Related papers: Discrete Thickness
The Dirichlet form associated with the intrinsic gradient on Poisson space is known to be quasi-regular on the complete metric space $\ddot\Gamma=$ $\{Z_+$-valued Radon measures on $\IR^d\}$. We show that under mild conditions, the set…
A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…
We investigate minimizers and critical points for scale-invariant tangent-point energies ${\rm TP}^{p,q}$ of closed curves. We show that a) minimizing sequences in ambient isotopy classes converge to locally critical embeddings in all but…
We consider the numerical computation of a variational problem that arises from materials science. The target functional is a type of elastic energy that is influenced by obstacles and adhesion. Owing to its strong nonlinearity and…
In this paper, we introduce a nonlocal, variational model for thin films. We consider convolution-type functionals defined on a thin domain whose thickness is of order $\gamma$, where the effective interactions range between points is of…
We generalize the notion of calibrated submanifolds to smooth maps and show that the several examples of smooth maps appearing in the differential geometry become the examples of our situation. Moreover, we apply these notion to give the…
We introduce pointwise map smoothness via the Dirichlet energy into the functional map pipeline, and propose an algorithm for optimizing it efficiently, which leads to high-quality results in challenging settings. Specifically, we first…
The ropelength of a knot is the quotient of its length and its thickness, the radius of the largest embedded normal tube around the knot. We prove existence and regularity for ropelength minimizers in any knot or link type; these are…
We study the existence and regularity of minimizers of the neo-Hookean energy in the closure of classes of deformations without cavitation. The exclusion of cavitation is imposed in the form of the divergence identities, which is equivalent…
We prove that a certain discrete energy for triangulated surfaces, defined in the spirit of discrete differential geometry, converges to the Willmore energy in the sense of $\Gamma$-convergence. Variants of this discrete energy have been…
In the first part of this paper, we apply a well known discrete-to-continuum approach to a Frenkel-Kontorova-type model of an infinitely long one-dimensional chain of atoms weakly interacting with a line of fixed atoms. The rescaled model…
We prove generalized Gaffney inequalities and the discrete compactness for finite element differential forms on $s$-regular domains, including general Lipschitz domains. In computational electromagnetism, special cases of these results have…
We identify the $\Gamma$-limit of a nanoparticle-polymer model as the number of particles goes to infinity and as the size of the particles and the phase transition thickness of the polymer phases approach zero. The limiting energy consists…
The presence of inhomogeneities modifies the cosmic distances through the gravitational lensing effect, and, indirectly, must affect the main cosmological tests. Assuming that the dark energy is a smooth component, the simplest way to…
We study a quantity called discrete layered entropy, which approximates the Shannon entropy within a logarithmic gap. Compared to the Shannon entropy, the discrete layered entropy is piecewise linear, approximates the expected length of the…
We investigate some of the effects of the lack of compactness in the critical Folland-Stein-Sobolev embedding in very general (possible non-smooth) domains, by proving via De Giorgi's $\Gamma$-convergence techniques that optimal functions…
In this letter, the wavelet transform is used to decompose the classical linearly polarized plane light wave into a series of discrete Morlet wavelets. It is found that the energy of the light wave can be discrete, associated with its…
What length of rope (of given diameter) is required to tie a particular knot? To answer this question, we define some new notions of thickness for a space curve, one based on Gromov's distortion, and another generalizing the thickness of…
In this paper we explore relationships between divergence and thick groups, and with the same techniques we estimate lengths of shortest conjugators. We produce examples, for every positive integer n, of CAT(0) groups which are thick of…
Let $\Sigma$ be a smooth Riemannian manifold, $\Gamma \subset \Sigma$ a smooth closed oriented submanifold of codimension higher than $2$ and $T$ an integral area-minimizing current in $\Sigma$ which bounds $\Gamma$. We prove that the set…