On the phenomenological rate equation in a model exchange reaction

The limits of validity of the phenomenological rate equation, and the phenomenological rate constant k_f and k_b are found for the exchange reaction $\text{A + BC}\textcolor{red}{}\text{AB + C}$ within the framework of simple multistate models. The possibility of macroscopically long transient times is discussed. The rate constants are shown to depend on the total densities n_A, n_B and n_C of the chemical species present in the mixture, when nonequilibrium effects are important. The distinction between a rate constant and a flux coefficient is illustrated. Differences among exchange, dissociation-recombination, and isomerization reactions in that regard are discussed.     

On the dependence of the condensation coefficient on surface curvature

It is concluded that there is as yet no adequate theoretical solution for the size dependence of the condensation coefficient, the Okuyama-Zung approach to this problem being discounted.     

Probabilistic inference of reaction rate parameters from summary statistics

This investigation tackles the probabilistic parameter estimation problem involving the Arrhenius parameters for the rate coefficient of the chain branching reaction H + O₂ → OH + O. This is achieved in a Bayesian inference framework that uses indirect data from the literature in the form of summary statistics by approximating the maximum entropy solution with the aid of approximate bayesian computation. The summary statistics include nominal values and uncertainty factors of the rate coefficient, obtained from shock-tube experiments performed at various initial temperatures. The Bayesian framework allows for the incorporation of uncertainty in the rate coefficient of a secondary reaction, namely OH + H₂ → H₂O + H, resulting in a consistent joint probability density on Arrhenius parameters for the two rate coefficients. It also allows for uncertainty quantification in numerical ignition predictions while conforming with the published summary statistics. The method relies on probabilistic reconstruction of the unreported data, OH concentration profiles from shock-tube experiments, along with the unknown Arrhenius parameters. The data inference is performed using a Markov chain Monte Carlo sampling procedure that relies on an efficient adaptive quadrature in estimating relevant integrals needed for data likelihood evaluations. For further efficiency gains, local Padé–Legendre approximants are used as surrogates for the time histories of OH concentration, alleviating the need for 0-D auto-ignition simulations. The reconstructed realisations of the missing data are used to provide a consensus joint posterior probability density on the unknown Arrhenius parameters via probabilistic pooling. Uncertainty quantification analysis is performed for stoichiometric hydrogen–air auto-ignition computations to explore the impact of uncertain parameter correlations on a range of quantities of interest.     

Friction coefficient and radius of curvature effects upon traffic flow on a curved Road

We investigate the friction coefficient and radius of curvature effects upon traffic flow analytically and numerically. A new model is proposed to describe the motion of vehicles running on a curved road. The stability condition is obtained by the use of control theories. The nonlinear analysis method is taken to derive the modified KdV (Korteweg–de Vries) equation and the kink–antikink solution is obtained near the critical point. Simulations are carried out to verify the double effects upon traffic flow. The flux increases but the stability decreases with an increase of the two parameters. Numerical results are in good agreement with the analytical results.     

Relativistic string model in a space-time of a constant curvature

The relativistic string model is investigated in a space-time of a constant curvature (de Sitter universe). The fundamental differential quadratic forms of the world surface of the string are considered as the dynamical variables. The coefficients of these forms obey two nonlinear equations $$\varphi _{,11} - \varphi _{,22} = e^\varphi \cos \theta + Ke^{ - \varphi } ,\theta _{,11} - \theta _{,22} = e^\varphi \sin \theta .$$ The Lax representation for this system is obtained.     

A model of neural control of the heart rate

A simple model of heart rate regulation is proposed, using the assumption that the nervous system regulates the generation of pulses of the pacemaker. Previous values of intervals between heart beats (RR intervals) are used for this regulation, which is described by a nonlinear feedback loop with time delay. The conductance of the excitation in the heart is phenomenologically described by one nonlinear function (recovery curve). The model reproduces time series of RR intervals. Different known patterns of heart rate variability are observed, depending on the type of control and the parameter values.     

Effect of curvature on a statistical model of quark-gluon-plasma fireball in the hadronic medium

The free energy of a quark-gluon plasma fireball in the hadronic medium is calculated in the Ramanathan et al statistical model after incorporating the effect of curvature. The result with the inclusion of curvature is found to produce significant improvements in all the parameters we calculated with respect to the earlier results. The surface tension with this curvature effect is found to be 0.17T _c³, which is two times the earlier value of surface tension which is 0.078T _c³, and this new result is nearly close to the lattice value 0.24T _c³. As far as transition is concerned, a thermodynamic variable like entropy shows weakly first-order phase transition and it shows continuity in the behaviour of specific heat.     

Slope and curvature of Isgur-Wise function using variationally improved perturbation theory in a quantum chromodynamics inspired potential model

We used variationally improved perturbation theory (VIPT) in calculating the slope and curvature of Isgur-Wise (I-W) function with the Cornell potential −$ \frac{{4\alpha _s }} {{3r}} $ \frac{{4\alpha _s }} {{3r}} +br + c instead of the usual stationary state perturbation theory as done earlier. We used −(4α _s /3r), i.e. the Coulombic potential, as the parent and the linear one, i.e. br+c as the perturbed potential in the theory and calculated the slope and curvature of Isgur-Wise function including three states in the summation involved in the first-order correction to wave function in the method.     

