Related papers: The Cost of Two-dimensional Rearrangement
A simplified calculation of the structure constants of the diffeomorphism group of the two-sphere is presented
In this paper, we prove sharp estimates for the average cost of the optimal matching problem on the flat 2-torus, using quantitative linearization and the method of trajectories.
We investigate the evaluation of the six-fold integral representation for the second order exchange contribution to the self energy of a three dimensional electron gas at the Fermi surface.
We discuss a discretisation of the de Rham-Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge-Dirac and Laplace operators in which key geometric aspects of…
The uniform norm of the differential of the n-th iteration of a diffeomorphism is called the growth sequence of the diffeomorphism. In this paper we show that there is no lower universal growth bound for volume preserving diffeomorphisms on…
We investigate the random bipartite optimal matching problem on a flat torus in two-dimensions, considering general strictly convex power costs of the distance. We extend the successful ansatz first introduced by Caracciolo et al. for the…
Diagonal flipping of a rhombus consisting of two triangles sharing a common edge with atoms (ions) in vertices of the triangles is considered as an elementary act of the polymorphic transformation in metals. The estimation of the energy…
This paper introduces and studies a metamorphosis framework for geometric measures known as varifolds, which extends the diffeomorphic registration model for objects such as curves, surfaces and measures by complementing diffeomorphic…
Let $A$ be a $2\times 2$ integral matrix with an eigenvalue of modulus strictly less than 1. Let $T$ be the natural endomorphism on the torus $\mathbb{T}^2=\mathbb{R}^2/\mathbb{Z}^2$, induced by $A$. Given $\tau>0$, let \[ R_\tau =\{\, x\in…
The energetic cost of creating a defect within a host material is given by the formation energy. Here we present a formulation allowing the calculation of formation energies in one-dimensional nanostructures, which overcomes the…
This essay summarizes the state of the art on some aspects of the dynamics of polynomial diffeomorphsms in complex dimension two, and it presents a number of open questions.
We estimate the energy and Hausdorff dimensions of the Riesz products on the unit sphere of $\mathbb{C}^n$, $n\ge 2$. Also, we obtain similar results for the pluriharmonic measures on the torus.
In this note we prove estimates for the average cost in the quadratic optimal transport problem on the two-dimensional flat torus which are optimal up to a double logarithm. We also prove sharp estimates on the displacement. This is based…
The aim of this note is two-fold. In the first part of the paper we are going to investigate an inverse problem related to additive energy. In the second, we investigate how dense a subset of a finite structure can be for a given additive…
Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral…
We propose a method to compute complex volume of 2-bridge link complements. Our construction sheds light on a relationship between cluster variables with coefficients and canonical decompositions of link complements.
We study both analytically and numerically how the electronic structure and the transport properties of a two-dimensional disordered system are modified in the presence of resonances. The energy dependence of the density of states and the…
The energy, area and excess energy of a decorated vertex in a 2D foam are calculated. The general shape of the vertex and its decoration are described analytically by a reference pattern mapped by a parametric Moebius transformation. A…
We explain a correspondence between some invariants in the dynamics of color exchange in a 2d coloring problem, which are polynomials of winding numbers, and linking numbers in 3d. One invariant is visualized as linking of lines on a…
We describe results on the dynamics of polynomial diffeomorphisms of ${\bf C^2}$ and draw connections with the dynamics of polynomial maps of ${\bf C}$ and the dynamics of polynomial diffeomorphisms of ${\bf R^2}$ such as the H\'enon…