Saturday, January 29, 2011

Great Bards of QbD: Lewis Fry Richardson

Integration in time (and space) of the equations of mass, momentum and energy conservation plays a growing role in QbD.  An early contributor to this field was Lewis Fry Richardson, whose 1922 book, Weather Prediction by Numerical Process, laid the basis for modern weather prediction techniques.  Richardson also occupied himself with understanding turbulence and like Corrsin, was briefly moved to write a verse about his ideas.  Corrsin was inspired by Shakespeare; Richardson by Jonathan Swift and Augustus de Morgan to write about the cascade of energy from large to small scales:
  Big whorls have little whorls,
  Which feed on their velocity;
  And little whorls have lesser whorls,
  And so on to viscosity
  (in the molecular sense).
Many subsequent students of turbulence and mixing built on Richardson's work, and the Richardson Number is named in his honour. He also analyzed wars using mathematics and had early ideas about fractals while studying the lengths of shared borders between countries. Recipients of the Lewis Fry Richardson Medal have included Benoit Mandelbrot.

De Morgan had written:
  Great fleas have little fleas upon their backs to bite 'em,
  And little fleas have lesser fleas, and so ad infinitum.
  And the great fleas themselves, in turn, have greater fleas to go on;
  While these again have greater still, and greater still, and so on.
Swift originally wrote (in 1733):
  So, naturalists observe, a flea
  Hath smaller fleas that on him prey;
  And these have smaller still to bite 'em;
  And so proceed ad infinitum.
  Thus every poet, in his kind,
  Is bit by him that comes behind.

Great Bards of QbD: Stanley Corrsin

When we calculate mixing timescales in reactors and crystallizers [Liquid mixing: batch and fed batch mixing times], we leverage the work of Stanley Corrsin, one of many pre-Internet scientists who laid foundations for our predictive abilities.  His paper, [Simple theory of an idealized turbulent mixer,  AIChE Journal, Volume 3, Issue 3, pages 329–330, September 1957] showed how the time constant for mixing depended on the rate of dissipation of turbulent kinetic energy.  

Stanley loved his subject so much that he was moved to poetry.  He is responsible for the following sonnet, inspired by one of Shakespeare's (Sonnet 18 Shall I compare thee to a Summer's day?): 

For Hans Liepmann [2] on the occasion of his 70th birthday, with apologies to Bill S. and Liz B.B.

Shall we compare you to a laminar flow?
You are more lovely and more sinuous.
Rough winter winds shake branches free of snow,
And summer’s plumes churn up in cumulus.
How do we perceive you? Let me count the ways.
A random vortex field with strain entwined.
Fractal? Big and small swirls in the maze
May give us paradigms of flows to find.
Orthonormal forms non-linearly renew
Intricate flows with many free degrees
Or, in the latest fashion, merely few —
As strange attractor. In fact, we need Cray 3’s [3].
Experiment and theory, unforgiving;
For serious searcher, fun ... and it’s a living!

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