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  • 1
    Electronic Resource
    Electronic Resource
    The modeling of mixed-mode and chaotic oscillations in electrochemical systems (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 7797-7813 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We develop a simple but general three-variable model skeleton to describe complex nonlinear behaviors in electrochemical processes taking place at either a hanging mercury drop electrode (HMDE) or a rotating-disk electrode (RDE). We apply our formalism to the reduction of indium(III) at a HMDE in the presence of thiocyanate, a reaction known to exhibit complex mixed-mode and chaotic oscillations. Besides the role of the negative Faradaic impedance in destabilizing the electrochemical system, mass transport appears to be crucial as the model explicitly takes into account, in a truncated fashion, the time-dependent relaxation of the concentration profile. We study in detail the nonlinear dynamic behavior of our model of the indium/thiocyanate system and a RDE model. The models support mixed-mode sequences that appear either as incomplete Farey sequences or as periodic-chaotic sequences, which we discuss in terms of an incomplete homoclinic scenario whose definition and properties are worked out here. Our results compare very well to the experimental observations in the indium/thiocyanate system and the electrodissolution of a rotating copper disk in phosphoric acid. This satisfactory agreement strongly suggests that diffusion relaxation is an important phenomenon in electrochemical oscillations and could be the essential third variable in many dynamical electrochemical processes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.462377
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  • 2
    Electronic Resource
    Electronic Resource
    Influence of vibrational frequency mismatch on phase-space bottlenecks to intramolecular energy redistribution and molecular fragmentation (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 1775-1789 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report studies of classical models of unimolecular fragmentation of van der Waals complexes using the methodologies of Hamiltonian mappings and flows. The effect of frequency mismatch between harmonic molecular vibrations of a host molecule and the van der Waals bond-stretching motion is shown to dominate vibrational energy redistribution and fragmentation. Our results show that a crossover exists when the frequency mismatch is increased from a stochastic regime of resonances between the nonlinear oscillators to a regular regime where the system behaves like an integrable system. Our model systems include both collinear and T-shaped oscillator displacement configurations, as well as a many-oscillator system that included both classes of motions. Oscillator parameter ranges were used that approximate vibrations in C6H6⋅He and C6H6⋅Ar van der Waals complexes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458059
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  • 3
    Electronic Resource
    Electronic Resource
    Exact quantization of the scattering from a classically chaotic repellor (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 2255-2262 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The S matrix for the scattering of a point particle from three hard discs fixed on a plane is calculated exactly using Green's theorem. The S matrix is obtained explicitly from S=I−iCM−1D, where the matrix M describes the multiple scattering between the three discs and the matrices C and D describe the free propagation from the edges of the three discs to large distances. The scattering resonances are located in the complex wave number plane as the zeros of the determinant of the matrix M, and their symmetry representations are determined. The results of this calculation are compared with the results obtained from the semiclassical approximation described in the preceding paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456019
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  • 4
    Electronic Resource
    Electronic Resource
    Erratum: Semiclassical quantization of the scattering from a classically chaotic repellor [J. Chem. Phys. 90, 2242 (1989)] (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 3279-3279 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457672
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  • 5
    Electronic Resource
    Electronic Resource
    On using shaped light pulses to control the selectivity of product formation in a chemical reaction: An application to a multiple level system (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 1670-1680 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A previously reported method for shaping electromagnetic field pulses to achieve chemical selectivity is extended and applied to a simple multiple level model system. The pulse shaping approach is based on optimal control theory, where both the time-dependent Schrödinger equation and the constant pulse energy are used as constraints on the variational scheme. A conjugate gradient direction method is used to direct the convergence of the iterative process used to calculate the optimum pulse shape. The method is applied to a five-level system interacting with an optical (laser) field. Results demonstrating selectivity and stability are compared to those of other recent related investigations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459680
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  • 6
    Electronic Resource
    Electronic Resource
    Erratum: Scattering from a classically chaotic repellor [J. Chem. Phys. 90, 2225 (1989)] (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 3279-3279 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457669
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  • 7
    Electronic Resource
    Electronic Resource
    Scattering from a classically chaotic repellor (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 2225-2241 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report a study of the classical scattering of a point particle from three hard circular discs in a plane, which we propose as a model of an idealized unimolecular fragmentation. The system possesses a fractal and chaotic metastable classical state. On the basis of a coding of the system dynamics, we develop a method to construct the invariant probability measure and to calculate the particle escape rate, the Hausdorff dimension, the Kolmogorov–Sinai entropy per unit time and the mean largest Lyapunov exponent of the repellor. The relations between these characteristics of the system dynamics are discussed. In particular, we show that, in general, chaos inhibits escaping from the metastable state. The theory is compared with numerical simulations. We also introduce the classical tools necessary for the semiclassical quantization of the dynamics; the latter is discussed in the following paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456017
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  • 8
    Electronic Resource
    Electronic Resource
    Erratum: Exact quantization of the scattering from a classically chaotic repellor [J. Chem. Phys. 90, 2255 (1989)] (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 3280-3280 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457670
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  • 9
    Electronic Resource
    Electronic Resource
    Semiclassical quantization of the scattering from a classically chaotic repellor (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 2242-2254 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The scattering of a point particle from three hard discs in a plane is studied in the semiclassical approximation, using the Gutzwiller trace formula. Using a previously introduced coding of the classical dynamics, the needed summation over the classical periodic orbits is performed. The trace function is then given in terms of Ruelle zeta functions. A semiclassical limit upper bound is obtained on the lifetimes of the scattering resonances. This bound is larger than the classical lifetime when the classical repellor is chaotic but coincides with it when the repellor is periodic. We conclude that classical chaos dramatically influences the lifetimes of the scattering resonances. Our upper bound for the resonance lifetime is compared with the results of numerical calculation of the full quantum dynamics. The distribution of the imaginary parts of the complex wave numbers of the resonances is also calculated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456018
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  • 10
    Electronic Resource
    Electronic Resource
    Measurement of the instability rate of a far-from-equilibrium steady state at an infinite period bifurcation (1990)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 94 (1990), S. 1-3 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/j100364a001
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