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We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore…
Being motivated by the delivery of drugs and vaccines through subcutaneous (SC) injection in human bodies, a theoretical investigation is performed using a two-dimensional mathematical model in the cartesian coordinate. In general, a large…
The morphogenesis of cells and tissues involves an interplay between chemical signals and active forces on their surrounding surface layers. The complex interaction of hydrodynamics and material flows on such active surfaces leads to…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
Motivated to understand the behavior of biological filaments interacting with membranes of various types, we study a theoretical model for the shape and thermodynamics of intrinsically-helical filaments bound to curved membranes. We show…
As an injury heals, an embryo develops, or a carcinoma spreads, epithelial cells systematically change their shape. In each of these processes cell shape is studied extensively, whereas variation of shape from cell-to-cell is dismissed most…
Cells in tissues can organize into a broad spectrum of structures according to their function. Drastic changes of organization, such as epithelial-mesenchymal transitions or the formation of spheroidal aggregates, are often associated…
Cell-cell adhesion is an inherently nonlocal phenomenon. Numerous partial differential equation models with nonlocal term have been recently presented to describe this phenomenon, yet the mathematical properties of nonlocal adhesion model…
We examine emergent properties of 2D supramolecular networks, using enumeration of configurations formed by interacting dominoes on square lattices as a simple model system. Possible ground states are identified using a convex hull…
The folding of cellular monolayers pervades embryonic development and disease. It results from stresses out of the plane of the tissue, often caused by cell shape changes including cell wedging via apical constriction. These local cellular…
A continuum description is built to characterize the stationary and transient deformations of confluent tissues subject to heterogeneous activities. By defining a coarse-grained texture matrix field to represent the shape and size of cells,…
Cell shape is fundamental in biology. The average cell shape can influence crucial biological functions, such as cell fate and division orientation. But cell-to-cell shape variability is often regarded as noise. In contrast, recent works…
We use an elastic model to explore faceting of solid-wall vesicles with elastic heterogeneities. We show that faceting occurs in regions where the vesicle wall is softer, such as areas of reduced wall thicknesses or concentrated in…
Tissue growth can be modeled in two dimension by only using circular granular cells, which can grow and produce child. Linear spring-dashpot model is used to bind the cells with a cut-off interaction range of 1.1 times sum of radii of…
Ion transport in biological tissues is crucial in the study of many biological and pathological problems. Some multi-cellular structures, like smooth muscles on the vessel walls, could be treated as periodic bi-domain structures, which…
Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be…
Two-scale topology optimization, combined with the design of microstructure families with a broad range of effective material parameters, is increasingly widely used in many fabrication applications to achieve a target deformation behavior…
The initiation of directional cell motion requires symmetry breaking that can happen both with or without external stimuli. During cell crawling, forces generated by the cytoskeleton and their transmission through mechanosensitive adhesions…
Although tissues are usually studied in isolation, this situation rarely occurs in biology, as cells, tissues, and organs, coexist and interact across scales to determine both shape and function. Here, we take a quantitative approach…
The shape of a cell influences and it is influenced by interactions with its neighbouring partners. Here, we introduce a coarse-grained model of non-reciprocal interactions between single-cell organisms to study emergent morphologies during…