Výsledky vyhledávání - "Poppe, Johannes"

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Sensitivities in complex-time flows: phase transitions, Hamiltonian structure and differential geometry

Reminiscent of physical phase transitions separatrices divide the phase space of dynamical systems with multiple equilibria into regions of distinct flow behavior and asymptotics. We introduce complex time in order to study corresponding Riemann surf

Externí odkaz: http://arxiv.org/abs/2410.06018

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On Differential Geometric Formulations of Slow Invariant Manifold Computation: Geodesic Stretching and Flow Curvature

Autor: Poppe, Johannes, Lebiedz, Dirk

The theory of slow invariant manifolds (SIMs) is the foundation of various model-order reduction techniques for dissipative dynamical systems with multiple time-scales, e.g. in chemical kinetic models. The construction of SIMs and many approximation

Externí odkaz: http://arxiv.org/abs/1912.00676

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Stretching-Based Diagnostics in a Differential Geometry Setting

Autor: Poppe, Johannes, Lebiedz, Dirk

The identification of slow invariant manifolds (SIMs) is an essential part in model-order reduction for reactive systems. The mathematical definition of the SIM by Fenichel can be considered unsatisfactory, because it is only applicable to so-called

Externí odkaz: http://arxiv.org/abs/1905.02311

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Analytic continuation and differential geometry views on slow manifolds and separatrices

Autor: Lebiedz, Dirk, Dietrich, Jörn, Heitel, Marcus, Poppe, Johannes

We start from a mechano-chemical analogy considering the time evolution of a homogeneous chemical reaction modeled by a nonlinear dynamical system (ordinary differential equation, ODE) as the movement of a phase space point on the solution manifold s

Externí odkaz: http://arxiv.org/abs/1904.04613

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