Related papers: Developed Smectics: When Exact Solutions Agree

A theoretical framework is developed to link the density profiles in the Scrape Off Layer (SOL) with the fluctuations (filaments) that generate them. The framework is based on the dynamics of independent filaments and their statistical…

Topological materials occupy the central stage in the modern condensed matter physics because of their robust metallic edge or surface states protected by the topological invariant, characterizing the electronic band structure in the bulk.…

In this paper, we deal with the gluing of two surfaces, where the gluing locus is assumed to be a curve. We consider a moving frame along the gluing locus, and define developable surfaces with respect to the frame. Considering geometric…

We prove a general fusion theorem for complete orientable minimal surfaces in $\mathbb{R}^3$ with finite total curvature. As a consequence, complete orientable minimal surfaces of weak finite total curvature with exotic geometry are…

Diffusion models excel at generation, but their latent spaces are high dimensional and not explicitly organized for interpretation or control. We introduce ConDA (Contrastive Diffusion Alignment), a plug-and-play geometry layer that applies…

We derive constraints on the existence of walls for Bridgeland stability conditions for general projective surfaces. We show that in suitable planes of stability conditions the walls are bounded and derive conditions for when the number of…

We study the interplay between an isostructural critical point and dislocation mediated two-dimensional melting, using a combination of Landau and continuum elasticity theory. If dislocations are excluded, coupling to the elastic degrees of…

Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by…

We discover that at the edge of optical lattice imprinted in saturable nonlinear media one-dimensional surface solitons exist only within a band of light intensities, and that they cease to exist when the lattice depth exceeds an upper…

Following the remarkable success of diffusion models on image generation, recent works have also demonstrated their impressive ability to address a number of inverse problems in an unsupervised way, by properly constraining the sampling…

Texture synthesis has proven successful at imitating a wide variety of textures. Adding additional constraints (in the form of a low-resolution version of the texture to be synthesized) makes it possible to use texture synthesis methods for…

This paper presents a density-based topology optimization method for designing 3D thin-walled structures with adaptive meshing. Uniform wall thickness is achieved by simultaneously constraining the minimum and maximum feature sizes using…

In this paper we consider developable surfaces which are isometric to planar domains and which are piecewise differentiable, exhibiting folds along curves. The paper revolves around the longstanding problem of existence of the so-called…

Motivated by the relation between (twisted) K3 surfaces and special cubic fourfolds, we construct moduli spaces of polarized twisted K3 surfaces of any fixed degree and order. We do this by mimicking the construction of the moduli space of…

We propose a novel approach to continuum modelling of dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…

We prove that any compact surface with constant positive curvature and conical singularities can be decomposed into irreducible components of standard shape, glued along geodesic arcs connecting conical singularities. This is a spherical…

Standard finite element methods employ an element-wise assembly strategy. The element's contribution to the system matrix is formed by a loop over quadrature points. This concept is also used in fictitious domain methods, which perform…

This paper presents a new method for modelling the dynamic behaviour of developable ribbons, two dimensional strips with much smaller width than length. Instead of approximating such surface with a general triangle mesh, we characterize it…

Controlling the topology of structures self-assembled from a set of heterogeneous building blocks is highly desirable for many applications, but is poorly understood theoretically. Here we show that the thermodynamic theory of self-assembly…

3D generation methods have shown visually compelling results powered by diffusion image priors. However, they often fail to produce realistic geometric details, resulting in overly smooth surfaces or geometric details inaccurately baked in…