arXiv subjects

Uwe Thiele

Publications and source records attributed to Uwe Thiele.

At least 19 recordsLinked to original sources

arXiv2026

Strong Mpemba Effect Through a Reentrant Phase Transition

We investigate temperature quenches across the reentrant phase transition of the antiferromagnetic Ising model in a magnetic field and show that it provides a natural mechanism for strong direct and inverse Mpemba effects. For quenches terminating in the paramagnetic phase, the slowest relaxation mode is purely staggered. Initial states in the paramagnetic phase therefore have exactly zero overlap with this mode and exhibit a strong Mpemba effect, whereas antiferromagnetic initial states excite it and develop a slow-relaxation tail. Moreover, reentrance makes the equilibrium staggered magnetization nonmonotonic, producing conventional direct and inverse Mpemba effects when both initial states lie in the antiferromagnetic phase and the quench terminates in the paramagnetic phase. By varying the lattice coordination number, we show that this mechanism disappears in the absence of reentrance. Our results provide the first demonstration of (strong) Mpemba effects in the antiferromagnetic Ising model within the pair approximation and establish a direct link between anomalous relaxation and equilibrium phase behavior.

cond-mat.stat-mech↗

arXiv2026

Mean-Field Theory of Chiral Active Model B: Arrested Coarsening and Chiral Fingering Instabilities

We derive and analyze a mean-field theory of the chiral Ising model recently introduced by Wang, Pietzonka, and Jülicher in "Edge Currents Shape Condensates in Chiral Active Matter", arXiv:2603.20064. Starting from the master equation for clockwise and counterclockwise rotations of 2x2 spin blocks, we first obtain spatially discrete evolution equations for the spatially resolved average magnetization. On this discrete level, we show that a chiral bias strongly affects phase coarsening: domains coarsen anisotropically, develop nearly rectangular shapes, and eventually display chirality-induced arrested coarsening. Taking the continuum limit of these equations yields an active field theory that has the structure of a relaxational Model-B-type dynamics supplemented by a chiral current that permanently drives the system out of equilibrium. The coarse graining explicitly shows how microscopic rotational bias generates tangential currents localized at interfaces. Using this continuum theory, we perform a linear stability analysis of radially symmetric clusters and identify a chiral fingering instability in which angular perturbations of the interface are amplified and eventually lead to radially asymmetric rotating states or disordered states.

nlin.PS↗

arXiv2026

What is active wetting?

In recent years the term \textit{active wetting} has gained some traction in works describing, analyzing and modeling a wide variety of wetting phenomena, for instance, in the contexts of biomolecular condensates, of cell layers or cell aggregates, and of active Brownian particles. The present perspective discusses a coarse classification of wetting phenomena that accounts for this. First, different categories of static and dynamic wetting of passive liquids are briefly introduced, in particular, distinguishing equilibrium wetting, relaxational wetting, driven wetting, and reactive wetting. Second, an overview is given of the various phenomena recently described as active wetting. We conclude by discussing a possible definition of active wetting together with a number of caveats that one might want to keep in mind when using such classifications.

cond-mat.soft↗

arXiv2026

Gradient dynamics model for chemically driven running drops

We present a thermodynamically consistent model for chemically driven running drops on a solid substrate with reversible substrate adsorption of a wettability-changing chemical species. We consider drops confined to a vertical gap, thereby allowing us to first obtain a gradient dynamics description of the closed system, corresponding to a set of coupled dynamical equations for the drop profile and the chemical concentration profiles of species on the substrate and in both fluids (drop, ambient medium). Chemostatting the species in the drop and the ambient medium, we then derive a reduced model for the dynamics of the drop and the adsorbate on the substrate. When the externally imposed chemical potentials are distinct, the system is driven away from thermodynamic equilibrium, allowing for sustained drop self-propulsion across the substrate due to a wettability contrast maintained by chemical reactions. We numerically study the resulting running drops and show how they emerge from drift-pitchfork bifurcations.

cond-mat.soft↗

arXiv2026

Interface-dominated sliding compound drops

We investigate compound drops composed of two immiscible nonvolatile partially wetting liquids that slide down an inclined homogeneous smooth solid substrate based on a mesoscopic hydrodynamic two-layer model in full-curvature formulation. First, drops of one liquid stationarily sliding on a layer of the other liquid are briefly investigated with a focus on the dependence of drop velocity and interface profiles on inclination and mean thickness of the adaptive substrate. Then, stationary sliding compound drops are studied with a focus on the dependence of their configuration, velocity, dynamic Young and Neumann angles on three control parameters, namely, the inclination, the volume ratio and the viscosity ratio. The reasons for the encountered dependence of the velocity on configuration are clarified based on a discussion of the lateral dissipation profile. Finally, we briefly consider the time-periodic fusion-overtaking-splitting behavior found outside the existence range of the stationary sliding compound drops as determined by saddle-node bifurcations.

