Direct Observation of the Ethyl Radical in the Pyrolysis of Ethane

We report the first direct detection of ethyl radical in the pyrolysis of ethane. Observation of this vital intermediate was made possible in this extremely reactive environment by the use of a microreactor coupled with synchrotron radiation and photoelectron photoion coincidence (PEPICO) spectroscopy, despite its short lifetime and low concentration. Together with ab-initio master equation-calculated rates and fully coupled computational fluid dynamics simulations, our measurements show that even under the low pressures and short residence times in our experiment, ethyl formation can only be explained by bimolecular reactions; the most important is the catalytic attack of ethane by H atoms, which are then regenerated by decomposition of the nascent ethyl radicals. Our results complete the observation of all hypothesized intermediates in this industrially important process and highlight the need for further studies under additional conditions using similar methods to improve existing models and optimize process chemistries.     

What is the opposite of cat? A gentle introduction to group theory

This paper has originated from our interest in approaching mathematical concepts starting from people's common-sense intuitions and building up from there. This goal is challenging both in designing the didactical transposition and sequencing of the mathematical subject matter, and in adopting the open and interactive teaching approach needed to achieve students' active participation and reflection. To demonstrate these challenges, and our experience of trying to cope with them, we have chosen the concept of ‘inverses’ as used in group theory, and its common-sense precursor ‘opposites’. We present our approach via a series of workshop iterations, which summarizes our experience in the many actual workshops we ran in Israel and in Denmark.     

The maximum edit distance from hereditary graph properties

For a graph property , the edit distance of a graph G from , denoted , is the minimum number of edge modifications (additions or deletions) one needs to apply to G in order to turn it into a graph satisfying . What is the largest possible edit distance of a graph on n vertices from ? Denote this distance by .A graph property is hereditary if it is closed under removal of vertices. In a previous work, the authors show that for any hereditary property, a random graph essentially achieves the maximal distance from , proving: with high probability. The proof implicitly asserts the existence of such , but it does not supply a general tool for determining its value or the edit distance.In this paper, we determine the values of and for some subfamilies of hereditary properties including sparse hereditary properties, complement invariant properties, (r,s)-colorability and more. We provide methods for analyzing the maximum edit distance from the graph properties of being induced H-free for some graphs H, and use it to show that in some natural cases G(n,1/2) is not the furthest graph. Throughout the paper, the various tools let us deduce the asymptotic maximum edit distance from some well studied hereditary graph properties, such as being Perfect, Chordal, Interval, Permutation, Claw-Free, Cograph and more. We also determine the edit distance of G(n,1/2) from any hereditary property, and investigate the behavior of as a function of p.The proofs combine several tools in Extremal Graph Theory, including strengthened versions of the Szemerédi Regularity Lemma, Ramsey Theory and properties of random graphs.     

Entropic attraction condenses like-charged interfaces composed of self-assembled molecules

Like-charged solid interfaces repel and separate from one another as much as possible. Charged interfaces composed of self-assembled charged-molecules such as lipids or proteins are ubiquitous. The present study shows that although charged lipid-membranes are sufficiently rigid, in order to swell as much as possible, they deviate markedly from the behavior of typical like-charged solids when diluted below a critical concentration (ca. 15 wt %). Unexpectedly, they swell into lamellar structures with spacing that is up to four times shorter than the layers should assume (if filling the entire available space). This process is reversible with respect to changing the lipid concentration. Additionally, the research shows that, although the repulsion between charged interfaces increases with temperature, like-charged membranes, remarkably, condense with increasing temperature. This effect is also shown to be reversible. Our findings hold for a wide range of conditions including varying membrane charge density, bending rigidity, salt concentration, and conditions of typical living systems. We attribute the limited swelling and condensation of the net repulsive interfaces to their self-assembled character. Unlike solids, membranes can rearrange to gain an effective entropic attraction, which increases with temperature and compensates for the work required for condensing the bilayers. Our findings provide new insight into the thermodynamics and self-organization of like-charged interfaces composed of self-assembled molecules such as charged biomaterials and supramolecular assemblies that are widely found in synthetic and natural constructs.     

