Related papers: Textile D forms and $D_{4d}$
We use unimodular ribbon categories to construct quantum invariants of ribbon surfaces in $4$-dimensional $2$-handlebodies up to $1$-isotopy. In the process, we recover invariants due to Bobtcheva-Messia, Broda-Petit,…
Using a formalism developed to include collective coordinates, we calculate the contributions to S-matrix elements due to off-shell D-branes in a string coupling expansion. The formalism is further used to establish a two-dimensional…
In this article we are examining extensions and some basic diagrammatic properties of modules, in both cases from a new, "virtual" point of view. As natural background for investigating the kind of problems we are dealing with, the virtual…
This thesis is devoted to the construction and study of D-branes in some curved space-times in string theory. On the one hand, those D-branes are described geometrically as submanifolds subject to Born-Infeld effective dynamics. On the…
Texture is an essential property of physical objects that affects aesthetics, usability, and functionality. However, designing and applying textures to 3D objects with existing tools remains difficult and time-consuming; it requires…
Well-fitted clothing is essential for both real and virtual garments to enable self-expression and accurate representation for a large variety of body types. Common practice in the industry is to provide a pre-made selection of distinct…
This project is focused on investigating the structural performance of parts and structures produced using the latest additive manufacturing techniques. For additive manufacturing of test coupons, fused deposition modeling of…
Patterns and textures are defining characteristics of many natural objects: a shirt can be striped, the wings of a butterfly can be veined, and the skin of an animal can be scaly. Aiming at supporting this analytical dimension in image…
Optical vortices, as a kind of structured beam with helical phase wavefronts and doughnut shape intensity distribution, have been used for fabricating chiral structures in metal and spiral patterns in anisotropic polarization-dependent…
Designing real and virtual garments is becoming extremely demanding with rapidly changing fashion trends and increasing need for synthesizing realistic dressed digital humans for various applications. This necessitates creating simple and…
We introduce a new class of thin flexible structures that morph from a flat shape into prescribed 3D shapes without an external stimulus such as mechanical loads or heat. To achieve control over the target shape, two different concepts are…
Modular forms are highly self-symmetric functions studied in number theory, with connections to several areas of mathematics. But they are rarely visualized. We discuss ongoing work to compute and visualize modular forms as 3D surfaces and…
The problem of text-guided image generation is a complex task in Computer Vision, with various applications, including creating visually appealing artwork and realistic product images. One popular solution widely used for this task is the…
Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. We present here an efficient Fourier-space based…
We discuss the use of 3D printing to physically visualize (materialize) fluid flow structures. Such 3D models can serve as a refreshing hands-on means to gain deeper physical insights into the formation of complex coherent structures in…
The aim of this paper is to present a unified theory of many Kato type representation theorems in terms of solvable forms on Hilbert spaces. In particular, for some sesquilinear forms $\Omega$ on a dense domain $\mathcal{D}$ one looks for…
We uncover 2-group symmetries in 6d superconformal field theories. These symmetries arise when the discrete 1-form symmetry and continuous flavor symmetry group of a theory mix with each other. We classify all 6d superconformal field…
We introduce theoretical methods for describing the optical response of two-dimensional (2D) materials patterned at the nanoscale into both arrays of ribbons along a planar surface and spherical particles. Fourier-Floquet decompositions of…
3D printing technologies are currently enabling the fabrication of objects with complex architectures and tailored properties. In such framework, the production of 3D optical structures, which are typically based on optical transparent…
Novel technologies and new materials are in high demand for future energy-efficient electronic devices to overcome the fundamental limitations of miniaturization of current silicon-based devices. Two-dimensional (2D) materials show…