Phase separation dynamics in a symmetric binary mixture of ultrasoft particles.

Phase separation plays a key role in determining the self-assembly of biological and soft-matter systems. In biological systems, liquid-liquid phase separation inside a cell leads to the formation of various macromolecular aggregates. The interaction among these aggregates is soft, i.e., they can significantly overlap at a small energy cost. From a computer simulation point of view, these complex macromolecular aggregates are generally modeled by soft particles. The effective interaction between two particles is defined via the generalized exponential model of index n, with n = 4. Here, using molecular dynamics simulations, we study the phase separation dynamics of a size-symmetric binary mixture of ultrasoft particles. We find that when the mixture is quenched to a temperature below the critical temperature, the two components spontaneously start to separate. Domains of the two components form, and the equal-time order parameter reveals that the domain sizes grow with time in a power-law manner with an exponent of 1/3, which is consistent with the Lifshitz-Slyozov law for conserved systems. Furthermore, the static structure factor shows a power-law decay with an exponent of 4, consistent with the Porod law.

On some growth properties of entire functions using their maximum moduli focusing (p, q)th relative order.

We discuss some growth rates of composite entire functions on the basis of the definition of relative (p, q)th order (relative (p, q)th lower order) with respect to another entire function which improve some earlier results of Roy (2010) where p and q are any two positive integers.

Growth Analysis of Composite Entire and Meromorphic Functions in the Light of Their Relative Orders.

We study some comparative growth properties of composite entire and meromorphic functions on the basis of their relative orders (relative lower orders).