Related papers: Curvature-Induced Defect Unbinding in Toroidal Geo…
The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…
We construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form $H(X)=1+{A}{|X|^{-\gamma}}$ for $|X|$ large, when $A<0$ and…
We study the graded geometric point of view of curvature and torsion of Q-manifolds (differential graded manifolds). In particular, we get a natural graded geometric definition of Courant algebroid curvature and torsion, which correctly…
We show that the outcome of disc instability models is strongly influenced by boundary conditions such as the position of the inner and outer disc edges. We discuss other sources of uncertainties, such as the tidal torque, and we conclude…
We investigate topography-driven generation of defects in liquid crystals films coating frozen surfaces of spatially varying Gaussian curvature whose topology does not automatically require defects in the ground state. We study in…
This work studies existence and regularity questions for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations. Our main result is a constructive method of computer assisted proof which…
The tidal effects generated by a nonlinear gravitational wave are investigated in double-null v - u coordinates, as an exact solution of Einstein's field equations. The components $\xi^{v}$ and $\xi^{u}$ of the separation vector behave as…
Topological properties of quantum materials are intimately related to symmetry. Here, we tune the magnetic order of the axion insulator candidate EuIn$_2$As$_2$ from its broken-helix ground state to the field-polarized phase by applying an…
This note presents two observations which have in common that they lie at the boundary of toric geometry. The first one because it concerns the deformation of affine toric varieties into non toric germs in order to understand how to avoid…
We present a novel framework for the study of disclinations in two-dimensional active nematic liquid crystals, and topological defects in general. The order tensor formalism is used to calculate exact multi-particle solutions of the…
We use molecular dynamics to study the ordering of a nematic liquid crystal around a spherical particle or droplet. Homeotropic boundary conditions and strong anchoring create a hedgehog director configuration on the particle surface and in…
We investigate the geometry of a quantum universe with the topology of the four-torus. The study of non-contractible geodesic loops reveals that a typical quantum geometry consists of a small semi-classical toroidal bulk part, dressed with…
In this paper, we consider an incompressible viscous flow without surface tension in a finite-depth domain of three dimensions, with free top boundary and fixed bottom boundary. This system is governed by a Naiver-Stokes equation in above…
Topological or deconfined phases of matter exhibit emergent gauge fields and quasiparticles that carry a corresponding gauge charge. In systems with an intrinsic conserved U(1) charge, such as all electronic systems where the Coulombic…
We use genus zero free energy functions of Hermitian matrix models to define spectral curves and their special deformations. They are special plane curves defined by formal power series with integral coefficients generalizing the Catalan…
We provide a quantitative analysis of all kinds of topological defects present in 2D passive and active repulsive disk systems. We show that the passage from the solid to the hexatic is driven by the unbinding of dislocations. Instead,…
We simulate colloids (radius $R \sim 1\mu$m) trapped at the interface between a cholesteric liquid crystal and an immiscible oil, at which the helical order (pitch p) in the bulk conflicts with the orientation induced at the interface,…
Almost all available results in elasticity on curved topographies are obtained within either a small curvature expansion or an empirical covariant generalization that accounts for screening between Gaussian curvature and disclinations. In…
We consider the shape and topology optimization problem to design a structure that minimizes a weighted sum of material consumption and (linearly) elastic compliance under a fixed given boundary load. As is well-known, this problem is in…
We consider curvature depending variational models for image regularization, such as Euler's elastica. These models are known to provide strong priors for the continuity of edges and hence have important applications in shape-and image…