Search results for "53"
showing 10 items of 2908 documents
On-surface covalent linking of organic building blocks on a bulk insulator.
2011
On-surface synthesis in ultrahigh vacuum provides a promising strategy for creating thermally and chemically stable molecular structures at surfaces. The two-dimensional confinement of the educts, the possibility of working at higher (or lower) temperatures in the absence of solvent, and the templating effect of the surface bear the potential of preparing compounds that cannot be obtained in solution. Moreover, covalently linked conjugated molecules allow for efficient electron transport and are, thus, particularly interesting for future molecular electronics applications. When having these applications in mind, electrically insulating substrates are mandatory to provide sufficient decoupli…
Effect of mixing and spatial dimension on the glass transition
2009
We study the influence of composition changes on the glass transition of binary hard disc and hard sphere mixtures in the framework of mode coupling theory. We derive a general expression for the slope of a glass transition line. Applied to the binary mixture in the low concentration limits, this new method allows a fast prediction of some properties of the glass transition lines. The glass transition diagram we find for binary hard discs strongly resembles the random close packing diagram. Compared to 3D from previous studies, the extension of the glass regime due to mixing is much more pronounced in 2D where plasticization only sets in at larger size disparities. For small size disparitie…
Structure and dynamics in amorphous tellurium and Te-n clusters: A density functional study
2012
Density functional/molecular dynamics simulations have been performed on amorphous tellurium (a melt-quenched sample of 343 atoms at 300 K) and on Te clusters with up to 16 atoms. The former extend our calculations on liquid Te at 560, 625, 722, and 970 K [Phys. Rev. B 81, 094202 (2010)]. We discuss trends in structures (including those of other group-16 elements), electronic densities of states, and vibration frequencies. Chain structures are common in S and Se, but the chains in amorphous Te are short, and branching sites with threefold-coordinated atoms are common. The energy difference between two- and threefold local coordination depends sensitively on the exchange-correlation function…
Almost Sharp Global Well-Posedness for a class of Dissipative and Dispersive Equations on R in Low Regularity Sobolev Spaces
2014
In this paper we obtain global well-posedness in low order Sobolev spaces of higher order KdV type equations with dissipation. The result is optimal in the sense that the flow-map is not twice continuously differentiable in rougher spaces. The solution is shown to be smooth for positive times.
Short time existence of the classical solution to the fractional mean curvature flow
2019
Abstract We establish short-time existence of the smooth solution to the fractional mean curvature flow when the initial set is bounded and C 1 , 1 -regular. We provide the same result also for the volume preserving fractional mean curvature flow.
Sard property for the endpoint map on some Carnot groups
2016
In Carnot-Caratheodory or sub-Riemannian geometry, one of the major open problems is whether the conclusions of Sard's theorem holds for the endpoint map, a canonical map from an infinite-dimensional path space to the underlying finite-dimensional manifold. The set of critical values for the endpoint map is also known as abnormal set, being the set of endpoints of abnormal extremals leaving the base point. We prove that a strong version of Sard's property holds for all step-2 Carnot groups and several other classes of Lie groups endowed with left-invariant distributions. Namely, we prove that the abnormal set lies in a proper analytic subvariety. In doing so we examine several characterizat…
Semianalyticity of isoperimetric profiles
2009
It is shown that, in dimensions $<8$, isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic.
Geodesic ray transform with matrix weights for piecewise constant functions
2019
We show injectivity of the geodesic X-ray transform on piecewise constant functions when the transform is weighted by a continuous matrix weight. The manifold is assumed to be compact and nontrapping of any dimension, and in dimension three and higher we assume a foliation condition. We make no assumption regarding conjugate points or differentiability of the weight. This extends recent results for unweighted transforms.
Local Gauge Conditions for Ellipticity in Conformal Geometry
2013
In this article we introduce local gauge conditions under which many curvature tensors appearing in conformal geometry, such as the Weyl, Cotton, Bach, and Fefferman-Graham obstruction tensors, become elliptic operators. The gauge conditions amount to fixing an $n$-harmonic coordinate system and normalizing the determinant of the metric. We also give corresponding elliptic regularity results and characterizations of local conformal flatness in low regularity settings.
p-harmonic coordinates for H\"older metrics and applications
2015
We show that on any Riemannian manifold with H\"older continuous metric tensor, there exists a $p$-harmonic coordinate system near any point. When $p = n$ this leads to a useful gauge condition for regularity results in conformal geometry. As applications, we show that any conformal mapping between manifolds having $C^\alpha$ metric tensors is $C^{1+\alpha}$ regular, and that a manifold with $W^{1,n} \cap C^\alpha$ metric tensor and with vanishing Weyl tensor is locally conformally flat if $n \geq 4$. The results extend the works [LS14, LS15] from the case of $C^{1+\alpha}$ metrics to the H\"older continuous case. In an appendix, we also develop some regularity results for overdetermined el…