Non-equilibrium effects in spinodal decomposition of a binary system

Modelling of Microstructural Transformations in the Systems Subject to Radiation Influence

“…Очевидно, що вираз (112) є стохастичним представленням закону дисперсії, зазвичай розглядуваного для чисто детерміністичного випадку [102].…”

Pattern selection processes and noise induced pattern-forming transitions in periodic systems with transient dynamics

“…As in the previous study the equation obtained (23) admits a solution of the form S ∝ ( ) , where the phase ( ), in general, can have real and imaginary parts, = ( ) + ( ). In the spinodal decomposition theory with hyperbolic transport (τ D = 0), where the spatial interaction is governed by the term |∇ | 2 the real part ( ) + is known as an amplification rate R( ) = − ( ) + , where S ∝ −R( ) ; the imaginary part ( ) is responsible for pattern selection processes [52]. Next, using the formalism proposed in Ref.…”

On the 2D Cahn–Hilliard Equation with Inertial Term

“…Then, given some T > 0, we take sequences such that 18) and, for all n ∈ N, we consider the solution U n = (u n , u n,t ) to 19) coupled with the new initial datum U 0,n = (u 0,n , u 1,n ). By the linear theory, this satisfies…”

“…It has been noted that, in certain materials like glasses, (1.1) needs to be modified in order to describe strongly non-equilibrium decomposition generated by deep supercooling into the spinodal region (cf. [17,18,19] and references therein). In this respect, P. Galenko et al proposed a modification based on the relaxation of the diffusion flux (see, for instance, [15,16]) which yields the following evolution equation ǫu tt + u t − ∆(−∆u + f (u)) = 0, (1.2) where ǫ > 0 is a relaxation time.…”