MONAD GRAPhi-X
Vedecké laboratórium · jeden graf na stránku
Bio a difúzia
Science lab page · one study surface at a time.
Diffusion · living field
∂c/∂t = D·∂²c/∂x²
∂c/∂t = D·∂²c/∂x² D = 0.35
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Diffusion — Fick's second law
∂c/∂t = D·∂²c/∂x², solved on 96 cells with an explicit scheme and zero-flux membranes. Total mass is conserved while the profile spreads as σ ∝ √(2Dt) — the macroscopic face of a random walk.
t
0
integration steps
peak c
0.983
decays as 1/√t
σ spread
2.72
√(2Dt) random-walk width
entropy
2.418
mass 6.81 conserved
Osmosis
Water crosses a semipermeable membrane toward higher solute concentration until the chemical potentials equalise: Π = i·M·R·T.
Le Chatelier
A system at equilibrium counteracts an imposed change. Raising a reactant concentration shifts the reaction to consume it.
Michaelis-Menten
Enzyme rate v = Vmax·[S]/(Km + [S]) — binding saturates, so kinetics turn from first-order to zero-order.