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Digitale Medien

Slowing down near the critical point in optically bistable ZnSe (1992)

Wolff, Anita N. ; Ross, J. ; Harding, Robert H.

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 96 (1992), S. 1602-1608

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ISSN: 1089-7690

Quelle: AIP Digital Archive

Thema: Physik , Chemie und Pharmazie

Notizen: We measure relaxation rates near the critical point and the left hysteresis limit of an optically bistable system, a ZnSe interference filter. Our ZnSe system has an inhomogeneous geometry where a long, narrow illuminated region has boundaries at a temperature near and below that of the lower state. We determine the critical angle, the angle of incidence of light at which the hysteresis limits coalesce to form a critical point, and perturb the system by changing the input power beyond the critical point. For incidence angles equal to or slightly greater than the critical angle, we find that relaxation rates increase exponentially as the critical point is approached. The critical exponents for perturbations which increase the input power beyond the critical point are greater than those for perturbations which decrease the input power. In either case, the critical exponents increase as the angle of incidence approaches the critical angle. When the hysteresis region is large, we find slowing down near the left hysteresis limit in accordance with our calculations based on a one-dimensional inhomogeneous model.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.462144

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Theory and experiments on the effects of perturbations on nonlinear chemical systems: Generation of multiple attractors and efficiency (1990)

Hjelmfelt, Allen ; Harding, Robert H. ; Tsujimoto, Kim K. ; [weitere]

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 92 (1990), S. 3559-3568

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ISSN: 1089-7690

Quelle: AIP Digital Archive

Thema: Physik , Chemie und Pharmazie

Notizen: Periodic perturbations are applied to the input fluxes of reactants in a system which exhibits autonomous oscillations, the combustion of acetaldehyde (ACH) and oxygen, and a system which exhibits damped oscillations, the combustion of methane and oxygen. The ACH system is studied by experiments and numerical analysis and the methane system is studied by numerical analysis. The periodic perturbations are in the form of a two-term Fourier series. Such perturbations may generate multiple attractors, which are either periodic or chaotic. We discuss two types of bistable responses: a new phase bistability, in which a subharmonic frequency is added to a sinusoidal perturbation at different phases relative to the periodic response; and jump phenomena, in which the resonant frequency of a nonlinear oscillator depends on the amplitude of the periodic perturbation. Both the ACH and the methane systems confirm the phase bistability. The additional complex behavior of bistability due to jump phenomena is seen only in calculations in the methane system. In both types of bistability a hysteresis loop is formed as we vary the form of the periodic perturbation. In the methane system, we find period doubling to chaos occuring on one branch of the hysteresis loop while the other branch remains periodic. The methane system has been studied in the context of the efficiency of power production. We calculate the efficiency corresponding to each bistable attractor and find one branch of each pair to be the more efficient mode of operation. In the case of the coexisting periodic and chaotic attractors the chaotic attractor is the more efficient mode of operation.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.457865

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Comparison of theory and experiment on relative stability in a bistable (ZnSe) system (1990)

Harding, Robert H. ; Paoli, Paolo ; Ross, John

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 92 (1990), S. 1947-1955

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ISSN: 1089-7690

Quelle: AIP Digital Archive

Thema: Physik , Chemie und Pharmazie

Notizen: We compare theory and experiments on relative stability of the two stable stationary states in optically bistable ZnSe interference filters. We examine the equistability predictions of the master equation, the Fokker–Planck equation, and a deterministic analysis. For this effectively one-variable system there exists a potential for each of these descriptions. We derive a master and Fokker–Planck equation for the fluctuations in temperature expected in our system and find that the three theoretical potentials differ significantly for homogeneous geometries of the system, but the stochastic predictions agree with the deterministic equistability point for inhomogeneous systems. We also examine the effect of external noise, which is independent of the state variable, and find that a very small amount of noise reduces the equistability prediction of the homogeneous master and Fokker–Planck equations to that of the deterministic potential. Noise in the constraints (such as light intensity) results in a new effective potential.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.458025

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4

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The relation of fluxes and forces to work in nonequilibrium systems (1991)

Ross, John ; Harding, Robert H. ; Wolff, Anita N. ; [weitere]

