51 citations · 168 across the 26 of their papers we have counts for
30 papers
Rolls and Snaking in a Swift-Hohenberg Equation with Non-smooth Nonlinearity
Lütfiye Masur, Jens D. M. Rademacher
We study rolls and homoclinic snaking in a variation of the one-dimensional Swift-Hohenberg equation, whose standard forms are prototypical order-parameter models for pattern forma…
Energetic consistency and heat transport in Fourier-Galerkin truncations of free slip 3D rotating convection
Jens D. M. Rademacher, Roland Welter
This paper examines the effects of energetic consistency in Fourier truncated models of the 3D Boussinesq-Coriolis (BC) equations as a case-study towards improving the realism of c…
Numerical Continuation and Bifurcation in Nonlinear PDEs: Stability, invasion and wavetrains in the Swift-Hohenberg equation
David Lloyd, Ryan Goh, Jens D. M. Rademacher
We discuss some aspects of numerical continuation and bifurcation for partial differential equations, specifically pattern formation and coherent structures. For the sake of clarit…
Chaotic motion and singularity structures of front solutions in multi-component FitzHugh-Nagumo-type systems
Martina Chirilus-Bruckner, Peter van Heijster, Jens D. M. Rademacher
We study the dynamics of front solutions in a certain class of multi-component reaction-diffusion systems, where one fast component governed by an Allen-Cahn equation is weakly cou…
Fractional Dissipative PDEs
Franz Achleitner, Goro Akagi, Christian Kuehn +4
In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their dynamics. The class of PDEs we…
Rotating convection and flows with horizontal kinetic energy backscatter
Paul Holst, Jens D. M. Rademacher, Jichen Yang
Numerical simulations of large scale geophysical flows typically require unphysically strong dissipation for numerical stability. Towards energetic balance various schemes have bee…
Time averages and periodic attractors at high Rayleigh number for Lorenz-like models
Ivan Ovsyannikov, Jens D. M. Rademacher, Roland Welter +1
Revisiting the Lorenz '63 equations in the regime of large of Rayleigh number, we study the occurrence of periodic solutions and quantify corresponding time averages of selected qu…
Rotating shallow water equations with bottom drag: bifurcations and growth due to kinetic energy backscatter
Artur Prugger, Jens D. M. Rademacher, Jichen Yang
The rotating shallow water equations with f-plane approximation and nonlinear bottom drag are a prototypical model for mid-latitude geophysical flow that experience energy loss thr…
Bifurcation control for a ship maneuvering model with nonsmooth nonlinearities
Miriam Steinherr Zazo, Jens D. M. Rademacher
We consider a widely used form of models for ship maneuvering, whose nonlinearities entail continuous but nonsmooth second-order modulus terms. For such models bifurcations of stra…
Weak and strong interaction of excitation kinks in scalar parabolic equations
Antoine Pauthier, Jens D. M. Rademacher, Dennis Ulbrich
Motivated by studies of the Greenberg-Hastings cellular automata (GHCA) as a caricature of excitable systems, in this paper we study kink-antikink dynamics in the perhaps simplest…
Domain wall motion in axially symmetric spintronic nanowires
Jens D. M. Rademacher, Lars Siemer
This article is concerned with the dynamics of magnetic domain walls (DWs) in nanowires as solutions to the classical Landau-Lifschitz-Gilbert equation augmented by a typically non…
Lyapunov coefficients for Hopf bifurcations in systems with piecewise smooth nonlinearity
Miriam Steinherr Zazo, Jens D. M. Rademacher
Motivated by models that arise in controlled ship maneuvering, we analyze Hopf bifurcations in systems with piecewise smooth nonlinear part. In particular, we derive explicit formu…
Pulse replication and accumulation of eigenvalues
Paul Carter, Jens D. M. Rademacher, Björn Sandstede
Motivated by pulse-replication phenomena observed in the FitzHugh--Nagumo equation, we investigate traveling pulses whose slow-fast profiles exhibit canard-like transitions. We sho…
Explicit superposed and forced plane wave generalized Beltrami flows
Artur Prugger, Jens D. M. Rademacher
We revisit and present new linear spaces of explicit solutions to incompressible Euler and Navier-Stokes equations on , as well as the rotating Boussinesq equations o…
The impact of advection on the stability of stripes on lattices near planar Turing instabilities
Jichen Yang, Jens D. M. Rademacher, Eric Siero
Striped patterns are known to bifurcate in reaction-diffusion systems with differential isotropic diffusions at a supercritical Turing instability. In this paper we study the impac…
The impact of advection on large-wavelength stability of stripes near planar Turing instabilities
Jichen Yang, Jens D. M. Rademacher, Eric Siero
It is well known that for reaction-diffusion systems with differential isotropic diffusions, a Turing instability yields striped solutions. In this paper we study the impact of wea…
Reaction-subdiffusion systems and memory: spectra, Turing instability and decay estimates
Jichen Yang, Jens D. M. Rademacher
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial…
Inhomogeneous domain walls in spintronic nanowires
Lars Siemer, Ivan Ovsyannikov, Jens D. M. Rademacher
In case of a spin-polarized current, the magnetization dynamics in nanowires are governed by the classical Landau-Lifschitz equation with Gilbert damping term, augmented by a typic…
Dynamics and topological entropy of 1D Greenberg-Hastings cellular automata
Marc Kesseböhmer, Jens D. M. Rademacher, Dennis Ulbrich
In this paper we analyse the non-wandering set of 1D-Greenberg-Hastings cellular automata models for excitable media with excited and refractory state…
Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system
Martina Chirilus-Bruckner, Peter van Heijster, Hideo Ikeda +1
This manuscript extends the analysis of a much studied singularly perturbed three-component reaction-diffusion system for front dynamics in the regime where the essential spectrum…
Spectra and stability of spatially periodic pulse patterns: Evans function factorization via Riccati transformation
Björn de Rijk, Arjen Doelman, Jens Rademacher
In the spectral stability analysis of localized patterns to singular perturbed evolution problems, one often encounters that the Evans function respects the scale separation. In su…
pde2path - version 2.0: faster FEM, multi-parameter continuation, nonlinear boundary conditions, and periodic domains - a short manual
Tomas Dohnal, Jens D. M. Rademacher, Hannes Uecker +1
pdepath 2.0 is an upgrade of the continuation/bifurcation package pde2path for elliptic systems of PDEs over bounded 2D domains, based on the Matlab pdetoolbox. The new features in…
Patterns formation in axially symmetric Landau-Lifshitz-Gilbert-Slonczewski equations
Christof Melcher, Jens D. M. Rademacher
The Landau-Lifshitz-Gilbert-Slonczewski equation describes magnetization dynamics in the presence of an applied field and a spin polarized current. In the case of axial symmetry an…
Quasilinear parabolic reaction-diffusion systems: user's guide to well-posedness, spectra and stability of travelling waves
Martin Meyries, Jens D. M. Rademacher, Eric Siero
This paper is concerned with quasilinear parabolic reaction-diffusion-advection systems on extended domains. Frameworks for well-posedness in Hilbert spaces and spaces of continuou…