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Paul Bird's Scientific Research

This is a blog containing some scientific research I have done in various fields. My scientific interests are in the areas of physics, mathematics, and the brain. They mostly consist of theories I come up with now and again. Some of them are a bit unconventional or speculative for traditional media.

Double Torus Gear

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September 16, 2015

Invention

A pair of interlocking tori with a helical grooves may serve as a transmission gear???

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Vortex Solution to Navier Stokes Equations

August 01, 2011

This is a solution I found to the Navier Stokes equations . It uses the flow lines of the Hopf Fibration (which is basically just a way of covering the entire 3D space in circles). The flow lines can be seen in this image below: You can see my paper here. Solution to Navier-Stokes equation . Unfortunately I won't get a million pounds for winning the Clay Millennium prize because this is a compressible not incompressible solution. :( Oh, well. Nice try! I think it's pretty nice anyway. :) Also it uses the nice identity: which paramaterizes the Pythagorean quadruples!

Tarski-Seidenberg theorem

April 21, 2014

Tarski-Seidenberg theorem States that a set of equalities and inequalities f(x1,x2,x3,....xn)>=0 can be reduced down to a set of equalities and inequalities f(x1,x2,x3,....xn-1)>=0 with one less variable. Thus all equations can be reduced to a set of equalities and inequalities on their coefficients. See also: cylindrical algebraic decomposition See: Elimination These algorithms aren't very simple.

N=8 Supergravity coupled to E8xE8 N=4 Super Yang-Mills unified in 19 Dimensions?

April 01, 2014

N=8 Supergravity coupled to E 8 xE 8 N=4 Super Yang-Mills unified in 19 Dimensions? Pure N=8 supergravity can be derived from a compactification of an 11 dimensional action. The massless(?) sector of Heterotic String Theory contains 256 + 248x2x16 = 2 13 particles. This suggests that it could be the compactification of a higher dimension action in 19 dimensions . It should be related to a 16 dimensional lattice. Only up to 11D has group structure . fermion = (D-3)x2 (D-3)/2 graviton = (D-2)(D-1)/2-1 antisymmetric n-tensor (D-2)(D-3)(D-4)..(D-n-1)/n! 11D: graviton ( 44 ) + antisymmetric-3-tensor( 84 ) + fermion ( 128 ) = 2 8 components. (Root vectors of E8 240 roots, 16 less) 19D: graviton ( 152 ) + 232 x vector( 17 )+ fermion ( 4096 ) = 2 13 components. (136, 680, 2380, 6188) (Root vectors of 16D lattice...? E 8 xE 8 ? D 16 ? (too small) Coexter? ~ 8160 roots? 32 less? 4320 densest in 16 dimensions?) 27D: 196608 components. ...