Related papers: Defective nematogenesis: Gauss curvature in progra…
A nematic liquid crystal confined to the surface of a sphere exhibits topological defects of total charge $+2$ due to the topological constraint. In equilibrium, the nematic field forms four $+1/2$ defects, located at the corners of a…
We solve the forward and inverse problems associated with the transformation of flat sheets to surfaces of revolution with non-trivial topography, including Gaussian curvature, without a stretch elastic cost. We deal with systems slender…
We present a simple three-dimensional model to describe the autonomous expansion of a substrate which grows driven by the local mean curvature of its surface. The model aims to reproduce the nest construction process in arboreal…
Graph Neural Networks (GNNs) are characterized by their capacity of processing graph-structured data. However, due to the sparsity of labels under semi-supervised learning, they have been found to exhibit biased performance on specific…
Focusing on a small set of proteins that i) fold in a concerted, all-or-none fashion and ii) do not contain knots or slipknots, we show that the Gauss linking integral, the torsion and the number of sequence-distant contacts provide…
The gravitational evolution of the genus and other statistics of isodensity contours of the density field is derived analytically in a weakly nonlinear regime using second-order perturbation theory. The effect of final smoothing in…
A model describing cell membranes as optimal shapes with regard to the $L^2$-deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is shown that the corresponding energy functional is lower…
Topological defects play a fundamental role in the investigation of symmetries in quantum field theories. For conformal field theories in two space-time dimensions, it is possible to construct these defects using lattice models allowing…
Given a planar graph derived from a spherical, euclidean or hyperbolic tessellation, one can define a discrete curvature by combinatorial properties, which after embedding the graph in a compact 2d-manifold, becomes the Gaussian curvature.
Growth processes in many living organisms create thin, soft materials with an intrinsically hyperbolic geometry. These objects support novel types of mesoscopic defects - discontinuity lines for the second derivative and branch points -…
Shape transformations of epithelial tissues in three dimensions, which are crucial for embryonic development or in vitro organoid growth, can result from active forces generated within the cytoskeleton of the epithelial cells. How the…
We develop a fully coupled theoretical description of dislocation dynamics on deformable crystalline surfaces, using continuum modeling and the amplitude-phase-field crystal (APFC) framework extended to curved geometries. We derive a…
We consider three-dimensional reshaping of a thin nematoelastic film upon nematic-isotropic transition in the field of a charge one topological defect, leading to either cone or anticone (d-cone) shells. The analysis is based on the…
Soft materials with layered structure such as membranes, block copolymers, and smectics exhibit intriguing morphologies with nontrivial curvatures. We report on restructuring the Gaussian and mean curvatures of smectic A films with free…
A topology optimization approach for designing large deformation contact-aided shape morphing compliant mechanisms is presented. Such mechanisms can be used in varying operating conditions. Design domains are described by regular hexagonal…
Curved structures in soft matter and biological systems commonly emerge as a result of self-assembly processes where building blocks aggregate in a controlled manner, giving rise to specific system structure and properties. Learning how to…
The high degrees of freedom and complex structure of garments present significant challenges for clothing manipulation. In this paper, we propose a general topological dynamics model to fold complex clothing. By utilizing the visible…
We investigate the nucleation, growth, and spatial organization of topological defects with a ribbon shaped elastic sheet which is stretched and twisted. Singularities are found to spontaneously arrange in a triangular lattice in the form…
We investigate the out-of-plane shape morphing capability of single-material elastic sheets with architected cut patterns that result in arrays of tiles connected by flexible hinges. We demonstrate that a non-periodic cut pattern can cause…
To definite and compute differential invariants, like curvatures, for triangular meshes (or polyhedral surfaces) is a key problem in CAGD and the computer vision. The Gaussian curvature and the mean curvature are determined by the…