On the spherical prototype of a complex dissipative late-stage formation seen in terms of least action Vojta-Natanson principle

Rate of Entropy Production in Evolving Interfaces and Membranes under Astigmatic Kinematics: Shape Evolution in Geometric-Dissipation Landscapes

This paper presents theory and simulation of viscous dissipation in evolving interfaces and membranes under kinematic conditions, known as astigmatic flow, ubiquitous during growth processes in nature. The essential aim is to characterize and explain the underlying connections between curvedness and shape evolution and the rate of entropy production due to viscous bending and torsion rates. The membrane dissipation model used here is known as the Boussinesq-Scriven fluid model. Since the standard approaches in morphological evolution are based on the average, Gaussian and deviatoric curvatures, which comingle shape with curvedness, this paper introduces a novel decoupled approach whereby shape is independent of curvedness. In this curvedness-shape landscape, the entropy production surface under constant homogeneous normal velocity decays with growth but oscillates with shape changes. Saddles and spheres are minima while cylindrical patches are maxima. The astigmatic flow trajectories on the entropy production surface, show that only cylinders and spheres grow under the constant shape. Small deviations from cylindrical shapes evolve towards spheres or saddles depending on the initial condition, where dissipation rates decrease. Taken together the results and analysis provide novel and significant relations between shape evolution and viscous dissipation in deforming viscous membrane and surfaces.

On (sub)mesoscopic scale peculiarities of diffusion driven growth in an active matter confined space, and related (bio)material realizations

Diffusion in a confined space becomes an extremely important problem with many versatile applications, ranging from biomedical to biotechnological, and involving functional and smart (bio)materials. In this study, we have shown that the well-known Mullins-Sekerka approach to morphological stability of the diffusional non-ideal sphere's growth, for which a confinement factor disappears, is a firm starting point for further questions. It has two modifications and/or extensions for which the confinement factor is involved readily and becomes (in)finite firstly for microscale (or micrometer scale) involving biomatter packing phenomena. They are also applicable for nanoscopic biomaterial arrangements for which very tightly packed material and active-matter including outcomes of subdiffusive proveniency would manifest, as it has already been observed for the protein crystal growth in pores and globule-to-coil crossover phenomena.