@misc{SposiniKrapfMarinarietal.2022, author = {Sposini, Vittoria and Krapf, Diego and Marinari, Enzo and Sunyer, Raimon and Ritort, Felix and Taheri, Fereydoon and Selhuber-Unkel, Christine and Benelli, Rebecca and Weiss, Matthias and Metzler, Ralf and Oshanin, Gleb}, title = {Towards a robust criterion of anomalous diffusion}, series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {1313}, issn = {1866-8372}, doi = {10.25932/publishup-58596}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-585967}, pages = {10}, year = {2022}, abstract = {Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion emerges due to a variety of physical mechanisms, e.g., trapping interactions or the viscoelasticity of the environment. However, sometimes systems dynamics are erroneously claimed to be anomalous, despite the fact that the true motion is Brownian—or vice versa. This ambiguity in establishing whether the dynamics as normal or anomalous can have far-reaching consequences, e.g., in predictions for reaction- or relaxation-laws. Demonstrating that a system exhibits normal- or anomalous-diffusion is highly desirable for a vast host of applications. Here, we present a criterion for anomalous-diffusion based on the method of power-spectral analysis of single trajectories. The robustness of this criterion is studied for trajectories of fractional-Brownian-motion, a ubiquitous stochastic process for the description of anomalous-diffusion, in the presence of two types of measurement errors. In particular, we find that our criterion is very robust for subdiffusion. Various tests on surrogate data in absence or presence of additional positional noise demonstrate the efficacy of this method in practical contexts. Finally, we provide a proof-of-concept based on diverse experiments exhibiting both normal and anomalous-diffusion.}, language = {en} } @misc{deCarvalhoMetzlerCherstvy2014, author = {de Carvalho, Sidney J. and Metzler, Ralf and Cherstvy, Andrey G.}, title = {Critical adsorption of polyelectrolytes onto charged Janus nanospheres}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-98783}, pages = {12}, year = {2014}, abstract = {Based on extensive Monte Carlo simulations and analytical considerations we study the electrostatically driven adsorption of flexible polyelectrolyte chains onto charged Janus nanospheres. These net-neutral colloids are composed of two equally but oppositely charged hemispheres. The critical binding conditions for polyelectrolyte chains are analysed as function of the radius of the Janus particle and its surface charge density, as well as the salt concentration in the ambient solution. Specifically for the adsorption of finite-length polyelectrolyte chains onto Janus nanoparticles, we demonstrate that the critical adsorption conditions drastically differ when the size of the Janus particle or the screening length of the electrolyte are varied. We compare the scaling laws obtained for the adsorption-desorption threshold to the known results for uniformly charged spherical particles, observing significant disparities. We also contrast the changes to the polyelectrolyte chain conformations close to the surface of the Janus nanoparticles as compared to those for simple spherical particles. Finally, we discuss experimentally relevant physico-chemical systems for which our simulations results may become important. In particular, we observe similar trends with polyelectrolyte complexation with oppositely but heterogeneously charged proteins.}, language = {en} } @misc{BauerGodecMetzler2014, author = {Bauer, Maximilian and Godec, Aljaž and Metzler, Ralf}, title = {Diffusion of finite-size particles in two-dimensional channels with random wall configurations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76199}, year = {2014}, abstract = {Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda [J. Chem. Phys., 2012, 137, 024107].}, language = {en} } @misc{BodrovaChechkinCherstvyetal.2016, author = {Bodrova, Anna S. and Chechkin, Aleksei V. and Cherstvy, Andrey G. and Safdari, Hadiseh and Sokolov, Igor M. and Metzler, Ralf}, title = {Underdamped scaled Brownian motion}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-97158}, pages = {16}, year = {2016}, abstract = {It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.}, language = {en} } @misc{MolinaGarciaSandevSafdarietal.2019, author = {Molina-Garcia, Daniel and Sandev, Trifce and Safdari, Hadiseh and Pagnini, Gianni and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Crossover from anomalous to normal diffusion}, series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, number = {507}, issn = {1866-8372}, doi = {10.25932/publishup-42259}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-422590}, pages = {28}, year = {2019}, abstract = {Abstract The emerging diffusive dynamics in many complex systems show a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent power-laws. A prominent example for a subdiffusive-diffusive crossover are viscoelastic systems such as lipid bilayer membranes, while superdiffusive-diffusive crossovers occur in systems of actively moving biological cells. We here consider the general dynamics of a stochastic particle driven by so-called tempered fractional Gaussian noise, that is noise with Gaussian amplitude and power-law correlations, which are cut off at some mesoscopic time scale. Concretely we consider such noise with built-in exponential or power-law tempering, driving an overdamped Langevin equation (fractional Brownian motion) and fractional Langevin equation motion. We derive explicit expressions for the mean squared displacement and correlation functions, including different shapes of the crossover behaviour depending on the concrete tempering, and discuss the physical meaning of the tempering. In the case of power-law tempering we also find a crossover behaviour from faster to slower superdiffusion and slower to faster subdiffusion. As a direct application of our model we demonstrate that the obtained dynamics quantitatively describes the subdiffusion-diffusion and subdiffusion-subdiffusion crossover in lipid bilayer systems. We also show that a model of tempered fractional Brownian motion recently proposed by Sabzikar and Meerschaert leads to physically very different behaviour with a seemingly paradoxical ballistic long time scaling.}, language = {en} }