Obtaining bifurcation diagrams with a thermoacoustic network model

Linear techniques can predict whether the non-oscillating (steady) state of a thermoacoustic system is stable or unstable. With a sufficiently large impulse, however, a thermoacoustic system can reach a stable oscillating state even when the steady state is also stable. A nonlinear analysis is required to predict the existence of this oscillating state. Continuation methods are often used for this but they are computationally expensive. In this paper, an acoustic network code called LOTAN is used to obtain the steady and the oscillating solutions for a horizontal Rijke tube. The heat release is modelled as a nonlinear function of the mass flow rate. Several test cases from the literature are analysed in order to investigate the effect of various nonlinear terms in the flame model. The results agree well with the literature, showing that LOTAN can be used to map the steady and oscillating solutions as a function of the control parameters. Furthermore, the nature of the bifurcation between steady and oscillating states can be predicted directly from the nonlinear terms inside the flame model. Copyright © 2012 by ASME.

Facilitated ion-transfer of sodium cation by (anthraquinone-1-yloxy) methane-15-crown-5 across the water/1,2-dichloroethane microinterface

The transfer of sodium cation facilitated by (anthraquinone-1-yloxy) methane-15-crown-5(L) has been investigated at the water/1,2-dichloroethane microinterface supported at the tip of a micropipette. The diffusion coefficient of (anthraquinone-1-yloxy) methane-15-crown-5 obtained was (3.42 +/- 0.20) x 10(-6) cm(2) s(-1). The steady-state voltammograms were observed for forward and backward scans due to sodium ion transfer facilitated by L with 1:1 stoichiometry. The mechanism corresponded to an interfacial complexation (TIC) and interfacial dissociation (TID) process. The association constant was calculated to be log beta(o) = 11.08 +/- 0.03 in the DCE phase. The association constant of other alkali metals (Li+, K+, Rb+) were also obtained.

Alkali metal ions transfer across a water/1,2-dichloroethane interface facilitated by a novel monoaza-B15C5 derivative

In this paper, a novel monoaza-B15C5 derivative, N-(2-tosylamino)-isopentyl-monoaza-15-crown-5 (L), is used as an ionophore to facilitate alkali metal cations transfer across a water/1,2-dichloroethane (W/DCE) interface. Well-defined voltammetric behaviors are observed at the polarized W/DCE interfaces supported at micro- and nano-pipets except Cs+. The diffusion coefficient of this ionophore in the DCE phase is calculated to be equal to (3.3+/-0.2) x 10(-6) cm(2) s(-1). The experimental results indicate that a 1:1 (metal: ionophore) complex is formed at the interface with a TIC/TID mechanism. The selectivity of this ionophore towards alkali ions follows the sequence Na+ > Li+ > K+ > Rb+ > Cs+. The logarithm of the association constants (log beta(1)(0)) of the LiL+, NaL+, KL+ and RbL+ complexes in the DCE phase are calculated to be 10.6, 11.6, 9.0 and 7.1, respectively. The kinetic parameters are determined by steady-state voltammograms using nanopipets. The standard rate constants (k(0)) for Li+, Na+, K+ and Rb+ transfers facilitated by L are 0.54+/-0.05, 0.63+/-0.09, 0.51+/-0.04 and 0.46+/-0.06 cm s(-1), respectively. The pH values of aqueous solution have little effect on the electrochemical behaviors of these facilitated processes. The results predicate that this new type of ionophore might be useful to fabricate electrochemical sensor of sodium ion.

Systematic investigation of alkali metal ion transfer across the micro- and nano-water/1,2-dichloroethane interfaces facilitated by dibenzo-18-crown-6

Facilitated alkali metal ion (M+= Li+, Na+, K+, Rb+, and Cs+) transfers across the micro- and nano-water/1,2-dichloroethane (W/DCE) interfaces supported at the tips of micro- and nanopipets by dibenzo-18-crown-6 (DB18C6) have been investigated systematically using cyclic voltammetry. The theory developed by Matsuda et al. was applied to estimate the association constants of DB18C6 and M+ in the DCE phase based on the experimental voltammetric results. The kinetic measurements for alkali metal ion transfer across the W/DCE interface facilitated by DB18C6 were conducted using nanopipets or-submicropipets, and the standard rate constants (k(0)) were evaluated by analysis of the experimental voltammetric data. They increase in the following order: k(Cs+)(0) < k(Li+)(0) < k(Rb+)(0) < k(Na+)(0) < k(K+)(0), which is in accordance with their association constants except Cs+ and Li+.

