Related papers: Geometry, Analysis and Morphogenesis: Problems and…
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
We present results of a long-term team collaboration of mathematicians and biologists. We focus on building a mathematical framework for the shape space constituted by a collection of homologous bones or teeth from many species. The…
The understanding of morphogenesis in living organisms has been renewed by tremendous progressin experimental techniques that provide access to cell-scale, quantitative information both on theshapes of cells within tissues and on the genes…
The process of self-morphing in curved surfaces found in nature, such as with the growth of flowers and leaves, has generated interest in the study of self-morphing bilayers, which has been used in many soft robots or switchers. However,…
3D shape editing is widely used in a range of applications such as movie production, computer games and computer aided design. It is also a popular research topic in computer graphics and computer vision. In past decades, researchers have…
A new model for biological growth is introduced that couples the geometry of an organism (or part of the organism) to the flow and deposition of material. The model has three dynamical variables (a) a Riemann metric tensor for the geometry,…
Although thin films are typically manufactured in planar sheets or rolls, they are often forced into three-dimensional shapes, producing a plethora of structures across multiple length-scales. Existing theoretical approaches have made…
We review the recent literature on the simulation of the structure and deformation of amorphous glasses, including oxide and metallic glasses. We consider simulations at different length and time scales. At the nanometer scale, we review…
Studying shape changing thick surfaces induced by differential growth helps us understand morphogenesis in biology and offers opportunities for device design. While ideal 2D differential growth maps have been well studied for both isotropic…
We consider a free boundary problem for a system of PDEs, modeling the growth of a biological tissue. A morphogen, controlling volume growth, is produced by specific cells and then diffused and absorbed throughout the domain. The geometric…
This paper presents bone adaptation as a geometric flow. The proposed method is based on two assumptions: first, that the bone surface is smooth (not fractal) permitting the definition of a tangent plane and, second, that the interface…
Throughout biology, hierarchy is a recurrent theme in the geometry of structures where strength is achieved with minimal use of material. Acting over vast timescales, evolution has brought about beautiful solutions to problems of…
Tissues are subjected to large external forces and undergo global deformations during morphogenesis. We use synthetic analogues of tissues to study the impact of cell-cell adhesion on the response of cohesive cellular assemblies under such…
Collective cell motions underlie structure formation during embryonic development. Tissues exhibit emergent multicellular characteristics such as jamming, rigidity transitions, and glassy dynamics, but there remain questions about how those…
In Nature, liquids often circulate in channels textured with leaflets, cilia or porous walls that deform with the flow. These soft structures are optimized to passively control flows and inspire the design of novel microfluidic and soft…
A stochastic model is used to assess the effect of external parameters on the development of submerged biofilms on smooth and rough surfaces. The model includes basic cellular mechanisms, such as division and spreading, together with an…
Smooth and curved microstructural topologies found in nature - from soap films to trabecular bone - have inspired several mimetic design spaces for architected metamaterials and bio-scaffolds. However, the design approaches so far have been…
Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…
Deployable structures, essential across various engineering applications ranging from umbrellas to satellites, are evolving to include soft, morphable designs where geometry drives transformation. However, a major challenge for soft…
Animal morphogenesis often involves significant shape changes of epithelial tissue sheets. Great progress has been made in understanding the underlying cellular driving forces and their coordination through biomechanical feedback loops.…