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- ItemA diuranium carbide cluster stabilized inside a C80 fullerene cage(London : Nature Publishing Group, 2018) Zhang, X.; Li, W.; Feng, L.; Chen, X.; Hansen, A.; Grimme, S.; Fortier, S.; Sergentu, D.-C.; Duignan, T.J.; Autschbach, J.; Wang, S.; Wang, Y.; Velkos, G.; Popov, A.A.; Aghdassi, N.; Duhm, S.; Li, X.; Li, J.; Echegoyen, L.; Schwarz, W.H.E.; Chen, N.Unsupported non-bridged uranium-carbon double bonds have long been sought after in actinide chemistry as fundamental synthetic targets in the study of actinide-ligand multiple bonding. Here we report that, utilizing I h(7)-C80 fullerenes as nanocontainers, a diuranium carbide cluster, U=C=U, has been encapsulated and stabilized in the form of UCU@I h(7)-C80. This endohedral fullerene was prepared utilizing the Krätschmer-Huffman arc discharge method, and was then co-crystallized with nickel(II) octaethylporphyrin (NiII-OEP) to produce UCU@I h(7)-C80·[NiII-OEP] as single crystals. X-ray diffraction analysis reveals a cage-stabilized, carbide-bridged, bent UCU cluster with unexpectedly short uranium-carbon distances (2.03 Å) indicative of covalent U=C double-bond character. The quantum-chemical results suggest that both U atoms in the UCU unit have formal oxidation state of +5. The structural features of UCU@I h(7)-C80 and the covalent nature of the U(f1)=C double bonds were further affirmed through various spectroscopic and theoretical analyses.
- ItemBraid equivalences and the L-moves(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Lambropoulou, SofiaIn this survey paper we present the L–moves between braids and how they can adapt and serve for establishing and proving braid equivalence theorems for various diagrammatic settings, such as for classical knots, for knots in knot complements, in c.c.o. 3–manifolds and in handlebodies, as well as for virtual knots, for flat virtuals, for welded knots and for singular knots. The L–moves are local and they provide a uniform ground for formulating and proving braid equivalence theorems for any diagrammatic setting where the notion of braid and diagrammatic isotopy is defined, the statements being first geometric and then algebraic.
- ItemSpatial "rocking" for improving the spatial quality of the beam of broad area semiconductor lasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Radziunas, Mindaugas; Staliunas, KestutisThe spatial ``rocking'' is a dynamical effect converting a phase-invariant oscillatory system into a phase-bistable one, where the average phase of the system locks to one of two values differing by pi. We demonstrate theoretically the spatial rocking in experimentally accessible and practically relevant systems -- the broad area semiconductor lasers. By numerical integration of the laser model equations we show the phase bistability of the optical fields and explore the bistability area in parameter space. We also predict the spatial patterns, such as phase domain walls and phase solitons, which are characteristic for the phase-bistable spatially extended pattern forming systems.
- ItemPhase transitions for the Boolean model of continuum percolation for Cox point processes(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Jahnel, Benedikt; Tóbiás, András; Cali, EliWe consider the Boolean model with random radii based on Cox point processes. Under a condition of stabilization for the random environment, we establish existence and non-existence of subcritical regimes for the size of the cluster at the origin in terms of volume, diameter and number of points. Further, we prove uniqueness of the infinite cluster for sufficiently connected environments.
- ItemSINR percolation for Cox point processes with random powers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Jahnel, Benedikt; Tóbiás, AndrásSignal-to-interference plus noise ratio (SINR) percolation is an infinite-range dependent variant of continuum percolation modeling connections in a telecommunication network. Unlike in earlier works, in the present paper the transmitted signal powers of the devices of the network are assumed random, i.i.d. and possibly unbounded. Additionally, we assume that the devices form a stationary Cox point process, i.e., a Poisson point process with stationary random intensity measure, in two or higher dimensions. We present the following main results. First, under suitable moment conditions on the signal powers and the intensity measure, there is percolation in the SINR graph given that the device density is high and interferences are sufficiently reduced, but not vanishing. Second, if the interference cancellation factor γ and the SINR threshold τ satisfy γ ≥ 1/(2τ), then there is no percolation for any intensity parameter. Third, in the case of a Poisson point process with constant powers, for any intensity parameter that is supercritical for the underlying Gilbert graph, the SINR graph also percolates with some small but positive interference cancellation factor.