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The spike is thus an obstacle for growth that must be broken through in order for diffusion-controlled growth to turn partitionless.

Fig. 6 Arrhenius-type plots of samples a 3Y-TZP (DIPE) and b TZ-3Y (TOSOH) Table 2 Activation energy and the order of diffusion mechanisms for the samples TZ-3Y (TOSOH) and 3Y-TZP (DIPE) Powders Number Q (kJ/mol) TZ-3Y (TOSOH) 1/3 840 ± 40 3Y-TZP (DIPE) 1/2 667 ± 40.

In order for the diffusion approximation to be valid two conditions must be fulfilled: μ a ≪ μ s ′ and μ ′ s ⋅ r > > 1.

The obtained activation energy and the order of diffusion mechanisms (n = 0.33 0.51) for the samples are shown in Table 2.

For the ED scheme, we have applied the strategies recommended in [17], including B(3) smoothing for image data, zero extension for boundary points, and serpentine scan order for the error diffusion.

A Langmuir isotherm model has been assumed and chemical potential gradient is considered as the driving force for diffusion in order to represent the concentration dependence of crystal diffusivity.

The value of this coefficient was De = 1.9 × 10−5 cm2/s, of the same order as free diffusion for l-asparaginase.

A model for diffusion in ordered phases with B2-b.c.c.

The current work focuses on developing high-order realizable finite-volume schemes for diffusion.

Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.

Differential architectures for both first order error diffusion and first order sigma delta modulators are presented in this paper.