0000000000873319
AUTHOR
R. Mahnke
How to solve Fokker-Planck equation treating mixed eigenvalue spectrum?
An analogy of the Fokker-Planck equation (FPE) with the Schr\"odinger equation allows us to use quantum mechanics technique to find the analytical solution of the FPE in a number of cases. However, previous studies have been limited to the Schr\"odinger potential with a discrete eigenvalue spectrum. Here, we will show how this approach can be also applied to a mixed eigenvalue spectrum with bounded and free states. We solve the FPE with boundaries located at x=\pm L/2 and take the limit L\rightarrow\infty, considering the examples with constant Schr\"{o}dinger potential and with P\"{o}schl-Teller potential. An oversimplified approach was proposed earlier by M.T. Araujo and E. Drigo Filho. A…
Nucleation in physical and nonphysical systems
Abstract The aggregation of particles out of an initially homogeneous situation is well known in physics. Depending on the system under consideration and its control parameters, the cluster formation in a supersaturated (metastable or unstable) situation has been observed in nucleation physics as well as in other branches. We investigate the well-known example of condensation (formation of liquid droplets) in an undercooled vapour to conclude that the formation of bound states as a phase transition is related to transportation science. We present a comparison of nucleation in an isothermal–isochoric container with traffic congestion on a circular one-lane freeway. The analysis is based, in …