Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Scholtes, Sebastian"'
We explore recent progress and open questions concerning local minima and saddle points of the Cahn--Hilliard energy in $d\geq 2$ and the critical parameter regime of large system size and mean value close to $-1$. We employ the String Method of E, R
Externí odkaz:
http://arxiv.org/abs/2104.03689
We discuss a discretization by polygonal lines of the Euler-Bernoulli bending energy and of Euler elasticae under clamped boundary conditions. We show Hausdorff convergence of the set of almost minimizers of the discrete bending energy to the set of
Externí odkaz:
http://arxiv.org/abs/1901.02228
In this paper we derive optimal algebraic-in-time relaxation rates to the kink for the Cahn-Hilliard equation on the line. We assume that the initial data have a finite distance---in terms of either a first moment or the excess mass---to a kink profi
Externí odkaz:
http://arxiv.org/abs/1806.02519
We establish metastability of the one-dimensional Cahn-Hilliard equation for initial data that is order-one in energy and order-one in $\dot{H}^{-1}$ away from a point on the so-called slow manifold with $N$ well-separated layers. Specifically, we sh
Externí odkaz:
http://arxiv.org/abs/1705.10985
Autor:
Scholtes, Sebastian
The present chapter gives an overview on results for discrete knot energies. These discrete energies are designed to make swift numerical computations and thus open the field to computational methods. Additionally, they provide an independent, geomet
Externí odkaz:
http://arxiv.org/abs/1603.02464
Autor:
Havenith, Thomas, Scholtes, Sebastian
When computing the average speed of a car over different time periods from given GPS data, it is conventional wisdom that the maximal average speed over all time intervals of fixed length decreases if the interval length increases. However, this intu
Externí odkaz:
http://arxiv.org/abs/1501.06391
Autor:
Scholtes, Sebastian
We investigate the relationship between a discrete version of thickness and its smooth counterpart. These discrete energies are defined on equilateral polygons with $n$ vertices. It will turn out that the smooth ropelength, which is the scale invaria
Externí odkaz:
http://arxiv.org/abs/1401.5651
Autor:
Scholtes, Sebastian
We investigate a discrete version of the M\"obius energy, that is of geometric interest in its own right and is defined on equilateral polygons with $n$ segments. We show that the $\Gamma$-limit regarding $L^{q}$ or $W^{1,q}$ convergence, $q\in [1,\i
Externí odkaz:
http://arxiv.org/abs/1311.3056
Autor:
Scholtes, Sebastian
We give new characterisations of sets of positive reach and show that a closed hypersurface has positive reach if and only if it is of class $C^{1,1}$. These results are then used to prove new alternating Steiner formul{\ae} for hypersurfaces of posi
Externí odkaz:
http://arxiv.org/abs/1304.4179
Autor:
Scholtes, Sebastian
In this brief note we show that the integral Menger curvature $\mathcal{M}_{p}$ is finite for all simple polygons if and only if $p\in (0,3)$. For the intermediate energies $\mathcal{I}_{p}$ and $\mathcal{U}_{p}$ we obtain the analogous result for $p
Externí odkaz:
http://arxiv.org/abs/1202.0504