Zobrazeno 1 - 10
of 357
pro vyhledávání: '"Lebiedz P"'
Autor:
Lebiedz, Dirk, Poppe, Johannes
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
Autor:
Kainz, Nicolas, Lebiedz, Dirk
In this follow-up paper to [Local geometry of Equilibria and a Poincare-Bendixson-type Theorem for Holomorphic Flows, Nicolas Kainz, Dirk Lebiedz (2024)] we investigate the global topology and geometry of dynamical systems $\dot{x} = F(x)$ with entir
Externí odkaz:
http://arxiv.org/abs/2410.04895
Autor:
Kainz, Nicolas, Lebiedz, Dirk
In this paper, we explore the local geometry of dynamical systems $\dot{x}=F(x)$ with real time parameterization, where $F$ is holomorphic on connected open subsets of $\mathbb{C}\stackrel{\sim}{=}\mathbb{R}^2$. We describe the geometry of first-orde
Externí odkaz:
http://arxiv.org/abs/2402.07612
Flatness-based control design is a well established method to generate open-loop control signals. Several articles discuss the application of flatness-based control design of (reaction-) diffusion problems for various scenarios. Beside the pure analy
Externí odkaz:
http://arxiv.org/abs/2307.16764
Autor:
Dietrich, Jörn, Lebiedz, Dirk
The numerical simulation of realistic reactive flows is a major challenge due to the stiffness and high dimension of the corresponding kinetic differential equations. Manifold-based model reduction techniques address this problem by projecting the fu
Externí odkaz:
http://arxiv.org/abs/2210.07938
In his famous book entitled \textit{Theory of Oscillations}, Nicolas Minorsky wrote: "\textit{each time the system absorbs energy the curvature of its trajectory decreases} and \textit{vice versa}". According to the \textit{Flow Curvature Method}, th
Externí odkaz:
http://arxiv.org/abs/2101.01927
Autor:
Lebiedz, Dirk
With a view on the formal analogy between Riemann-von-Mangoldts explicit formula and semiclassical quantum mechanics in terms of the Gutzwiller trace formula we construct a complex-valued Hamiltonian $H(q,p)=\xi(q)p$ from the holomorphic flow $\dot{q
Externí odkaz:
http://arxiv.org/abs/2006.09165
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
Autor:
Dietrich, Jörn, Lebiedz, Dirk
Many real-analytic flows, e.g. in chemical kinetics, share a multiple time scale spectral structure. The trajectories of the corresponding dynamical systems are observed to bundle near so-called slow invariant manifolds (SIMs), which are usually addr
Externí odkaz:
http://arxiv.org/abs/1912.00748
Autor:
Heitel, Marcus, Lebiedz, Dirk
Separatrices divide the phase space of some holomorphic dynamical systems into separate basins of attraction or 'stability regions' for distinct fixed points. 'Bundling' (high density) and mutual 'repulsion' of trajectories are often observed at sepa
Externí odkaz:
http://arxiv.org/abs/1911.10963