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Single-particle tracking (SPT) is the observation of the motion of individual particles within a medium. The coordinates time series, which can be either in two dimensions (x, y) or in three dimensions (x, y, z), is referred to as a trajectory. The trajectory is typically analyzed using statistical methods to extract information about the ...
This observation is useful in defining Brownian motion on an m-dimensional Riemannian manifold (M, g): a Brownian motion on M is defined to be a diffusion on M whose characteristic operator in local coordinates x i, 1 ≤ i ≤ m, is given by 1 / 2 Δ LB, where Δ LB is the Laplace–Beltrami operator given in local coordinates by ...
A WISP (weakly interacting slender particle) is any one of a number of low mass particles that might explain dark matter (such as the axion) A GIMP (gravitationally interacting massive particle) is a particle which provides an alternative explanation of dark matter, instead of the aforementioned WIMP
Tracer diffusion describes the motion of individual adparticles on a surface at relatively low coverage levels. At these low levels (< 0.01 monolayer), particle interaction is low and each particle can be considered to move independently of the others. The single atom diffusing in figure 1 is a nice example of tracer diffusion.
The particle's Mean squared displacement from its original position is: =, where is the dimension of the particle's Brownian motion. For example, the diffusion of a molecule across a cell membrane 8 nm thick is 1-D diffusion because of the spherical symmetry; However, the diffusion of a molecule from the membrane to the center of a eukaryotic ...
Contrary to brownian motion, which is the diffusion of a single particle, interactions between particles may have to be considered, unless the particles form an ideal mix with their solvent (ideal mix conditions correspond to the case where the interactions between the solvent and particles are identical to the interactions between particles ...
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