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 95 (1991), S. 5206-5211

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ISSN: 1089-7690

Quelle: AIP Digital Archive

Thema: Physik , Chemie und Pharmazie

Notizen: Prior work has shown that an excess work is necessary to displace a chemical or physical system from a stationary state, and this excess work determines the stationary distribution of a stochastic birth–death master equation. We derive the augmentation of this master equation for a one-variable system in the presence of external noise. When this noise is much larger than internal noise, but still small compared to macroscopic averages, then the stationary distribution reduces to a form suggested by Landau and Schlögl, which is the integral of the flux of the deterministic kinetic equation. A similar result was obtained on the basis of an assumed Fokker–Planck equation. Hence, in the presence of external forces exceeding in intensity the internal fluctuations, fluxes are proportional to forces without linearization in concentrations.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.461689

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Experimental measurement of the relative stability of two stationary states in optically bistable ZnSe interference filters (1990)

Harding, Robert H. ; Ross, John

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 92 (1990), S. 1936-1946

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ISSN: 1089-7690

Quelle: AIP Digital Archive

Thema: Physik , Chemie und Pharmazie

Notizen: We report the first measurement of the relative stability of two stable stationary states in a bistable system, that of an optically bistable ZnSe interference filter. A thin ZnSe rectangle is illuminated and bounded by nonilluminated regions at room temperature. This geometry allows the observation of a boundary between the upper and lower stationary state. We describe the inhomogeneous experiments, discuss relative stability in such systems, and compare them with the relative stability of the related homogeneous system. The right marginal stability point of the hysteresis loop is marked by the appearance of the upper stationary state. The homogeneous left marginal stability point is determined by a measurement of the transient relaxation in our inhomogeneous experiment. At the constraint of illumination corresponding to equistability of the two stable stationary states, the upper state becomes unstable for inhomogeneous conditions. We find close agreement between our experiments and the predictions of deterministic physical kinetics. In an accompanying article we discuss the issue of the relative stability of bistable states with thermodynamic fluctuations for inhomogeneous conditions and homogeneous conditions with noise that is independent of the state variable.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.458024

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Digitale Medien

Symptoms of chaos in observed oscillations near a bifurcation with noise (1988)

Harding, Robert H. ; Ross, John

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 89 (1988), S. 4743-4751

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ISSN: 1089-7690

Quelle: AIP Digital Archive

Thema: Physik , Chemie und Pharmazie

Notizen: We examine an experimental transition from periodic to aperiodic and back to periodic dynamics in the combustion of acetaldehyde(ACH) in a continuous stirred tank reactor (CSTR) with power spectra, autocorrelation functions, phase portraits, Poincar´e sections, the Wolf–Swift–Swinney–Vastano (WSSV) method for determining the largest Lyapounov exponent, and the Grassberger–Procaccia (GP) method for determining correlation dimension. Each technique gives some indications of a transition to chaos, but there are discrepancies in that the largest Lyapounov exponent is positive but does not converge and the GP method results in a correlation dimension between one and two for two aperiodic data sets. We explore in instructive detail possible explanations for false indications of chaos by comparing our results with calculations on the Rössler chaotic attractor and the van der Pol periodic attractor modified to examine the effects of uneven point distribution and three types of experimental noise. An uneven distribution of points results in a decreased range of length scales for convergence and a larger required embedding dimension for the GP method, but does not explain our experimental results. Observation noise (a Gaussian noise added to each term in the time series but not entering in the equations of motion) and constraint shift (the motion relaxes to an attractor but a constraint changes monotonically during the course of measurement) added to a periodic attractor both result in a low length scale cutoff below which the attractor dimension does not converge with embedding dimension, and above which it converges to 1. Constraint variation noise (a Gaussian noise is added to each term in the time series and enters into the equations of motion as a stochastic perturbation) does yield correlation dimensions between 1 and 2. The experimental transition shows many similarities to a Hopf bifurcation found in another experiment on the same system and to a theoretical Hopf bifurcation with constraint variation noise. A modification of the WSSV Lyapounov exponent analysis for this experimental transition shows the random walk separation of trajectories expected for constraint variation noiseadded to the dynamics of a periodic attractor with a Hopf bifurcation. We therefore identify the experimental transition as an arc in constraint space which does not cross but is nearly tangent to a Hopf bifurcation set.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.455668

