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Discrete rearranging patterns include cellular patterns, for instance liquid foams, biological tissues, grains in polycrystals; assemblies of particles such as beads, granular materials, colloids, molecules, atoms; and interconnected…
Chemical heterogeneity of solid surfaces disrupts the adsorption of surfactants from the bulk liquid. While its presence can hinder the performance of some formulations, bespoke chemical patterning could potentially facilitate controlled…
3D printing methods which enable control over the position and orientation of embedded particles have promising applications in cell patterning and composite scaffolds. Extrusion-based additive manufacturing techniques such as fused…
Extrusion 3D-printing of biopolymers and natural fiber-based biocomposites allows for the fabrication of complex structures, ranging from gels for healthcare applications to eco-friendly structural materials. However, traditional polymer…
A fake quadric is a smooth projective surface that has the same rational cohomology as a smooth quadric surface but is not biholomorphic to one. We provide an explicit classification of all irreducible fake quadrics according to the…
In this work, we provide a local classification of certain special classes of surfaces determined by the prescription of the radial mean curvature in terms of the height and angle functions. Moreover, we introduce a special class of…
Current 3D representations like meshes, voxels, point clouds, and NeRF-based neural implicit fields exhibit significant limitations: they are often task-specific, lacking universal applicability across reconstruction, generation, editing,…
The surface reconstruction problem from sets of planar parallel slices representing cross sections through 3D objects is presented. The final result of surface reconstruction is always based on the correct estimation of the structure of the…
Starting with the irreducible triangulations of a fixed surface and splitting vertices, all the triangulations of the surface up to a given number of vertices can be generated. The irreducible triangulations have previously been determined…
Amorphous solids, such as glasses, have complex responses to deformations, with significant consequences in material design and applications. In this respect two intertwined aspects are important: stability and reversibility. It is crucial…
PCB (printed circuit board) substrates are often single-use, leading to material waste in electronics making. We introduce PCB Renewal, a novel technique that "erases" and "reconfigures" PCB traces by selectively depositing conductive epoxy…
Intermolecular forces are known to precipitate adhesion events between solid bodies. Inspired by a macro-scale experiment showing the hysteretic adhesion of a piece of flexible tape over a plastic substrate, we develop here a model of…
Heavy plastic shear deformation at relatively low homologous temperatures is called high-pressure torsion (HPT) deformation, which is one method of severe plastic deformation (SPD). The aim of the paper is to give an overview of a new…
The reconstruction of shredded documents consists of coherently arranging fragments of paper (shreds) to recover the original document(s). A great challenge in computational reconstruction is to properly evaluate the compatibility between…
A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the surface. In this work we propose an algorithm that constructs the set of irreducible triangulations of any surface with…
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…
Poisson surface reconstruction (PSR) remains a popular technique for reconstructing watertight surfaces from 3D point samples thanks to its efficiency, simplicity, and robustness. Yet, the existing PSR method and subsequent variants work…
This paper presents a method to obtain geometric registrations between high-genus ($g\geq 1$) surfaces. Surface registration between simple surfaces, such as simply-connected open surfaces, has been well studied. However, very few works…
Two-dimensional (2D) materials are widely used in various applications due to their extraordinary properties. In particular, their electrochemical stability, low electrical resistance, and huge specific surface area make them very…
Two-dimensional materials can be combined by placing individual layers on top of each other, so that they are bound only by their van der Waals interaction. The sequence of layers can be chosen arbitrarily, enabling an essentially…