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The phase field model replaces the sharp discontinuities with a scalar damage field representing the diffuse crack topology through controlling the amount of diffusion by a regularization parameter.
where △ represents the graph Laplacian of the network, α > 0 is a real number that scales the amount of diffusion across the nodes, and σ d ω is white noise with scale σ.
The diffusion length increases at recombination because the mean free path does, with less photon scattering occurring; this increases the amount of diffusion and damping.
The extent of the activation was reduced by the amount of diffusion weighting, as described in our earlier work [28].
Soft tissue and bone particles differ significantly in the amount of diffusion resistance they present (Figure 6).
We also included additional supports for the cover slip at the top and bottom of the chamber, which increases the stability of the gradient by limiting the amount of diffusion as well as providing support.
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The results showed that, although there was no significant effect on the diffusion length, bottom ash in high-strength concrete can significantly reduce the amount of chloride diffusion.
As a measures to stabilize the tracking, the amount of random diffusion is effectively adjusted using a Kalman updating of the covariance matrix.
The choice of variables used for limiting the fluxes affects the amount of numerical diffusion and an appropriate choice of the gradient in volume fraction is used.
In both model formulations, nonlinear high-resolution techniques minimizing the amount of artificial diffusion were applied, so that fictitious mixing is exclusively due to grid-orientation effects.
Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes are found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme.
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