The Smooth Dance of Two Spheres
An Exact Calculation in Fluid Mechanics

Kengo Ichiki

Two spheres face each other in a viscous fluid. This book calculates their interaction not approximately but exactly — and tells the story of the research along the way. The English edition of the Japanese original 厳密な計算 ふたつの球のなめらかなダンス, translated by the author.

Paperback/Kindle on Amazon.com/Amazon.co.jp: paperbackKindle

Also in Kindle Unlimited.

Six numbered billiard balls on a blue-grey checkered background with pale curves suggesting flow

What does it take to calculate something exactly?

Two spheres move through a viscous fluid. Follow their hydrodynamic interaction from the equations of Stokes flow to C code and 1,414 exact coefficient values.

From approximation to exact results. From equations to code. And into the human story of research.

A finite decimal, 0.333333, giving way to the exact fraction one third

From approximation to exact calculation

Instead of stopping at a "good enough" floating-point approximation, this book uses exact rational arithmetic with GMP to obtain exact coefficient values.

A diagram leading from the Stokes equations to C code and a table of coefficients

From equations to code and tables

Follow Stokes flow, Lamb's general solution, and the Jeffrey–Onishi recurrence relations into working C code, then onward to tables containing 1,414 exact coefficient values.

A blurred bookshelf filled with books on fluid mechanics, mathematics, and physics

The human story of research

Meet the mentors and collaborators, the wrong turns and failures, and the passion, struggles, and dogged persistence: the human story that formal papers leave out.

A close-up of Table A.1 showing long integers densely filling two columns of an exact coefficient table

1,414 exact coefficient values fill the page.

A technical doujinshi: neither a textbook nor a specialist monograph. An independently produced technical book that works through the mathematics, writes the code, and calculates and verifies the exact coefficients. For curious readers who want both the mathematics and the human story behind the research.

Where it comes from

The book works through the core ideas of a 1984 paper on two spheres in Stokes flow — the kind of problem the author worked on as a researcher in microhydrodynamics — all the way to exact results. The code is C with the GNU Multiple Precision library; the same lineage continues in the author's open-source libstokes.

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