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Rigoberto Hernandez - One of the best experts on this subject based on the ideXlab platform.

  • Invariant manifolds and rate constants in driven chemical reactions
    2019
    Co-Authors: Matthias Feldmaier, Thomas Bartsch, Philippe Schraft, Robin Bardakcioglu, Johannes Reiff, Melissa Lober, Martin Tschope, Andrej Junginger, Jorg Main, Rigoberto Hernandez
    Abstract:

    Reaction rates of chemical reactions under nonequilibrium conditions can be determined through the construction of the normally hyperbolic invariant manifold (NHIM) [and moving dividing surface (DS)] associated with the transition State Trajectory. Here, we extend our recent methods by constructing points on the NHIM accurately even for multidimensional cases. We also advance the implementation of machine learning approaches to construct smooth versions of the NHIM from a known high-accuracy set of its points. That is, we expand on our earlier use of neural nets and introduce the use of Gaussian process regression for the determination of the NHIM. Finally, we compare and contrast all of these methods for a challenging two-dimensional model barrier case so as to illustrate their accuracy and general applicability

  • communication transition State Trajectory stability determines barrier crossing rates in chemical reactions induced by time dependent oscillating fields
    Journal of Chemical Physics, 2014
    Co-Authors: Galen T. Craven, Thomas Bartsch, Rigoberto Hernandez
    Abstract:

    When a chemical reaction is driven by an external field, the transition State that the system must pass through as it changes from reactant to product—for example, an energy barrier—becomes time-dependent. We show that for periodic forcing the rate of barrier crossing can be determined through stability analysis of the non-autonomous transition State. Specifically, strong agreement is observed between the difference in the Floquet exponents describing stability of the transition State Trajectory, which defines a recrossing-free dividing surface [G. T. Craven, T. Bartsch, and R. Hernandez, “Persistence of transition State structure in chemical reactions driven by fields oscillating in time,” Phys. Rev. E 89, 040801(R) (2014)], and the rates calculated by simulation of ensembles of trajectories. This result opens the possibility to extract rates directly from the intrinsic stability of the transition State, even when it is time-dependent, without requiring a numerically expensive simulation of the long-time...

  • persistence of transition State structure in chemical reactions driven by fields oscillating in time
    Physical Review E, 2014
    Co-Authors: Galen T. Craven, Thomas Bartsch, Rigoberto Hernandez
    Abstract:

    : Chemical reactions subjected to time-varying external forces cannot generally be described through a fixed bottleneck near the transition-State barrier or dividing surface. A naive dividing surface attached to the instantaneous, but moving, barrier top also fails to be recrossing-free. We construct a moving dividing surface in phase space over a transition-State Trajectory. This surface is recrossing-free for both Hamiltonian and dissipative dynamics. This is confirmed even for strongly anharmonic barriers using simulation. The power of transition-State theory is thereby applicable to chemical reactions and other activated processes even when the bottlenecks are time dependent and move across space.

Luc Jaulin - One of the best experts on this subject based on the ideXlab platform.

  • Exact bounded-error continuous-time linear State estimator
    Systems and Control Letters, 2021
    Co-Authors: Simon Rohou, Luc Jaulin
    Abstract:

    This paper proposes an interval-based method for estimating the State of a linear continuous-time dynamical system. In this work, we assume that the measurements are provided at discrete times and that all errors are bounded. Interval analysis is used to propagate the interval uncertainties continuously over time. The resulting method is guaranteed to never lose any feasible solution and provides an optimal polygonal enclosure of the State Trajectory. A reproducible example illustrates the principle of the method.

Galen T. Craven - One of the best experts on this subject based on the ideXlab platform.

  • communication transition State Trajectory stability determines barrier crossing rates in chemical reactions induced by time dependent oscillating fields
    Journal of Chemical Physics, 2014
    Co-Authors: Galen T. Craven, Thomas Bartsch, Rigoberto Hernandez
    Abstract:

    When a chemical reaction is driven by an external field, the transition State that the system must pass through as it changes from reactant to product—for example, an energy barrier—becomes time-dependent. We show that for periodic forcing the rate of barrier crossing can be determined through stability analysis of the non-autonomous transition State. Specifically, strong agreement is observed between the difference in the Floquet exponents describing stability of the transition State Trajectory, which defines a recrossing-free dividing surface [G. T. Craven, T. Bartsch, and R. Hernandez, “Persistence of transition State structure in chemical reactions driven by fields oscillating in time,” Phys. Rev. E 89, 040801(R) (2014)], and the rates calculated by simulation of ensembles of trajectories. This result opens the possibility to extract rates directly from the intrinsic stability of the transition State, even when it is time-dependent, without requiring a numerically expensive simulation of the long-time...

  • persistence of transition State structure in chemical reactions driven by fields oscillating in time
    Physical Review E, 2014
    Co-Authors: Galen T. Craven, Thomas Bartsch, Rigoberto Hernandez
    Abstract:

    : Chemical reactions subjected to time-varying external forces cannot generally be described through a fixed bottleneck near the transition-State barrier or dividing surface. A naive dividing surface attached to the instantaneous, but moving, barrier top also fails to be recrossing-free. We construct a moving dividing surface in phase space over a transition-State Trajectory. This surface is recrossing-free for both Hamiltonian and dissipative dynamics. This is confirmed even for strongly anharmonic barriers using simulation. The power of transition-State theory is thereby applicable to chemical reactions and other activated processes even when the bottlenecks are time dependent and move across space.

Daniel W C Ho - One of the best experts on this subject based on the ideXlab platform.

  • sliding mode control for nonlinear State delayed systems using neural network approximation
    IEE Proceedings - Control Theory and Applications, 2003
    Co-Authors: Xingyu Wang, Daniel W C Ho
    Abstract:

    The sliding-mode control problem is studied for a class of State-delayed systems with mismatched parameter uncertainties, unknown nonlinearities and external disturbances. By integrating neural-network approximation and the Lyapunov theory into the sliding-mode technique, a neural-network-based sliding-mode control scheme is proposed. The major advantage of the present work over traditional sliding-mode designs is the relaxation of the requirement that the unknown nonlinearities are to be bounded. By means of linear matrix inequalities, a sufficient condition for ensuring the asymptotic stability of the sliding-mode dynamics restricted to the defined sliding surface is given. Further, by utilising a neural-network model to approximate the unknown nonlinearity, a sliding-mode control scheme is proposed to guarantee that the system State Trajectory is attracted to the designed sliding surface.

Simon Rohou - One of the best experts on this subject based on the ideXlab platform.

  • Exact bounded-error continuous-time linear State estimator
    Systems and Control Letters, 2021
    Co-Authors: Simon Rohou, Luc Jaulin
    Abstract:

    This paper proposes an interval-based method for estimating the State of a linear continuous-time dynamical system. In this work, we assume that the measurements are provided at discrete times and that all errors are bounded. Interval analysis is used to propagate the interval uncertainties continuously over time. The resulting method is guaranteed to never lose any feasible solution and provides an optimal polygonal enclosure of the State Trajectory. A reproducible example illustrates the principle of the method.