Random Parking, Sequential Adsorption,¶and the Jamming Limit

Identical cars are dropped sequentially from above into a large parking lot. Each car is positioned uniformly at random, subject to non-overlap with its predecessors, until jamming occurs. There have been many studies of the limiting mean coverage as the parking lot becomes large, but no complete proof that such a limit exists, until now. We prove spatial laws of large numbers demonstrating that for various multidimensional random and cooperative sequential adsorption schemes such as the one above, the jamming limit coverage is well-defined. Received: 18 August 2000 / Accepted: 13 November 2000     

Harmonic frequency scaling factors for Hartree-Fock, S-VWN, B-LYP, B3-LYP, B3-PW91 and MP2 with the Sadlej pVTZ electric property basis set

Scaling factors for obtaining fundamental vibrational frequencies from harmonic frequencies calculated at six of the most commonly used levels of theory have been determined from regression analysis for the polarized-valence triple-zeta (pVTZ) Sadlej electric property basis set. The Sadlej harmonic frequency scaling factors for first- and second-row molecules were derived from a comparison of a total of 900 individual vibrations for 111 molecules with available experimental frequencies. Overall, the best performers were the hybrid density functional theory (DFT) methods, Becke's three-parameter exchange functional with the Lee–Yang–Parr fit for the correlation functional (B3-LYP) and Becke's three-parameter exchange functional with Perdew and Wang's gradient-corrected correlation functional (B3-PW91). The uniform scaling factors for use with the Sadlej pVTZ basis set are 0.9066, 0.9946, 1.0047, 0.9726, 0.9674 and 0.9649 for Hartree–Fock, the Slater–Dirac exchange functional with the Vosko–Wilk–Nusair fit for the correlation functional (S-VWN), Becke's gradient-corrected exchange functional with the Lee–Yang–Parr fit for the correlation functional (B-LYP), B3-LYP, B3-PW91 and second-order M?ller–Plesset theory with frozen core (MP2(fc)), respectively. In addition to uniform frequency scaling factors, dual scaling factors were determined to improve the agreement between computed and observed frequencies. The scaling factors for the wavenumber regions below 1800 cm⁻¹ and above 1800 cm⁻¹ are 0.8981 and 0.9097, 1.0216 and 0.9857, 1.0352 and 0.9948, 0.9927 and 0.9659, 0.9873 and 0.9607, 0.9844 and 0.9584 for Hartree–Fock, S-VWN, B-LYP, B3-LYP, B3-PW91 and MP2(fc), respectively. Hybrid DFT methods along with the Sadlej pVTZ basis set provides reliable theoretical vibrational spectra in a cost-effective manner. Received: 22 May 2000 / Accepted: 30 August 2000 / Published online: 28 February 2001     

Dinuclear platinum(II) 4,6-diphenyl-2,2'-bipyridine complexes tethered by a rigid bridging ligand: synthesis and photophysics in solution and in LB film

Two dinuclear platinum(II) 4,6-diphenyl-2,2'-bipyridine (C^N^N) complexes (1 and 2) with a rigid bridging ligand cis-1,2-bis(diphenylphosphino)ethylene were synthesized and their photophysical properties were systematically investigated in solution for 1 and 2 and in LB film for 2. Similar to their corresponding mononuclear complexes, both complexes exhibit intense (1)π,π* absorption in the UV region and a broad, moderate absorption band in the visible region, which likely stems from the mixed (1)MLCT (metal-to-ligand charge transfer), (1)ILCT (intraligand charge transfer) and (1)π,π* transitions. Both complexes are emissive in solutions at room temperature and in glassy matrix at 77 K. The emitting state is tentatively assigned as (3)MLCT for 1 and (3)MLCT/(3)ILCT/(3)π,π* for 2 at room temperature. At 77 K, the emission observed for 1 is mainly from the emissive ground-state aggregates, which is concentration dependent; while in 2 the emission from the monomer dominates. Unlike the dinuclear platinum complex with flexible bridging ligand diphenylphosphinoethane, the electronic absorption and emission energies of 1 and 2 at room temperature are independent of their concentration, indicating a fixed conformation for these two complexes. In addition, the presence of alkoxyl substituents on the diphenylbipyridine ligands causes a bathochromic shift of the lowest-energy absorption band and the emission band at room temperature for 2, presumably due to the involvement of the ILCT character into the lowest excited states. The presence of alkoxyl substituents in 2 also makes 2 amphiphilic, allowing for the fabrication of LB films of 2. The electronic absorption and emission characteristics in the LB films of 2 are quite similar to those in solutions, indicating no intermolecular Pt-Pt interactions occur in the LB films. The dinuclear complex without alkoxyl substituent (1) exhibits vapochromic behavior to heteroatom-containing volatile organic compounds (VOC's).     

Structure elucidation of highly polar basic degradants by on-line hydrogen/deuterium exchange hydrophilic interaction chromatography coupled to tandem mass spectrometry

A hydrophilic interaction liquid chromatography (HILIC) method was used to separate a commonly used pharmaceutical starting material, 4-aminomethylpyridine (4-AMP), and its degradants. The structures of the major degradants were characterized and elucidated without prior isolation by accurate mass measurement, MS/MS analysis and on-line hydrogen/deuterium (H/D) exchange experiments. The mass spectra obtained from H/D exchange experiments are particularly useful to differentiate structural isomers, to elucidate the fragmentation pathways, and to aid in structure elucidation in the absence of MS/MS fragmentation information. The impact of deuterium oxide and temperature on HILIC separation has also been explored here. The integration of H/D exchange with HILIC has been described here for the first time and has been demonstrated to be a powerful structure elucidation tool via the study of degradants in 4-AMP.     

