References |
Cahn, J.W., Allen, S.M., A microscopic theory of domain wall motion and its experimental verification in Fe-Al alloy domain growth kinetics (1977) J. Phys. Colloq., 38 (C7), pp. 51-54; Allen, S.M., Cahn, J.W., A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening (1979) Acta Metall., 27, pp. 1085-1095; Wheeler, A., Boettinger, W.J., McFadden, G.B., Phase-field model for isothermal phase transitions in binary-alloys (1992) Phys. Rev. A, 45 (10), pp. 7240-7424; Gouyet, J.F., Generalized Allen-Calm equations to describe far-from-equilibrium order-disorder dynamics (1995) Phys. Rev. e, 51 (3), pp. 1695-1710; Fife, P.C., Lacey, A.A., Motion by curvature in generalized Calm-Allen models (1994) J. Stat. Phys., 77 (1-2), pp. 173-181; Benes, M., Chalupecky, V., Mikula, K., Geometrical image segmentation by the Allen-Calm equation (2004) Applied Numerical Mathematics, 51, pp. 187-205; Alfaro, M., Hilhorst, D., Generation of interface for an Allen-Calm equation with nonlinear diffusion (2010) Math. Model. Nat. Phenom., 5, pp. 1-12; Caginalp, G., Chen, X., Phase field equations in the singular limit of sharp interface problems (1992) IMA Volume of Mathematics and Its Applications, 43, pp. 1-28; Bates, P.W., Chen, F., Spectral analysis and multidimensional stability of traveling waves for nonlocal Allen-Calm equation (2002) J. Math. Anal. Appl, 273, pp. 45-57; Galenko, P., Jou, D., Diffuse-interface model for rapid phase transformations in nonequilibrium systems (2005) Phys. Rev. E, 71, pp. 0461251-04612513; Yang, Y., Humadi, H., Buta, D., Laird, B.B., Sun, D., Hoyt, J.J., Asta, M., Atomistic simulations of nonequilibrium crystal-growth kinetics from alloy melts (2011) Phys. Rev. Lett., 107, pp. 0255051-0255054; Jou, D., Galenko, P., Coarse graining for the phase-field model of fast phase transitions (2013) Phys. Rev. e, 88, pp. 0421511-0421518; Field, R.J., Burger, M., (1985) Oscillations and Traveling Waves in Chemical Systems, p. 681. , New York: Wiley; Galenko, P.K., Abramova, E.V., Jou, D., Danilov, D.A., Lebedev, V.G., Herlach, D.M., Solute trapping in rapid solidification of a binary dilute system: A phase-field study (2011) Phys. Rev. e, 84, pp. 0411431-04114317; Salhoumi, A., Galenko, P.K., Gibbs-Thomson condition for the rapidly moving interface in a binary system (2016) Physica A, 447, pp. 161-171; Feng, Zh., The first-integral method to study the Burgers-Korteweg-de Vries equation (2002) J. Phys. A: Math. Gen., 35, pp. 343-349; Lu, B., Zhang, H.-Q., Xie, F.-D., Traveling wave solutions of nonlinear partial differential equations by using the first integral method (2010) Applied Mathematics and Computations, 216, pp. 1329-1336; Bourbaki, N., (1998) Commutative Algebra, p. 625. , Springer; Feng, Zh., Wang, X., The first integral method to the two-dimensional Burgers-Korteweg-de Vries equation (2003) Physics Letters A, 308, pp. 173-178; Ahmed Ali, A.H., Raslan, K.R., New solutions for some important partial differential equations (2007) International Journal of Nonlinear Science, 4, pp. 109-117; Wazwaz, A.-M., The tanh method for traveling wave solutions of nonlinear equations (2004) Applied Mathematics and Computation, 154 (3), pp. 713-723; Taşcan, F., Bekir, A., Travelling wave solutions of Calm-Allen equation by using first integral method (2009) Applied Mathematics and Computation, 207 (1), pp. 279-282; Choi, J.-W., Lee, H.G., Jeong, D., Kim, J., An unconditionally gradient stable numerical method for solving the Allen-Calm equuation (2009) Physica A, 388, pp. 1791-1803; Herlach, D.M., Galenko, P.K., Holland-Moritz, D., (2007) Metastable Solids from Undercooled Melts, p. 432. , Amsterdam: Elsevier |