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7

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Optimization of kinetic and thermodynamic properties in irreversible open chemical and thermal engines (1989)

Hjelmfelt, Allen ; Harding, Robert H. ; Ross, John

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 91 (1989), S. 3677-3684

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ISSN: 1089-7690

Quelle: AIP Digital Archive

Thema: Physik , Chemie und Pharmazie

Notizen: Periodic variations of an external parameter or constraint of open chemical systems have been shown to induce changes in time averaged kinetic and thermodynamic quantities. We examine the effects of the analytic form of the periodic variation on the time averaged quantities and find the maximum changes obtainable through periodic variations. A variational procedure is proposed, based on a Fourier expansion of the form of the periodic perturbation, the laws of thermodynamics, conservation of matter, and the kinetics. The efficiency of power production in a combustion system is examined with this method in a numerical example. A unique maximum in the efficiency is found, with the gains achievable for more complex functions exceeding those for a sinusoidal perturbation. We interpret the changes in efficiency in terms of the magnitude of the response of the system (resonance) and phase shifts between the periodic perturbations and the response of the system. We illustrate the mechanisms of efficiency changes in this system with two examples; one in which the periodic perturbation affects the phase relations and one in which the periodic perturbation affects the magnitude of the response. Finally, we note that multiple attractors may coexist in this system for certain forms of the periodic perturbation, each with a distinct efficiency.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.456848

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Digitale Medien

Complex oscillations in the combustion of acetaldehyde (1988)

Harding, Robert H. ; Sevcikova, Hana ; Ross, John

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 89 (1988), S. 4737-4742

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ISSN: 1089-7690

Quelle: AIP Digital Archive

Thema: Physik , Chemie und Pharmazie

Notizen: Aperiodic dynamics are observed experimentally in the cool flame combustion region of acetaldehyde (ACH) in a continuous stirred tank reactor (CSTR). A gradual transition is seen, with variation of exit orifice size, from limit cycle oscillation to aperiodic variations in light emission, and then back to near periodic oscillations. We analyze this transition by calculating power spectra, autocorrelation functions, phase portraits, period distributions, and Poincaré sections. The variation in peak amplitude and peak-to-peak period of the temporal variations of light emission increases during the transition. There are many initial indications of a transition to chaos. However, after an in-depth analysis, given in the following article, we ascribe the transition to the presence of a Hopf bifurcation and noise: the path traced out in the constraint space by the change in exit orifice size is nearly tangent to a Hopf bifurcation set but does not cross this set.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.455667

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9

Digitale Medien

Catalytic cracking of alkylcyclohexanes: Modeling the reaction pathways and mechanisms (1997)

Watson, Beth A. ; Klein, Michael T. ; Harding, Robert H.

New York, NY : Wiley-Blackwell

International Journal of Chemical Kinetics 29 (1997), S. 545-560

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ISSN: 0538-8066

Schlagwort(e): Chemistry ; Physical Chemistry

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Chemie und Pharmazie

Notizen: The cracking reaction pathways and mechanisms of ethylcyclohexane and 1-cyclohexyloctane with a rare earth Y (REY) catalyst were studied. Experiments at 500°C indicated that the dominant reactions were ring opening with subsequent secondary cracking, cracking in the alkyl side chain, isomerization, and hydrogen transfer. A kinetic model of the catalytic cracking of 1-cyclohexyloctane was developed using a novel mechanism-based lumping scheme that exploits the chemical similarities within reaction families. The formal application of 17 reaction family matrices, which correspond to 13 reaction family classes, to the matrix representations of the reactants and derived products generated the model. The reaction family concept was further exploited to constrain the kinetics within each reaction family to follow a quantitative structure/reactivity Polanyi relationship. Ultimately, nine Polanyi relationship parameters and three coking/deactivation parameters were determined by optimizing the model fit to the experimental data. The resulting model correlations were excellent, as the overall parity between experimental and model values was yModel=-0.000470+0.986yExp with a correlation coefficient of 0.971. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet 29: 545-560, 1997.

Zusätzliches Material: 13 Ill.

Materialart: Digitale Medien

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