By A. M. Selvam

This booklet goals to advertise the knowledge of a few of the elemental mathematical and medical concerns within the topics on the subject of weather dynamics, chaos and quantum mechanics. it's in keeping with vast learn paintings in atmospheric technology performed over 20 years.

Atmospheric flows convey self related fractal fluctuations, a signature of long-range correlations on all space-time scales. sensible simulation and prediction of atmospheric flows calls for the incorporation of the physics of saw fractal fluctuation features in conventional meteorological conception. A normal structures idea version for fractal space-time fluctuations in turbulent atmospheric flows is gifted and utilized to the formation of rain in hot clouds. This version provides scale-free common governing equations for cloud development procedures. The version envisioned cloud parameters are in contract with suggested observations, particularly, the cloud drop-size distribution. Rain formation can take place in hot clouds inside half-hour as saw in perform lower than beneficial stipulations of moisture provide within the surroundings. conventional cloud actual options for rain improvement calls for over an hour for a full-sized raindrop to shape.

The booklet presents heritage studying for postgraduate scholars of Meteorology, Atmospheric Sciences/Physics, Environmental Sciences, and scientists operating within the box of the subject of the booklet in addition to the multidisciplinary box of Nonlinear Dynamics and Chaos.

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Sornette (2009) discusses the ubiquity of observed power law distributions in complex systems as follows. The extension of Boltzmann’s distribution to out-of-equilibrium systems is the subject of intense scrutiny. In the quest to characterize complex systems, two distributions have played a leading role: the normal (or Gaussian) distribution and the power law distribution. Power laws obey the symmetry of scale invariance. Power law distributions and more generally regularly varying distributions remain robust functional forms under a large number of operations, such as linear combinations, products, minima, maxima, order statistics, powers, which may also explain their ubiquity and attractiveness.

Cambridge University Press, Cambridge Checa R, Tapiador FJ (2011) A maximum entropy modelling of the rain drop size distribution. Entropy 13:293–315 Cohen EGD (2005) Boltzmann and Einstein: statistics and dynamics—an unsolved problem. PRAMANA 64(5):635–643 Damasceno P, Engel M, Glotzer S (2012) Predictive self-assembly of polyhedra into complex structures. Science 337(6093):453–457 Dennery P (1972) An introduction to statistical mechanics. George Allen and Unwin, London Devenish BJ, Bartello P, Brenguier J-L, Collins LR, Grabowski WW, IJzermans RHA, Malinowski SP, Reeks MW, Vassilicos JC, Wangi L-P, Warhaft Z (2012) Review Article: droplet growth in warm turbulent clouds.

7 General Systems Theory and Classical Statistical Physics A summary of Lebowitz’s (Lebowitz 1999) discussion on the essential role of classical statistical mechanical concepts underlying the formulation of precise physical laws for observed macroscale phenomena in nature is given below. Nature has a hierarchical structure, with time, length, and energy scales ranging from the submicroscopic to the supergalactic. Surprisingly it is possible and in many cases essential to discuss these levels independently—quarks are irrelevant for understanding protein folding and atoms are a distraction when studying ocean currents.

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