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The out-of-time-ordered correlator (OTOC) has emerged as an interesting object in both classical and quantum systems for probing the spatial spread and temporal growth of initially local perturbations in spatially extended chaotic systems. Here, we study the (classical) OTOC and its “light cone” in the nonlinear Kuramoto-Sivashinsky (KS) equation, using extensive numerical simulations. We also show that the linearized KS equation exhibits a qualitatively similar OTOC and light cone, which can be understood via a saddle-point analysis of the linearly unstable modes. Given the deep connection between the KS (deterministic) and the Kardar-Parisi-Zhang (KPZ, which is stochastic) equations, we also explore the OTOC in the KPZ equation. While our numerical results in the KS case are expected to hold in the continuum limit, for the KPZ case it is valid in a discretized version of the KPZ equation. More broadly, our work unravels the intrinsic interplay between noise/instability, nonlinearity, and dissipation in partial differential equations (deterministic or stochastic) through the lens of OTOC.
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Computationally Efficient Simulations of Stochastically Perturbed Nonlinear Dynamical Systems
Abstract A probabilistic approach is needed to address systems with uncertainties arising in natural processes and engineering applications. For computational convenience, however, the stochastic effects are often ignored. Thus, numerical integration routines for stochastic dynamical systems are rudimentary compared to those for the deterministic case. In this work, the authors present a method to carry out stochastic simulations by using methods developed for the deterministic case. Thereby, the well-developed numerical integration routines developed for deterministic systems become available for studies of stochastic systems. The convergence of the developed method is shown and the method's performance is demonstrated through illustrative examples.
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- Award ID(s):
- 1760366
- PAR ID:
- 10423299
- Date Published:
- Journal Name:
- Journal of Computational and Nonlinear Dynamics
- ISSN:
- 1555-1415
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4054932
