Nested hierarchies in planar graphs

We construct a partial order relation which acts on the set of 3-cliques of a maximal planar graph G and defines a unique hierarchy. We demonstrate that G is the union of a set of special subgraphs, named ‘bubbles’, that are themselves maximal planar graphs. The graph G is retrieved by connecting these bubbles in a tree structure where neighboring bubbles are joined together by a 3-clique. Bubbles naturally provide the subdivision of G into communities and the tree structure defines the hierarchical relations between these communities.     

Bump solutions for the mesoscopic Allen�CCahn equation in periodic media

Given a double-well potential F, a ${\mathbb{Z}^n}$ -periodic function H, small and with zero average, and ???>?0, we find a large R, a small ?? and a function H _?? which is ??-close to H for which the following two problems have solutions:

1. Find a set E _?? ,R whose boundary is uniformly close to ? B _R and has mean curvature equal to ?H _?? at any point,
2. Find u = u _?? ,R,?? solving $$ -\delta\,\Delta u + \frac{F'(u)}{\delta} +\frac{c_0}{2} H_\varepsilon = 0, $$ such that u _??,R,?? goes from a ??-neighborhood of +?1 in B _R to a ??-neighborhood of ?1 outside B _R .

     

Spin structure of surface-supported single-molecule magnets from isomorphous replacement and X-ray magnetic circular dichroism

Surface-supported arrays of Fe(4)-type Single-Molecule Magnets retain a memory effect and are of current interest in the frame of molecule-based information storage and spintronics. To reveal the spin structure of [Fe(4)(L)(2)(dpm)(6)] (1) on Au, an isomorphous compound [Fe(3)Cr(L)(2)(dpm)(6)] was synthesized and structurally and magnetically characterized (H(3)L is tripodal ligand 11-(acetylthio)-2,2-bis(hydroxymethyl)undecan-1-ol and Hdpm is dipivaloylmethane). The new complex contains a central Cr(3+) ion and has a S = 6 ground state as opposed to S = 5 in 1. Low-temperature X-ray Magnetic Circular Dichroism studies at Fe- and Cr-L(2,3) edges revealed that the antiparallel alignment between Fe and Cr spins is preserved on surfaces. Moreover, the different Fe-L(2,3) spectral features found in the homo- and heterometallic species disclose the opposing contribution of the central Fe(3+) ion in the former compound, proving that its ferrimagnetic spin structure is retained on surfaces.     

Graphene solutions

Thermodynamics drive the spontaneous dissolution of a graphite intercalation compound (GIC) KC(8) in NMP to form stable solutions. Reduction potential of graphene is measured at +22 mV vs. SCE. Single layer graphene flakes (ca. 1 μm(2)) have been unambiguously identified by electron diffraction.     

Giant field dependence of the low temperature relaxation of the magnetization in a dysprosium(III)-DOTA complex

The square antiprismatic Na[Dy(DOTA)(H(2)O)]·4H(2)O complex was characterised by single crystal X-ray diffraction and ac magnetic susceptometry. Two competing mechanisms for magnetic relaxation as well as the remarkable increase of six orders of magnitude in the relaxation time upon application of a static magnetic field were detected.     

Surface models and reaction barrier in Eley-Rideal formation of H2 on graphitic surfaces

The exothermic, collinearly-dominated Eley-Rideal hydrogen formation on graphite is studied with electronic structure and quantum dynamical means. In particular, the focus is on the importance of the model used to describe the graphitic substrate, in light of the marked discrepancies present in available literature results. To this end, the collinear reaction is considered and the potential energy surface is computed for a number of different graphitic surface models using Density Functional Theory (DFT) for different dynamical regimes. Quantum dynamics is performed with wavepacket techniques down to the cold collision energies relevant for the chemistry of the interstellar medium. Results show that the reactivity at moderate-to-high collision energies sensitively depends on the shape of the PES in the entrance channel, which in turn is related to the adopted surface model. At low energies we rule out the presence of any barrier to reaction, thereby highlighting the importance of quantum reflection in limiting the reaction efficiency.     

Extended viologen as a source of electric oscillations

A long organic molecule 1 with five bipyridinium functions separated by benzene rings (extended viologen) undergoes a reversible multi-step electron transfer. Here we show that this decacation accepts electrons at the heterogeneous interface with the occurrence of the periodically changing electric reduction currents. According to the applied bias voltage the observed current-time dependence changes from chaotic through periodic and irregular to sinusoidal and finally to monotonous. A careful choice of the controlling parameters yields the sustained periodic sinusoidal currents lasting for a prolonged time. Oscillations stem from a mutual interplay of the heterogeneous supply of electrons and the homogeneous redox reactions (disproportionation) between the transient redox forms. In difference to many other electrochemical oscillating systems the described oscillations do not require any additional external impedance. The principle of these oscillatory currents may serve as a model of a truly 'molecular oscillator'.     

How to embed three-dimensional flexible electrodes in microfluidic devices for cell culture applications

This communication describes a simple, rapid and cost effective method of embedding a conductive and flexible material within microfluidic devices as a means to realize uniform electric fields within cellular microenvironments. Fluidic channels and electrodes are fabricated by traditional soft-lithography in conjunction with chemical etching of PDMS. Devices can be deformable (thus allowing for a combination of electro-mechanical stimulation), they are made from inexpensive materials and easily assembled by hand; this method is thus accessible to a wide range of laboratories and budgets.     

Modified edge finite elements for photonic crystals

We consider Maxwell’s equations with periodic coefficients as it is usually done for the modeling of photonic crystals. Using Bloch/Floquet theory, the problem reduces in a standard way to a modification of the Maxwell cavity eigenproblem with periodic boundary conditions. Following [8], a modification of edge finite elements is considered for the approximation of the band gap. The method can be used with meshes of tetrahedrons or parallelepipeds. A rigorous analysis of convergence is presented, together with some preliminary numerical results in 2D, which fully confirm the robustness of the method. The analysis uses well established results on the discrete compactness for edge elements, together with new sharper interpolation estimates.