A test problem for molecular dynamics integrators

We derive a test problem for evaluating the ability of time-steppingmethods to preserve the statistical properties of systems inmolecular dynamics. We consider a family of deterministic systemsconsisting of a finite number of particles interacting on acompact interval. The particles are given random initial conditionsand interact through instantaneous energy- and momentum-conservingcollisions. As the number of particles, the particle density,and the mean particle speed go to infinity, the trajectory ofa tracer particle is shown to converge to a stationary Gaussianstochastic process. We approximate this system by one describedby a system of ordinary differential equations and provide numericalevidence that it converges to the same stochastic process. Wesimulate the latter system with a variety of numerical integrators,including the symplectic Euler method, a fourth-order Runge-Kuttamethod, and an energyconserving step-and-project method. Weassess the methods' ability to recapture the system's limitingstatistics and observe that symplectic Euler performs significantlybetter than the others for comparable computational expense.     

Structure and Structural Nonrigidity of Tetrachlorodibenzo-p-Dioxin Radical Cations

Ab initio calculations showed that the tetrachlorodibenzo-para-dioxin radical cations (TCDD RCs) with a planar structure have two steady states with asymmetric dioxin cycles. The activation barriers between these states are up to 2 kcal/mole, so that the RCs may be regarded as being structurally nonrigid within the dioxin cycle. The 2,3,7,8-TCDD RC is more stable than the 1,4,6,9-TCDD RC, the energy difference being 5.2 kcal/mole. The adiabatic ionization potential of 2,3,7,8-TCDD (7.54 eV) is 0.1 eV smaller than the corresponding potential of 1,4,6,9-TCDD. These factors account for the increased hemoproteide affinity and hence increased biological activity of 2,3,7,8-TCDD.     

An Application of Branch and Cut to Open Pit Mine Scheduling

The economic viability of the modern day mine is highly dependent upon careful planning and management. Declining trends in average ore grades, increasing mining costs and environmental considerations will ensure that this situation will remain in the foreseeable future. The operation and management of a large open pit mine having a life of several years is an enormous and complex task. Though a number of optimization techniques have been successfully applied to resolve some important problems, the problem of determining an optimal production schedule over the life of the deposit is still very much unresolved. In this paper we will critically examine the techniques that are being used in the mining industry for production scheduling indicating their limitations. In addition, we present a mixed integer linear programming model for the scheduling problems along with a Branch and Cut solution strategy. Computational results for practical sized problems are discussed.     

Computations of two passing‐by high‐speed trains by a relaxation overset‐grid algorithm

This paper presents a relaxation algorithm, which is based on the overset grid technology, an unsteady three‐dimensional Navier–Stokes flow solver, and an inner‐ and outer‐relaxation method, for simulation of the unsteady flows of moving high‐speed trains. The flow solutions on the overlapped grids can be accurately updated by introducing a grid tracking technique and the inner‐ and outer‐relaxation method. To evaluate the capability and solution accuracy of the present algorithm, the computational static pressure distribution of a single stationary TGV high‐speed train inside a long tunnel is investigated numerically, and is compared with the experimental data from low‐speed wind tunnel test. Further, the unsteady flows of two TGV high‐speed trains passing by each other inside a long tunnel and at the tunnel entrance are simulated. A series of time histories of pressure distributions and aerodynamic loads acting on the train and tunnel surfaces are depicted for detailed discussions. Copyright © 2004 John Wiley & Sons, Ltd.     

Photorefractive Four-Wave Mixing Switches Utilizing Pockels Effect -Longitudinal and Lateral Switches-

We carried out detailed calculations for photorefractive wave-mixing switches based on one of three crystals with high electro-optic coefficients, namely, BaTiO₃, Strontium Barium Niobate (SBN (0.75)), and Potasium Sodium Strontium Barium Niobate (KNSBN). A comparison of results for the three crystals shows that a 0_-cut BaTiO³ crystal is suitable for a longitudinal switch and requires a voltage of about 80 for a 2-mm-thick crystal to induce sufficient phase mismatch. The electrodes must be transparent for the incident and diffracted beams. A 45_-cut SBN (0.75) crystal, however, is suitable for a lateral switch and requires a voltage of about 150 for a 1-mm-wide crystal. The electrodes do not need to be transparent.     

Measurements of Time-Varying Characteristics of Optical Signals and Inhomogeneities of Tested Substances with Additional Phase Modulation

The problem of investigation of the amplitude and phase structure of a time-varying probing optical signal and the structure of time-varying inhomogeneities of a substance tested by this signal is considered. The analysis is concerned, in particular, with determination of the structure of signals and processes with resolution in the pico- and femtosecond range. The scheme used for the analysis is based on registration of four spatially separated spectra of the studied radiation. The spectra are formed in a four-channel scheme with a twin-wave Michelson interferometer and a spectral device. Modulators based on electrooptical crystals (perovskites) are placed in the channels. The sum spectra are formed: without modulators, with the effect of either of the modulators, and with both of them affecting the radiation. The effect of the studied substance implies either modulating the radiation (in this case it is described by multiplication) or redistributing the radiation (then it is described by convolution).     

