Applying pure mathematics: mathematics in the natural sciences

The book of nature is written in the language of mathematics. This quotation, attributed to Galileo, seemed to hold to an unreasonable1 extent in the era of quantum mechanics.

Natural frequencies and modes of tapered skew plates

The vibration of simply supported skew plates having a linear variation in thickness in one direction is considered. Approximate analysis is made by using Lagrange's equations employing the double Fourier sine series in oblique co-ordinates to represent the deflected surface. Natural frequencies are obtained for rhombic plates for several ranges of thickness variation and skew angle. The nodal patterns plotted for a few typical configurations show interesting metamorphoses with variation in thickness and skew angle.

Natural history and behaviour of the primitively eusocial wasp Ropalidia marginata (Hymenoptera: Vespidae): a comparison of the two sexes

We report the natural history and behaviour of the primitively eusocial wasp Ropalidia marginata with a special reference to the males. We found that just as nests of this species are found throughout the year, so are the males. Females spend all their life in their nests but males stay in their natal nests only for 1-12 days and leave to lead a nomadic life. Males maintained in the laboratory can live for up to 140 days. Like all eusocial hymenopteran males, R. marginata males also do not perform any colony maintenance activities. We found that males did not forage or feed larvae. Compared with females, males showed fewer dominance and subordinate behaviours and being solicited behaviour and more feeding self and soliciting behaviours. By comparing males with young females, we found similar differences, except that the males showed similar rates of feeding self and higher rates of subordinate behaviour.

A comparative analysis of regeneration in natural forests and joint forest management plantations in Uttara Kannada district, Western Ghats

Five villages undertaking joint forest management (JFM) were chosen in Uttara Kannada district, Karnataka for assessing regeneration in plantations and nearby natural forests of the village. Species number, stem density, diversity index, similarity in species composition in less disturbed and disturbed forests and plantations in the village were compared. Stem density was low in all the disturbed forests; however, the species number was low in disturbed forests of three villages and high in two villages. Plantations showed lower diversity values compared to the adjacent natural forests. Regeneration in all less disturbed forests was better compared to the disturbed counterparts. Villages were ranked based on number of landless families, per, capita forest available and number of cut stems. Assessment of village forests using ranks indicates that parameters such as per capita availability, cut stems in the forests may determine the success of JFM.

Natural Frequencies And Transient Responses Of 3-Phase Rotating Machine Windings

The analysis of transient electrical stresses in the insulation of high voltage rotating machines is rendered difficult because of the existence of capacitive and inductive couplings between phases. The Published theories ignore many of the couplings between phases to obtain the solution. A new procedure is proposed here to determine the transient voltage distribution on rotating machine windings. All the significicant capacitive and inductive couplings between different sections in a phase and between different sections in different phases have been considered in this analysis. The experimental results show good correlation with those computed.

Chemical modifications of natural triterpenes—glycyrrhetinic and boswellic acids: evaluation of their biological activity

Synthetic analogues of naturally occurring triterpenoids; glycyrrhetinic acid, arjunolic acid, and boswellic acids, by modification of A-ring with a cyano- and enone-functionality, have been reported. A novel method of synthesis of α-cyanoenones from isoxazoles is reported. Bioassays using primary mouse macrophages and tumor cell lines indicate potent anti-inflammatory and cytotoxic activities associated with cyano-enones of boswellic acid and glycyrrhetinic acid.

Effective thermal conductivity of a heat generating rod bundle dissipating heat by natural convection and radiation

A numerical study of conjugate natural convection and surface radiation in a horizontal hexagonal sheath housing 19 solid heat generating rods with cladding and argon as the fill gas, is performed. The natural convection in the sheath is driven by the volumetric heat generation in the solid rods. The problem is solved using the FLUENT CFD code. A correlation is obtained to predict the maximum temperature in the rod bundle for different pitch-to-diameter ratios and heat generating rates. The effective thermal conductivity is related to the heat generation rate, maximum temperature and the sheath temperature. Results are presented for the dimensionless maximum temperature, Rayleigh number and the contribution of radiation with changing emissivity, total wattage and the pitch-to-diameter ratio. In the simulation of a larger system that contains a rod bundle, the effective thermal conductivity facilitates simplified modelling of the rod bundle by treating it as a solid of effective thermal conductivity. The parametric studies revealed that the contribution of radiation can be 38-65% of the total heat generation, for the parameter ranges chosen. Data for critical Rayleigh number above which natural convection comes into effect is also presented. (C) 2011 Elsevier B.V. All rights reserved.