Voltammetric study of the sodium ion transfer across micro-water/1,2-dichloroethane interface facilitated by terminal-vinyl liquid crystal crown ether

Sodium ion transfer across micro-water/1,2-dichloroethane (DCE) interface facilitated by a novel ionophore, terminal-vinyl liquid crystal crown ether (LCCE) was studied by cyclic voltammetry. LCCEs have potential applications because of their physicochemical properties and the utilization of crown ethers as selective ionophoric units in other functionalized compounds are interesting. Host-guest-type behavior for such compounds in the liquid-crystalline state is studied. The experimental results suggest that the transfer of the sodium ion facilitated by LCCE was controlled by diffusion of LCCE from bulk solution of DCE to the interface. The diffusion coefficient of LCCE in DCE was calculated to be equal to (3.62 +/- 0.20) x 10(-6) cm(2)/s. Steady-state voltammograms are due to sodium ion transfer facilitated by the formation of 1: 1 metal (M)-LCCE complex at the interface and the mechanism tends to be transfer by interfacial complexation or dissociation (TIC or TID). The stability constant of the complex formed was determined to be log beta(o) = 5.5 in DCE phase. The influence of parameters such as concentration of sodium ion and concentration of LCCE on the sodium ion transfer was investigated.

Fabrication of nanometer-sized electrodes and tips for scanning electrochemical microscopy

A novel method for fabrication of nanometer-sized electrodes and tips suitable for scanning electrochemical microscopy (SECM) is reported. A fine etched Pt wire is coated with polyimide, which was produced by polymerization on the Pt surface initiated by heat. This method can prepare electrodes with effective radii varying from a few to hundreds of nanometers. Scanning electron microscopy, cyclic voltammetry, and SECM were used to characterize these electrodes. Well-defined steady-state voltammograms could be obtained in aqueous or in 1,2-dichloroethane solutions. Ibis method produced the nanoelectrodes with exposed Pit on the apex, and they can also be employed as the nanotips for SECM investigations. Different sizes of Pt nanotips made by this method were employed to evaluate the kinetics of the redox reaction of Ru(NH3)6(3+) on the surface of a large Pt electrode by SECM, and the standard rate constant kappa (o) of this system was calculated from the best fit of the SECM approach curve. This result is similar to the values obtained by analysis of the obtained voltammetric data.

Fabrication of agar-gel microelectrodes and their application in the study of ion transfer across the agar-water 1,2-dichloroethane interface

In this paper, we describe a simple procedure to make agar-gel microelectrodes by filling micropipettes. These microelectrodes were used to study K+ transfer across the agar-water \ 1,2-dichloroethane interface facilitated by dibenzo-18-crown-6 (DB18C6), and the transfer of tetraethylammonium (TEA(+)). The results observed were similar to those obtained at micro-liquid \ liquid interfaces. The effect of various amounts of agar in the aqueous phase was optimized and 3% agar was chosen based on the potential window and solidification time. The different shapes of micro-agar-gel electrodes were prepared in a similar way. The fabricated agar-gel microelectrodes obey the classical micro-disk steady-state current equation, which is different from the behavior of a normal micropipette filled with aqueous solution without silanization. (C) 2001 Elsevier Science B.V. All rights reserved.

