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A theoretical model for stratified epithelium is presented. The viscoelastic properties of the tissue is assumed to be dependent on the spatial distribution of proliferative and differentiated cells. Based on this assumption, a hydrodynamic…
Shell structure in the single particle spectrum of deformed harmonic oscillator potentials when a term proportional to $(\vec L)^2$ is added is analyzed for a large particle number. A scaling law which gives a dividing line between regular…
In this paper, I study the coarsening dynamics of two-dimensional dry foam sandwiched by deformable membranes. The time-varying deformation of the confining membranes gives rise to a significant alteration in the evolution of polygonal…
Two-dimensional maps can model interactions between populations. Despite their simplicity, these dynamical systems can show some complex situations, as multistability or fractal boundaries between basins that lead to remarkable pictures.…
Parallel Molecular Dynamics simulations are conducted for describing growth on surfaces with different kind of roughness: a perfect ordered crystalline flat graphite surface, a disordered rough graphite surface and flat surface with an…
Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies,…
A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating…
Inspired on the well known dynamical dichotomy predicted in voids, where some underdense regions expand whereas others collapse due to overdense surrounding regions, we explored the interplay between the void inner dynamics and its large…
Foam is a canonical example of disordered soft matter where local force balance leads to the competition of many metastable configurations. Here we present an experimental and theoretical framework for "active foam" where an individual…
We present a model for cell growth, division and packing under soft constraints that arise from the deformability of the cells as well as of a membrane that encloses them. Our treatment falls within the framework of diffuse interface…
Neural computation is associated with the emergence, reconfiguration and dissolution of cell assemblies in the context of varying oscillatory states. Here, we describe the complex spatio-temporal dynamics of cell assemblies through temporal…
Membrane particles such as proteins and lipids organize into zones that perform unique functions. Here, I introduce a topological and category-theoretic framework to represent particle and zone intra-scale interactions and inter-scale…
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template…
Using tools and concepts from contact topology we show that non-vanishing twist implies conservation of the layer structure in cholesteric liquid crystals. This leads to a number of additional topological invariants for cholesteric…
A fractal can be simply understood as a set or pattern in which there are far more small things than large ones, e.g., far more small geographic features than large ones on the earth surface, or far more large-scale maps than small-scale…
Morphogenetic dynamics of tissue sheets require coordinated cell shape changes regulated by global patterning of mechanical forces. Inspired by such biological phenomena, we propose a minimal mechanochemical model based on the notion that…
Based on extensive study of a dynamical systems model of the development of a cell society, a novel theory for stem cell differentiation and its regulation is proposed as the ``chaos hypothesis''. Two fundamental features of stem cell…
Autophagy is an intracellular degradation process that employs complex membrane dynamics to isolate and break down cellular components. However, many unanswered questions remain concerning remodeling of autophagic membranes. Here, we focus…
We present the computed phase diagram of columnar structures of soft spheres under pressure, of which the main feature is the appearance and disappearance of line slips, the shearing of adjacent spirals, as pressure is increased. A…
The emergence of nematic order on deformable closed surfaces plays a pivotal role in the morphogenesis of active biological matter, such as the regeneration of Hydra. In this work, we present a continuum model that couples the…