Geometry and boundary control of pattern formation and competition

Abstract

This paper presents the effective control of the formation and competition of cellular patterns. Simulation and theoretical analyses are carried out for pattern formation in a confined circular domain. The Cahn-Hilliard equation is solved with the zero-flux boundary condition to describe the phase separation of binary mixtures. A wavelet-based discrete singular convolution algorithm is employed to provide high-precision numerical solutions. By extensive numerical experiments, a set of cellular ordered state patterns are generated. Theoretical analysis is carried out by using the Fourier-Bessel series. Modal decomposition shows that the pattern morphology of an ordered state pattern is dominated by a principal Fourier-Bessel mode, which has the largest Fourier-Bessel decomposition amplitude. Interesting modal competition is also observed. It is found that the formation and competition of cellular patterns are effectively controlled by the confined geometry and boundary condition.

Modeling the Effects of Calcium Overload on Mitochondrial Ultrastructural Remodeling

“…The CH model can be derived from the classic conservation law and free energy minimization, with the free energy function determining the final composition of the binary system [ 63 , 64 ]. The pattern and morphology of the binary system is further determined by the domain size and geometric shape [ 65 , 66 ]. The CH model can be modified to describe the nucleation dynamics and process of a specific species in the mixture [ 67 , 68 ].…”

A special instrument for the defined modification of polymer properties in solutions and polymer layers

“…The surface properties of the substrate [39], the size and shape of the container [36,[40][41][42], the thermal history of the material [6] and solvent evaporation [24,43,44] also contribute to the complexity of the system. Consequently, it is virtually impossible to predict the behaviour of such a complicated system on the base of some idealised model [45][46][47][48]. Thus, it is still necessary to rely on a perfectly-performed experiment [37,43,44], the results of which will provide information about the practical application of the self-organised processes for the targeted modification of (not only) polymeric systems.…”

Preliminary investigation of factors determining self-organised structures preparation in polymer layers

“…A synoptic summary can be found in the work of Colinet et al [8] and some other recent works [12][13][14][15]. The study of this problem is still relevant, not only for the development of computer techniques and attempts to model the processes [16][17][18][19][20], but also for the need to solve technical challenges where these processes play major role. Examples include protein crystalization [21], Si-wafers drying [22], thermal field-flow fractionation [23,24], thin polymeric film preparation [17,25,26], and others.…”