Related papers: A geometrically controlled rigidity transition in …
The energetically optimal position of lattice defects on intrinsically curved surfaces is a complex function of shape parameters. For open surfaces, a simple condition predicts the critical size for which a central disclination yields lower…
The balance between stretching and bending deformations characterizes shape transitions of thin elastic sheets. While stretching dominates the mechanical response in tension, bending dominates in compression after an abrupt buckling…
Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as a important paradigm for relating these…
Organoids are in vitro cellular collectives from which brain-like, or gut-like, or kidney-like structures emerge. To make quantitative predictions regarding the morphology and rheology of a cellular collective in its initial stages of…
The task of learning patterns is typically associated with systems that update parameters on fixed architectures, such as neural networks, where learning proceeds through continuous optimization. Here, we demonstrate that pattern learning…
Disordered solids, straddling the solid-fluid boundary, lack a comprehensive continuum mechanical description. They exhibit a complex microstructure wherein multiple meta-stable states exist. Deforming disordered solids induces particles…
A liquid foam in contact with a solid surface forms a two-dimensional foam on the surface. We derive the equilibrium equations for this 2D foam when the solid surface is curved and smooth, generalising the standard case of flat Hele Shaw…
The vertex model is widely used to describe the dynamics of epithelial tissues, because of its simplicity and versatility and the direct inclusion of biophysical parameters. Here, it is shown that quite generally, when cells modify their…
An important open question in the modeling of biological tissues is how to identify the right scale for coarse-graining, or equivalently, the right number of degrees of freedom. For confluent biological tissues, both vertex and Voronoi…
Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of…
A mathematical model for crack-tip fields is proposed in this paper for the response of a three-dimensional (3-D) porous elastic solid whose material moduli are dependent on the density. Such a description wherein the generalized Lam\`e…
The optimal shapes attained by contractile cells on adhesive substrates are determined by the interplay between intracellular forces and adhesion with the extracellular matrix. We model the cell as a contractile film bounded by an elastic…
We study a shape evolution framework in which the deformation of shapes from time t to t + dt is governed by a regularized anisotropic elasticity model. More precisely, we assume that at each time shapes are infinitesimally deformed from a…
After a brief introduction to several variational problems in the study of shapes of thin thickness structures, we deal with variational problems on 2-dimensional surface in 3-dimensional Euclidian space by using exterior differential…
Cilia are motile biological appendages that are driven to bend by internal shear stresses between tubulin filaments. A continuum model of ciliary material is constructed that incorporates the essential ciliary constraints: (1)…
The mechanics of animal cells is strongly determined by stress fibers, which are contractile filament bundles that form dynamically in response to extracellular cues. Stress fibers allow the cell to adapt its mechanics to environmental…
Magnetic reconnection, a fundamental plasma process, is pivotal in understanding energy conversion and particle acceleration in astrophysical systems. While extensively studied in two-dimensional (2D) configurations, the dynamics of…
Cell deformability is an essential determinant for tissue-scale mechanical nature, such as fluidity and rigidity, and is thus crucial for understanding tissue homeostasis and stable developmental processes. However, numerical simulations…
Thin elastic solids are easily deformed into a myriad of three-dimensional shapes, which may contain sharp localized structures as in a crumpled candy wrapper, or have smooth and diffuse features like the undulating edge of a flower.…
The mechanics of epithelial tissues, which is governed by forces generated in various cell domains, is often investigated using two-dimensional models that account for the apically-positioned actomyosin structures but neglect basolateral…