@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{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{KourovSamoilovaStraube2025, author = {Kourov, Mikhail N. and Samoilova, Anna E. and Straube, Arthur}, title = {Dynamics of a chain of interacting magnetic particles in a one-dimensional periodic energy landscape}, volume = {89}, journal = {Bull. Russ. Acad. Sci. Phys.}, number = {7}, issn = {1062-8738}, doi = {10.1134/S1062873825711742}, pages = {1086 -- 1092}, year = {2025}, abstract = {We explore the dynamics of a one-dimensional chain of paramagnetic colloidal particles in a periodic potential. The model accounts for a constant external force, along with magnetic dipolar attraction and hard-core repulsive interactions between particles. Numerical simulations reveal the emergence of a traveling kink - a chain defect propagating along the chain. We show that the kink emerges beyond a critical force threshold and identify parameter regimes corresponding to distinct dynamic modes such as a pinned kink, a running kink, a cluster kink, and chain drift.}, language = {en} }