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  • 1
    Electronic Resource
    Electronic Resource
    An Electrochemical Mechanism for the Voltammetric Oxidation of Methanol and Its Relationship with Period-Doubling Bifurcations (1994)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 98 (1994), S. 12768-12775 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/j100099a047
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  • 2
    Electronic Resource
    Electronic Resource
    Superstable nonequilibrium states (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 3220-3226 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Relaxation times were measured from the decay to period-one attractors, a period-two attractor, and a period-three attractor in two reaction processes: the voltammetric oxidations of ethanol and 1-propanol. The results provide strong evidence that a periodic state that can undergo a subharmonic bifurcation is most stable near the point where the relaxation changes from a monotone to an alternating approach. The relation between the experimental results and theory is discussed and it is concluded that the reaction processes are in what is called the strongly contracting limit. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.468632
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  • 3
    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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  • 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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  • 5
    Electronic Resource
    Electronic Resource
    Mixed-mode oscillations in an electrochemical system. I. A Farey sequence which does not occur on a torus (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 813-821 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We analyze measurements of an oscillatory current in an electrochemical process in which copper dissolves into phosphoric acid from a rotating-disk electrode. The focus is on a set of states in which each member consists of a different combination of large and small oscillations (mixed-mode oscillations). This set of mixed-mode oscillations is shown to constitute a Farey sequence, i.e., a periodic sequence for which a one-to-one correspondence exists with an ordered sequence of rational numbers. Plots of a measured quantity known as the "firing number'' are presented which reveal a structure that is similar to a "devil's staircase.'' The states surrounding the mixed-mode oscillations are analyzed by examining one-dimensional maps, surfaces of section, and phase portraits constructed from experimental data. This analysis shows that the Farey sequence of these mixed-mode oscillations is of a different nature than the Farey sequences associated with phase locking on a torus.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456106
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  • 6
    Electronic Resource
    Electronic Resource
    Mixed-mode oscillations in an electrochemical system. II. A periodic–chaotic sequence (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 822-828 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We describe a sequence of alternating periodic and chaotic behaviors that occur in the anodic dissolution of copper from a rotating disk in phosphoric acid. Each dynamical state of the sequence possesses a different combination of large and small amplitude oscillations (mixed-mode oscillations). The sequence is generated by incrementing either the potential or rotation speed of the copper-disk electrode. We find that chaotic regimes are linked to periodic regimes through tangent and period-doubling bifurcations. Measured waveforms of the chaotic mixed-mode oscillations can appear as mixtures of the waveforms of the adjacent periodic states. Phase portraits and one-dimensional maps are used to characterize a transition to chaotic mixed-mode oscillations from small amplitude chaotic oscillations. A brief comparison is made with the sequences of mixed-mode oscillations found in the Belousov–Zhabotinski reaction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456107
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  • 7
    Electronic Resource
    Electronic Resource
    An experimental investigation of periodic and chaotic electrochemical oscillations in the anodic dissolution of copper in phosphoric acid (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 4312-4319 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The response of the current to an applied potential was monitored in an open electrochemical system consisting of a rotating copper disk as the working electrode, a calomel reference electrode, and a platinum counter electrode, all of which were in contact with a solution of 85% phosphoric acid. In addition to stable stationary states, the applied potential induced oscillatory states which were either periodic or chaotic. Transitions from a stationary state to sustained oscillations were found to take place either through a Hopf bifurcation or by way of a mechanism that gives rise to states possessing complex combinations of small and large amplitude oscillations (mixed-mode oscillations). Within the parameter ranges for which sustained oscillations occurred, we discovered sequences of period doubling bifurcations. Aperiodic oscillations were observed just beyond the limit at which a sequence terminated. Phase trajectories were constructed from time-series data for these aperiodic states from which we produced one-humped, one-dimensional maps. A trajectory was also constructed that closely resembled a homoclinic orbit. Mixed-mode oscillations were found which have the same properties as those previously observed in the Belousov–Zhabotinskii reaction. The production of copper was observed in this electrochemical system which suggests that the reaction of disproportionality may be part of a feedback mechanism that is responsible for the complex dynamical behavior.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453790
