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We introduce new results about the shape derivatives of scalar- and vector-valued functions, extending the results from (Dogan-Nochetto 2012) to more general surface energies. They consider surface energies defined as integrals over…
In this paper, we explore the algebraic and geometric structures that arise from a procedure we dub "gauging the gauge", which involves the promotion of a certain global, coordinate independent symmetry to a local one. By gauging the global…
We consider membranes as fluid deformable surface and allow for higher order geometric terms in the bending energy. The evolution equations are derived and numerically solved using surface finite elements. The higher order geometric terms…
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…
Using agent-based simulations of self-propelled particles subject to short-range repulsion and nematic alignment we explore the dynamical phases of a dense active material confined to the surface of a sphere. We map the dynamical phase…
Topological defects are increasingly being identified in various biological systems, where their characteristic flow fields and stress patterns are associated with continuous active stress generation by biological entities. Here, using…
The buckling of a soft elastic sample under growth or swelling has highlighted a new interest in materials science, morphogenesis, and biology or physiology. Indeed, the change of mass or volume is a common fact of any living species, and…
Formation of membrane necks is crucial for fission and fusion in lipid bilayers. In this work, we seek to answer the following fundamental question: what is the relationship between protein-induced spontaneous mean curvature and the…
We study the adhesion of an elastic sheet on a rigid spherical substrate. Gauss'Theorema Egregium shows that this operation necessarily generates metric distortions (i.e. stretching) as well as bending. As a result, a large variety of…
A variant of a gauge theory is formulated to describe disclinations on Riemannian surfaces that may change both the Gaussian (intrinsic) and mean (extrinsic) curvatures, which implies that both internal strains and a location of the surface…
Deep Learning methods, specifically convolutional neural networks (CNNs), have seen a lot of success in the domain of image-based data, where the data offers a clearly structured topology in the regular lattice of pixels. This…
Biological membranes are able to exhibit various morphology due to the fluidity of the lipid molecules within the monolayers. The shape transformation of membranes has been well described by the classical Helfrich theory, which consists…
Fracture networks are ubiquitous in nature, spanning scales from millimeter-sized cracks in botanical peels to hundred-kilometer-long lineae on planetary satellites. The propagation of a crack is a complex, nonlinear phenomenon governed by…
We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on…
Unoriented surface reconstructions based on the Gauss formula have attracted much attention due to their elegant mathematical formulation and excellent performance. However, the isotropic characteristics of the formulation limit their…
Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…
In this paper we investigate the curvature of conformal deformations by noncommutative Weyl factors of a flat metric on a noncommutative 2-torus, by analyzing in the framework of spectral triples functionals associated to perturbed…
If more than one curvaton dominate the Universe at different epochs from each other, curvature perturbations can be temporarily enhanced to a value much larger than the observed one 10^{-5}. The traces of the enhancement may be left as…
A description of dislocations and disclinations defects in terms of Riemann--Cartan geometry is given, with the curvature and torsion tensors being interpreted as the surface densities of the Frank and Burgers vectors, respectively. A new…
A model of pattern formation in living systems is presented. The pattern is achieved by the sequential interaction of two signaling pathways. The coupling of the pattern to the (thick) epithelial sheet changes is given, when the Gauss…