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  • 2020-2024  (3)
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  • 1
    Publication Date: 2023-08-14
    Description: Understanding the kinetics between the components of time-resolved spectra is a crucial step in the study of photo-activatedprocesses. However, modeling the kinetics requires usually some a priori knowledge about the system. In our approach, webuild a Markov State Model (MSM) from the spectral data, and obtain a Koopman transition matrix K(t). With genPCCA,an invariant subspace projection, we project the process into its metastable components. The result of the application of gen-PCCA is a transition matrix Kc(t), from which we can read the transition probability between the metastable components of the reaction. We discuss the application of this analysis method to the transient absorption spectrum of brominated Al-corrole
    Language: English
    Type: article , doc-type:article
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  • 2
    Publication Date: 2023-08-14
    Description: This article addresses the problem of estimating the Koopman generator of a Markov process. The direct computation of the infinitesimal generator is not easy because of the discretization of the state space, in particular because of the trade-off inherent in the choice of the best lag time to study the process. Short lag times implies a strong discretization of the state space and a consequent loss of Markovianity. Large lag times bypass events on fast timescales. We propose a method to approximate the generator with the computation of the Newton polynomial extrapolation. This technique is a multistep approach which uses as its input Koopman transfer operators evaluated for a series of lag times. Thus, the estimated infinitesimal generator combines information from different time resolutions and does not bias only fast- or slow-decaying dynamics. We show that the multi-scale Newton method can improve the estimation of the generator in comparison to the computation using finite difference or matrix logarithm methods.
    Language: English
    Type: article , doc-type:article
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  • 3
    Publication Date: 2024-03-18
    Description: Python implementation of severals tools (PCCA, AJC, SQRA, P/Q estimation) for the analysis of dynamical systems from the transfer operator perspective.
    Language: English
    Type: software , doc-type:Other
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