ifcis the concentration of the substance, and if the constant of proportionality isD,thenj= −D(dc/dx);dc/dxis the rate of change of concentration in the directionx,and the minus sign indicates the flow is from higher to lower concentration.Dis called thediffusivityand governs the rate of...
We reconsider the problem of diffusion of particles at constant speed and present ageneralization of the Telegrapher process to higher-dimensional stochastic media(d > 1) where the particle can move along 2d directions. We derive the equations for probability density function using the "formulae of...
Example calculations of collection efficiency were presented in dimensional terms for one representative set of process conditions (200 mm wafer, showerhead-to-wafer gap of 2.54 cm, mass flow rate of 1000 sccm argon, 1 torr, 300 K). In all cases, the efficiency curves exhibited a minimum nea...
We reconsider the problem of diffusion of particles at constant speed and present ageneralization of the Telegrapher process to higher-dimensional stochastic media(d > 1) where the particle can move along 2d directions. We derive the equations for probability density function using the "formulae of...
Here, we consider the following two-dimensional fractional heat-like problem (6.46)Dtαu=12(x2uxx+y2uyy)+x2+y2,0<x,y<1,0<α≤1,t>0, subject to the following initial condition (6.47)u(x,y,0)=x2+y2, and boundary conditions (6.48)u(0,y,t)=y2(2et−1),u(x,0,t)=x2...
Electrical resistance of disordered one-dimensional lattices. Philos. Mag. J. Theor. Exp. Appl. Phys. 21, 863–867 (1970). CAS Google Scholar Büttiker, M., Imry, Y., Landauer, R. & Pinhas, S. Generalized many-channel conductance formula with application to small rings. Phys. Rev. ...
We will consider the case in other domains such as rectangular and elliptic in the future. Otherwise, it would be interesting to investigate the unique continuation properties of the solution in a high dimensional case.Data availability No new data were created or analysed in this study....
In this section, we first introduce one-dimensional GMMs as the backbone of our model and recall some properties that are needed for the analysis in the following subsections. Then, we detail how we can utilize PoGMDMs based on filter, wavelet, and shearlet responses to model the distribution...
Depending on the threshold value, other threshold models can be classified into the following categories: (1) majority TM [4,20], where Tv=12D(v); (2) small TM [21], where the threshold value Ty is a very small constant; (3) Separated TM [22,23], with the exception of maintaining...
(the Stokes–Einstein equation). When the data are plotted as a two-dimensional graph with spectra on the horizontal axis and diffusion coefficients corresponding to each peak on the vertical axis, this is known as diffusion-ordered spectroscopy (DOSY). The approach can be used to distinguish ...