Related papers: Developed Smectics: When Exact Solutions Agree
This work proposes a new formulation to the long-standing problem of convex decomposition through learning feature fields, enabling the first feed-forward model for open-world convex decomposition. Our method produces high-quality…
Disordered metasurfaces offer unique properties unattainable with periodic or ordered metasurfaces, notably the absence of deterministic interference effects at specific wavelengths and angles. In this work, we introduce a lithography-free…
It is proved that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. The relevance of this result in the context of the dynamics of…
Addressing the limitations of text as a source of accurate layout representation in text-conditional diffusion models, many works incorporate additional signals to condition certain attributes within a generated image. Although successful,…
We show that any smooth one-dimensional link in the real projective three-plane is the fixed-point locus of a smooth symplectic surface in the complex projective three-plane which is invariant under complex conjugation. The degree of the…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
Working in infinite dimensional linear spaces, we deal with support for closed sets without interior. We generalize the Convexity Theorem for closed sets without interior. Finally we study the infinite dimensional version of Jordan…
Two-dimensional (2D) layered materials hosting dislocations have attracted considerable research attention in recent years. In particular, screw dislocations can result in a spiral topology and an interlayer twist in the layered materials,…
We prove that moduli spaces of torsion-free sheaves on a projective smooth complex surface are irreducible, reduced and of the expected dimension, provided the expected dimension is large enough. Actually we prove more: given a line bundle…
Complex geometric tasks such as geometric modeling, physical simulation, and texture parametrization often involve the embedding of many complex sub-domains with potentially different dimensions. These tasks often require evolving the…
Minimal surfaces are ubiquitous in nature. Here they are considered as geometric objects that bear a deformation content. By refining the resolution of the surface deformation gradient afforded by the polar decomposition theorem, we…
In many scenarios -- when we bite food or during a crash -- fracture is inevitable. Finding solutions to steer fracture to mitigate its impact or turn it into a purposeful functionality, is therefore crucial. Strategies using composites,…
We translate notions and results of decomposition and dimension theories for module categories, into the lattice environment. In particular we translate dimension theory in module categories to complete modular upper-continuous lattices.
Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
Given a complete non-compact surface embedded in R^3, we consider the Dirichlet Laplacian in a layer of constant width about the surface. Using an intrinsic approach to the layer geometry, we generalise the spectral results of an original…
Ordered phases on curved substrates experience a complex interplay of ordering and intrinsic curvature, commonly producing frustration and singularities. This is an especially important issue in crystals as ever-smaller scale materials are…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
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…
For any compact, connected, orientable, finite-type surface with marked points other than the sphere with three marked points, we construct a finite rigid set of its arc complex: a finite simplicial subcomplex of its arc complex such that…