Fig 1.
Results of the phase-field analysis (a) with (b) without using random term.
Fig 2.
Schematic of the coordinate system and the dendrite indices.
Fig 3.
Representation of the phase in the phase-field variable (a) image of the dendrite and (b) correspondence between the phase-field variable and the solid–liquid interface phase.
Fig 4.
Uniform distribution and Gaussian distribution of random number used in this study.
Fig 5.
Scaling of tip radius.
Table 1.
Table 2.
Phase-field computational parameters and properties of SCN.
Fig 6.
Coefficient aX for Fu in Eq (22) with respect to the sidebranch length Xact (a) Effect of difference in (b) Effect of difference in
.
Fig 7.
Coefficient bX for Fu in Eq (22) with respect to the sidebranch length Xact (a) Effect of difference in (b) Effect of difference in
.
Fig 8.
Coefficient aU for Fu in Eq (23) with respect to the contour length U (a) Effect of difference in (b) Effect of difference in
.
Fig 9.
Coefficient bU for Fu in Eq (23) with respect to the contour length U (a) Effect of difference in (b) Effect of difference in
.
Fig 10.
Coefficient aF for Fu in Eq (24) with respect to the area F (a) Effect of difference in (b) Effect of difference in
.
Fig 11.
Coefficient bF for Fu in Eq (24) with respect to the area F (a) Effect of difference in (b) Effect of difference in
.
Fig 12.
Comparison the shape of dendrites under different anisotropy strength. (a) anistropy strength is 0.015. (b) anistropy strength
is 0.025.
Fig 13.
Comparison of analysis results for different Fu values at the anisotropy strength .
(a) The magnitude of the noise Fu is . (b) The magnitude of the noise Fu is
.
Table 3.
Comparison of calculation time for each distribution and random terms in 100,000 time step.