physics.flu-dyn↗

arXiv2026

Nonlinear physics of axion inflation

An axion-like field coupled to an Abelian gauge field provides one of the simplest inflationary models that is free from the eta problem and possesses an efficient reheating mechanism. For sufficiently large coupling, this system enters a regime of strong gauge-field backreaction, exhibiting rich and intricate dynamics. In this work, we employ a semi-analytical method, the gradient-expansion formalism, to perform a comprehensive parameter scan and determine the precise conditions under which backreaction sets in. Previous studies have shown that the Anber-Sorbo solution, in which the potential-gradient force acting on the axion is balanced by Hubble friction and gauge-field backreaction, is unstable. Here, we broaden the parameter space and identify a new region in which the Anber-Sorbo solution remains stable despite strong backreaction. Although our analysis is restricted to a homogeneous axion field and to perturbations that depend only on time, we expect that this stability property can be extrapolated to generic time- and space-dependent perturbations. This newly identified region therefore represents a distinct type of backreaction - stable backreaction - which may not be accompanied by the rapid growth of perturbations. We further investigate the nonlinear behavior of solutions in the backreaction regime in a toy model (de Sitter, constant potential slope, no axion gradients), identifying a supercritical Hopf bifurcation at the onset of instability, a nontrivial limit cycle in the unstable regime, and burst-like oscillatory dynamics. Finally, we present a more stringent criterion for the onset of (unstable) backreaction, based on crossing the instability threshold, and apply this criterion to two benchmark inflationary models.

hep-ph↗

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↗

arXiv2025

From bipedal to chaotic motion of chemically fueled partially wetting liquid drops

We employ a thermodynamically consistent out-of-equilibrium continuum model to study the motion patterns of partially wetting liquid drops covered by autocatalytically reacting surfactants. When ambient chemostats feed a chemomechanical feedback loop involving a nonlinear reaction network, surface stresses caused by the Marangoni effect and the ensuing hydrodynamic motion, drops show a variety of increasingly complex biomimetic motility modes including shuttling, bipedal, rotational, intermittently chaotic and chaotic motion. We determine the corresponding nonequilibrium phase diagram and show that the complexity of the motion arises from competing length scales.

nlin.AO↗

arXiv2025

Dynamic Models for Two Nonreciprocally Coupled Fields: A Microscopic Derivation for Zero, One, and Two Conservation Laws

We construct dynamic models governing two nonreciprocally coupled fields for several cases with zero, one, and two conservation laws. Starting from two microscopic nonreciprocally coupled Ising models, and using the mean-field approximation, we obtain closed-form evolution equations for the spatially resolved magnetization in each lattice. Only allowing for single spin-flip dynamics, the macroscopic equations in the thermodynamic limit are closely related to the nonreciprocal Allen-Cahn equations, i.e. conservation laws are absent. Likewise, only accounting for spin-exchange dynamics within each lattice, the thermodynamic limit yields equations similar to the nonreciprocal Cahn-Hilliard model, i.e. with two conservation laws. In the case of spin-exchange dynamics within and between the two lattices, we obtain two nonreciprocally coupled equations that add up to one conservation law. For each of these cases, we systematically map out the linear instabilities that can arise. Moreover, combining the different dynamics gives a large number of further models. Our results provide a microscopic foundation for a broad class of nonreciprocal field theories, establishing a direct link between nonequilibrium statistical mechanics and macroscopic continuum descriptions.

cond-mat.stat-mech↗

arXiv2025

Chemomechanical motility modes of partially wetting liquid droplets

We consider a simple thermodynamically consistent model that captures the self-organized chemomechanical coupling resulting from the interplay between autocatalytically reacting surfactants, the Marangoni effect and wetting dynamics. An ambient bath of surfactant acts as a chemostat and provides the system with chemical fuel, thereby driving it away from thermodynamic equilibrium. We find that a positive feedback loop between the local reactions and the Marangoni effect induces surface tension gradients that allow for self-propelled droplets. Besides simple directional motion, we find crawling and shuttling droplets as well as droplets performing random walks, thus exploring the entire substrate. We study the occurring chemomechanical motility modes and show how the observed dynamic states emerge from local and global bifurcations. Due to the underlying generic thermodynamic structure, we expect that our results are relevant not only to directly related biomimetic droplet systems but also to structurally similar systems like chemically active phase-separating mixtures.

cond-mat.soft↗

arXiv2025

The effect of self-induced Marangoni flow on polar-nematic waves in active-matter systems

We study the formation of propagating large-scale density waves of mixed polar-nematic symmetry in a colony of self-propelled agents that are bound to move along the planar surface of a thin viscous film. The agents act as an insoluble surfactant, i.e. the surface tension of the liquid depends on their density. Therefore, density gradients generate a Marangoni flow. We demonstrate that for active matter in the form of self-propelled surfactants with local (nematic) aligning interactions such a Marangoni flow nontrivially influences the propagation of the density waves. Upon gradually increasing the Marangoni parameter, which characterises the relative strength of the Marangoni flow as compared to the self-propulsion speed, the density waves broaden while their speed may either increase or decrease depending on wavelength and overall mean density. A further increase of the Marangoni parameter eventually results in the disappearance of the density waves. This may occur either discontinuously at finite wave amplitude via a saddle-node bifurcation or continuously with vanishing wave amplitude at a wave bifurcation, i.e. a finite-wavelength Hopf bifurcation.

