How Many Timesteps for a Cycle? Analysis of the Wisdom-Holman Algorithm

The Wisdom-Holman algorithm is an effective method for numerically solving nearly integrable systems. It takes into account the exact solution of the integrable part. If the nearly integrable system is the solar system, for example, the Wisdom-Holman algorithm uses the solution consisting of Keplerian orbits obtained when the interplanetary interactions are ignored. The effectiveness of the algorithm lies in its ability to take long timesteps. We use the Duffing oscillator and Kepler's problem with forcing to deduce how long those timesteps can be. For nearly Keplerian orbits, the timesteps must be at least six per orbital period even when the orbital eccentricity is zero. High eccentricity of the Keplerian orbits constrains the algorithm and forces it to take shorter timesteps. The analysis is applied to the solar system and other problems.     

Further studies of the reaction kernel structure and stabilization of jet diffusion flames

The structure of axisymmetric laminar jet diffusion flames of ethane, ethylene, acetylene, and propane in quasi-quiescent air has been studied numerically in normal earth gravity (1g) and zero gravity (0g). The time-dependent full Navier–Stokes equations with buoyancy were solved using an implicit, third-order accurate numerical scheme, including a C₃-chemistry model and an optically thin-media radiation model for heat losses. Observations of the flames were also made at the NASA Glenn 2.2-Second Drop Tower. For all cases of the fuels and gravity levels investigated, a peak reactivity spot, i.e., reaction kernel, was formed in the flame base, thereby holding a trailing diffusion flame. The location of the reaction kernel with respect to the burner rim depended inversely on the reaction-kernel reactivity or velocity. In the C₂ and C₃ hydrocarbon flames, the H₂–O₂ chain reactions were important at the reaction kernel, yet the CH₃ + O → CH₂O + H reaction, a dominant contributor to the heat-release rate in methane flames studied previously, did not outweigh other exothermic reactions. Instead of the C₁-route oxidation pathway in methane flames, the C₂ and C₃ hydrocarbon fuels dehydrogenated on the fuel side and acetylene was a major hydrocarbon fragment burning at the reaction kernel. The reaction-kernel correlations between the reactivity (the heat-release or oxygen-consumption rate) and the velocity, obtained previously for methane, were developed further for various fuels in more universal forms using variables related to local Damköhler numbers and Peclet numbers.     

Interfacial insights on the dibenzo-based crown ether assisted cesium extraction in [BMIM][Tf2N]–water binary system

The distribution coefficient of Cs is estimated using dibenzo-21-crown-7 (DB21C7) and di-benzo-18-crown-6 (DB18C6) in 1-butyl-3-methylimidazolium bis (trifluroromethanesulphonyl) imide (BMIMTF2N) ionic liquid by performing solvent extraction experiments. In addition, molecular dynamics studies on the extraction of cesium (Cs⁺) ion transfer from the aqueous phase to the BMIMTF2N phase is reported. The experimental findings gave a cesium distribution coefficient of 0.218 and 0.326, which agrees closely with the values of 0.2 and 0.5 obtained from MD simulation for the ionophores DB18C6 and DB21C7, respectively. Thus MD simulation may be helpful in screening the solvents prior to the experiments.

     

Cup-burner flame structure and extinguishment by CF3Br and C2HF5 in microgravity

The effects of fire-extinguishing agents CF₃Br and C₂HF₅ on the structure and extinguishing processes of microgravity cup-burner flames have been studied numerically. Propane and a propane–ethanol–water fuel mixture, prescribed for a Federal Aviation Administration (FAA) aerosol can explosion simulator test, were used as the fuel. The time-dependent, two-dimensional numerical code, which includes a detailed kinetic model (177 species and 2986 reactions), diffusive transport, and a gray-gas radiation model, revealed unique flame structure and predicted the minimum extinguishing concentration of agent when added to the air stream. The peak reactivity spot (i.e., reaction kernel) at the flame base stabilized a trailing flame. The calculated flame temperature along the trailing flame decreased downstream due to radiative cooling, causing local extinction at <1250 K and flame tip opening. As the mole fraction of agent in the coflow (X_a) was increased gradually: (1) the premixed-like reaction kernel weakened (i.e., lower heat release rate) (but nonetheless formed at higher temperature); (2) the flame base stabilized increasingly higher above the burner rim, parallel to the axis, until finally blowoff-type extinguishment occurred; (3) the calculated maximum flame temperature remained at nearly constant (≈1700 K) or mildly increased; and (4) the total heat release of the entire flame decreased (inhibited) for CF₃Br but increased (enhanced) for C₂HF₅. In the lifted flame base with added C₂HF₅, H₂O (formed from hydrocarbon-O₂ combustion) was converted further to HF and CF₂O through exothermic reactions, thus enhancing the heat-release rate peak. In the trailing flame, “two-zone” flame structure developed: CO₂ and CF₂O were formed primarily in the inner and outer zones, respectively, while HF was formed in both zones. As a result, the unusual (non-chain branching) reactions and the combustion enhancement (increased total heat release) due to the C₂HF₅ addition occurred primarily in the trailing diffusion flame.     