Synthesis,characterization, and biological activity of [2‐oxo‐2‐(4‐acetyl) phenyl amino] ethylene methacrylate and its derivatives

A new type of methacrylate monomer, [2‐oxo‐2‐(4‐acetyl) phenyl amino] ethylene methacrylate (APEMA), was synthesized. The oxime, 2,4‐dinitrophenylhydrazone, and thiosemicarbazone derivatives of poly{[2‐oxo‐2‐(4‐acetyl) phenyl amino] ethylene methacrylate} [poly(APEMA)] were prepared with hydroxylamine hydrochloride, 2,4‐dinitrophenylhydrazine, and thiosemicarbazone hydrochloride, respectively. The radical homopolymerization of APEMA was performed at 65 °C in a 1,4‐dioxane solution with benzoyl peroxide as an initiator. The monomer and its homopolymer were characterized with Fourier transform infrared and NMR techniques. The thermal stabilities of poly(APEMA) and its derivatives were investigated with thermogravimetric analysis and differential scanning calorimetry. The ultraviolet stability of the polymers were compared. The solubility and inherent viscosity of the polymers were also determined. The number‐average and weight‐average molecular weights and polydispersity index of the polymers were determined with gel permeation chromatography. The antibacterial and antifungal effects of the monomer and the polymer and its derivatives were also investigated on various bacteria and fungi. The activation energies of the thermal degradation of the polymers were calculated with the Ozawa method. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3157–3169, 2004     

Desorption behavior of a surfactant in a linear low‐density polyethylene blend at elevated temperatures

The desorption behavior of a surfactant in a linear low‐density polyethylene (LLDPE) blend at elevated temperatures of 50, 70, and 80 °C was studied with Fourier transform infrared spectroscopy. The composition of the LLDPE blend was 70:30 LLDPE/low‐density polyethylene. Three different specimens (II, III, and IV) were prepared with various compositions of a small molecular penetrant, sorbitan palmitate (SPAN‐40), and a migration controller, poly(ethylene acrylic acid) (EAA), in the LLDPE blend. The calculated diffusion coefficient (D) of SPAN‐40 in specimens II, III, and IV, between 50 and 80 °C, varied from 1.74 × 10^?11 to 6.79 × 10^?11 cm²/s, from 1.10 × 10^?11 to 5.75 × 10^?11 cm²/s, and from 0.58 × 10^?11 to 4.75 × 10^?11 cm²/s, respectively. In addition, the calculated activation energies (E_D) of specimens II, III, and IV, from the plotting of ln D versus 1/T between 50 and 80 °C, were 42.9, 52.7, and 65.6 kJ/mol, respectively. These values were different from those obtained between 25 and 50 °C and were believed to have been influenced by the interference of Tinuvin (a UV stabilizer) at elevated temperatures higher than 50 °C. Although the desorption rate of SPAN‐40 increased with the temperature and decreased with the EAA content, the observed spectral behavior did not depend on the temperature and time. For all specimens stored over 50 °C, the peak at 1739 cm^?1 decreased in a few days and subsequently increased with a peak shift toward 1730 cm^?1. This arose from the carbonyl stretching vibration of Tinuvin, possibly because of oxidation or degradation at elevated temperatures. In addition, the incorporation of EAA into the LLDPE blend suppressed the desorption rate of SPAN‐40 and retarded the appearance of the 1730 cm^?1 peak. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1114–1126, 2004     

NMR investigation of concentrated alumina and silica slurries

The longitudinal relaxation times (T₁) of water in concentrated silica and alumina slurries were measured as a function of solids content. It was shown that the results could be fit very well with a two-phase fast-exchange model between free and surface-bound water. As expected, values of T₁ for bound water were in the order of 20–2000 times lower than that for free water, indicating a higher effective viscosity of the surface-bound water. The strength of the interaction depended on the particular surface, and all of the aluminas examined interacted more strongly with water than the two silicas studied, which themselves differed considerably. The chemical mechanical polishing (CMP) removal rate of tantalum by silica slurries was shown to be directly correlated with the interaction parameters, derived from the NMR relation times rather than with total surface hydroxyl group concentration.     

On the influence of the surfactant''s polar group on the local and terminal velocities of bubbles

The local and the terminal velocities, the size and the degree of bubbles’ shape deformations were determined as a function of distance from the position of the bubble formation (capillary orifice) in solutions of n-octyltrimethylammonium bromide, n-octyldimethylphosphine oxide, n-octyl-β-D-glucopyranoside and n-octanoic acid.

These surface-active compounds have different polar groups but an identical hydrocarbon chain (C8) in the molecule. The motion of the bubbles was monitored and recorded using a stroboscopic illumination, a CCD camera, and a JVC professional video. The recorded bubble images were analyzed by the image analysis software. The bubbles accelerated rapidly and their shape was deformed immediately after detachment from the capillary. The extent of the bubbles’ shape deformation (ratio of horizontal and vertical diameters) was 1.5 in distilled water and dropped rapidly down to a level of ca. 1.05–1.03 with increasing surfactant concentration. After the acceleration period the bubbles either attained a constant value of the terminal velocity (distilled water and high concentrations of the solutions), or a maximum in the velocity profiles was observed (low concentrations). The values of the terminal velocity diminished drastically with increasing concentration, from the value of 35 cm/s in water down to about 15 cm/s, while the bubble diameter decreased by ca. 10% only. The surfactant adsorption at the surface of the bubbles was evaluated and the minimum adsorption coverages required to immobilize the bubbles’ surface were determined. It was found that this minimum adsorption coverage was ca. 4% for n-octyldimethylphosphine oxide, n-octyl-β-D-glucopyranoside, n-octanoic acid and 25% for n-octyltrimethylammonium bromide. The difference in the adsorption coverage together with the surfactants’ surface activities indicate that it is mainly the adsorption kinetics of the surfactants that governs the fluidity of interfaces of the rising bubbles.