As Nelson proposed in6, the variance of the Brownian motion of the particle is equal to the ratio of Planck constant to the mass of the particle. That is why we express the square of the diffusion coefficient in (2) to be proportional to the \(\frac{\hbar }{m}\). $$\begin{aligne...
The source term appearing in the diffusion equation is discussed, followed by the derivation of Fick's law of diffusion for the neutron current. To gain better understanding of the diffusion approximation as compared with the rigorous transport theory, the chapter presents the use the energyand ...
\begin{aligned} & \int_{-\infty}^{\infty} h(Y(t)) \frac{\partial P[Y(t) \mid X(t_0)]}{\partial t} d Y \\ =&\lim_{\Delta t \rightarrow 0} {1 \over \Delta t} \int P\left[ Z(t)|X(t_0) \right] \mathrm{d} Z \int P\left[ Y(t+\Delta t)|Z(t) \right...
The derivation of the modified diffusion equations is presented. These equations of a relaxational type generalize Fick's law and are applicable for large spatial and temporal gradients. The telegraph equation for the concentration is found in the simplest case. The derivation and the equations thems...
MicroscopicDerivationofCausalDiffusionEquationusingProjectionOperatorMethod 系统标签: equationcausalprojectionmicroscopicderivationoperator arXiv:cond-mat/0501696v3[cond-mat.stat-mech]22Aug2005MicroscopicDerivationofCausalDiffusionEquationusingProjectionOperatorMethodT.Koide11InstitutodeFisica,UniversidadedeSaoPaulo,C.P...
1960. Derivation of an equation for the diffusion potential . Nature. 188 :944–945 10.1038/188944b0 [ Cross Ref ]PATLAK, C. S. (1960). Derivation of an equation for the diffusion potential. Nature, Lond. 188, 944-945.Patlak, C.S. (1960) Derivation of an equation for the diffusion ...
AN equation for the potential across a membrane arising from the steady-state diffusion of univalent ions was derived by D. Goldman 1 under the assumptions of a constant electric field and constant ionic mobilities across the membrane. His equation may be written as 2 : Open image in new win...
In the derivation, a discrete stochastic reaction-diffusion equation is first constructed from basic principles, that is, from the changes that occur in a small time interval. As the time interval goes to zero, the discrete stochastic model leads to a system of It stochastic differential equation...
DERIVATION OF THE NEUTRON DIFFUSION EQUATION The neutron diffusion equation is a basic balance equation that describes the transport of neutrons in space, energy, and time. This chapter discusses the ... JC Lee - Nuclear Reactor Physics and Engineering 被引量: 0发表: 2020年 The Diffusion Approxi...
We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance of the same order of magnitude of the materials in ...