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  • 8
    Electronic Resource
    Electronic Resource
    Efficiency of a combustion reaction in power production (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 2730-2734 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We analyze a thermal engine in which the source of heat is the combustion reaction CH4+2O2→CO2+2H2O. The efficiency of the thermal engine is defined as the ratio of the power output of the engine to the power input. We compare the efficiency in two modes of operation, one in which the input and output of chemical species are constants and one in which their corresponding fluxes have an imposed oscillatory component of a given amplitude and frequency. The ratio of efficiency in the oscillatory mode to the stationary flux mode can be as high as 1.3 for an amplitude of variation of the input and output fluxes plus or minus 40% of the stationary value. At low amplitudes of variation (10%), a single peak is present in a plot of the ratio of efficiency vs frequency of the fluxes. For higher amplitudes there are two peaks in that plot. One peak is associated with a response of the system that has the same period as the fluxes and the other occurs in a frequency range for which the periodic response is twice that of the perturbation. We calculate plots of the oscillatory output flux and the power output divided by that flux, which is an analog of a thermodynamic force, as a function of time, to show the importance of both resonance effects and the phase relation between the flux and the thermodynamic force in determining the ratio of efficiency.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454003
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  • 9
    Electronic Resource
    Electronic Resource
    Transition to Soret-driven convection in a system with nearly impermeable boundaries (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 1467-1474 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The transition to Soret-driven convection in a binary fluid located in a system with nearly impermeable boundaries is analyzed. An expansion is carried out around the critical conduction state in terms of the Biot number, the ratio of the solute diffusivity in the material composing the boundaries to the solute diffusivity in the binary fluid. At a large enough separation ratio three spatial convective structures, rolls, squares, and hexagons, can arise through a supercritical bifurcation and each of these structures is stable with respect to disturbances that possess wave vectors coincident to those of the steady solutions. However, it is shown that only squares are stable with respect to disturbances with wave vectors pointed in an arbitrary direction. The convective contributions to the heat flux and a concentration flux are calculated for each of the three spatial structures and they are found to be largest for squares. This result is in agreement with a stated relative stability criterion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857324
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  • 10
    Electronic Resource
    Electronic Resource
    Soret-driven convection coupled to the morphology of a solid–liquid interface (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 1597-1606 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The importance of Soret-driven convection in solidification processes is illustrated through an analysis of the coupling between convective currents and the deformations in a solid–liquid interface. The interface appears on freezing an upper portion of a layer of a dilute binary fluid. The presence of the interface and the amount of the solid strongly affect the stability properties of the liquid mixture and, in turn, the state of the liquid determines the patterns formed on the interface. Marginal stability curves are constructed by plotting the critical Rayleigh number and the critical wave number against the thickness of the solid layer. At small values of a positive separation ratio, increases in the thickness of the solid layer are found to have a destabilizing effect, the static state becomes unstable at smaller values of the Rayleigh number, whereas at larger values for the separation ratio this effect disappears. As the separation ratio is increased, a change of slope at zero thickness in the solid layer, from negative to positive, occurs in the plots of the critical wave number. For the case of a sufficiently large separation ratio, a weakly nonlinear analysis leads to the prediction of a bifurcation diagram that is characterized by two regions of bistability. A stable stationary convective structure consisting of down-hexagons appears through a subcritical bifurcation and for a small range of Rayleigh numbers coexists with the static state. Squares become stable at higher Rayleigh numbers and for a small parameter range coexist with down-hexagons. These stationary structures, down-hexagons and squares, are imprinted as patterns on the solid–liquid interface through the action of the convective currents. It is deduced that down-hexagons appear as a result of the coupling of the convective motion in the melt with the deformations in the interface and do not occur in the absence of solidification.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857567
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