Numerical solutions of the isotropic 3-wave kinetic equation

We show that the isotropic 3-wave kinetic equation is equivalent to the mean-field rate equations for an aggregation–fragmentation problem with an unusual fragmentation mechanism. This analogy is used to write the theory of 3-wave turbulence almost entirely in terms of a single scaling parameter. A new numerical method for solving the kinetic equation over a large range of frequencies is developed by extending Lee’s method for solving aggregation equations. The new algorithm is validated against some analytical calculations of the Kolmogorov–Zakharov (KZ) constant for some families of model interaction coefficients. The algorithm is then applied to study some wave turbulence problems in which the finiteness of the dissipation scale is an essential feature. Firstly, it is shown that for finite capacity cascades, the dissipation of energy becomes independent of the cut-off frequency as this cut-off is taken to infinity. This is an explicit indication of the presence of a dissipative anomaly. Secondly, a preliminary numerical study is presented of the so-called bottleneck effect in a wave turbulence context. It is found that the structure of the bottleneck depends non-trivially on the interaction coefficient. Finally, some results are presented on the complementary phenomenon of thermalisation in closed wave systems which demonstrates explicitly for the first time the existence of so-called mixed solutions of the kinetic equation which exhibit aspects of both KZ and equilibrium equipartition spectra.     

Double gradient ion chromatography using short monolithic columns modified with a long chained zwitterionic carboxybetaine surfactant

The rapid separation of inorganic anions on short monolithic columns permanently coated with a long chained zwitterionic carboxybetaine-type surfactant is shown. The surfactant, N-dodecyl-N,N-(dimethylammonio)undecanoate (DDMAU), was used to coat 2.5, 5.0 and 10 cm long reversed-phase silica monoliths, resulting in a permanent zwitterionic exchange surface when used with aqueous based eluents. The unique structure of the surfactant results in a charge double layer structure on the surface of the stationary phase, with strong internal anionic and weak external cationic exchange groups. The dissociation of the weak external carboxylic acid group acts to shield the inner anionic exchange site, resulting in substantial effective capacity changes with eluent pH. Utilising this effect with the application of an eluent pH gradient, simultaneously combined with eluent flow-rate gradients, very rapid simultaneous separations of both weakly retained anions and strongly retained polarisable anions was possible, with up to 10-fold decreases in overall run times. Coating stability and retention times under isocratic and isofluentic eluent conditions were shown to be reproducible over >450 repeat injections, with peak efficiency values averaging 29,000 N/m for the 2.5 cm column and 42,000 N/m for the 10 cm monolithic column, again under isocratic elution conditions.     

Performance enhancement of 10 Gb/s direct modulation optical OFDM by external optical injection

We show experimentally and by simulation a performance enhancement of a directly modulated 10 Gb/s optical Orthogonal Frequency Division Multiplexing (OFDM) system due to external optical injection. The experiment is performed back to back and over 12 km of single mode fiber. The injection extends the range of linear operation of the laser and therefore extends the usable bandwidth for direct modulation formats which are susceptible to nonlinearity, such as OFDM. Nonlinearity in the system and its reduction due to injection are estimated by means of a two tone test. Additionally the performance enhancement on OFDM systems was verified in both simulation and experimentally by the comparisons of the average Bit Error Rate (BER) and Error Vector Magnitude (EVM).     

多晶粒银纳米线形变机理对温度依赖性的分子动力学研究

基于大规模分子动力学仿真,本文研究了包含多个晶粒的柱状银纳米线在不同温度下,沿轴向拉伸形变的行为。结果表明,当温度低于200 K时,含较大晶粒的体系中位错滑移是其形变的主要机理,最大应力随温度变化不显著。当环境温度高于200 K时,晶粒的滑动逐渐成为形变的主导因素,这一特征在含更小晶的体系内表现更明显。同时最大应力随温度显著降低。基于上述结果,进一步讨论了温度对Hall-Petch关系的影响。     

Taking Account of Correlations Between Streams in Queueing Network Approximations

