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Prototype2009: Energy Distribution

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This is the maths used to derive the velocity of generated particles in generator/molecule . The base maths are taken from evogrid-analysis/temperature, which is taken from gmxdump.

ekin = ((vel.x * vel.x * mass ) / 2) + ((vel.y * vel.y * mass ) / 2) + ((vel.z * vel.z * mass ) / 2)

temp = (2 * ekin) / ( 3 * BOLTZ ) // 3 * due to 3 axis

2 * ekin = temp * 3 * BOLTZ

ekin = ( temp * 3 * BOLTZ ) / 2

((vel.x * vel.x * mass ) / 2) + ((vel.y * vel.y * mass ) / 2) + ((vel.z * vel.z * mass ) / 2) = ( temp * 3 * BOLTZ ) / 2

(vel.x * vel.x * mass ) + (vel.y * vel.y * mass ) + (vel.z * vel.z * mass ) = ( temp * 3 * BOLTZ )

mass * ( (vel.x * vel.x ) + (vel.y * vel.y ) + (vel.z + vel.z) ) = temp * 3 * BOLTZ

(vel.x * vel.x ) + (vel.y * vel.y ) + (vel.z + vel.z) = (temp * 3 * BOLTZ / mass)

To get a single component, we'll consider as if we've divided both sides by three. We'll use a Maxwell-Boltzman distribution to make this randomly distributed over all three axis

vel.x * vel.x = (DIST * temp * BOLTZ ) / mass

vel.x = sqrt( ( DIST * temp * BOLTZ ) / mass )

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