The transfer of chloride ion across an anion exchange membrane

The transfer of chloride ions into a low resistance anion exchange membrane (AEM) was investigated by cyclic voltammetry (CV) and electrochemical impedance spectra. In all cases, concentration polarization of Cl- ions is exterior to the membrane. It controls the flux and produces the limiting currents: either steady state or transient (peak type) current. In CV experiments, when the size of the holes in the membrane was much smaller than the distance between membrane holes, the Cl- anion transfer showed steady state voltammetric behavior. Each hole in the membrane can be regarded as a microelectrode and the membrane was equivalent to a microelectrode array in this condition. When the hole in the membrane was large or the distance between membrane holes was small, the CV curve of the Cl- anion transfer across the membrane showed a peak shape, which was attributed to linear diffusion. In AC impedance measurement, the impedance spectrum of the membrane system was composed of two semicircles at low DC bias, corresponding to the bulk characteristics of the membrane and the kinetic process of ion transfer, respectively. The bulk membrane resistance increases with increasing DC bias and only one semicircle was observed at higher DC bias. The parameters related to kinetic and membrane properties were discussed.

Study on ferrocene derivatives diffusion dynamics in polymer electrolyte by solid-state voltammetry

The diffusion rates of seven ferrocene derivatives have been estimated in polyelectrolyte PEG . LiClO4 by using non-steady-state chronoamperometry. The D-app of ferrocene derivatives increases with temperature, and the dependency of D-app on temperature obeys the Arrhenius equation. The D-app of ferrocene derivatives decreases with increasing size of electroactive species. The Delta D-app values of D-T>Tm and D-T T-m in the polyelectrolyte. On the other hand, the diffusion behaviour of ferrocene derivatives is qualitatively analyzed by using cyclic voltammetry. Copyright (C) 1996 Elsevier Science Ltd

PREPARATION AND CHARACTERIZATION OF A MULTICYLINDER MICROELECTRODE COUPLED WITH A CONVENTIONAL GLASSY-CARBON ELECTRODE AND ITS APPLICATION TO THE DETECTION OF DOPAMINE

A multi-cylinder microelectrode coupled with a conventional glassy carbon disc electrode (MCM/GC) was prepared and characterized using cyclic voltammetry and chronoamperometry. It was demonstrated that in the same way as one observed a steady-state current at closely spaced microelectrodes when redox recycling takes place, the same effect can be obtained with the MCM/GC device. The experimental results obtained with K3Fe(CN)6 solutions were compared with a previously developed theory. Further, it was demonstrated that with a carbon fibre MCM/GC device, the voltammetric behaviour of dopamine is greatly improved by virtue of redox recycling, hence giving high sensitivity. The steady-state collection current was linearly related to dopamine concentration in the range 1 X 10(-4) to 5 x 10(-7) Mol l-1, and the detection limit was 2 x 10(-7) mol l-1. The influence of coexisting ascorbic acid was also investigated. This device was applied successfully in the determination of dopamine hydrochloride in pharmaceutical preparations.

Qualitative Modelling of Linear Networks in ECAD Applications

Lee M.H., Qualitative Modelling of Linear Networks in ECAD Applications, Expert Update, Vol. 3, Num. 2, pp23-32, BCS SGES, Summer 2000. Qualitative modeling of linear networks in ecad applications (1999) by M Lee Venue: Pages 146?152 of: Proceedings 13th international workshop on qualitative reasoning, QR ?99

PROPAGATION OF SONIC BOOMS THROUGH A REAL, STRATIFIED ATMOSPHERE

Sonic boom propagation in a quiet) stratified) lossy atmosphere is the subject of this dissertation. Two questions are considered in detail: (1) Does waveform freezing occur? (2) Are sonic booms shocks in steady state? Both assumptions have been invoked in the past to predict sonic boom waveforms at the ground. A very general form of the Burgers equation is derived and used as the model for the problem. The derivation begins with the basic conservation equations. The effects of nonlinearity) attenuation and dispersion due to multiple relaxations) viscosity) and heat conduction) geometrical spreading) and stratification of the medium are included. When the absorption and dispersion terms are neglected) an analytical solution is available. The analytical solution is used to answer the first question. Geometrical spreading and stratification of the medium are found to slow down the nonlinear distortion of finite-amplitude waves. In certain cases the distortion reaches an absolute limit) a phenomenon called waveform freezing. Judging by the maturity of the distortion mechanism, sonic booms generated by aircraft at 18 km altitude are not frozen when they reach the ground. On the other hand, judging by the approach of the waveform to its asymptotic shape, N waves generated by aircraft at 18 km altitude are frozen when they reach the ground. To answer the second question we solve the full Burgers equation and for this purpose develop a new computer code, THOR. The code is based on an algorithm by Lee and Hamilton (J. Acoust. Soc. Am. 97, 906-917, 1995) and has the novel feature that all its calculations are done in the time domain, including absorption and dispersion. Results from the code compare very well with analytical solutions. In a NASA exercise to compare sonic boom computer programs, THOR gave results that agree well with those of other participants and ran faster. We show that sonic booms are not steady state waves because they travel through a varying medium, suffer spreading, and fail to approximate step shocks closely enough. Although developed to predict sonic boom propagation, THOR can solve other problems for which the extended Burgers equation is a good propagation model.

