.

Completeness of the Coulomb wave functions in quantum mechanics

We give an explicit, direct, and fairly elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses only some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory; therefore it would form useful supplementary reading for a graduate course on quantum mechanics.

The Mechanics and Statistics of Active Matter

Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their motile constituents such as molecular motors. This article reviews recent progress in applying the principles of nonequilibrium statistical mechanics and hydrodynamics to form a systematic theory of the behavior of collections of active particles-active matter-with only minimal regard to microscopic details. A unified view of the many kinds of active matter is presented, encompassing not only living systems but inanimate analogs. Theory and experiment are discussed side by side.

Nonlinear fracture properties of concrete-concrete interfaces

The fracture properties of different concrete-concrete interfaces are determined using the Bazant's size effect model. The size effect on fracture properties are analyzed using the boundary effect model proposed by Wittmann and his co-workers. The interface properties at micro-level are analyzed through depth sensing micro-indentation and scanning electron microscopy. Geometrically similar beam specimens of different sizes having a transverse interface between two different strengths of concrete are tested under three-point bending in a closed loop servo-controlled machine with crack mouth opening displacement control. The fracture properties such as, fracture energy (G(f)), length of process zone (c(f)), brittleness number (beta), critical mode I stress intensity factor (K-ic), critical crack tip opening displacement CTODc (delta(c)), transitional ligament length to free boundary (a(j)), crack growth resistance curve and micro-hardness are determined. It is seen that the above fracture properties decrease as the difference between the compressive strength of concrete on either side of the interface increases. (C) 2010 Elsevier Ltd. All rights reserved.

Evaluation of ductile-brittle transition temperature (DBTT) of aluminide bond coats by micro-tensile test method

A method has been suggested to accurately determine the DBTT of diffusion aluminide bond coats. Micro-tensile testing of free-standing coating samples has been carried out. The DBTT was determined based on the variation of plastic strain-to-fracture with temperature. The positive features of this method over the previously reported techniques are highlighted. (C) 2010 Elsevier B.V. All rights reserved.

Effect of interface friction on the mechanics of indentation of a finite layer resting on a rigid substrate

Copper strips of 2.5 mm thickness resting on stainless steel anvils were normally indented by wedges under nominal plane strain conditions. Inflections in the hardness-penetration characteristics were identified. Inflections separate stages where each stage has typical mechanics of deformation. These are arrived at by studying the distortion of 0.125 mm spaced grids inscribed on the deformation plane of the strip. The sensitivity of hardness and deformation mechanics to wedge angle and the interfacial friction between strip and anvil were investigated within the framework of existing slip line field models of indentation of semi-infinite and finite blocks.