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Triangular meshes are the most popular representations of 3D objects, but many mesh surfaces contain topological singularities that represent a challenge for displaying or further processing them properly. One such singularity is the…
This is an invited commentary on "Geometrically incompatible confinement of solids", B. Davidovitch, Y. Sun and G. M. Grason (PNAS, doi:10.1073/pnas.1815507116 , arxiv:1809.06919).
Functionals that penalize bending or stretching of a surface play a key role in geometric and scientific computing, but to date have ignored a very basic requirement: in many situations, surfaces must not pass through themselves or each…
We present a new method for performing Boolean operations on volumes represented as triangle meshes. In contrast to existing methods which treat meshes as 3D polyhedra and try to partition the faces at their exact intersection curves, we…
Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared to…
This paper considers the dynamics of edges in a network. The Dynamic Bond Percolation (DBP) process models, through stochastic local rules, the dependence of an edge $(a,b)$ in a network on the states of its neighboring edges. Unlike…
Under hard-agar and nutrient-rich conditions, a cell of $Bacillus$ $subtilis$ grows as a single filament owing to the failure of cell separation after each growth and division cycle. The self-elongating filament of cells shows sequential…
With the evolution of new manufacturing technologies such as multi-material 3D printing, one can think of new type of objects that consist of considerably less, yet heterogeneous, material, consequently being porous, lighter and cheaper,…
Unstable growth of cracks (rough crack surface and crack branching) in dynamic fracture has long been observed in various materials. Until now, there was no universally agreed upon explanation for these instabilities. Here, we demonstrate…
Metal-organic frameworks (MOFs) marry inorganic nodes, organic edges, and topological nets into programmable porous crystals, yet their astronomical design space defies brute-force synthesis. Generative modeling holds ultimate promise, but…
Large language models produce repetitive output when prompted independently across many batches, a phenomenon we term cross-batch mode collapse: the progressive loss of output diversity when a language model is prompted repeatedly without…
Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We…
Buckling instabilities driven by tissue growth underpin key developmental events such as the folding of the brain. Tissue growth is disordered due to cell-to-cell variability, but the effects of this variability on buckling are unknown.…
We introduce Curvy-an interactive design tool to generate varying density support structures for 3D printing. Support structures are essential for printing models with extreme overhangs. Yet, they often cause defects on contact areas,…
Marine obstacle detection demands robust segmentation under challenging conditions, such as sun glitter, fog, and rapidly changing wave patterns. These factors degrade image quality, while the scarcity and structural repetition of marine…
Liquid droplets on soft solids, such as soft polymeric gels, can induce substantial surface deformations, leading to the formation of wetting ridges at contact points. While these contact ridges have been shown to govern the rich surface…
Mesh saliency enhances the adaptability of 3D vision by identifying and emphasizing regions that naturally attract visual attention. To investigate the interaction between geometric structure and texture in shaping visual attention, we…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
We investigate symmetric grain boundaries in a lamellar diblock copolymer system. The form of the interface between two grains strongly depends on the angle $\theta$, between the normals of the grains. When this angle is small, the lamellae…
We study the evolution from a liquid to a crystal phase in two-dimensional curved space. At early times, while crystal seeds grow preferentially in regions of low curvature, the lattice frustration produced in regions with high curvature is…