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  • 1985-1989  (44)
  • 1950-1954  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Explicit solutions of normal form of driven oscillatory systems (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 6538-6543 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider an oscillatory dissipative system driven by external sinusoidal perturbations of given amplitude Q and frequency ω. The kinetic equations are transformed to normal form and solved for small Q, near a Hopf bifurcation to oscillations in the autonomous system, for ratios ωn to the autonomous frequency of irrational so that the response of the system is quasiperiodic. The system is assumed to have either two variables or is adequately described by two variables near the bifurcation, and we obtain explicit solutions for this general case. The equations show interesting effects of external perturbations on limit cycles, both stable and unstable. Next we treat a specific model (Brusselator) and show by comparison with results of numerical integration that the theory predicts well the shape of the perturbed limit cycle, its variation with changes in constraints and parameters, and the point of transition from quasiperiodic to periodic response.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453437
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  • 2
    Electronic Resource
    Electronic Resource
    Effects of periodic perturbations on the oscillatory combustion of acetaldehyde (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 868-878 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Periodic perturbations are applied to the input rates of acetaldehyde and oxygen, one at a time, in the combustion of acetaldehyde in a CSTR. We measure periodic responses in five entrainment bands as we vary the frequency and amplitude of the external periodic perturbation. Outside of entrainment bands we find quasiperiodic responses. Next-phase maps of the experimental results are constructed in real time and used in the observation and interpretation of entrainment and quasiperiodic behavior. Within the fundamental entrainment band, we measure critical slowing down and enhancement of the response amplitude. As the bath temperature is increased, so that the oscillatory system approaches a Hopf bifurcation, we observe an increase in the amplitude enhancement. The predictions of a five-variable thermokinetic model agree with the experimental results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.451242
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Theory of Ostwald ripening for open systems (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 4710-4714 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Diffusion-controlled coarsening (Ostwald ripening) of a precipitate is analyzed for the case of an open system, immersed in a reservoir of constant solute concentration. Equivalence of the evolution of such open systems and closed systems studied previously is established in the limit of infinite systems. The cause of this equivalence is screening of the bulk of the system from the reservoir by diffusive interactions between the precipitated particles. The applicability to large, but finite systems is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.448995
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  • 4
    Electronic Resource
    Electronic Resource
    Effects of time delay in rate processes (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 6489-6503 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Time delay processes in chemical kinetics occur naturally and can be imposed by means of a delayed feedback. We study the temporal evolution of homogeneous chemical reaction mechanisms (the autonomous system) describable by ordinary differential equations subjected to an imposed time delay, a delayed feedback. A natural delay process can be decomposed into analogous components. At short delays the delayed feedback is shown to stabilize different types of unstable stationary states of the autonomous systems, as well as induce bistability in a monostable system. At longer delays transitions into chaos are predicted. First we study the chaotic response of autonomous bistable systems which support only stationary states. A recipe for finding chaos is given. Chaos occurs for a small parameter range in which the delayed feedback repeatedly reinjects trajectories into the neighborhood of one of the marginally stable points of the autonomous system. Secondly, we consider the imposition of a delayed feedback to a system in which periodic oscillations occur and show this leads to both chaos and hyperchaos when memory effects in the delay cause the system to be reinjected into the neighborhood of a saddle-focus point. The examples studied in detail are thermo-illuminated chemical reactions, but we also consider the applicability of our results to reactions in continuously stirred tank reactors and biochemical processes. The results of this study show that natural time delays can regulate a wide range of dynamical behavior in biochemical processes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.451429
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Reduction of dissipation in a thermal engine by means of periodic changes of external constraintsa) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 82 (1985), S. 2453-2456 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider a thermal engine driven by chemical reactions, which take place in a continuous flow, stirred tank reactor fitted with a movable piston. Work can be produced by means of a heat engine coupled to the products and to an external heat bath, and by the piston. Two modes of operation are compared, each with fixed input rate of chemicals: one with periodic variation of an external constraint [mode (b)], in which we vary the external pressure, and one without such variation [mode (a)]. We derive equations for the total power output in each of the two modes. The power output in mode (b) can be larger than that of mode (a) for the same chemical throughput and for the same average value of the external pressure. For a particularly simple case it is shown that the total power output in mode (b) is larger than that in (a) if work is done by the piston. At the same time the entropy production is decreased and the efficiency is increased. The possibility of an increased power output is due to the proper control of the relative phase of the externally varied constraint and its conjugate variable, the external pressure and the volume. This control is achieved by the coupling of nonlinear kinetics to the externally varied constraint. Details of specific mechanisms and the occurrence of resonance phenomena are presented in the following article.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.448289
