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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.
Forced Rayleigh scattering (FRS) is an experimental method in physics and chemistry based on light scattering and is usually used to measure diffusion on length scales of roughly 10 μm.
Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low ...
This is a truly microscopically irreversible process. But even without molecular diffusion taking care of the last step, one can reasonably claim that spatial concentration is altered due to eddy diffusion. In practice, concentration is defined using a very small but finite control volume in which particles of the relevant species are counted.
Three examples of Turing patterns Six stable states from Turing equations, the last one forms Turing patterns. The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state.
Hypothetical dynamic light scattering of two samples: Larger particles on the top and smaller particles on the bottom. Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. [1]
where is a diffusion matrix specifying hydrodynamic interactions, Oseen tensor [4] for example, in non-diagonal entries interacting between the target particle and the surrounding particle , is the force exerted on the particle , and () is a Gaussian noise vector with zero mean and a standard deviation of in each vector entry.
Physically, the turbulence kinetic energy is characterized by measured root-mean-square (RMS) velocity fluctuations. In the Reynolds-averaged Navier Stokes equations, the turbulence kinetic energy can be calculated based on the closure method, i.e. a turbulence model.