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Brownian Motion Hoodie

NO STEP REMEMBERS THE LAST | Pixelated Physics

\[\langle r^2\rangle = 4Dt\quad\text{(2D)}\]
$54.99 USD
$54.99 USD
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Size guide S–5XL · inches

In 1827 Robert Brown watched tiny particles from pollen grains jitter in water under his microscope, and could not make them stop. A 24,000-step Brownian path in a microscope field, coloured by time. Mean squared distance grows as 4Dt in 2D, so spread goes as √t. Pixel-art unisex hoodie in black; equation, symbols and sources in the physics panel below.

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Details

Size & fitS–5XL

Unisex Heavy Blend hoodie (Gildan 18500), classic fit.

SizeWidthLengthSleeve
S202733.5
M222834.5
L242935.5
XL263036.5
2XL283137.5
3XL303238.5
4XL323339.5
5XL343440.5

Measurements in inches. Width and length ±1 in, sleeve (from center back) ±0.75 in.

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Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

A pollen grain in water is knocked around by countless molecules, so it wanders randomly with no memory of its previous step. Its mean-square distance grows in proportion to time, and Einstein linked the rate to temperature and the fluid's viscosity, which made atoms measurable.

In 1827 Robert Brown watched tiny particles from pollen grains jitter in water under his microscope, and could not make them stop.

They are kicked by water molecules, enormous numbers of times a second, from random directions. Each step forgets the last. Einstein showed in 1905 that the mean squared distance grows in proportion to time, so the typical distance grows only as the square root of time.

Jean Perrin measured this in 1908 and used it to count molecules. It helped convince the remaining sceptics that atoms are real.

The art is one random walk of 24,000 Gaussian steps, coloured from cyan at the start to amber at the end, where the particle sits now.

No step remembers the last.

Equations

\[\langle r^2\rangle = 4Dt\quad\text{(2D)}\]
\[D = \frac{k_BT}{6\pi\eta a}\]
\[m\ddot{x} = -\gamma\dot{x} + F(t)\]
SymbolMeaningUnit
\(\langle r^2\rangle\) mean squared displacement \(\mathrm{m^2}\)
\(D\) diffusion coefficient \(\mathrm{m^2/s}\)
\(t\) time \(\mathrm{s}\)
\(k_B\) Boltzmann constant \(\mathrm{J/K}\)
\(T\) temperature \(\mathrm{K}\)
\(\eta\) viscosity of the fluid \(\mathrm{Pa·s}\)
\(a\) particle radius \(\mathrm{m}\)
\(\gamma\) drag coefficient \(\mathrm{kg/s}\)
\(F(t)\) random force from molecular kicks \(\mathrm{N}\)

Sources

  1. Brown (1828) A brief account of microscopical observations, Phil. Mag. 4, 161
  2. Einstein (1905) Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen, Ann. Phys. 322, 549
  3. Perrin (1909) Mouvement brownien et réalité moléculaire, Ann. Chim. Phys. 18, 5
  4. Langevin (1908) Sur la théorie du mouvement brownien, C. R. Acad. Sci. 146, 530

Source Einstein, A. (1905). Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik 322, 549–560.doi.org/10.1002/andp.19053220806

Field notes

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