Thermodynamics of the rupture in a Morse lattice

The rupture of a Morse lattice is considered in the presentpaper. The critical rupture force F _cr is found todecrease with the number of particles N as F _cr ~ 1/\(\sqrt{N}\). The partition function is obtained for two states ofthe lattice – with all equal bond lengths and one broken bond.In the first case an accurate expressions for thermodynamicparameters are obtained, and thermodynamic expressions arederived in the harmonic approximation in the latter case. Theanalytical predictions are confirmed by extensive MD simulations.Cis-trans isomerization is considered as an example. Volumefractions of trans- and cis-isomers versus number ofmonomer units N are found depending on the torsion stiffnesses.     

The Index of a 1-Form on a Real Quotient Singularity

Let G be a finite Abelian group acting (linearly) on space ?ⁿ and, therefore, on its complexification ?ⁿ, and let W be the real part of the quotient ?ⁿ/G (in the general case, W ≠ ?ⁿ/G). The index of an analytic 1-form on the space W is expressed in terms of the signature of the residue bilinear form on the G-invariant part of the quotient of the space of germs of n-forms on (?ⁿ, 0) by the subspace of forms divisible by the 1-form under consideration.     

McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularities

We give a uniform and, to a large extent, geometrical proof that the Poincaré series of the coordinate algebra of a Kleinian singularity and of a Fuchsian singularity of genus 0 is the quotient of the characteristic polynomials of two Coxeter elements. These Coxeter elements are interpreted geometrically, using 2-Calabi-Yau triangulated categories and spherical twist functors.     

A Review of Wine Authentication Using Spectroscopic Approaches in Combination with Chemometrics

In a global context where trading of wines involves considerable economic value, the requirement to guarantee wine authenticity can never be underestimated. With the ever-increasing advancements in analytical platforms, research into spectroscopic methods is thriving as they offer a powerful tool for rapid wine authentication. In particular, spectroscopic techniques have been identified as a user-friendly and economical alternative to traditional analyses involving more complex instrumentation that may not readily be deployable in an industry setting. Chemometrics plays an indispensable role in the interpretation and modelling of spectral data and is frequently used in conjunction with spectroscopy for sample classification. Considering the variety of available techniques under the banner of spectroscopy, this review aims to provide an update on the most popular spectroscopic approaches and chemometric data analysis procedures that are applicable to wine authentication.     

Active Brownian motion models and applications to ratchets

We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircaselike and Mateos ratchet potentials, also with the additional loads modelled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This stochastically driven directionality effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed.     

Interface formation in CdTe solar cells: Nucleation of CdTe on CdS(0001) and (10$ \bar 1 $0)

The growth of CdTe on (0001) and (10 0) surfaces of CdS was studied using low energy electron diffraction and photoelectron spectroscopy. The results indicate oriented growth of the CdTe films with a faster nucleation of CdTe on CdS(0001), explaining the preferred (111) orientation of CdTe films on polycrystalline substrates. The faster nucleation on the (0001) surface is attributed to the formation of a stable CdS(0001):Te surface termination, which is identified from surface sensitive Te 4d spectra and a 2√3 × 2√3 surface reconstruction. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nucleophilic Aromatic Substitution at Benzene with Powerful Strontium Hydride and Alkyl Complexes

Key to the isolation of the first alkyl strontium complex was the synthesis of a strontium hydride complex that is stable towards ligand exchange reactions. This goal was achieved by using the super bulky β‐diketiminate ligand ^DIPePBDI (CH[C(Me)N‐DIPeP]₂, DIPeP=2,6‐diisopentylphenyl). Reaction of ^DIPePBDI‐H with Sr[N(SiMe₃)₂]₂ gave (^DIPePBDI)SrN(SiMe₃)₂, which was converted with PhSiH₃ into [(^DIPePBDI)SrH]₂. Dissolved in C₆D₆, the strontium hydride complex is stable up to 70 °C. At 60 °C, H–D isotope exchange gave full conversion into [(^DIPePBDI)SrD]₂ and C₆D₅H. Since H–D exchange with D₂ is facile, the strontium hydride complex served as a catalyst for the deuteration of C₆H₆ by D₂. Reaction of [(^DIPePBDI)SrH]₂ with ethylene gave [(^DIPePBDI)SrEt]₂. The high reactivity of this alkyl strontium complex is demonstrated by facile ethylene polymerization and nucleophilic aromatic substitution with C₆D₆, giving alkylated aromatic products and [(^DIPePBDI)SrD]₂.     

Lewis Acid Directed Regioselective Metalations of Pyridazine

Mono‐ or bidentate boron Lewis acids trigger a regioselective magnesiation or zincation of pyridazine in position C3 (ortho product) or C4 (meta product). The regioselectivity of the metalation was rationalized with the help of calculated pK_a values of both pyridazine and pyridazine/Lewis acid complexes.     

Fast f-to-2f interferometer for a direct measurement of the carrier-envelope phase drift of ultrashort amplified laser pulses

We propose a novel method to directly extract the phase from spectral interferograms, without the need for digital signal processing. This method is demonstrated with single-shot measurement and stabilization of the carrier-envelope phase of a 3 kHz amplifier system. Our scheme allows for real-time monitoring of the carrier-envelope drift and an increased loop width for stabilization. We find that in our amplifier laser system fast carrier-envelope phase jitter is mainly inherited from the oscillator stabilization loop but we also find previously unreported indications for a rapid pulse-to-pulse jitter from the amplifier pump laser.     

Dextramabs: A Novel Format of Antibody-Drug Conjugates Featuring a Multivalent Polysaccharide Scaffold

Antibody-drug conjugates (ADCs) are multicomponent biomolecules that have emerged as a powerful tool for targeted tumor therapy. Combining specific binding of an immunoglobulin with toxic properties of a payload, they however often suffer from poor hydrophilicity when loaded with a high amount of toxins. To address these issues simultaneously, we developed dextramabs, a novel class of hybrid antibody-drug conjugates. In these architectures, the therapeutic antibody trastuzumab is equipped with a multivalent dextran polysaccharide that enables efficient loading with a potent toxin in a controllable fashion. Our modular chemoenzymatic approach provides an access to synthetic dextramabs bearing monomethyl auristatin as releasable cytotoxic cargo. They possess high drug-to-antibody ratios, remarkable hydrophilicity, and high toxicity in vitro.