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The kinetic theory of gases is a simple classical model of the thermodynamic behavior of gases. It treats a gas as composed of numerous particles, too small to see with a microscope, which are constantly in random motion.
The atoms (or particles) that might stop a beam particle are shown in red. The magnitude of the mean free path depends on the characteristics of the system. Assuming that all the target particles are at rest but only the beam particle is moving, that gives an expression for the mean free path: ℓ=(σn)−1,{\displaystyle \ell =(\sigma n)^{-1},}
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 ...
The van der Waals equation, named for its originator, the Dutch physicist Johannes Diderik van der Waals, is an equation of state that extends the ideal gas law to include the non-zero size of gas molecules and the interactions between them (both of which depend on the specific substance). As a result the equation is able to model the liquid ...
In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected [clarification needed] connection revealed independently by William Sutherland in 1904, [ 1 ][ 2 ][ 3 ] Albert Einstein in 1905, [ 4 ] and by Marian Smoluchowski in 1906 [ 5 ] in their works on Brownian motion.
μ is the mobility of the particle in the fluid or gas, which can be calculated using the Einstein relation (kinetic theory). m is the mass of the particle. t is time. At long time scales, Einstein's result is recovered, but short time scales, the ballistic regime are also explained.
Brownian motion. Simulation of the Brownian motion of a large particle, analogous to a dust particle, that collides with a large set of smaller particles, analogous to molecules of a gas, which move with different velocities in different random directions. Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas).
The Vicsek model is a mathematical model used to describe active matter. One motivation of the study of active matter by physicists is the rich phenomenology associated to this field. Collective motion and swarming are among the most studied phenomena. Within the huge number of models that have been developed to catch such behavior from a ...