arXiv subjects

Daniel Greve

Publications and source records attributed to Daniel Greve.

5 recordsLinked to original sources

arXiv2026

Higher-codimension points as organizing centers in nonreciprocal pattern-forming systems with O(2)-symmetry

Focusing on a two-field Swift-Hohenberg model with linear nonreciprocal interactions, this study investigates how emerging higher-codimension points act as organizing centers for the nonequilibrium phase diagram that features various steady and dynamic phases. Complementing the numerical analysis of the field equations with time simulations and path continuation techniques, we derive a reduced dynamical system corresponding to a one-mode approximation for the critical-wavenumber modes. Furthermore, we derive the normal form equations that are valid in the vicinity of the Takens-Bogdanov bifurcation with O(2)-symmetry, which allows us to draw on corresponding literature results. Comparing results obtained on the different levels of description, we discuss the bifurcation structure relating trivial uniform and inhomogeneous steady states as well as traveling, standing and modulated waves. We also contextualize the relevance of recently highlighted features of the linear mode structure, i.e., of the dispersion relations, termed "critical exceptional points" for the transitions between the nonequilibrium phases.

nlin.PS↗

arXiv2024

An amplitude equation for the conserved-Hopf bifurcation -- derivation, analysis and assessment

We employ weakly nonlinear theory to derive an amplitude equation for the conserved-Hopf instability, i.e., a generic large-scale oscillatory instability for systems with two conservation laws. The resulting equation represents in the conserved case the equivalent of the complex Ginzburg-Landau equation obtained in the nonconserved case as amplitude equation for the standard Hopf bifurcation.Considering first the case of a relatively simple symmetric Cahn-Hilliard model with purely nonreciprocal coupling, we derive the nonlinear nonlocal amplitude equation with real coefficients and show that its bifurcation diagram and time evolution well agree with results for the full model. The solutions of the amplitude equation and their stability are analytically obtained thereby showing that in oscillatory phase separation the suppression of coarsening is universal. Second, we lift the two restrictions and obtain the amplitude equation in the generic case that has complex coefficients, that also shows very good agreement with the full model as exemplified for some transient dynamics that converges to traveling wave states.

nlin.PS↗

arXiv2024

Coexistence of uniform and oscillatory states resulting from nonreciprocity and conservation laws

Employing a two-species Cahn-Hilliard model with nonreciprocal interactions we show that the interplay of nonreciprocity and conservation laws results in the robust coexistence of uniform stationary and oscillatory phases as well as of uniform and crystalline phases. For nonequilibrium models with a spurious gradient dynamics structure such coexistencies between two or more nonequilibrium phases and resulting phase diagrams can nevertheless be predicted by a Maxwell double-tangent construction. This includes phases with sustained regular or irregular out-of-equilibrium dynamics as further corroborated by bifurcation studies and time simulations.

nlin.PS↗

arXiv2023

Drops on polymer brushes -- advances in thin-film modelling of adaptive substrates

We briefly review recent advances in the hydrodynamic modeling of the dynamics of droplets on adaptive substrates, in particular, solids that are covered by polymer brushes. Thereby, the focus are long-wave and full-curvature variants of mesoscopic hydrodynamic models in gradient dynamics form. After introducing the approach for films/drops of nonvolatile simple liquids on rigid smooth solid substrate, it is first expanded to an arbitrary number of coupled degrees of freedom, before considering the specific case of drops of volatile liquids on brush-covered solids. After presenting the model its usage is illustrated by briefly considering the natural and forced spreading of drops of nonvolatile liquids on a horizontal brush-covered substrate as well as drops sliding down a brush-covered incline. Finally, also volatile liquids are considered.

physics.flu-dyn↗

arXiv2023

Stick-slip Dynamics in the Forced Wetting of Polymer Brushes

We study the static and dynamic wetting of adaptive substrates using a mesoscopic hydrodynamic model for a liquid droplet on a solid substrate covered by a polymer brush. First, we show that on the macroscale Young's law still holds for the equilibrium contact angle and that on the mesoscale a Neumann-type law governs the shape of the wetting ridge. Following an analytic and numeric assessment of the static profiles of droplet and wetting ridge, we examine the dynamics of the wetting ridge for a liquid meniscus that is advanced at constant speed. In other words, we consider an inverse Landau-Levich case where a brush-covered plate is introduced into (and not drawn from) a liquid bath. We find a characteristic stick-slip motion that emerges when the dynamic contact angle of the stationary moving meniscus decreases with increasing velocity, and relate the onset of slip to Gibbs' inequality and to a cross-over in relevant time scales.

physics.flu-dyn↗