Interaction of additive and quantization noises in digital PLLs

Phase-locked loops (PLLs) are a crucial component in modern communications systems. Comprising of a phase-detector, linear filter, and controllable oscillator, they are widely used in radio receivers to retrieve the information content from remote signals. As such, they are capable of signal demodulation, phase and carrier recovery, frequency synthesis, and clock synchronization. Continuous-time PLLs are a mature area of study, and have been covered in the literature since the early classical work by Viterbi [1] in the 1950s. With the rise of computing in recent decades, discrete-time digital PLLs (DPLLs) are a more recent discipline; most of the literature published dates from the 1990s onwards. Gardner [2] is a pioneer in this area. It is our aim in this work to address the difficulties encountered by Gardner [3] in his investigation of the DPLL output phase-jitter where additive noise to the input signal is combined with frequency quantization in the local oscillator. The model we use in our novel analysis of the system is also applicable to another of the cases looked at by Gardner, that is the DPLL with a delay element integrated in the loop. This gives us the opportunity to look at this system in more detail, our analysis providing some unique insights into the variance `dip' seen by Gardner in [3]. We initially provide background on the probability theory and stochastic processes. These branches of mathematics are the basis for the study of noisy analogue and digital PLLs. We give an overview of the classical analogue PLL theory as well as the background on both the digital PLL and circle map, referencing the model proposed by Teplinsky et al. [4, 5]. For our novel work, the case of the combined frequency quantization and noisy input from [3] is investigated first numerically, and then analytically as a Markov chain via its Chapman-Kolmogorov equation. The resulting delay equation for the steady-state jitter distribution is treated using two separate asymptotic analyses to obtain approximate solutions. It is shown how the variance obtained in each case matches well to the numerical results. Other properties of the output jitter, such as the mean, are also investigated. In this way, we arrive at a more complete understanding of the interaction between quantization and input noise in the first order DPLL than is possible using simulation alone. We also do an asymptotic analysis of a particular case of the noisy first-order DPLL with delay, previously investigated by Gardner [3]. We show a unique feature of the simulation results, namely the variance `dip' seen for certain levels of input noise, is explained by this analysis. Finally, we look at the second-order DPLL with additive noise, using numerical simulations to see the effects of low levels of noise on the limit cycles. We show how these effects are similar to those seen in the noise-free loop with non-zero initial conditions.

Thin-zone TAP reactor as a basis of �state-by-state transient screening

Thin-zone TAP reactor is presented as a basis of the new state-by-state transient screening approach which has been proposed by the authors for non-steady-state kinetic characterization of industrial catalysts. The general thin-zone TAP reactor model is described, and its mathematical status is justified analytically. It is shown that this model provides high enough accuracy to be applicable in the wide conversion interval (up to 90%), which is an important advantage of this approach compared with the traditional differential reactor.

Charge-state distribution and Doppler effect in an expanding photoionized plasma.

The charge state distributions of Fe, Na, and F are determined in a photoionized laboratory plasma using high resolution x-ray spectroscopy. Independent measurements of the density and radiation flux indicate unprecedented values for the ionization parameter ���¾=20 25 erg cm s-1 under near steady-state conditions. Line opacities are well fitted by a curve-of-growth analysis which includes the effects of velocity gradients in a one-dimensional expanding plasma. First comparisons of the measured charge state distributions with x-ray photoionization models show reasonable agreement.