Next, the three models are numerically compared under Langmuir isotherm conditions, assuming a constant diffusion coefficient of guest species in the host material.
Here, we have to note that Ide (2010) reported that the migration followed a curve with a constant diffusion coefficient ( overline{d} ) of 104 m2 s−1, which was defined as ( pi {r}^2=overline{d}t ), where r and t denote the distance and duration of the migration, respectively.
In the case of a constant diffusion matrix (varSigma(t)=varSigmainmathbb{R}^{3times3}), the covariance matrix is given as (Delta t varSigma^{2}).
The assumption of a constant diffusion coefficient in the CO2 water is reasonable, because the CO2 concentration in water is generally low under the test conditions.
The applicability of these equations is limited because they are deduced under the assumption of a constant diffusion coefficient.
For the case of a constant diffusion coefficient it is well established that a MC method using a steplength chosen from the appropriate Gaussian distribution gives accurate results.
Formal results are given stating that, at least in the case of a constant diffusion, RT0M is significantly more accurate than RT0, although both elements have essentially the same implementation cost.
In such an age, the constant diffusion of information can become just as dangerous as it is empowering.
Pilot studies showed that the shade cloth facilitated steady, constant diffusion of warm water from the heated metal plate to the surrounding water layer, while providing a suitable surface for rapid colonisation by marine fauna.
The actual value of R is calculated at each step for each region of the virtual Petri dish (called "patch" in Netlogo) as the equilibrium between the quantity that is consumed by the cells and the constant diffusion of the substance from the surrounding culture medium.