High-throughput salting-out assisted liquid/liquid extraction with acetonitrile for the simultaneous determination of simvastatin and simvastatin acid in human plasma with liquid chromatography

Simvastatin (SS) is an effective cholesterol-lowering medicine, and is hydrolyzed to simvastatin acid (SSA) after oral administration. Due to SS and SSA inter-conversion and its pH and temperature dependence, SS and SSA quantitation is analytically challenging. Here we report a high-throughput salting-out assisted liquid/liquid extraction (SALLE) method with acetonitrile and mass spectrometry compatible salts for simultaneous LC-MS/MS analysis of SS and SSA. The sample preparation of a 96-well plate using SALLE was completed within 20 min, and the SALLE extract was diluted and injected into an LC-MS/MS system with a cycle time of 2.0 min/sample. The seamless interface of SALLE and LC-MS eliminated drying down step and thus potential sample exposure to room or higher temperature. The stability of SS and SSA in various concentration ratios in plasma was evaluated at room and low (4 °C) temperature and the low temperature (4 °C) was found necessary to maintain sample integrity. The short sample preparation time along with controlled temperature (2-4 °C) and acidity (pH 4.5) throughout sample preparation minimized the conversion of SS → SSA to ≤0.10% and the conversion of SSA → SS to 0.00% The method was validated with a lower limit of quantitation (LLOQ) of 0.094 ng mL⁻¹ for both SS and SSA and a sample volume of 100 μL. The method was used for a bioequivalence study with 4048 samples. Incurred sample reproducibility (ISR) analysis of 362 samples from the study exceeded ISR requirement with 99% re-analysis results within 100 ± 20% of the original analysis results.     

Humidity sensor based on a single-mode hetero-core fiber structure

Using a small-core single-mode fiber (SCSMF), a novel relative humidity (RH) sensor based on an SMF28-SCSMF-SMF28 fiber structure was proposed in this paper. By depositing a humidity sensitive material, such as poly (ethylene oxide) (PEO) on the bare SCSMF fiber, the proposed structure can act as an RH sensor with high sensitivity. Experiments demonstrated that the proposed RH sensor with PEO coating can achieve a sensitivity of 430 nm per relative humidity unit (RHU) in the RH range from 80% to 83% RH and a sensitivity of 50 nm per RHU in the RH range from 83% to 95% RH.     

Exact and analytical solutions for a nonlinear sigma model

We consider wave solutions to nonlinear sigma models in n dimensions. First, we reduce the system of governing PDEs into a system of ODEs through a traveling wave assumption. Under a new transform, we then reduce this system into a single nonlinear ODE. Making use of the method of homotopy analysis, we are able to construct approximate analytical solutions to this nonlinear ODE. We apply two distinct auxiliary linear operators and show that one of these permits solutions with lower residual error than the other. This demonstrates the effectiveness of properly selecting the auxiliary linear operator when performing homotopy analysis of a nonlinear problem. From here, we then obtain residual error‐minimizing values of the convergence control parameter. We find that properly selecting the convergence control parameter makes a drastic difference in the magnitude of the residual error. Together, appropriate selection of the auxiliary linear operator and of the convergence control parameter is shown to allow approximate solutions that quickly converge to the true solution, which means that few terms are needed in the construction of such solution. This, in turn, greatly improves computational efficiency. Copyright © 2013 John Wiley & Sons, Ltd.     

Competition through capacity investment under asymmetric existing capacities and costs

This paper discusses the way that different operational characteristics including existing capacity, scale economies, and production policy have an important influence on the capacity outcomes when firms compete in the market place. We formulate a game-theoretical model where each firm has an existing capacity and faces both fixed and variable costs in purchasing additional capacity. Specifically, the firms simultaneously (or sequentially) make their expansion decisions, and then simultaneously decide their production decisions with these outputs being capacity constrained. We also compare our results with cases where production has to match capacity. By characterizing the firms’ capacity and production choices in equilibrium, our analysis shows that the operational factors play a crucial role in determining what happens. The modeling and analysis in the paper gives insight into the way that the ability to use less production capacity than has been built will undermine the commitment value of existing capacity. If a commitment to full production is not possible, sinking operational costs can enable a firm to keep some preemptive advantage. We also show that the existence of fixed costs can introduce cases where there are either no pure strategy equilibrium or multiple equilibria. The managerial implications of our analysis are noted in the discussion. Our central contribution in this paper is the innovative integration of the strategic analysis of capacity expansion and well-known (s,S)$(s\text{,}S)$ policy in operations and supply chain theory.     

On the choice of auxiliary linear operator in the optimal homotopy analysis of the Cahn-Hilliard initial value problem

Analytical solutions for the Cahn-Hilliard initial value problem are obtained through an application of the homotopy analysis method. While there exist numerical results in the literature for the Cahn-Hilliard equation, a nonlinear partial differential equation, the present results are completely analytical. In order to obtain accurate approximate analytical solutions, we consider multiple auxiliary linear operators, in order to find the best operator which permits accuracy after relatively few terms are calculated. We also select the convergence control parameter optimally, through the construction of an optimal control problem for the minimization of the accumulated L ²-norm of the residual errors. In this way, we obtain optimal homotopy analysis solutions for this complicated nonlinear initial value problem. A variety of initial conditions are selected, in order to fully demonstrate the range of solutions possible.