Magnons localised on surface steps: a theoretical model

We present the solution of the full magnetic problem arising from the absence of magnetic translation symmetry in two dimensions due to an extended magnetic surface step on the surface boundary of an insulating magnetic substrate. The calculation concerns in particular the spin fluctuation dynamics of a magnetic atomic step in the surface of a ferromagnetic simple cubic lattice, the spin order being in the direction normal to surface boundary. Only exchange interactions are considered between the spins in the model. The theoretical approach determines the evanescent spin fluctuation field in the two dimensional plane normal to the direction of the step edge. This field arises owing to the absence of magnetic translation symmetry in this plane, and is completely independent of the form of the surface defect, underlying the general character of the calculation. We show the existence of optical localised magnon modes propagating along the step, their fields being evanescent in the plane normal to the step direction. Received 17 February 1999     

Colliding Solitons for the Nonlinear Schrödinger Equation

We study the collision of two fast solitons for the nonlinear Schrödinger equation in the presence of a slowly varying external potential. For a high initial relative speed ||v|| of the solitons, we show that, up to times of order ||v|| after the collision, the solitons preserve their shape (in L ²-norm), and the dynamics of the centers of mass of the solitons is approximately determined by the external potential, plus error terms due to radiation damping and the extended nature of the solitons. We remark on how to obtain longer time scales under stronger assumptions on the initial condition and the external potential.     

Innovative beneficial reuse of reverse osmosis concentrate using bipolar membrane electrodialysis and electrochlorination processes

Reverse osmosis (RO) is a widely used and rapidly growing desalination technology. A major disadvantage of this process is that the concentrate from the RO process, which could be as much as 25% of the feed stream, represents a polluting stream. This waste stream could pose a significant challenge to the implementation of this process, particularly for inland communities which do not have the option of ocean disposal. An excellent environmentally benign approach to disposal could be beneficial reuse of the waste stream. This study presents two innovative beneficial reuse strategies for RO concentrate produced by an integrated membrane system (IMS) from a wastewater reclamation facility. The technologies evaluated in this study included bipolar membrane electrodialysis (BMED) for conversion of RO concentrate into mixed acid and mixed base streams, and electrochlorination (EC) for onsite chlorine generation. Bench-scale studies conducted with BMED demonstrated that RO concentrate could be desalted while producing mixed acids and mixed bases with concentrations as high as 0.2N. Similarly, the EC process was capable of producing a 0.6% hypochlorite solution from RO concentrate. The acids and bases as well as the hypochlorite produced could be directly applied to the RO process as well as upstream pre-treatment processes. A preliminary economic evaluation of the viability of these two approaches was conducted by conducting rough order of magnitude cost estimates based on the bench-scale performance of these processes on RO concentrate. A comparison of the overall costs of an Integrated Membrane System utilizing these innovative reuse strategies with conventional disposal options and thermal zero liquid discharge treatment is presented. This comparison indicates that a reuse approach might be economically viable for inland wastewater reuse facilities that utilize RO membranes and have limited options for concentrate disposal.     

Naphthyridines. Part 3: First example of the polyfunctionally substituted 1,2,4-triazolo[1,5-g][1,6]naphthyridines ring system

Treatment of 1,2,4-triazoles (1) with diethylmalonate in bromobenzene gave 1,2,4-triazolo-[1,5-a]pyridines 2. Chlorination of 2 using POCl₃/DMF (Vilsmeier reagent) led to the isolation of 7-chloro-6-formyl-1,2,4-triazolo[1,5-a]pyridine derivative 4, which reacted with the stabilized ylid 5 to afford 6-ethoxycarbonylvinyl-1,2,4-triazolo[1,5-a]-pyridines 6. Azidation of 6 yielded the corresponding azido compound 7, (Scheme 2). Reduction of 7 with Na₂S₂O₄ gave the corresponding 7-amino compound 8, which cyclized in boiling DMF to give the novel 1,2,4-triazolo[1,5-g][1,6]naphthyridines 9. On the other hand, reacting 7 with one equivalent of PPh₃ (aza-Wittig reaction) in CH₂Cl₂ gave 7-imino-phosphorane derivative 10, and subsequent cyclization in boiling DMF afforded the new 1,2,4-triazolo[1,5-g][1,6]naphthyridine derivative 11 (Scheme 3). However, treatment of 10 with phenyl isothiocyanate in 1,2-dichlorobenzene at reflux temperature gave the new 1,2,4-triazolo[1,5-g][1,6]naphthyridine derivative 14 (Scheme 4). Refluxing 6 with excess of a primary amines 15a,b in absolute. EtOH yielded the corresponding 7-alkyl-amino-1,2,4-triazolo[1,5-a]pyridines 16a,b. These obtained amines 16a,b underwent intramolecular heterocyclization in boiling DMF to give the novel 9-alkyl-1,2,4-triazolo[1,5-g][1,6]-naphthyridines 17a,b, in excellent yields (Scheme 5).     

