# Brownian Motion

## Contents

## Definition

Brownian motion was identified by Robert Brown in 1827 after looking at the jittery movement of pollen on water. It can be defined as the apparent random motion of particles suspended on a fluid. The term is often associated with the 'random walk' phenomenon.

## Applications

Brownian motion, and the mathematical models that describe it, have been used for over a century to describe a multitude of phenomena. For example, Einstein used Brownian motion to describe both the existence of atoms, and the kinetic model of thermal equilibrium. Among other things, economists have been using Brownian motion since the early 20th century to model the stock market. For a study of the diffusion of brownian spheres, see Hydrodynamic Coupling of two brownian spheres to a planar survace.

### Biological Movements

In biology, Brownian motion can be the driving force behind supramolecular ratchets. The principle of operation is that polymerizing filaments can push on an object. When this object's position fluctuates due to Brownian motion, polymer subunits can attach to the growing filament, biasing the movement of the object in a certain direction. These filaments are cross-linked into a gel which provides the force for movement.

## References

## Links

http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/brownian/brownian.html

## Papers

1. Einstein, A. "On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat", *Annalen der Physik*, 17, 1905, 549-560

## Keyword in references:

Mechanoelectrical transduction assisted by Brownian motion: a role for noise in the auditory system

Brownian Dynamics of a Sphere Between Parallel Walls

Single-particle Brownian dynamics for characterizing the rheology of fluid Langmuir monolayers

The Elementary Theory of the Brownian Motion

Like Charge Attraction through Hydrodynamic Interaction

Noise underlies switching behavior of the bacterial flagellum

The force-velocity relationship for the actin-based motility of Listeria-Monocytogenes

Gravitational stability of suspensions of attractive colloidal particles

Physiological and pathological population dynamics of circulating human red blood cells

Motility powered by supramolecular springs and ratchets

Single molecule statistics and the polynucleotide unzipping transition

Minimal model for kinetic arrest

Patterned Colloidal Coating Using Adhesive Emulsions

Optical Measurements of Frequency-Dependent Linear Viscoelastic Moduli of Complex Fluids

Elasticity of Compressed Emulsions

Janus Microgels Produced from Functional Precursor Polymers

Perturbation Spreading in Many-Particle Systems: A Random Walk Approach

Dealing with mechanics: mechanisms of force transduction in cells

Actin Filament Length Tunes Elasticity of Flexibly Cross-Linked Actin Networks

Nanomechanics of vimentin intermediate filament networks

Surface roughness directed self-assembly of patchy particles into colloidal micelles

Does size matter? Elasticity of compressed suspensions of colloidal- and granular-scale microgels

Origin of de-swelling and dynamics of dense ionic microgel suspensions