pp 155-159 February 2020 Editorial
pp 162-162 February 2020 Science Smiles
pp 163-168 February 2020 Article-in-a-Box
pp 169-175 February 2020 General Article
pp 177-190 February 2020 General Article
In this article1, I reminisce about my fond interactions withJohn Torrence Tate (13 March, 1925–16 October, 2019), myteacher, mentor and PhD advisor. It is hard to trace theinfluence of Tate’s work on other works accurately, as thebasic objects, ideas and theorems that he introduced havepermeated (and have been generalized by others into widelyused theories) throughout mathematics. I briefly describehis many fundamental contributions to number theory andarithmetic geometry, and end with some personal anecdotes.
pp 191-213 February 2020 General Article
A rigid body accelerated through a frictionless fluid appearsto gain mass. Swimmers, air bubbles, submarines and airshipsare slowed down by the associated ‘added mass’ forcewhich is distinct from viscous drag and buoyancy. In particlephysics, an otherwise massless electron, quark, W or Z boson,moving through the Higgs field acquires a mass. In thisarticle, we introduce the fluid mechanical added mass effectthrough examples and use its analogy with the Higgs mechanismto intuitively explain how the carriers of the weak force(W and Z bosons) get their masses while leaving the photonmassless.
pp 215-231 February 2020 General Article
Nanoparticle research is an exciting field. Serving as a linkbetween bulk materials and atoms, these materials, existingon a nanometre scale (10−9m), display some fascinating properties.One such property is the depression of melting point.As the particle size decreases, the melting temperature decreasesdramatically. This article describes a model explainingthe origin of this behaviour of nanomaterials (Figure 1).To reinforce the concept in the text and force the reader tothink carefully about the quantitative aspects, short problemshave been included in the end.
pp 233-247 February 2020 General Article
In mammals, including humans, males and females differ notonly in physical appearance but in every cell of their body:male cells have a tiny Y-chromosome which females lack. Femalesinstead have two X-chromosomes whilemales have onlyone. It is not universally true though, as majority of fishes,frogs, lizards and turtles have no sex chromosomes. Their sexis generally determined based on the environment (e.g. temperature)in which the eggs grow. Though, the Y-chromosomegene, Sry, triggers male development, it alone is not enoughto differentiate the two sexes; orderly expression of a numberof genes, generally present on the autosomes, is requiredto ensure differentiation of a specific gonad – testis or ovary.Individuals bearing testes become male while those havingovaries become female. Excepting the Y-chromosomal Sry,almost all other genes in this cascade are evolutionarily conservedthroughout vertebrates. Mutually antagonistic interactionsof the male and female pathway genes lead to the formationof the gonads that eventually determine the sex of theindividual. Most disorders of sexual development occur dueto mutations in any of these genes.
pp 249-268 February 2020 General Article
We make a pedagogical survey on why the charge carriers(electrons) in graphene are called massless Dirac fermions.Our analysis begins at the beginning, namely, we start fromthe quantum chemistry of two nearby carbon (C) atoms andshow how their hybridized orbitals ‘valence-bond’ with eachother to form an energy-band in the solid-state. This yieldsa two-dimensional honeycomb lattice of graphene, which canbe viewed as two inter-penetrating triangular sublattices. Thatrecognition provides a perfect setting for describing the dynamicsof the last weakly-localized valence electron of C ina tight-binding model, which captures all the unusual electronicphenomena of graphene. The latter emerges from aresemblance to the relativistic Dirac theory of electrons because,in the long-wavelength limit, the energy dispersion islinear in the wave vector. We build up – step by step – this remarkabletransition of a carbon-based material to an exotictwo-dimensional Dirac solid, in which much of the quantumaspects of modern condensed matte physics can be tested inthe laboratory.
pp 269-296 February 2020 Series Article
Wonderful as they are, insects do not by any means exhaustthe possibilities of suitable organisms to conduct fascinating,cutting-edge, low-cost research, especially in animal behavior.Having seen how insects can be used to this end, in all theprevious articles in this series, I will now deliberately chooseexamples from studies done on vertebrates, starting with fishand navigating through the evolutionary tree of life, all theway to humans. In this article, we will see how simple, cleverexperiments can reveal that when fish fight, the outcome isnot only based on their intrinsic fighting abilities but alsoon extrinsic factors such as prior winning and losing experiences,and indeed, on a sophisticated interaction betweenintrinsic and extrinsic factors. In particular, we will studythe phenomenon of winner-effects and loser-effects and learnthat this is a near-virgin field of research waiting to be exploitedand eminently suitable for cutting-edge research at atrifling cost.
pp 297-307 February 2020 Classroom
I have been asked several times, by teachers, students andfriends, how I create math problems, specifically the ones thatappear in olympiads. For me, olympiad problems are a byproductof my explorations of mathematics. In this write-upI will explain this with a particular example. We will startwith a simple problem and create many more problems ofdifferent flavours and levels.
pp 309-312 February 2020 Reflections
pp 313-325 February 2020 Classics
pp 326-326 February 2020 Birds in the Backyard
Volume 25 | Issue 7