Related papers: Geometry, Analysis and Morphogenesis: Problems and…
The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows…
The physics of disordered media, from metallic glasses to colloidal suspensions, granular matter and biological tissues, offers difficult challenges because it often occurs far from equilibrium, in materials lacking symmetries and evolving…
Accretion of mineralized thin wall-like structures via localized growth along their edges is observed in a range of physical and biological systems ranging from molluscan and brachiopod shells to carbonate-silica composite precipitates. To…
Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of…
Many organs of higher organisms are heavily branched structures and arise by an at first sight similar process of branching morphogenesis. Yet the regulatory components and local interactions that have been identified differ greatly in…
The prediction of the three-dimensional native structure of proteins from the knowledge of their amino acid sequence, known as the protein folding problem, is one of the most important yet unsolved issues of modern science. Since the…
Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…
The shape of materials is often subject to a number of geometric constraints that limit the size of the system or fix the structure of its boundary. In soft and biological materials, however, these constraints are not always hard, but are…
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
Controlling the self-assembly of supramolecular structures is vital for living cells, and a central challenge for engineering at the nano- and microscales. Nevertheless, even particles without optimized shapes can robustly form well-defined…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
A basic paradigm underlying the Hookean mechanics of amorphous, isotropic solids is that small deformations are proportional to the magnitude of external forces. However, slender bodies may undergo large deformations even under minute…
Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [Pizer et al., 2003]) yield rich geometrical features that can be useful for analyzing the shape of sheet-like biological…
Experimental methods allow the shape and chemical composition of solid surfaces to be controlled at a mesoscopic level. Exposing such structured substrates to a gas close to coexistence with its liquid can produce quite distinct adsorption…
Understanding how growth induces form is a longstanding biological question. Many studies concentrated on the shapes of plant cells, fungi or bacteria. Some others have shown the importance of the mechanical properties of bacterial walls…
Mathematical models of biological growth commonly attempt to distinguish deformation due to growth from that due to mechanical stresses through a hypothesised multiplicative decomposition of the deformation gradient. Here we demonstrate…
Soft and biological matter come in a variety of shapes and geometries. When soft surfaces that do not fit into each other due to a mismatch in Gaussian curvatures form an interface, beautiful geometry-induced patterns emerge. In this paper,…
The process of morphogenesis is an evolution of the shape of an organism together with the differentiation of its parts. This process encompasses numerous biological processes ranging from embryogenesis to regeneration following crisis such…
Predicting the large-amplitude deformations of thin elastic sheets is difficult due to the complications of self-contact, geometric nonlinearities, and a multitude of low-lying energy states. We study a simple two-dimensional setting where…
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel,…