Complexation of N-methyl-4-(p-methyl benzoyl)-pyridinium methyl cation and its neutral analogue by cucurbit[7]uril and β-cyclodextrin: a computational study

In this work, molecular dynamics (MD) simulations have been conducted to study the inclusion complexes between cucurbit[7]uril (CB7) and β-cyclodextrin (β-CD) with N-methyl-4-(p-methyl benzoyl)-pyridinium methyl cation, and N-methyl-4-(p-methyl benzoyl)-pyridine in aqueous solutions to gain detailed information about the dynamics and mechanism of the inclusion complexes. The obtained MD trajectories were used to estimate the binding free energy of the studied complexes using the molecular mechanics/Poisson Bolzmann surface area (MM–PBSA) method. Results indicate preference of CB7 to bind to the cationic guest more than the neutral guest, whereas β-CD exhibits more or less the same affinity to complex with either species. Furthermore it was interesting to note that β-CD forms more stable complexes with both guests than CB7. Average structure of each complex and the distances between the center of masses of the guest and the host were also discussed.     

Effect of the acyl group and the dodecylsulfonate chain on the inclusion of pyrene inside the cavity of β-cyclodextrin

The solubilization of pyrene in aqueous solution of β-cyclodextrin (β-CD) or its derivatives such as β-CD-hexanoyl, β-CD-benzoyl and β-CD-dodecylsulfonate was investigated by spectrophotometry. Linear and non-linear regression methods were used to estimate the association constants (K₁). A 1:1 stoichiometric ratio and different effects of the hexanoyl, benzoyl and dodecylsulfonate groups on the association constant were observed for the binary inclusion complex between pyrene and β-CD. The formation constant was shown to decrease when β-CD was modified by a dodecylsulfonate chain. The value of K₁ was 190 ± 10 L mol⁻¹ for the [pyrene/β-CD] complex and 145 L mol⁻¹ for the [pyrene/β-CD-dodecylsulfonate] complex. Partitioning of the pyrene molecules between the dodecylsulfonate chains and cyclodextrin cavities can explain the decrease in the association constant value. In the cases of β-CD-hexanoyl and β-CD-benzoyl derivatives, no association constants were detected. Results suggest that the high hydrophobicity of the hexanoyl and benzoyl groups prevents the inclusion of pyrene molecules inside the cyclodextrin cavity.     

Robust improvement schemes for road networks under demand uncertainty

This paper is concerned with development of improvement schemes for road networks under future travel demand uncertainty. Three optimization models, sensitivity-based, scenario-based and min–max, are proposed for determining robust optimal improvement schemes that make system performance insensitive to realizations of uncertain demands or allow the system to perform better against the worst-case demand scenario. Numerical examples and simulation tests are presented to demonstrate and validate the proposed models.     

Ultrashort pulse generation using fiber FM laser

Ultrashort optical pulse generation using a fiber FM laser is presented and analyzed in detail. Fiber FM laser operation is realized using a fiber ring with an internal phase modulator and an erbium-doped fiber amplifier. To compress FM laser pulses, an external dispersive single-mode fiber is employed. Furthermore, by external intensity modulation, the pulse background is removed. The background ratio of the generated ultrashort pulse is calculated and compared with the experimental results. The experimental results show an output optical pulse width of 1.77 ps and a spectral bandwidth of 0.5 THz.     

Reactions of 2‐amino‐3‐cyano‐4,5,6,7‐tetrahydrobenzo[b]thiophene and 2‐amino‐3‐cyano‐4,7‐diphenyl‐5‐methyl‐4H‐pyrano[2,3‐c] pyrazole with phenylisocyanate,carbon disulfide,and thiourea

2‐Amino‐3‐cyano‐4,5,6,7‐tetrahydrobenzo[b]thiophene 1a or 2‐amino‐3‐cyano‐4,7‐di‐ phenyl‐5‐methyl‐4H‐pyrano[2,3‐c]pyrazole 2a reacted with phenylisocyanate in dry pyridine to give 2‐(3‐phenylureido)‐3‐cyanobenzo[b]thiophene 1b or 2‐disubstituted amino‐3‐cyanopyranopyrazole 2b derivative. However, when 1a and 2a were refluxed with carbon disulfide in 10% ethanolic sodium hydroxide solution, they afforded the thieno[2,3‐d]pyrimidin‐2,4‐dithione derivative 5 in the former case, 2,4‐dicyano‐1,3‐bis(dithio carboxamino)cyclobuta‐1,3‐ diene 6 and pyrazolopyranopyrido[2,3‐d]pyrimidin‐ 2,4‐dithione derivative 7 in the latter one. Treatment of 2a with thiourea in refluxing ethanol in the presence of potassium carbonate gave 2,2′‐dithiobispyrimidine derivative 9 (major) in addition to pyranopyrazole derivative 10 and 2,2′‐dithiobis ethoxypyrimidine derivative 11 in minor amounts. The structures of all products were evidenced by microanalytical and spectral data. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:6–11, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.20070