QED limits for many-server systems under a priority policy

A multi-class many-server priority system operating in the quality-and-efficiency-driven regime is considered. Both arrival processes and service times are general. The many-server heavy-traffic diffusion asymptotic is characterized in terms of the corresponding limiting infinite-server process.     

Qualitative Features of Periodic Solutions of KdV

In this paper we prove new qualitative features of solutions of KdV on the circle. The first result says that the Fourier coefficients of a solution of KdV in Sobolev space H ^N , N ≥ 0, admit a WKB type expansion up to first order with strongly oscillating phase factors defined in terms of the KdV frequencies. The second result provides estimates for the approximation of such a solution by trigonometric polynomials of sufficiently large degree.     

Simplified approach to modelling the catalytic degradation of low-density polyethylene (LDPE) by applying catalyst-free LDPE-TG profiles and the Friedman method

The course of the thermogravimetric degradation of LDPE in the presence of different aluminosilicate catalysts was modelled by applying a differential isoconversional Friedman approach. An analysis of catalyst-free PE-TG profiles confirmed that the degradation profiles predicted by various reaction models overlap over the entire conversion range once the data are analysed using a differential isoconversional Friedman approach. The results demonstrate that the catalytic degradation of LDPE can be predicted by a correlation twin, i.e. the two specific functional relations between the activation energy, pre-exponential factor and conversion. The crucial step for ensuring good agreement between the predicted and the measured profiles is to extrapolate the discrete values of the activation energies and pre-exponential factors to the zero conversion. It turns out that linear extrapolation and interpolation from the discrete values outperforms regression functions based on various order polynomials, and that apparent deviations from the global trend at lower conversions are not a consequence of the misinterpretation of the experimental results but are an experimental fact. The assumption about the compensation effect between the pre-exponential factor and activation energy holds within the conversion range from 10 to 90%. However, it is generally unsuitable for modelling purposes due to the uncertain extrapolation of the kinetic parameters to the zero conversion.

     

Synthesis and characterization of novel (9H‐fluoren‐9‐ylamino) carbonylaminomethylphosphonic acid

The new α‐aminophosphonic acids are synthesized, reacting (9H‐fluoren‐9‐yl)urea with formaldehyde and phosphorus trichloride. (9H‐Fluoren‐9‐yl)urea was prepared from spiro(fluoren‐9,4′‐imidazolidine)‐2′,5′‐dione by alkaline hydrolysis with Ba(OH)₂. The structure of the title compounds was proved by means of IR, ¹H, ¹³C, and ³¹P NMR spectroscopy. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:719–722, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20500     

Elucidating Molecule–Plasmon Interactions in Nanocavities with 2 nm Spatial Resolution and at the Single‐Molecule Level

The fundamental understanding of the subtle interactions between molecules and plasmons is of great significance for the development of plasmon‐enhanced spectroscopy (PES) techniques with ultrahigh sensitivity. However, this information has been elusive due to the complex mechanisms and difficulty in reliably constructing and precisely controlling interactions in well‐defined plasmonic systems. Herein, the interactions in plasmonic nanocavities of film‐coupled metallic nanocubes (NCs) are investigated. Through engineering the spacer layer, molecule–plasmon interactions were precisely controlled and resolved within 2 nm. Efficient energy exchange interactions between the NCs and the surface within the 1–2 nm range are demonstrated. Additionally, optical dressed molecular excited states with a huge Lamb shift of ≈7 meV at the single‐molecule (SM) level were observed. This work provides a basis for understanding the underlying molecule–plasmon interaction, paving the way for fully manipulating light–matter interactions at the nanoscale.     

On the symplectic phase space of KdV

We prove that the Birkhoff map for KdV constructed on can be interpolated between and . In particular, the symplectic phase space can be described in terms of Birkhoff coordinates.

     

Nanostructured Crosslinkable Micropatterns by Amphiphilic Dendrimer Stamping

Summary: Microcontact printing was used to deposit stable, nanostructured, amphiphilic and crosslinkable patterns of poly(amidoamine organosilicon) (PAMAMOS)‐dimethoxymethylsilyl (DMOMS) dendrimer multilayers onto silicon wafers, glass, and polyelectrolyte multilayers. The effects of dendrimer ink concentration, contact time, and inking method, on the thickness, uniformity, and stability of the resulting patterns were studied using optical microscopy, fluorescence microscopy, atomic force microscopy (AFM), and contact‐angle analysis. Microarrayed dendrimer film thickness was found to be controllable by conditions used during spin self‐assembly.

Optical micrograph of the circular patterns, obtained from a 0.5% PAMAMOS dendrimer solution, on a glass substrate.     

Heterocyclizations of hydroxyketones with two‐coordinated (trimethylsilylamino)phosphines, (Me3Si)2N?PE?SiMe3

The reaction of two‐coordinated (trimethylsilylamino)phosphines (Me₃Si)₂N PE SiMe₃ 1 (E = N) and 2 (E = CH) with hydroxycarbonyl compounds proceeded with four‐ or five‐member heterocyclization to yield derivatives of oxaphosphetane, oxaphospholanes, and oxaphospholes. The reaction rate depends on the structure of hydroxyketones as well as on the type of the two‐coordinated phosphorus compound in accordance with the polarity of the P=N and P=C bonds. Thus, reaction was completed in 30 min in the case of the ortho carbonyl phenoxy derivatives with the phosphine 1 , but required 2 h in the case of the alkyl hydroxy carbonyls. All reactions with the phosphine 2 took about 24 h. © 2004 Wiley Periodicals, Inc. Heteroatom Chem 15:413–417, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.20033     

Novel branched blockcopolymers from poly(vinylpyridine) by chromium allyl compounds

Novel branched blockcopolymers from polyvinylpyridine are formed by chromium allyl compounds. Our present work shows results for the homopolymerization of vinylpiridine (VP), dimethylacrylamide (DMAA), tert - butylacrylate (t - BA) as well as the graftcopolymerization of poly(vinylpyridine) (PVP), using tris (π - allyl) chromium (TPC) as initiator. PVP activated by TPC was used for grafting with DMAA - “grafting from”. On the other hand living PDMAA polymerized by TPC, was able to react with PVP chain - “grafting onto”.     

Self-consistent simulations of quantum cascade laser structures for frequency comb generation

Maxwell–Bloch equations are widely used to model the dynamics due to coherent light-matter interaction in quantum cascade laser (QCL) structures, which plays an essential role especially for the generation of frequency combs and mode-locked pulses. While the modest numerical complexity of the Maxwell–Bloch system allows for a full spatiotemporal treatment, its main disadvantage is the inclusion of dissipation by empirical dephasing rates and electron lifetimes. We present a self-consistent multi-domain approach which couples the Maxwell–Bloch equations to advanced carrier transport simulations based on a density matrix Monte Carlo technique, yielding the scattering and dephasing rates. In this way, the compact spatiotemporal modeling of the carrier-light dynamics by the Maxwell–Bloch system can be combined with the versatility and reliability of self-consistent carrier transport approaches. Simulation results are shown for a QCL-based terahertz frequency comb source, and good agreement with experiment is obtained.