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  • 6
    Electronic Resource
    Electronic Resource
    Effects of two periodic perturbations on the oscillatory combustion of acetaldehyde (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 879-886 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Periodic perturbations are applied to the input rates of acetaldehyde and oxygen simultaneously in the combustion of acetaldehyde in a CSTR. With the two perturbations at the same frequency, we measure bistability in entrainment and hysteresis as a function of the phase shift between the two perturbations. The application of a perturbation in the flowrate of one reactant to the system already entrained to a perturbation of the flowrate of the second reactant can cause the system: to become quasiperiodic in both perturbations; to become entrained to both perturbations; to remain entrained, but not phase locked, to the first perturbation; or to become quasiperiodic in the first perturbation but entrained to the second perturbation. We measure the effects of frequency modulated and amplitude modulated acetaldehyde flowrate perturbations; the results compare well with predictions made by a five-variable thermokinetic model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.451243
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  • 7
    Electronic Resource
    Electronic Resource
    Monte Carlo study of a model of diffusion-controlled reactions (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 3857-3864 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Diffusion-controlled reactions between solute particles and immobile spherical sinks are studied, using the Monte Carlo method to perform averages over sink configurations. The average steady-state solute concentration profile c¯(r) in a locally perturbed solution is determined for sink volume fractions φ≤0.3, by numerically solving the diffusion equation in the monopolar+dipolar approximation of diffusive couplings between the sinks. At low volume fractions the analytical result c¯(r)∝r−1 exp(−r/λ), with the screening length λ∝φ−1/2, is recovered, whereas for φ(approximately-greater-than)0.1 significant deviations from this functional form are found. The Monte Carlo method is shown to be most accurate and efficient in the region 10−3(approximately-less-than)φ(approximately-less-than)10−1 in which (a) a system of only 25 sinks suffices, and (b) the monopolar approximation alone is sufficiently accurate. In this regime the reaction rate coefficient calculated numerically is found to be in good agreement with previous analytical theories.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.450805
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  • 8
    Electronic Resource
    Electronic Resource
    Propagation of a chemical pulse in an illuminated thermochemical bistable system (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 1492-1499 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Propagating chemical pulses are observed in the illuminated dimerization reaction of S2O6F2 when this bistable system is suitably perturbed. The dependence of the speed of propagation on incident laser power and the temporal evolution of the absorption profile along the laser beam are measured. The results compare well with calculations based on a previously developed model. The propagating chemical pulse is compared to chemical waves in an excitable medium.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.450495
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  • 9
    Electronic Resource
    Electronic Resource
    Stabilization of unstable states, relaxation, and critical slowing down in a bistable system (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 6234-6241 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The unstable branch of stationary states in an illuminated thermochemical bistable system is stabilized with an external feedback loop which does not otherwise alter the autonomous system. The technique allows the measurement of the entire set of stationary states available to the system. Trajectories of transition between branches of stationary states (relaxation) are investigated theoretically and experimentally. Critical slowing down in the speed of the trajectories is predicted and measured as the points of marginal stability are approached. Trajectories are observed to spread as they depart from the unstable stationary state and then to coalesce as they approach a stable stationary state. These results are obtained due to experimental spread in initial conditions and not from noise along the relaxation trajectory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449571
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  • 10
    Electronic Resource
    Electronic Resource
    Propagating and stationary structures in chemical reaction–diffusion systemsf a@f ) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 82 (1985), S. 113-122 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider propagating fronts and stationary patterns in chemical reaction–diffusion systems with nonlinear rate mechanisms maintained far from equilibrium. We study analytically and numerically the dependence on diffusion coefficients of the direction of propagation of the concentration profile which is obtained when two homogeneous steady states are placed in contact under identical constraints. We analyze the possible concentration profiles in a two-variable system with two stable stationary states for various values of diffusion coefficients and reaction time scales, and show that the direction of propagation depends on the diffusion coefficients. Finally, we show that a stationary pattern can develop behind the propagating concentration profile, a process for which there is some experimental evidence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.448784
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