Related papers: Resolvent-Based Optimisation for Approximating the…
In this paper we consider filtering and smoothing of partially observed chaotic dynamical systems that are discretely observed, with an additive Gaussian noise in the observation. These models are found in a wide variety of real…
When considering a general system of equations describing the space-time evolution (flow) of one or several variables, the problem of the optimization over a finite period of time of a measure of the state variable at the final time is a…
We extend our approach for the exact solution of the Riemann problem in relativistic hydrodynamics to the case in which the fluid velocity has components tangential to the initial discontinuity. As in one-dimensional flows, we here show…
Spatio-temporally chaotic dynamics of transitional plane Couette flow may give rise to regular turbulent-laminar stripe patterns with a large-scale pattern wavelength and an oblique orientation relative to the laminar flow direction. A…
Spatially-periodic channels are increasingly attracting attention as an efficient alternative to packed columns for a number of analytical and engineering processes. In incompressible flows, the periodic geometry allows to compute the flow…
Self-consistent chaotic transport is studied in a Hamiltonian mean-field model. The model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in…
For appropriately chosen weights, temporal averages in chaotic systems can be approximated as a weighted sum of averages over reference states, such as unstable periodic orbits. Under strict assumptions, such as completeness of the orbit…
We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…
We provide resolvent asymptotics as well as various operator-norm estimates for the system of linear partial differential equations describing the thin infinite elastic rod with material coefficients which periodically highly oscillate…
We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data is not sufficient for estimating time derivatives of state variables but enough to…
Grebogi, Ott and Yorke (Phys. Rev. A 38(7), 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits ($T$) of a dynamical system scales as a…
Many chaotic dynamical systems of physical interest present a strong form of nonhyperbolicity called unstable dimension variability (UDV), for which the chaotic invariant set contains periodic orbits possessing different numbers of unstable…
In this paper, based on real-time nonlinear receding horizon control methodology, a novel approach is developed for parameter estimation of time invariant and time varying nonlinear dynamical systems in chaotic environments. Here, the…
As originally formulated, the Generalized Alignment Index (GALI) method of chaos detection has so far been applied to distinguish quasiperiodic from chaotic motion in conservative nonlinear dynamical systems. In this paper we extend its…
A new resolvent-based method is developed to predict the space-time properties of the flow field. To overcome the deterioration of the prediction accuracy with the increasing distance between the measurements and predictions in the…
Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down…
Invariant manifolds of unstable periodic orbits organize the dynamics of chaotic orbits in phase space. They provide insight into the mechanisms of transport and chaotic advection and have important applications in physical situations…
In this work, we discuss the long-time behavior of non-rotating quasi-2D viscous flows over topographies. We develop a novel theoretical and numerical framework for the analysis of these flows, derived as a dimensional reduction of the 3D…
Time-delayed feedback control, attributed to Pyragas (1992 Physics Letters 170(6) 421-428), is a method known to stabilise periodic orbits in low dimensional chaotic dynamical systems. A system of the form…
The present work demonstrates the use of resolvent analysis to obtain physical insights for open-cavity flows. Resolvent analysis identifies the flow response to harmonic forcing, given a steady base state, in terms of the response and…