Residence Time Interval Research Articles

Modelling of JP-8 distributed combustion using a HyChem mechanism under gas turbine conditions

The critical advantages of liquid fuels in aviation over alternative energy carriers imply their dominance in the upcoming decades. The Mixture Temperature Controlled (MTC) combustion concept allows spatially homogeneous, efficient burning (distributed combustion) with low pollutant emission. MTC combustion of jet fuel JP-8 was investigated in an atmospheric burner, and the measured pollutant concentrations in the flue gas were reproduced using the Hybrid Chemistry (HyChem) approach employing Perfectly Stirred Reactor simulations. Using this robust approach comes with losing spatiotemporal characteristics if the mixture homogeneity assumption is globally valid. The effect of residence time and pressure under typical gas turbine operating conditions was investigated. Stable combustion was present above 3 ms residence time at pressures up the 60 bar, which was the upper limit of the investigated regime, while the lower residence time limit of stable combustion was 0.3 ms. The residence time interval of stable operation could be extended by applying flue gas recirculation. NO emission can be reduced by increasing the operating pressure, while the N2O production is dominant only up to 20 bar and in the 10–100 ms residence time range. CO emission vanishes above 10 ms residence time. Ultra-low emission operation requires >20 bar pressure and 10 ms residence time with distributed combustion, requiring larger combustion chambers for future jet engines.

Dynamical complexity of FitzHugh–Nagumo neuron model driven by Lévy noise and Gaussian white noise

In this paper, on the basis of information theory measures (statistical complexity and normalized Shannon entropy), the dynamical complexity of FitzHugh–Nagumo (FHN) neuron model under the co-excitation of Lévy noise and Gaussian white noise is studied. Because the potential function of the neuron system is asymmetric, we consider not only the total residence time interval of the system, but also the residence time interval of the left and right potential wells respectively. Here, we use Bandt–Pompe algorithm to calculate the three interval sequences, and obtain the statistical complexity and normalized Shannon entropy of the total system as well as the left and right potential wells. Finally, the effects of additive noise intensity, multiplicative noise intensity and system parameter on complexity of system are analyzed. We find that the total dynamical complexity of the system is obviously different from that of a single potential well. In addition, Gaussian white noise and Lévy noise have different effects on the complexity of the system.

On the asymptotic hyperstability of switched systems under integral-type feedback regulation Popovian constraints

This paper deals with the asymptotic hyperstability of switched time-varying dynamic systems involving switching actions among linear time-invariant parametrizations in the feed-forward loop for any feedback regulator controller potentially being also subject to switching through time while being within a class which satisfies a Popov-type integral inequality. Asymptotic hyperstability is proved to be achievable under very generic switching laws if at least one of the feed-forward parametrization possesses a strictly positive real transfer function, a minimum residence time interval is respected for each activation time interval of such a parametrization and a maximum allowable residence time interval is simultaneously maintained for all active parametrizations which are not positive real, if any. In the case where all the feed-forward parametrizations possess a common Lyapunov function, asymptotic hyperstability of the switched closed-loop system is achieved under arbitrary switching.

Flux distributions as robust diagnostics of stratosphere‐troposphere exchange

We perform the first analysis of stratosphere‐troposphere exchange in terms of distributions that partition the one‐way flux across the thermal tropopause according to stratospheric residence time τ and the regions where air enters and exits the stratosphere. These distributions robustly quantify one‐way flux without being rendered ill defined by the short‐τ eddy‐diffusive singularity. Diagnostics are computed with an idealized circulation model with topography only in the Northern Hemisphere (NH) run under perpetual NH winter conditions. Suitable integrations of the flux distribution are used to determine the stratospheric mean residence time and the mass fraction of the stratosphere in any given residence time interval. We find that the largest mass fraction is destined for isentropic cross‐tropopause transport, with one‐way fluxes that are sustained over a broad range of residence times. Air exiting the stratosphere in the winter hemisphere has significantly longer mean residence times than air exiting in the summer hemisphere because the winter hemisphere has a deeper circulation and stronger eddy diffusion. We also explore the sensitivity of the stratosphere‐troposphere exchange to changes in the circulation by increasing the amplitude of the topography. The resulting more vigorous residual mean circulation dominates over increased eddy diffusion, leading to decreased except for air exiting at high NH latitudes, for which increases. These findings underline that the flux distributions diagnose the integrated advective‐diffusive tropopause‐to‐tropopause transport and not merely advection by the residual mean circulation.

Non-Markovian stochastic resonance: Three-state model of ion channel gating

Stochastic resonance in single voltage-dependent ion channels is investigated within a three-state non-Markovian modeling of the ion channel conformational dynamics. In contrast to a two-state description one assumes the presence of an additional closed state for the ion channel which mimics the manifold of voltage-independent closed subconformations (inactivated "state"). The conformational transition into the open state occurs through a domain of voltage-dependent closed subconformations (closed "state"). At distinct variance with the standard two-state and also the three-state Markovian approach, the inactivated state is characterized by a broad, nonexponential probability distribution of corresponding residence times. The linear response to a periodic voltage signal is determined for arbitrary distributions of the channel's recovery times. Analytical results are obtained for the spectral amplification of the applied signal and the corresponding signal-to-noise ratio. Alternatively, these results are also derived by use of a corresponding two-state non-Markovian theory which is based on driven integral renewal equations [I. Goychuk and P. Hänggi, Phys. Rev. E 69, 021104 (2004)]. The non-Markovian features of stochastic resonance are studied for a power law distribution of the residence time intervals in the inactivated state which exhibits a large variance. A comparison with the case of biexponentially distributed residence times possessing the same mean value, i.e., the simplest non-Markovian two-state description, is also presented.

