Related papers: Topological State Space Inference for Dynamical Sy…
Topological pumping of edge states in finite crystals or quasicrystals with non-trivial topological phases provides a powerful means for robust excitation transfer. In most schemes of topological pumping, the edge states become delocalized…
A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the…
We present several topics involving the computation of dynamical systems. The emphasis is on work in progress and the presentation is informal -- there are many technical details which are not fully discussed. The topics are chosen to…
Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with respect to a dynamical frame, i.e. a sequence of sampling vectors constructed by the…
In this paper we apply the method of Lagrangian descriptors to explore the geometrical structures in phase space that govern the dynamics of dissipative systems. We demonstrate through many classical examples taken from the nonlinear…
The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…
We show how to generalize the concepts of identifying and classifying symmetry protected topological phases in 1D to the case of an arbitrary mixed state. The pure state concepts are reviewed using a concrete spin-1 model. For the mixed…
The results of a combined experimental and numerical study of the flow in slowly diverging pipes are presented. Interestingly, an axisymmetric conical recirculation cell has been observed. The conditions for its existence and the length of…
This paper focuses on multiscale dynamics occurring in steam supply systems. The dynamics of interest are originally described by a distributed-parameter model for fast steam flows over a pipe network coupled with a lumped-parameter model…
A phase-space formulation of non-stationary nonlinear dynamics including both Hamiltonian (e.g., quantum-cosmological) and dissipative (e.g., dissipative laser) systems reveals an unexpected affinity between seemly different branches of…
Control schemes for dynamical systems typically involve stabilizing unstable periodic orbits. In this paper we introduce a new paradigm of control that involves `trapping' the dynamics arbitrarily close to any desired trajectory. This is…
Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the framework of Topological Data Analysis.…
Active emulsions and liquid crystalline shells are intriguing and experimentally realisable types of topological matter. Here we numerically study the morphology and spatiotemporal dynamics of a double emulsion, where one or two passive…
In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD)…
Two dynamical systems are topologically equivalent when their phase-portraits can be morphed into each other by a homeomorphic coordinate transformation on the state space. The induced equivalence classes capture qualitative properties such…
Phase-space path-integrals are used in order to illustrate various aspects of a recently proposed interpretation of quantum mechanics as a gauge theory of metaplectic spinor fields.
We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…
The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…