## How to calculate mean squared displacement?

MSD is defined as MSD=average(r(t)-r(0))^2 where r(t) is the position of the particle at time t and r(0) is the initial position, so in a sense it is the distance traveled by the particle over time interval t.

**What do you expect the mean displacement of a particle undergoing Brownian motion to be?**

zero

For a pure Brownian motion, mean displacements are obviously zero.

### What is the mean squared displacement of the particles?

In statistical mechanics, the mean squared displacement (MSD, also mean square displacement, average squared displacement, or mean square fluctuation) is a measure of the deviation of the position of a particle with respect to a reference position over time.

**When to use mean square displacement versus time?**

Mean-square displacement versus time for diffusion + ﬂow, pure normal diffusion, sub-diffusion, and conﬁned diffusion Single-particle Tracking: Application to Membrane Dynamics

## How do you calculate diffusion mean squared displacement?

We observe the particle positions at every timestep and run the simulation for a given amount of steps.

**What is the relationship between Brownian motion and mean-squared displacement?**

Brownian motion and mean-squared displacement The discovery of Green Fluorescent Protein (GFP) has revolutionized in vivobiology Aequorea victoria GFP Extraction, purification and properties of Aequorin, a bioluminescent protein from the Luminous Hydromedusan, Aequorea. Shimomura, Johnson, and Saiga J Cell Comp Physiol59: 223 (1962)

### How to calculate the slope of a diffusion coefficient?

The slope (diffusion coefficient) is changing with time. which part of the curve to be considered to calculate the slope (diffusion coefficient)? =sqrt (2nD*t) where is your displacement, t is the observation time over which the displacement occurred and n is the allowed dimensionality of the diffusion process.