A novel Zn(4)O-based triazolyl benzoate MOF: synthesis, crystal structure, adsorption properties and solid state 13C NMR investigations

The newly synthesized Zn(4)O-based MOF (3)(∞)[Zn(4)(μ(4)-O){(Metrz-pba)(2)mPh}(3)]·8 DMF (1·8 DMF) of rare tungsten carbide (acs) topology exhibits a porosity of 43% and remarkably high thermal stability up to 430 °C. Single crystal X-ray structure analyses could be performed using as-synthesized as well as desolvated crystals. Besides the solvothermal synthesis of single crystals a scalable synthesis of microcrystalline material of the MOF is reported. Combined TG-MS and solid state NMR measurements reveal the presence of mobile DMF molecules in the pore system of the framework. Adsorption measurements confirm that the pore structure is fully accessible for nitrogen molecules at 77 K. The adsorptive pore volume of 0.41 cm(3) g(-1) correlates well with the pore volume of 0.43 cm(3) g(-1) estimated from the single crystal structure.     

On Growth Types of Quotients of Coxeter Groups by Parabolic Subgroups

The principal objects studied in this note are infinite, non-affine Coxeter groups W. A well-known result of de la Harpe asserts that such groups have exponential growth. We study the growth type of quotients of W by parabolic subgroups and by a certain class of reflection subgroups. Our main result is that these quotients have exponential growth as well.     

Photolytic-interference-free, femtosecond two-photon fluorescence imaging of atomic hydrogen

We discuss photolytic-interference-free, high-repetition-rate imaging of reaction intermediates in flames and plasmas using femtosecond (fs) multiphoton excitation. The high peak power of fs pulses enables efficient nonlinear excitation, while the low energy nearly eliminates interfering single-photon photodissociation processes. We demonstrate proof-of-principle, interference-free, two-photon laser-induced fluorescence line imaging of atomic hydrogen in hydrocarbon flames and discuss the method's implications for certain other atomic and molecular species.     

Multiple laminar-turbulent transition cycles around a swept leading edge

Certain interesting flow features involving multiple transition/relaminarization cycles on the leading edge of a swept wing at low speeds are reported here. The wing geometry tested had a circular nose and a leading edge sweep of 60°. Tests were made at a chord Reynolds number of 1.3 × 10⁶ with model incidence α varied in the range of 3°?18° in discrete steps. Measurements made included wing chord-wise surface pressure distributions and wall shear stress fluctuations (using hot-film gages) within about 10 % of the chord in the leading edge zone. Results at α = 16° and 18° showed that several (often incomplete) transition cycles between laminar-like and turbulent-like flows occurred. These rather surprising results are attributable chiefly to the fact that the Launder acceleration parameter K (appropriately modified for swept wings) can exceed a critical range more than once along the contour of the airfoil in the leading edge region. Each such crossing results in a relaminarization followed by direct retransition to turbulence as K drops to sufficiently low values. It is further shown that the extent of each observed transition zone (of either type) is consistent with earlier data acquired in more detailed studies of direct transition and relaminarization. Swept leading edge boundary layers therefore pose strong challenges to numerical modelling.     

Formation of two-dimensional structures by tuning the driving force of chemical reactions: an interpretation of kinetic control

Understanding shape control during wet chemical synthesis is important for rational synthesis of nanostructures. Here, we show that two-dimensional metal structures can be obtained from metal salts by reducing the driving force of the reduction reaction that directly translates to the growth of the metal taking place by the two-dimensional nucleation (layer-by-layer growth) mechanism. Experimental evidence is provided for Au, Ag, Pt and Pd systems by choosing appropriate reaction conditions without using any external surfactant. The results are analyzed in terms of the calculations of driving force under different conditions. The results show that surfactants may not be important for producing shape control for the case of 2-D structures while they are required to obtain size control. It is shown that the regime of low driving force is also one where the kinetics of the process is slow and thus a new interpretation of the kinetic control hypothesis is provided.