Geometric interpretation of Murphy bases and an application

In this article we study the representations of general linear groups which arise from their action on flag spaces. These representations can be decomposed into irreducibles by proving that the associated Hecke algebra is cellular. We give a geometric interpretation of a cellular basis of such Hecke algebras which was introduced by Murphy in the case of finite fields. We apply these results to decompose representations which arise from the space of submodules of a free module over principal ideal local rings of length two with a finite residue field.     

Second harmonic generation and confined acoustic phonons in highly excited semiconductor nanocrystals

The photo-induced enhancement of second harmonic generation and the effect of nanocrystal shape and pump intensity on confined acoustic phonons in semiconductor nanocrystals have been investigated with time-resolved scattering and absorption measurements. The second harmonic signal showed a sublinear increase of the second-order susceptibility with respect to the pump pulse energy, indicating a reduction of the effective one-electron second-order nonlinearity with increasing electron-hole density in the nanocrystals. The coherent acoustic phonons in spherical and rod-shaped semiconductor nanocrystals were detected in a time-resolved absorption measurement. Both nanocrystal morphologies exhibited oscillatory modulation of the absorption cross section, the frequency of which corresponded to their coherent radial breathing modes. The amplitude of the oscillation also increased with the level of photoexcitation, suggesting an increase in the amplitude of the lattice displacement as well.     

Synthesis of InAs/CdSe/ZnSe core/shell1/shell2 structures with bright and stable near-infrared fluorescence

A complex InAs/CdSe/ZnSe core/shell1/shell2 (CSS) structure is synthesized, where the intermediate CdSe buffer layer decreases strain between the InAs core and the ZnSe outer shell. This structure leads to significantly improved fluorescence quantum yield as compared to previously prepared core/shell structures and enables growth of much thicker shells. The shell growth is done using a layer-by-layer method in which the shell cation and anion precursors are added sequentially allowing for excellent control, and a good size distribution is maintained throughout the entire growth process. The CSS structure is characterized using transmission electron microscopy, as well as by X-ray diffraction and X-ray photoelectron spectroscopy which provide evidence for shell growth. The quantum yield for CSS with small InAs cores reaches over 70%-exceptional photoluminescence intensity for III-V semiconductor nanocrystals. In larger InAs cores there is a systematic decrease in the quantum yield, with a yield of approximately 40% for intermediate size cores down to a few percent in large cores. The CSS structures also exhibit very good photostability, vastly improved over those of organically coated cores, and transformation into water environment via ligand exchange is performed without significant decrease of the quantum yield. These new InAs/CdSe/ZnSe CSS nanocrystals are therefore promising near-IR chromophores for biological fluorescence tagging and optoelectronic devices.     

Vibrational anharmonicity effects in electronic tunneling through molecular bridges

Effects of anharmonic bridge vibrations on electronic tunneling in donor-bridge-acceptor complexes are studied using a model of anharmonic bridge vibration coupled nonlinearly to an electronic degree of freedom. An anharmonicity parameter is introduced, enabling to reproduce the standard harmonic model with linear coupling as a limiting case. The frequency of electronic tunneling oscillations between the donor and acceptor sites is shown to be sensitive to the nuclear anharmonicity, where stretching and compression modes have an opposite effect on the electronic frequency. This phenomenon, that cannot be accounted for within the harmonic approximation, is analyzed and explained.     

An Embedding Theorem for Automorphism Groups of Cartan Geometries

We study the automorphism group of a Cartan geometry, and prove an embedding theorem analogous to a result of Zimmer for automorphism groups of G-structures. Our embedding theorem leads to general upper bounds on the real rank or nilpotence degree of a Lie subgroup of the automorphism group. We prove that if the maximal real rank is attained in the automorphism group of a geometry of parabolic type, then the geometry is flat and complete.     

Fast Surface Mesh Denoising with Regularization and Edge Preservation

We describe a hybrid algorithm that is designed to smooth, but not only smooth, noisy polygonal surface meshes with sharp edges. While denoising, our method simultaneously regularizes triangle meshes on flat regions for further mesh processing and preserves edge sharpness for faithful reconstruction. A clustering technique, which combines K-means and geometric a priori information, is first developed and refined. It is then used to implement vertex classification so that we can subsequently apply different smoothing operators on different vertex groups. This yields a highly efficient robust algorithm that is capable of handling both edge sharpness and mesh sampling irregularity without any significant cost increase. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)