Rate processes with non-Markovian dynamical disorder

Rate processes with dynamical disorder are investigated within a simple framework provided by unidirectional electron transfer (ET) with fluctuating transfer rate. The rate fluctuations are assumed to be described by a non-Markovian stochastic jump process which reflects conformational dynamics of an electron transferring donor-acceptor molecular complex. A tractable analytical expression is obtained for the relaxation of the donor population (in the Laplace-transformed time domain) averaged over the stationary conformational fluctuations. The corresponding mean transfer time is also obtained in an analytical form. The case of two-state fluctuations is studied in detail for a model incorporating substate diffusion within one of the conformations. It is shown that an increase of the conformational diffusion time results in a gradual transition from the regime of fast modulation characterized by the averaged ET rate to the regime of quasistatic disorder. This transition occurs at the conformational mean residence time intervals fixed much less than the inverse of the corresponding ET rates. An explanation of this paradoxical effect is provided. Moreover, its presence is also manifested for the simplest, exactly solvable non-Markovian model with a biexponential distribution of the residence times in one of the conformations. The nontrivial conditions for this phenomenon to occur are found.

Fractional diffusion modeling of ion channel gating

An anomalous diffusion model for ion channel gating is put forward. This scheme is able to describe nonexponential, power-law-like distributions of residence time intervals in several types of ion channels. Our method presents a generalization of the discrete diffusion model by Millhauser, Salpeter, and Oswald [Proc. Natl. Acad. Sci. U.S.A. 85, 1503 (1988)] to the case of a continuous, anomalous slow conformational diffusion. The corresponding generalization is derived from a continuous-time random walk composed of nearest-neighbor jumps which in the scaling limit results in a fractional diffusion equation. The studied model contains three parameters only: the mean residence time, a characteristic time of conformational diffusion, and the index of subdiffusion. A tractable analytical expression for the characteristic function of the residence time distribution is obtained. In the limiting case of normal diffusion, our prior findings [Proc. Natl. Acad. Sci. U.S.A. 99, 3552 (2002)] are reproduced. Depending on the chosen parameters, the fractional diffusion model exhibits a very rich behavior of the residence time distribution with different characteristic time regimes. Moreover, the corresponding autocorrelation function of conductance fluctuations displays nontrivial power law features. Our theoretical model is in good agreement with experimental data for large conductance potassium ion channels.

Theory of non-Markovian stochastic resonance.

We consider a two-state model of non-Markovian stochastic resonance (SR) within the framework of the theory of renewal processes. Residence time intervals are assumed to be mutually independent and characterized by some arbitrary nonexponential residence time distributions which are modulated in time by an externally applied signal. Making use of a stochastic path integral approach we obtain general integral equations governing the evolution of conditional probabilities in the presence of an input signal. These equations generalize earlier integral renewal equations by Cox and others to the case of driving-induced nonstationarity. On the basis of these equations a response theory of two-state renewal processes is formulated beyond the linear response approximation. Moreover, a general expression for the linear response function is derived. The connection of the developed approach with the phenomenological theory of linear response for manifest non-Markovian SR put forward [I. Goychuk and P. Hänggi, Phys. Rev. Lett. 91, 070601 (2003)] is clarified and its range of validity is scrutinized. The theory is then applied to SR in symmetric non-Markovian systems and to the class of single ion channels possessing a fractal kinetics.

Hydrogenation reactions of iron/tin treated and acid-washed Morwell coal in a time-sampled autoclave

Liquefaction of iron/tin treated acid-washed Morwell coal has been studied in a time-sampled reactor which rapidly charges reactants into a preheated autoclave and samples its contents throughout the course of the reaction. A large increase in conversion at short residence times compared to that of untreated coal was observed, and almost 100% conversion was achieved for residence times greater than 30 min. The increased conversion was mainly to oil, whereas in conventional batch autoclaves the increase is mainly to asphaltenes. Strong evidence was obtained for the formation of a viscous product after 5 to 10 min of reaction; this viscous product made sampling unreliable and sometimes blocked the sampling lines completely. It decomposed after 10 to 20 min of reaction. The fate of the iron and tin additives was followed by 57Fe and 119Sn Mössbauer spectroscopy. Most of the iron was converted from Fe(III) oxyhydroxide to magnetite (Fe 3O 4) and troilite (FeS) during the residence time interval, 6 to 8 min, when the viscous product was present. The tin was reduced from its initial SnO 2. xH 2 O form but the reaction was much slower than that of iron. Acid-washing the Morwell coal increased the conversion at short reaction times in the time-sampled autoclave, as was observed earlier in batch autoclave studies.