Analytical solutions of Cahn-Hillard phase-field model for spinodal decomposition of a binary system

Abstract

PACS 44.05.+e -Analytical and numerical techniques PACS 02.90.+p -Other topics in mathematical methods in physics Abstract -Spinodal decomposition is a very important and challenging issue not for only materials science but for also many other fields in science. Phase-field models, which have become very popular in recent years, are very promising for the evaluation of phase transformations such as spinodal decomposition. In this study, the Cahn-Hillard equation which is one of the most trending phase-field models is analytically solved by the double exp-function and the modified extended exp-function methods. Spatio-temporal energy and concentration distributions were evaluated by applying two of the ten obtained analytical solutions to the free energy equation. The results obtained were found to be successful in predicting spinodal decomposition as is expected from the Cahn-Hillard model.

Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical Physics

“…Recently, many powerful methods for obtaining exact solutions of nonlinear partial differential equations (NLPDEs) have been presented, such as exponential rational function method [21], exp a function, and the hyperbolic function methods [22]. ðG ′ /GÞexpansion method [23,24], ðG′/G, 1/GÞ-expansion method [25,26], Sardar-subequation method [27], new subequation method [28], Riccati equation method [29], homotopy perturbation method [30], extended direct algebraic method [31], Kudryashov method [32], Exp-function method [33], the modified extended exp-function method [34], F-expansion method [35], the Backlund transformation method [36], the extended tanh-method [37], Jacobi elliptic function expansion methods [38], extended sinh-Gordon equation expansion method [39], and different other methods [40][41][42][43].…”

New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation

“…In recent years, analytical and numerical solutions of fractional differential partial differential equations have been obtained by different methods [7,[13][14][15][16]. (1/G )-expansion method has been widely used to obtain analytical solutions of partial differential equations [17][18][19].…”

“…Many different nonlinear differential equations have been the subject of studies to explain various nonlinear phenomena. Some of the most famous of these equations are Korteweg -de Vries (KdV) [5], Boussinesq [6], Cahn-Hilliard [7], nonlinear Schrödinger [8] and Ginzburg-Landau [9], etc. Especially complex form of Ginzburg-Landau equation (CGLE) is very interesting due to its capability of explaining very complex events in physics such as superconductivity, superfluidity [10], strings in field theory [11], Bose-Einstein condensation [12], etc.…”