physics.flu-dyn↗

arXiv2025

Hyperparameter Optimization in the Estimation of PDE and Delay-PDE models from data

We propose an improved method for estimating partial differential equations and delay partial differential equations from data, using Bayesian optimization and the Bayesian information criterion to automatically find suitable hyperparameters for the method itself or for the equations (such as a time-delay). We show that combining time integration into an established model estimation method increases robustness and yields predictive models. Allowing hyperparameters to be optimized as part of the model estimation results in a wider modelling scope. We demonstrate the method's performance on a number of synthetic benchmark problems of different complexity, representing different classes of physical behaviour. This includes the Allen-Cahn and Cahn-Hilliard models, as well as different reaction-diffusion systems without and with time-delay.

physics.comp-ph↗

arXiv2025

Mesoscopic hydrodynamic model for spreading, sliding and coarsening compound drops

We revisit the mesoscopic hydrodynamic description of the dynamics of sessile partially wetting compound drops, i.e., of drops that consist of two immiscible nonvolatile partially wetting liquids and are situated on a smooth rigid solid substrate. We briefly discuss and complete existing dynamic models employing a gradient dynamics approach. Thereby, the underlying energy features capillarity and wettability contributions for all relevant interfaces in full-curvature formulation. Establishing transparent consistency relations between macroscopic and mesoscopic parameters, we obtain mesoscopic Neumann and Young laws that are also fully consistent with the macroscopic ones. In particular, we discuss the minimal requirements for the wetting energy that ensure the full spectrum of macroscopic parameters {for partially wetting cases} is addressed by the mesoscopic model. Subsequently, we distinguish long-wave and full-curvature variants of the dynamical model based on properties of the energy, and employ the latter to illustrate the usage of the mesoscopic model. As examples, we chose the spreading of individual compound drops on one-dimensional horizontal substrates, sliding compound drops on one-dimensional inclined substrates, and the coarsening of drop ensembles on one- and two-dimensional horizontal substrates. In each case, the discussion emphasizes occurring qualitative changes in the drop configurations.

physics.flu-dyn↗

arXiv2025

Gradient dynamics approach to reactive thin-film hydrodynamics

Wetting and dewetting dynamics of simple and complex liquids is described by kinetic equations in gradient dynamics form that incorporates the various coupled dissipative processes in a fully thermodynamically consistent manner. After briefly reviewing this, we also review how chemical reactions can be captured by a related gradient dynamics description, assuming detailed balanced mass action type kinetics. Then, we bring both aspects together and discuss mesoscopic reactive thin-film hydrodynamics illustrated by two examples, namely, models for reactive wetting and reactive surfactants. These models can describe the approach to equilibrium but may also be employed to study out-of-equilibrium chemo-mechanical dynamics. In the latter case, one breaks the gradient dynamics form by chemostatting to obtain active systems. In this way, for reactive wetting we recover running drops that are driven by chemically sustained wettability gradients and for drops covered by autocatalytic reactive surfactants we find complex forms of self-propulsion and self-excited oscillations.

physics.flu-dyn↗

arXiv2025

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↗

arXiv2025

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↗

arXiv2025

Local Order Controls the Onset of Oscillations in the Nonreciprocal Ising Model

We elucidate the generic bifurcation behavior of local and global order in the nonreciprocal Ising model evolving under Glauber dynamics. We show that a critical magnitude of nearest-neighbor correlations within the respective lattices controls the emergence of coherent oscillations of global order as a result of frustration. Local order is maintained during these oscillations, implying nontrivial spatiotemporal correlations. Long-lived states emerge in the strong-interaction regime. The residence time in either of these states eventually diverges, giving rise to ordered non-equilibrium trapped states and a loss of ergodic behavior via a saddle-node-infinite-period bifurcation. Our work provides a comprehensive microscopic understanding of the nonreciprocal Ising model beyond the mean-field approximation.

cond-mat.stat-mech↗

arXiv2024

The role of substrate mechanics in osmotic biofilm spreading

Bacteria invade surfaces by forming dense colonies encased in a polymer matrix. Successful settlement of founder bacteria, early microcolony development and later macroscopic spreading of these biofilms on surfaces rely on complex physical mechanisms. Recent data show that on soft hydrogels, substrate rigidity is an important determinant for biofilm initiation and spreading, through mostly unknown mechanisms. Using a thermodynamically consistent thin-film approach for suspensions on soft elastic surfaces supplemented with biomass production we investigate in silico the role of substrate softness in the osmotic spreading of biofilms. We show that on soft substrates with an imposed osmotic pressure spreading is considerably slowed down and may be completely halted depending on the biomass production rate. We find, that the critical slowing down of biofilm spreading on soft surfaces is caused by a reduced osmotic influx of solvent into the biofilm at the edges, which results from the thermodynamic coupling between substrate deformation and interfacial forces. By linking substrate osmotic pressure and mechanical softness through scaling laws, our simple model semi-quantitatively captures a range of experimentally observed biofilm spreading dynamics on hydrogels with different architectures, underscoring the importance of inherent substrate properties in the spreading process.

cond-mat.soft↗