Physics / advanced
From collisions to transport equations
Derive kinetic descriptions and transport coefficients, tracking collision assumptions, conservation laws, and the emergence of hydrodynamic behavior.
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Module 01 advanced
From collisions to transport equations
Derive kinetic descriptions and transport coefficients, tracking collision assumptions, conservation laws, and the emergence of hydrodynamic behavior.
- 01
Normalize the distribution before taking moments
Separate particle number, mean motion, and random momentum transport.
27 min - 02
Account for gains and losses in velocity space
Build the dilute-gas collision operator from relative speed and elastic scattering.
27 min - 03
Find the arrow of time in the closure assumption
Derive the sign of Boltzmann entropy production without confusing it with fine-grained entropy.
27 min - 04
Identify the five slow fields of a monatomic gas
Use collision invariants to derive conservation and a local Maxwellian closure.
27 min - 05
Relax toward a Maxwellian without losing conservation
Use moment matching and separate physical relaxation from numerical stepping.
27 min - 06
Organize the hydrodynamic limit by a small parameter
Separate solvability, moment matching, and the order of dissipative corrections.
27 min - 07
Transport momentum and energy between neighboring layers
Compute dilute-gas transport coefficients with their signs, units, and model limitations.
27 min - 08
Relate thermal spreading to drift under a weak force
Derive the Einstein relation from equilibrium flux balance and a Langevin model.
27 min - 09
Keep velocity memory when diffusion is premature
Derive a finite-time spreading law and locate the continuum regime.
27 min - 10
Let conserved momentum remember a molecular impulse
Connect collective fluctuations, correlation tails, and limits of simple relaxation models.
27 min