Sentence examples for corresponding Wulff shapes from inspiring English sources

In the bottom row, the final shapes (black lines) are overlapped by the corresponding Wulff shapes (magenta lines), due to the appropriate surface energy plots (blue lines).

In the bottom row, the final ((t=600)) results (black lines) are overlapped by the corresponding Wulff shapes (magenta lines), due to the appropriate surface energy plots (blue lines).

In the bottom row, the final ((t=600)) results (black lines) are overlapped by the polar plots of the corresponding Wulff shapes (magenta lines), due to the appropriate interface energy plots (blue lines).

Built on the presented simulation results, we reveal the applicability and the limitation of every approach, with added focus on the consistency between the numerical equilibrium shape and the corresponding Wulff shape.

(9) and  (10), in the cases with (F_{alpha beta }ge 1/15) and (I_{alpha beta }ge 2), the surface stiffness becomes negative, and the corresponding Wulff shape with "ears" belongs to these missing orientations.

Nevertheless, if the corresponding Wulff shape is well defined, the interfacial energy in the diffuse interface equates to the sharp interface form (gamma (varvec{n})=sigma (varvec{n})), in spite of the model.

In two dimensions, the expression reduces to a function of only one angle (theta =arctan {frac{n_y}{n_x}}), and the corresponding Wulff shape is a convex hull (Mullins 1962) bounded by the perpendiculars to (varvec{n}), at a distance (sigma (varvec{n})), from the origin (Sekerka 2005).

The shape and site composition ranges were also compared to previously calculated Wulff shapes and showed good agreement.

Thus, in the bottom row, the numerically stationary states (t=600) (black lines) as well as the anisotropy plot (blue lines) with the Wulff shapes (magenta lines) are demonstrated.

We study the dynamics of interfaces under strong anisotropy and compare near-equilibrium diffuse interface solutions to the sharp interface Wulff shapes in 2D and 3D.

One possibility is to change the formulation of the interface energy (sigma (varvec{n})rightarrow sigma ^{(c)} varvec{n})) (Taylor and Cahn 1998) to its "convexified" form, but with equivalent Wulff shapes.