In this paper we describe a new variation on QNA, the Queueing Network Analyzer (Whitt [38]). QNA calculates approximate congestion measures for a network of queues. The variant proposed here allows us to relax QNA’s assumption that certain counts of events in the network are uncorrelated. Following QNA, the network is approximated in terms of three basic operations on streams, namely, queueing, splitting and superposition, and random quantities of interest are characterized approximately by two moments. The approach differs from QNA in that instead of expressing the network operations as transformations applied to two-moment characterizations of the inputs, it expresses these operations as regression relations between counts in the output streams and the input streams. In essence, we substitute approximate regression relationships between random variables for QNA’s approximate moment relationships. This device allows us to enhance QNA’s moment relationships with information about correlations between the streams. We compare the performance of the proposed approach with QNA on a simple feed-forward network to demonstrate the need for taking account of correlation. We also discuss some of the limitations of this approach, particularly its difficulty in handling feedback, and give some ideas to improve accuracy.AMS subject classification: 60K25, 68M20, 90B22Colm O’Cinneide has left Purdue University after 10 wonderful years of research and teaching, and now works for Deutsche Asset Management in New York. This research has been supported in part under NSF grant DMI-9713730.This revised version was published online in June 2005 with corrected coverdate     

Surface-immobilized pyridine-functionalized gamma-cyclodextrin: alkanethiol co-adsorption-induced reorientation

Monolayers of di-6A,6B-deoxy-6-(4-pyridylmethyl)amino-gamma-cyclodextrin (gamma-CD-(py)2) have been formed on polycrystalline platinum electrodes and investigated using electrochemical and surface-enhanced Raman spectroscopy (SERS). The behavior of self-assembled monolayers of (gamma-CD-(py)2) alone, (gamma-CD-(py)2) backfilled with 1-nonanethiol, and 1-nonanethiol are reported. The potential dependence of the capacitance indicates that the film capacitance is higher for the backfilled CD layers than for 1-nonanethiol layers, most likely due to ion flux through the CD cavity. SERS spectra of the backfilled layer exhibit features associated with both pyridine-functionalized CD and alkane moieties. Investigations using [Fe(CN)6]4- as a solution-phase probe indicate that the backfilled CD-alkane thiol layer exhibits enhanced blocking properties compared to gamma-CD-(py)2 films alone. Complete blocking was achieved by a combination of backfilling and insertion of a high-affinity guest 1-adamantylamine into the cavity. Significantly, an electroactive guest with high affinity for gamma-CD, [Co(biptpy)2]2+, does not exhibit a redox response at the gamma-CD-(py)2 layer but molecular recognition is turned on by backfilling the CD layer with 1-nonanethiol molecules. This switching on of the electrochemical activity suggests that the CD hosts are initially inaccessible but reorientate upon backfilling, exposing the CD opening to solution and permitting a supramolecular host-guest complex to form. The binding of [Co(biptpy)2]2+ to gamma-CD in the backfilled monolayer depends on the bulk concentration of guest and is modeled by the Langmuir isotherm, yielding an association constant for the Co2+ state of 1.45 +/- 0.46 x 105 M-1 and a limiting surface coverage 1.49 +/- 0.25 x 10-11 mol cm-2. The surface coverage of the divalent state is higher than the trivalent state, reflecting the dynamic nature of the inclusion.     

Palladium‐Templated Subcomponent Self‐Assembly of Macrocycles,Catenanes, and Rotaxanes

The reaction of 2,6‐diformylpyridine with diverse amines and Pd^II ions gave rise to a variety of metallosupramolecular species, in which the Pd^II ion is observed to template a tridentate bis(imino)pyridine ligand. These species included a mononuclear complex as well as [2+2] and [3+3] macrocycles. The addition of pyridine‐containing macrocyclic capping ligands allows for topological complexity to arise, thereby enabling the straightforward preparation of structures that include a [2]catenane, a [2]rotaxane, and a doubly threaded [3]rotaxane.     

A Triphasic Sorting System: Coordination Cages in Ionic Liquids

Host–guest chemistry is usually carried out in either water or organic solvents. To investigate the utility of alternative solvents, three different coordination cages were dissolved in neat ionic liquids. By using ¹⁹F NMR spectroscopy to monitor the presence of free and bound guest molecules, all three cages were demonstrated to be stable and capable of encapsulating guests in ionic solution. Different cages were found to preferentially dissolve in different phases, allowing for the design of a triphasic sorting system. Within this system, three coordination cages, namely Fe₄L₆ 2 , Fe₈L₁₂ 3 , and Fe₄L₄ 4 , each segregated into a distinct layer. Upon the addition of a mixture of three different guests, each cage (in each separate layer) selectively bound its preferred guest.