Resonance 

About: Resonance is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Science education & Earthquake engineering. It has an ISSN identifier of 0971-8044. Over the lifetime, 2290 publications have been published receiving 27123 citations. The journal is also known as: Resonance.

Introduction to algorithms: 4. Turtle graphics

Abstract: The primary purpose of a programming language is to assist the programmer in the practice of her art. Each language is either designed for a class of problems or supports a different style of programming. In other words, a programming language turns the computer into a ‘virtual machine’ whose features and capabilities are unlimited. In this article, we illustrate these aspects through a language similar tologo. Programs are developed to draw geometric pictures using this language.

A method for the construction of minimum-redundancy codes

Abstract: An optimum method of coding an ensemble of messages consisting of a finite number of members is developed. A minimum-redundancy code is one constructed in such a way that the average number of coding digits per message is minimized.

Inhomogeneous electron gas

Abstract: Shobhana Narasimhan’s article ‘A Tryst With Density’ in this issue of Resonance describes a remarkable theorem proved by Hohenberg and Kohn in 1964, and its aftermath. These authors considered a system of electrons in an external potential. This is an excellent idealised model of an atom, molecule or solid because the nuclei are so much heavier than the electrons and can be treated as an external potential. The difficulty lies in accounting for the interaction between the electrons – what one electron is doing depends on what all the others are doing. It therefore came as a shock when the ground state energy of this very general and nontrivial system was shown by Hohenberg and Kohn to be the result of minimising an expression which only contained a function of three variables. This function was just the number of electrons per unit volume as a function of position, something which chemists and crystallographers had long dealt with as a very meaningful and measurable quantity. The theorem showed that such an expression exists, but did not provide the form, which could contain nonlinear terms, derivatives, and integrals of the electron density. While approximate theories of this kind had been proposed before, it was unexpected that the idea of using the electron density could be made exact. What a marvellous turn of events that an existence theorem, proved by contradiction in a modestly written paper would revolutionise the modeling of materials half a century later and win a Nobel Prize in Chemistry for one of the authors!

There’s plenty of room at the bottom

Abstract: The theory of chemical processes is based on theoretical physics. In this sense, physics supplies the foundation of chemistry. The biological example of writing information on a small scale has inspired to think of something that should be possible. Suppose, to be conservative, that a bit of information is going to require a little cube of atoms 5 times 5 times 5 – that is 125 atoms. The magnetic properties on a very small scale are not the same as on a large scale; there is the "domain" problem involved. The electron microscope is not quite good enough, with the greatest care and effort, it can only resolve about 10 angstroms. The wave length of the electron in such a microscope is only 1/20 of an angstrom. Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics.