Volume and macroscopic scalar curvature

We prove the macroscopic cousins of three conjectures: (1) a conjectural bound of the simplicial volume of a Riemannian manifold in the presence of a lower scalar curvature bound, (2) the conjecture that rationally essential manifolds do not admit metrics of positive scalar curvature, (3) a conjectural bound of ℓ$^{2}$-Betti numbers of aspherical Riemannian manifolds in the presence of a lower scalar curvature bound. The macroscopic cousin is the statement one obtains by replacing a lower scalar curvature bound by an upper bound on the volumes of 1-balls in the universal cover

Volume and macroscopic scalar curvature

We prove the macroscopic cousins of three conjectures: 1) a conjectural bound of the simplicial volume of a Riemannian manifold in the presence of a lower scalar curvature bound, 2) the conjecture that rationally essential manifolds do not admit metrics of positive scalar curvature, 3) a conjectural bound of $L^2$-Betti numbers of aspherical Riemannian manifolds in the presence of a lower scalar curvature bound. The macroscopic cousin is the statement one obtains by replacing a lower scalar curvature bound by an upper bound on the volumes of $1$-balls in the universal cover.Comment: 48 pages; added a statement about integral foliated simplicial volume in the introduction and made minor corrections; to be published in GAF

Osteuropäische Partnerschaft und Nachbarschaftsabkommen

Die beispiellose Erweiterung der Europäischen Union (EU) in den Jahren 2004 und 2007 brachte neue Herausforderungen für die Idee der europäischen Integration mit sich. Der Beitritt der zentral- und osteuropäischen Länder, die früher zu der sowjetischen Einflusssphäre gehört haben und jetzt eine gemeinsame Grenze mit der EU haben, hat neue Trennungslinien zwischen den neuen EU-Mitgliedstaaten und den osteuropäischen Staaten, die außerhalb der EU bleiben, kreiert. Damals musste die Außenpolitik der EU eine dringende Antwort auf diese Herausforderungen geben, um mögliche Wirtschafts-, Sicherheits- und Gerechtigkeitskrisen aufgrund der EU-Erweiterung zu verhindern

From one to NN Cooper pairs, step by step

We extend the one-pair Cooper configuration towards Bardeen-Cooper-Schrieffer (BCS) model of superconductivity by adding one-by-one electron pairs to an energy layer where a small attraction acts. To do it, we solve Richardson's equations analytically in the dilute limit of pairs on the one-Cooper pair scale. We find, through only keeping the first order term in this expansion, that the $N$ correlated pair energy reads as the energy of $N$ isolated pairs within a $N(N-1)$ correction induced by the Pauli exclusion principle which tends to decrease the average pair binding energy when the pair number increases. Quite remarkably, extension of this first-order result to the dense regime gives the BCS condensation energy exactly. This leads us to suggest a different understanding of the BCS condensation energy with a pair number equal to the number of pairs feeling the potential and an average pair binding energy reduced by Pauli blocking to half the single Cooper pair energy - instead of the more standard but far larger superconducting gap.Comment: 14 pages, 2 figure

Spatially mapping thermal transport in graphene by an opto-thermal method

Mapping the thermal transport properties of materials at the nanoscale is of critical importance for optimizing heat conduction in nanoscale devices. Several methods to determine the thermal conductivity of materials have been developed, most of them yielding an average value across the sample, thereby disregarding the role of local variations. Here, we present a method for the spatially resolved assessment of the thermal conductivity of suspended graphene by using a combination of confocal Raman thermometry and a finite-element calculations-based fitting procedure. We demonstrate the working principle of our method by extracting the two-dimensional thermal conductivity map of one pristine suspended single-layer graphene sheet and one irradiated using helium ions. Our method paves the way for spatially resolving the thermal conductivity of other types of layered materials. This is particularly relevant for the design and engineering of nanoscale thermal circuits (e.g. thermal diodes)

Emergence of skew distributions in controlled growth processes

Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the evolution quation, to obtain such skew distributions as power-law, log-normal, and Weibull distributions, depending on the growth or division and production. Specifically, repeated production of elements of uniform size leads to power-law distributions, whereas production of elements with the size distributed according to the current distribution as well as no production of new elements results in log-normal distributions. Finally, division into two, or binary fission, bears Weibull distributions. Numerical simulations are also carried out, confirming the validity of the obtained solutions.Comment: 9 pages, 3 figure

The Herschel Exploitation of Local Galaxy Andromeda (HELGA) II: Dust and Gas in Andromeda

We present an analysis of the dust and gas in Andromeda, using Herschel images sampling the entire far-infrared peak. We fit a modified-blackbody model to ~4000 quasi-independent pixels with spatial resolution of ~140pc and find that a variable dust-emissivity index (beta) is required to fit the data. We find no significant long-wavelength excess above this model suggesting there is no cold dust component. We show that the gas-to-dust ratio varies radially, increasing from ~20 in the center to ~70 in the star-forming ring at 10kpc, consistent with the metallicity gradient. In the 10kpc ring the average beta is ~1.9, in good agreement with values determined for the Milky Way (MW). However, in contrast to the MW, we find significant radial variations in beta, which increases from 1.9 at 10kpc to ~2.5 at a radius of 3.1kpc and then decreases to 1.7 in the center. The dust temperature is fairly constant in the 10kpc ring (ranging from 17-20K), but increases strongly in the bulge to ~30K. Within 3.1kpc we find the dust temperature is highly correlated with the 3.6 micron flux, suggesting the general stellar population in the bulge is the dominant source of dust heating there. At larger radii, there is a weak correlation between the star formation rate and dust temperature. We find no evidence for 'dark gas' in M31 in contrast to recent results for the MW. Finally, we obtained an estimate of the CO X-factor by minimising the dispersion in the gas-to-dust ratio, obtaining a value of (1.9+/-0.4)x10^20 cm^-2 [K kms^-1]^-1.Comment: 19 pages, 18 figures. Submitted to ApJ April 2012; Accepted July 201

Tunable Quantum Dots from Atomically Precise Graphene Nanoribbons Using a Multi‐Gate Architecture

Atomically precise graphene nanoribbons (GNRs) are increasingly attracting interest due to their largely modifiable electronic properties, which can be tailored by controlling their width and edge structure during chemical synthesis. In recent years, the exploitation of GNR properties for electronic devices has focused on GNR integration into field-effect-transistor (FET) geometries. However, such FET devices have limited electrostatic tunability due to the presence of a single gate. Here, on the device integration of 9-atom wide armchair graphene nanoribbons (9-AGNRs) into a multi-gate FET geometry, consisting of an ultra-narrow finger gate and two side gates is reported. High-resolution electron-beam lithography (EBL) is used for defining finger gates as narrow as 12 nm and combine them with graphene electrodes for contacting the GNRs. Low-temperature transport spectroscopy measurements reveal quantum dot (QD) behavior with rich Coulomb diamond patterns, suggesting that the GNRs form QDs that are connected both in series and in parallel. Moreover, it is shown that the additional gates enable differential tuning of the QDs in the nanojunction, providing the first step toward multi-gate control of GNR-based multi-dot systems