@article{StraubeKowalikNetzetal.2020, author = {Straube, Arthur and Kowalik, Bartosz G. and Netz, Roland R. and H{\"o}fling, Felix}, title = {Rapid onset of molecular friction in liquids bridging between the atomistic and hydrodynamic pictures}, volume = {3}, journal = {Commun. Phys.}, publisher = {Nature}, doi = {10.1038/s42005-020-0389-0}, pages = {126}, year = {2020}, abstract = {Friction in liquids arises from conservative forces between molecules and atoms. Although the hydrodynamics at the nanoscale is subject of intense research and despite the enormous interest in the non-Markovian dynamics of single molecules and solutes, the onset of friction from the atomistic scale so far could not be demonstrated. Here, we fill this gap based on frequency-resolved friction data from high-precision simulations of three prototypical liquids, including water. Combining with theory, we show that friction in liquids emerges abruptly at a characteristic frequency, beyond which viscous liquids appear as non-dissipative, elastic solids. Concomitantly, the molecules experience Brownian forces that display persistent correlations. A critical test of the generalised Stokes-Einstein relation, mapping the friction of single molecules to the visco-elastic response of the macroscopic sample, disproves the relation for Newtonian fluids, but substantiates it exemplarily for water and a moderately supercooled liquid. The employed approach is suitable to yield insights into vitrification mechanisms and the intriguing mechanical properties of soft materials.}, language = {en} } @article{StraubeHoefling2024, author = {Straube, Arthur and H{\"o}fling, Felix}, title = {Memory effects in colloidal motion under confinement and driving}, volume = {57}, journal = {J. Phys. A: Math. Theor.}, publisher = {IOP Publishing}, issn = {1751-8113}, doi = {10.1088/1751-8121/ad5b2d}, pages = {295003}, year = {2024}, abstract = {The transport of individual particles in inhomogeneous environments is complex and exhibits non-Markovian responses. The latter may be quantified by a memory function within the framework of the linear generalised Langevin equation (GLE). Here, we exemplify the implications of steady driving on the memory function of a colloidal model system for Brownian motion in a corrugated potential landscape, specifically, for one-dimensional motion in a sinusoidal potential. To this end, we consider the overdamped limit of the GLE, which is facilitated by separating the memory function into a singular (Markovian) and a regular (non-Markovian) part. Relying on exact solutions for the investigated model, we show that the random force entering the GLE must display a bias far from equilibrium, which corroborates a recent general prediction. Based on data for the mean-square displacement (MSD) obtained from Brownian dynamics simulations, we estimate the memory function for different driving strengths and show that already moderate driving accelerates the decay of the memory function by several orders of magnitude in time. We find that the memory may persist on much longer timescales than expected from the convergence of the MSD to its long-time asymptote. Furthermore, the functional form of the memory function changes from a monotonic decay to a non-monotonic, damped oscillatory behaviour, which can be understood from a competition of confined motion and depinning. Our analysis of the simulation data further reveals a pronounced non-Gaussianity, which questions the Gaussian approximation of the random force entering the GLE.}, language = {en} } @article{HoeflingStraube2025, author = {H{\"o}fling, Felix and Straube, Arthur}, title = {Langevin equations and a geometric integration scheme for the overdamped limit of rotational Brownian motion of axisymmetric particles}, volume = {7}, journal = {Physical Review Research}, arxiv = {http://arxiv.org/abs/2403.04501}, doi = {10.1103/wzdn-29p4}, pages = {043034}, year = {2025}, abstract = {The translational motion of anisotropic or self-propelled colloidal particles is closely linked with the particle's orientation and its rotational Brownian motion. In the overdamped limit, the stochastic evolution of the orientation vector follows a diffusion process on the unit sphere and is characterized by an orientation-dependent ("multiplicative") noise. As a consequence, the corresponding Langevin equation attains different forms depending on whether Itō's or Stratonovich's stochastic calculus is used. We clarify that both forms are equivalent and derive them in a top-down approach from a geometric construction of Brownian motion on the unit sphere, based on infinitesimal random rotations. Our approach suggests further a geometric integration scheme for rotational Brownian motion, which preserves the normalization constraint of the orientation vector exactly. We show that a simple implementation of the scheme, using Gaussian random rotations, converges weakly at order 1 of the integration time step, and we outline an advanced variant of the scheme that is weakly exact for an arbitrarily large time step. Due to a favorable prefactor of the discretization error, already the Gaussian scheme allows for integration time steps that are one order of magnitude larger compared to a commonly used algorithm for rotational Brownian dynamics simulations based on projection on the constraining manifold. For torques originating from constant external fields, we prove by virtue of the Fokker-Planck equation that the constructed diffusion process satisfies detailed balance and converges to the correct equilibrium distribution. The analysis is restricted to time-homogeneous rotational Brownian motion (i.e., a single rotational diffusion constant), which is relevant for axisymmetric particles and also chemically anisotropic spheres, such as self-propelled Janus particles.}, language = {en} } @article{StraubeHoefling2024, author = {Straube, Arthur and H{\"o}fling, Felix}, title = {Depinning transition of self-propelled particles}, volume = {110}, journal = {Physical Review E}, number = {6}, arxiv = {http://arxiv.org/abs/2306.09150}, doi = {10.1103/PhysRevE.110.L062601}, pages = {L062601}, year = {2024}, abstract = {For self-propelled particles in a corrugated potential landscape, we describe a discontinuous change of the classical depinning transition and a host of unique behaviors sensitive to the persistence of the propulsion direction. Exact and semianalytic results for active Brownian particles corroborate a creep regime with a superexponentially suppressed drift velocity upon lowering the force towards the threshold value. This unusual nonlinear response emerges from the competition of two critical scaling laws with exponents of 1/2 for rapidly reorienting particles and 𝑑/2 for particles with a persistent orientation; the latter case depends on the dimensionality 𝑑 of rotational motion and also includes run-and-tumble particles. Additionally, different giant diffusion phenomena occur in the two regimes. Our findings extend to random dynamics with bounded noise near a saddle-node bifurcation and have potential applications in various nonequilibrium problems, including arrested active matter and cell migration.