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  • 1
    Electronic Resource
    Electronic Resource
    Projected dynamics: Analysis of a chemical reaction model (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 5528-5543 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The rate processes corresponding to barrier crossing dynamics in a symmetric double-well potential driven by a white-noise source are investigated. The rate kernels in the generalized phenomenological rate law describing the reaction involve time evolution through a projected Fokker–Planck operator. The spectral properties of the projected Fokker–Planck operator are studied, and the rate kernels are expressed in terms of the eigenvalues and eigenfunctions of this operator. The formal results are illustrated with numerical calculations. The results provide information on the nature of the generalized chemical rate law for fast processes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457556
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  • 2
    Electronic Resource
    Electronic Resource
    Reactive dynamics in a deterministic thermal bath (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 5602-5612 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A study of barrier crossing dynamics is presented for a simple two-degree-of-freedom system coupled to a Nosé–Hoover heat bath. The characteristics of the deterministic heat bath are found to give rise to a variety of rate processes. Examination of the microscopic dynamics indicates how bath fluctuations drive the reactive dynamics and gives insight into how different deterministic heat baths can be constructed to model specific bath fluctuation effects.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457563
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  • 3
    Electronic Resource
    Electronic Resource
    Transition rates in a bistable system driven by external dichotomous noise (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 7468-7477 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A study of dichotomous noise-induced transitions is presented for a simple one-dimensional system exhibiting deterministic bistability between two steady states. A phenomenological rate law for the kinetics of such transitions is derived and the corresponding rate coefficient is evaluated. Critical slowing down for such transitions is shown to be possible and an asymptotic scaling form for the rate coefficient is derived. Finally, memory effects and the breakdown of the phenomenological rate law due to the magnitude of the noise correlation time are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454311
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Bistable limit cycle oscillations in chemical systems. I. Basins of attraction (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 86 (1987), S. 3357-3365 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: When bistable oscillations occur in nonlinear chemical systems, the concentration space can be separated into regions that asymptotically tend to each of the oscillatory states. The structure of such basins of attraction is studied for Rössler's model of a far-from-equilibrium chemical system. Starting with a set of local pictures of the basins, their three-dimensional structure is deduced. The idea of a phase basin is introduced. For a multilooped limit cycle, the phase basin is the set of those initial phase points that tend to the same discrete phase of the cycle, defined in a plane that cuts the cycle transversely. The nature of such basins of attraction is important for studies of noise-induced transitions between coexisting limit cycles or loss of phase coherence in a single limit cycle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.451993
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  • 5
    Electronic Resource
    Electronic Resource
    Noise-induced transitions in an excitable system (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 4285-4298 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A numerical study of dichotomous noise-induced transitions is presented for an example of a two-dimensional excitable system exhibiting bistability between a limit cycle and a fixed point: the simple Oregonator model. The decay of the average population number in the fixed-point region is investigated for various noise correlation times and for two different initial system preparations. The mean first passage time taken to leave the fixed-point region is determined and is compared with analytical results obtained from a simple stochastic model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456809
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Phase transformation kinetics in finite inhomogeneously nucleated systems (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 7146-7152 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Phase transformation kinetics that occurs by a nucleation and growth process is investigated. A simple discrete space and time model is used for the dynamics and analytical results are obtained for the volume fraction of the material transformed for both finite systems and a special example of an inhomogeneously nucleated system. The theory is developed for two cases, initial nucleation, and continuous nucleation. The results are compared with simulations of the model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457330
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  • 7
    Electronic Resource
    Electronic Resource
    Bistable limit cycle oscillations in chemical systems. II. Mechanisms for noise-induced transitions (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 86 (1987), S. 3366-3372 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: External noise coupled to Rössler's model of a nonlinear chemical system is considered, and noise-induced transitions between coexisting three-looped limit cycles are studied. Two mechanisms account for these transitions. These are analogs of mechanisms which have been identified for the noise-induced transitions of a stochastic, discrete-time dynamical system. The effects of changing the statistical properties of the external noise process are also investigated. The dynamical response of the system has a straightforward interpretation in terms of the structure of the basins of attraction. The correlation time of the noise process is one important determinant of the system's response to the fluctuations. In particular, if the correlation time is short, compared to the characteristic time for the oscillations of the system, the analogy with the discrete-time mechanisms for transitions breaks down.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.451994
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  • 8
    Electronic Resource
    Electronic Resource
    Dynamics of ion pair interconversion in a polar solvent (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 7137-7147 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The reaction rate and mechanism of the interconversion between a contact ion pair and solvent separated ion pair in model polar solvents is investigated by molecular dynamics (MD) simulation. The full rate constant for the model reaction is estimated from the product of the transition state theory (TST) rate constant, determined from the potential of mean force between the ions in an equilibrium solvent, and the transmission coefficient, which depends on the details of the dynamics. The collective character of the solvent motion in the reaction barrier crossing is examined in some detail, and the important role of solvent dynamics in causing the reaction rate to markedly deviate from the TST rate is discussed. The MD results are compared with the predictions of Kramers and Grote–Hynes theories.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459437
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  • 9
    Electronic Resource
    Electronic Resource
    Phase resetting dynamics for a discrete reaction–diffusion model (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 7315-7322 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The results of a study of spatial pattern formation in a two-dimensional oscillatory reaction–diffusion system are presented. The calculations are carried out on a discrete model of the Brusselator reaction. The system responds to inhomogeneous perturbations in two different ways. For most perturbations it relaxes back to a spatially homogeneous state with a phase shift. However, special perturbations produce persistent structures which consist of spiral waves and target patterns. The nature of these spatio-temporal states is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458216
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  • 10
    Electronic Resource
    Electronic Resource
    Inhomogeneous perturbations and phase resetting in an oscillatory reaction–diffusion system (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 7302-7314 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The response of the Brusselator reaction–diffusion system to inhomogeneous perturbations is studied. The main focus of this work is on a spatial generalization of the phase resetting problem. A randomly chosen fraction p of an initially homogeneous oscillatory system is locally perturbed and driven off the limit cycle. The asymptotic local phase is monitored and averaged over local regions and realizations of the perturbation process. From this information a phase response curve can be constructed which depends both on the local stimulus amplitude and on p. The system exhibits two qualitatively different kinds of response depending on the stimulus amplitude and the phase at which the perturbation is applied. It either relaxes to a spatially homogeneous oscillatory state or develops persistent spatial patterns. The origin of this behavior is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458215
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