Sentence examples for mean field solution from inspiring English sources

The disorder is treated without the use of replica method, in which an exact mean field solution is obtained for two different types of quenched disorders: the bimodal and the gaussian ones.

Also, in layered structure of bulk materials (in quasi two-dimensional systems), Cronström and Noga [9] noted that some rather unexpected properties (new mean field solution) are observed at non-zero temperature.

For the global hopping model, the mean field solution is exact, even for small h.

The mean field solution is an approximate solution for the case with local hopping rules.

For large h, the mean field solution is close to the well-mixed limit, as expected.

A useful way to understand the effects of the limited diffusion rate in this model is to calculate the mean field solution.

Starting from the mean-field solution given by the Poisson-Boltzmann equation, an original approach is proposed to numerically sample fluctuations around it, through the propagation of a Langevin-like stochastic partial differential equation (SPDE).

Figure 12(a) compares the mean-field solution (red) and full numerical solutions (dashed lines) for Ω / γ = 1.5 and U / γ = 2 as the tunneling rate J is increased.

Here the numerical solutions converge to the mean-field solution as the cut-off number is increased, indicating that the mean-field approach is a very accurate approximation throughout.

These should be interpreted as a failure of the mean-field approach for larger J. Figure 12(b) in turn compares the mean-field solution (red) and full numerical solutions (dashed lines) for J / γ = 0.2 and U / γ = 0.5 as the drive strength Ω is increased.

We found that the percentage error made by the mean-field solution of the Master equation was only 6% in absolute values by 2009; this 6% error translates into an overestimation (during the last quarter of 2008) of the cumulative incidence of transmitted resistance by ∼74 individuals out of a total number of 12302.