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The fluctuation–dissipation theorem is a general result of statistical thermodynamics that quantifies the relation between the fluctuations in a system that obeys detailed balance and the response of the system to applied perturbations.
Multicomponent diffusion is diffusion in mixtures, and diffusiophoresis is the special case where we are interested in the movement of one species that is usually a colloidal particle, in a gradient of a much smaller species, such as dissolved salt such as sodium chloride in water. or a miscible liquid, such as ethanol in water.
This random motion is described by a differential equation, known as the diffusion equation. The diffuson is the Green's function of the diffusion equation. [1] The diffuson plays an important role in the theory of electron transport in disordered systems, especially for phase coherent effects such as universal conductance fluctuations. [3]
The process of osmosis over a semipermeable membrane.The blue dots represent particles driving the osmotic gradient. Osmosis (/ ɒ z ˈ m oʊ s ɪ s /, US also / ɒ s-/) [1] is the spontaneous net movement or diffusion of solvent molecules through a selectively-permeable membrane from a region of high water potential (region of lower solute concentration) to a region of low water potential ...
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 ...
There are some notable similarities in equations for momentum, energy, and mass transfer [7] which can all be transported by diffusion, as illustrated by the following examples: Mass: the spreading and dissipation of odors in air is an example of mass diffusion. Energy: the conduction of heat in a solid material is an example of heat diffusion.
Another method to describe the motion of a Brownian particle was described by Langevin, now known for its namesake as the Langevin equation.) (,) = (,), given the initial condition (, =) = (); where () is the position of the particle at some given time, is the tagged particle's initial position, and is the diffusion constant with the S.I. units ...
Atomic diffusion on the surface of a crystal. The shaking of the atoms is an example of thermal fluctuations. Likewise, thermal fluctuations provide the energy necessary for the atoms to occasionally hop from one site to a neighboring one. For simplicity, the thermal fluctuations of the blue atoms are not shown.