Molecule matters Dinitrogen

Dinitrogen (N₂) is a very stable and inert molecule due to the formation of a triple bond between the two atoms. Surprisingly isoelectronic molecules are quite reactive making dinitrogen very useful and unique.     

Electronic commerce 1. What is e-commerce?

In this part of the series, we define different types of e-commerce and list their advantages and disadvantages     

The Indian monsoon 5. Prediction of the monsoon

In this article we first consider the importance of prediction of the monsoon, and events such as the intense rainfall event over Mumbai in July 2005. We then discuss how meteorologists make short-, medium-, and long-range forecasts and the concept of the limit of predictability in a chaotic system such as the atmosphere. Problems and prospects of prediction on different time-scales are discussed by using one example of short-range forecasts and the prediction of the monsoon by dynamical and statistical methods. Finally we consider measures of the skill of a forecast and how high the skill has to be for it to be useful for applications.     

Fascinating organic transformations 2. The ubiquitous hydrogen bond

Hydrogen bonds can transform simple molecules into beautiful architectures. This is well illustrated in this article.     

G?del’s proof 3. Incompleteness theorems

After presenting the technique developed by G?del to examine questions about a theory such as Number Theory, Set Theory by the theory itself, we present the surprising Incompleteness Theorems of G?del.     

Quantum computing 1. Building blocks of a quantum computer

In this article we have seen how the principles of quantum physics can be exploited in making a computational device. However, we still haven’t seen the kind of algorithms a quantum computer would use and how they would be different from traditional algorithms. We will look at these issues in the next part of this article, with the help of Shor’s famous factorization algorithm. We will also briefly mention some practical issues and the progress achieved so far.     

Silicon photonics Silicon Raman lasers

The increased use of optoelectronic devicessuch as TV screens and computer monitors in everyday life, calls for a material on which integration of all circuits may be performed. Silicon, the most widely used material in electronics, has limited application in optoelectronics due to its poor light emission property. In this article, the need for silicon photonics in present day ICs, and communication, the reason for its inefficient light emission, and recent breakthrough in the form of Si Raman laser are discussed.     

Fire synthesis Preparation of alumina products

The novel ‘solution combustion method’ or ‘fire synthesis’ has been used to make high temperature synthesised ceramic materials. The process, which can be initiated at low temperature, is self-propagating and gas-producing. Fine-particle alumina and its related oxides can be easily prepared in bulk by the redox mixture method.     

Mangroves The most fragile forest ecosystem

Mangroves, an exclusive group of plants with remarkable ecological importance, inhabit mostly the zones washed by the back and forth movement of tides. They are disappearing rapidly from their natural habitat due to various reasons. Mangroves create a unique ecological environment that is composed of rich assemblages of species. Economic importance of mangroves is also noteworthy.     

Symmetries and conservation laws in classical and quantum mechanics 2. Quantum mechanics

In Part 1 of this two-part article we have spelt out, in some detail, the link between symmetries and conservation principles in the Lagrangian and Hamiltonian formulations of classical mechanics (CM). In this second part, we turn our attention to the corresponding question in quantum mechanics (QM). The generalization we embark upon will proceed in two directions: from the classical formulation to the quantum mechanical one, and from a single (infinitesimal) symmetry to a multi-dimensional Lie group of symmetries. Of course, we always have some definite physical system in mind. We also assume that the reader is familiar with the elements of quantum mechanics at the level of a standard first course on the subject. Operators will be denoted with an overhead caret, e.g., $ \hat A,\hat G,\hat U $ \hat A,\hat G,\hat U , etc., while $ [\hat A,\hat B] = \hat A\hat B - \hat B\hat A $ [\hat A,\hat B] = \hat A\hat B - \hat B\hat A is the commutator of $ \hat A $ \hat A and $ \hat B $ \hat B .     

Symmetries and conservation laws in classical and quantum mechanics 1. Classical mechanics

We describe the connection between continuous symmetries and conservation laws in classical mechanics. This is done at successively more sophisticated levels, bringing out important features at each level: the Newtonian, the Euler-Lagrange, and the Hamiltonian phase-space forms of mechanics. The role of the Action Principle is emphasised, and many examples are given.