Linked from

The 56 pages that link to Brownian motion, each with the reason it gives.

• DiffusionRelated: Its random molecular collisions provide a visible example of the motion underlying diffusion.

• Albert EinsteinRelated: Einstein’s 1905 analysis showed how this motion could provide evidence for atoms.

• Statistical mechanicsRelated: Its fluctuations reveal the statistical effects of a fluid’s unseen molecules.

• LocomotionCompared with: Random particle displacement resembles travel but is not organism-driven locomotion.

• Heat equationRelated: Its probability density evolves according to a heat equation under standard assumptions.

• Aquatic locomotionCompared with: At microscopic scales, passive random motion can rival an organism's directed propulsion.

• Kinetic energyRelated: It reveals the motion and kinetic energy of molecules through visible particle movement.

• AerosolRelated: Molecular collisions keep the smallest aerosol particles moving unpredictably.

• FlagellumCompared with: It can displace microscopic objects, but unlike flagellar propulsion it produces no directed thrust.

• Ludwig BoltzmannRelated: Its later quantitative analysis tested the molecular picture Boltzmann had argued for.

• Avogadro constantRelated: Perrin used its measurable statistics to estimate the number of molecules per mole.

• Effective temperatureRelated: Diffusion and mobility offer measurable quantities for estimating an effective temperature.

• AtomismRelated: Its measurable statistics provided evidence for unseen molecular motion.

• ColloidRelated: It helps keep colloidal particles moving instead of settling quickly.

• Wiener processRelated: The Wiener process formalizes the random motion first observed in suspended particles.

• FractalRelated: A Brownian path has fractal dimension two despite being a curve.

• FlocculationRelated: It drives collisions among fine particles in slowly mixed suspensions.

• Carryover cookingCompared with: It is microscopic particle motion, not the macroscopic inward heat transfer that drives carryover cooking.

• Molecular diffusionRelated: It provides observable evidence of the random motion underlying molecular diffusion.

• Optical tweezersRelated: Thermal fluctuations continually displace trapped particles and set limits on force measurements.

• SuspensionRelated: It can oppose gravitational settling for sufficiently small particles.

• Dynamic equilibriumRelated: Visible molecular fluctuations continue at equilibrium even when average properties remain unchanged.

• Diffusion coefficientRelated: Random microscopic steps produce the macroscopic spreading measured by a diffusion coefficient.

• Fluctuation–dissipation theoremBroader topic: The Einstein relation connects particle diffusion to mobility through thermal fluctuations.

• Diffusion equationRelated: Its probability density evolves according to a diffusion equation.

• Thermal fluctuationsBroader topic: It is a visible consequence of unresolved thermal fluctuations in a fluid.

• Dust coagulationRelated: It brings the smallest dust grains into collisions before larger grains dominate.

• NanoparticleRelated: Thermal collisions keep sufficiently small particles moving through liquids and influence their dispersion.

• BiophysicsRelated: It describes how thermal motion drives molecules through cells.

• Maxwell's demonRelated: It supplies the thermal fluctuations that feedback demons measure and attempt to rectify.

• Molecular machineRelated: Brownian motion is the unavoidable background against which molecular machines operate.

• Benoit MandelbrotRelated: Mandelbrot studied its mathematical structure and its connections to irregular paths.

• Cytoplasmic streamingCompared with: Unlike directed streaming, it produces no coordinated bulk flow.

• Insect locomotionCompared with: Unlike insect locomotion, Brownian motion is passive displacement rather than controlled movement.

• Jean PerrinRelated: Perrin tested Einstein’s account of this motion to estimate Avogadro’s number.

• Active matterRelated: Thermal fluctuations compete with the persistent propulsion characteristic of active units.

• Brownian ratchetNarrower topic: It supplies the random fluctuations that the ratchet rectifies.

• Itô's lemmaRelated: Its increments scale so their squared contributions persist in the differential limit.

• Theodor SvedbergRelated: It provided a complementary way to investigate the microscopic scale of colloidal particles.

• Fluorescence correlation spectroscopyRelated: Diffusing fluorescent molecules enter and leave the observation volume through Brownian motion.

• History of atomic theoryRelated: Its quantitative analysis provided evidence for atoms and molecules as physically real.

• UltracentrifugeRelated: Diffusion from Brownian motion counteracts sedimentation in equilibrium experiments.

• Annalen der PhysikRelated: A 1905 paper in Annalen der Physik used it to support the molecular theory of matter.

• Classical statistical mechanicsRelated: Its statistics reveal microscopic thermal activity through observable particle motion.

• Fractional dimensionRelated: A planar Brownian path has Hausdorff dimension two, illustrating dimensions of random traces.

• Oil-drop experimentRelated: Thermal fluctuations jostled the droplets and limited the precision of their observed motion.

• Complex fluidsRelated: Thermal motion competes with flow in structuring colloidal complex fluids.

• Diffusion and random walksBroader topic: It is the observable particle motion that helped establish molecular explanations of diffusion.

• Fluctuations and noiseBroader topic: It provides a direct mechanical picture of fluctuations in a fluid.

• Interactions in fluidsRelated: It makes molecular impacts visible through the erratic motion of suspended particles.