The reaction of allyl radicals with oxygen atoms—rate coefficient and product branching

The primary product formation of the C₃H₅ + O reaction in the gas phase has been studied at room temperature. Allyl radicals (C₃H₅) and O atoms were generated by laser flash photolysis at λ = 193 nm of the precursors C₃H₅Cl, C₃H₅Br, C₆H₁₀ (1,5-hexadiene), and SO₂, respectively. The educts and the products were detected by using quantitative FTIR spectroscopy. The combined product analysis of the experiments with the different precursors leads to the following relative branching fractions: C₃H₅ + O → C₃H₄O + H (47%), C₂H₄ + H + CO (41%), H₂CO + C₂H₂ + H (7%), CH₃CCH + OH and CH₂CCH₂ + OH (<5%). The rate of reaction has been studied relative to CH₃OCH₂ + O and C₂H₅ + O in the temperature range from 300 to 623 K. Here, the radicals were produced via the fast reactions of propene, dimethyl ether, and ethane, respectively, with atomic fluorine. Laser-induced multiphoton ionization combined with TOF mass spectrometry and molecular beam sampling from a flow reactor was used for the specific and sensitive detection of the C₃H₅, C₂H₅, and CH₃COCH₂ radicals. The rate coefficient of the reaction C₃H₅ + O was derived with reference to the reaction C₂H₅ + O leading to k(C₃H₅ + O) = (1.11 ± 0.2) × 10¹⁴ cm³/(mol s) in the temperature range 300-623 K. The C₃H₅ + O rate and channel branching, when incorporated in a suitable detailed reaction mechanism, have a large influence on benzene and allyl concentration profiles in fuel-rich propene flames, on the propene flame speed, and on propene ignition delay times.     

A novel approach for the potential parameters selection of Peyrard-Bishop model

The selection of the potential parameters is a very difficult question because the potentials entering the model are effective potentials. In this Letter, an approach for selecting potential parameters of the Peyrard-Bishop model by mean Lyapunov exponent is presented. Using the theory introduced by Shibata [H. Shibata, Physica A 264 (1999) 226] on the Peyrard-Bishop model shows that, the system is very sensitive to the parameters selection. The obtained results demonstrate that the best range for parameters are where the mean Lyapunov exponent has low values. Furthermore, there is a good correspondence between our results and other reports.     

Cell structure and stability of detonations with a pressure-dependent chain-branching reaction rate model

We examine detonation waves with a four-step chain-branching reaction model that exhibits explosion limits close to the two lower limits of hydrogen–oxygen chemistry. The reaction model consists of a chain-initiation step and a chain-branching step, both temperature-dependent with Arrhenius kinetics, followed by two pressure-dependent termination steps. Increasing the chain-branching activation energy or the overdrive shortens the reaction length in the ZND wavelength and leads to more unstable detonations, according to multi-dimensional linear stability analysis. Corresponding numerical simulations show that detonations with weak chain-branching reactions have a wave structure similar to those with a single-step reaction; strong chain-branching detonations show distinct keystone features. Keystone regions are bounded by a discontinuity in reactivity across the shear layers emanating from the triple points at the intersection of the transverse waves and the main front. Especially in the strong case, chain-branching occurs within a thin front at the back side of the keystone figure, or immediately behind Mach stems.     

Synthesis of tetracyclic pyrido-fused dibenzodiazepines via a catalyst-free cascade reaction

Molecular Diversity - An efficient, eco-friendly protocol has been described for the chemoselective synthesis of tetracyclic pyrido-fused dibenzodiazepines derivatives via catalyst-free,...     

三级自动复叠制冷中制冷剂配比计算方法研究

自动复叠制冷循环有其特殊的优点,但是混合制冷剂的配比选取仍需进一步研究。通过搭建一个三级自动复叠制冷循环实验台,并采用常规复叠制冷循环的方法,粗定制冷剂配比,再使用CSD方程微调,实验数据证明该方法的结果比较合理。     

Note on the reaction rate in non-ideal mixtures

The form of the reaction rates in the birth-and-death formalism of a chemical reaction is obtained by applying the principle of stationarity of the thermodynamic equilibrium distribution.     

Experimental determination of cascade parameters of a hearing-aid microphone via the two-load method

Presented in this article is a computer-aided experimental method for obtaining the cascade parameters of the two-port model of a miniature hearing-aid microphone. The method is an adaptation of the "two-load" method [D.P. Egolf and R.G. Leonard, J. Acoust. Soc. Am. 62, 1013-1023 (1977)] to acoustoelectric, rather than electroacoustic, transducers. The cascade parameters of a particular microphone, determined by this method, were within 2.5 dB of the manufacturer's published open-circuit sensitivity data. In an attempt to further verify the numerical cascade-parameter data, a two-port model of the microphone was used to simulate experimental voltages developed across two different complex electrical load impedances attached to the microphone. The results showed experimental/simulation differences of no greater than 3.0 dB at any frequency. The two-port microphone model and associated cascade parameters are currently being incorporated into a computer-based plan for mathematical simulation of an entire in situ hearing aid.     

Simulation of transmission coefficient through a triangular potential barrier

An analytical expression of the transmission coefficient for the electron transport through a triangular potential barrier has been modified for solution using the method of numerical simulation. The triangular potential barrier has been modelled as a staircase function. The performance of this numerical simulation method is briefly described. The simulation has been developed for personal computer IBM PC AT.