Abstract
By using N/sup -2/ phi (g sub i - g sub j) regular pair interactions, it is shown that, for n approaching infinity, the Vlasovdynamics is the omega meson resonances -limit of the classical canonical N-particle-dynamics. Propagation of molecular chaos holds in this limit and the fluctuations converge to a Gaussian stochastic process, which is, however, non-Markovian. A model of a nerve membrane is studied in the limit of singular interaction with Fermion reservoirs. The resulting axon equations have the same structure as the Hodgkin Huxley equations. Recently proven theorems are used on nonlinear diffusion equations to show the existance of a propagating pulse solution.
Citation Formats
Braun, W A.
On the limit dynamics of systems with infinite multiple degrees of freedom.
Switzerland: N. p.,
1977.
Web.
Braun, W A.
On the limit dynamics of systems with infinite multiple degrees of freedom.
Switzerland.
Braun, W A.
1977.
"On the limit dynamics of systems with infinite multiple degrees of freedom."
Switzerland.
@misc{etde_6518467,
title = {On the limit dynamics of systems with infinite multiple degrees of freedom}
author = {Braun, W A}
abstractNote = {By using N/sup -2/ phi (g sub i - g sub j) regular pair interactions, it is shown that, for n approaching infinity, the Vlasovdynamics is the omega meson resonances -limit of the classical canonical N-particle-dynamics. Propagation of molecular chaos holds in this limit and the fluctuations converge to a Gaussian stochastic process, which is, however, non-Markovian. A model of a nerve membrane is studied in the limit of singular interaction with Fermion reservoirs. The resulting axon equations have the same structure as the Hodgkin Huxley equations. Recently proven theorems are used on nonlinear diffusion equations to show the existance of a propagating pulse solution.}
place = {Switzerland}
year = {1977}
month = {Jan}
}
title = {On the limit dynamics of systems with infinite multiple degrees of freedom}
author = {Braun, W A}
abstractNote = {By using N/sup -2/ phi (g sub i - g sub j) regular pair interactions, it is shown that, for n approaching infinity, the Vlasovdynamics is the omega meson resonances -limit of the classical canonical N-particle-dynamics. Propagation of molecular chaos holds in this limit and the fluctuations converge to a Gaussian stochastic process, which is, however, non-Markovian. A model of a nerve membrane is studied in the limit of singular interaction with Fermion reservoirs. The resulting axon equations have the same structure as the Hodgkin Huxley equations. Recently proven theorems are used on nonlinear diffusion equations to show the existance of a propagating pulse solution.}
place = {Switzerland}
year = {1977}
month = {Jan}
}