}, language = {en} } @article{StraubeOliconMendezWinkelmannetal.2025, author = {Straube, Arthur and Olic{\´o}n M{\´e}ndez, Guillermo and Winkelmann, Stefanie and H{\"o}fling, Felix and Engel, Maximilian}, title = {Unfolding the geometric structure and multiple timescales of the urea-urease pH oscillator}, arxiv = {http://arxiv.org/abs/2508.07275}, year = {2025}, abstract = {We study a two-variable dynamical system modeling pH oscillations in the urea-urease reaction within giant lipid vesicles - a problem that intrinsically contains multiple, well-separated timescales. Building on an existing, deterministic formulation via ordinary differential equations, we resolve different orders of magnitude within a small parameter and analyze the system's limit cycle behavior using geometric singular perturbation theory (GSPT). By introducing two different coordinate scalings - each valid in a distinct region of the phase space - we resolve the local dynamics near critical fold points, using the extension of GSPT through such singular points due to Krupa and Szmolyan. This framework enables a geometric decomposition of the periodic orbits into slow and fast segments and yields closed-form estimates for the period of oscillation. In particular, we link the existence of such oscillations to an underlying biochemical asymmetry, namely, the differential transport across the vesicle membrane.}, language = {en} } @article{delRazoFroembergStraubeetal.2022, author = {del Razo, Mauricio and Fr{\"o}mberg, Daniela and Straube, Arthur and Sch{\"u}tte, Christof and H{\"o}fling, Felix and Winkelmann, Stefanie}, title = {A probabilistic framework for particle-based reaction-diffusion dynamics using classical Fock space representations}, volume = {112}, journal = {Letters in Mathematical Physics}, number = {49}, arxiv = {http://arxiv.org/abs/arXiv:2109.13616}, doi = {10.1007/s11005-022-01539-w}, year = {2022}, language = {en} } @article{StraubeWinkelmannSchuetteetal.2021, author = {Straube, Arthur and Winkelmann, Stefanie and Sch{\"u}tte, Christof and H{\"o}fling, Felix}, title = {Stochastic pH oscillations in a model of the urea-urease reaction confined to lipid vesicles}, volume = {12}, journal = {J. Phys. Chem. Lett.}, doi = {10.1021/acs.jpclett.1c03016}, pages = {9888 -- 9893}, year = {2021}, abstract = {The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We numerically study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules. For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller. The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm, but the periodicity of the rhythm is gradually destroyed for smaller vesicles. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators.}, language = {en} } @article{StraubeWinkelmannHoefling2023, author = {Straube, Arthur and Winkelmann, Stefanie and H{\"o}fling, Felix}, title = {Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles}, volume = {127}, journal = {The Journal of Physical Chemistry B}, number = {13}, arxiv = {http://arxiv.org/abs/arXiv:2212.14503}, doi = {10.1021/acs.jpcb.2c09092}, pages = {2955 -- 2967}, year = {2023}, abstract = {This theoretical study concerns a pH oscillator based on the urea-urease reaction confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyse the structure of the phase flow and of the limit cycle, which controls the dynamics for giant vesicles and dominates the pronouncedly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, which are amenable to analytic treatments that are complemented by numerical solutions, and obtain the period and amplitude of the oscillations as well as the parameter domain, where oscillatory behavior persists. We show that the accuracy of these predictions is highly sensitive to the employed reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The faithful modeling of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms.}, language = {en} } @misc{StraubeWinkelmannHoefling2022, author = {Straube, Arthur and Winkelmann, Stefanie and H{\"o}fling, Felix}, title = {Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles}, issn = {1438-0064}, doi = {10.12752/8817}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88179}, year = {2022}, abstract = {Our theoretical study concerns an urea-urease-based pH oscillator confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyse the structure of the limit cycle, which controls the dynamics for giant vesicles and dominates the strongly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, amenable to analytic treatments, and show that the accuracy of predictions, including the period of oscillations, is highly sensitive to the choice of the reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The accurate description of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms.}, language = {en} } @article{delRazoWinkelmannKleinetal.2023, author = {del Razo, Mauricio and Winkelmann, Stefanie and Klein, Rupert and H{\"o}fling, Felix}, title = {Chemical diffusion master equation: formulations of reaction-diffusion processes on the molecular level}, volume = {64}, journal = {Journal of Mathematical Physics}, number = {1}, arxiv = {http://arxiv.org/abs/2210.02268}, doi = {10.1063/5.0129620}, year = {2023}, abstract = {The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction--diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112:49, 2022]; it can be considered the master equation for reaction--diffusion processes. The CDME consists of an infinite ordered family of Fokker--Planck equations, where each level of the ordered family corresponds to a certain number of particles and each particle represents a molecule. The equations at each level describe the spatial diffusion of the corresponding set of particles, and they are coupled to each other via reaction operators --linear operators representing chemical reactions. These operators change the number of particles in the system, and thus transport probability between different levels in the family. In this work, we present three approaches to formulate the CDME and show the relations between them. We further deduce the non-trivial combinatorial factors contained in the reaction operators, and we elucidate the relation to the original formulation of the CDME, which is based on creation and annihilation operators acting on many-particle probability density functions. Finally we discuss applications to multiscale simulations of biochemical systems among other future prospects.}, language = {en} }