@article{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 = {Communications Physics}, volume = {5}, journal = {Communications Physics}, publisher = {Springer Nature}, address = {London}, issn = {2399-3650}, doi = {10.1038/s42005-022-01079-8}, 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} } @article{XuZhouMetzleretal.2022, author = {Xu, Pengbo and Zhou, Tian and Metzler, Ralf and Deng, Weihua}, title = {Stochastic harmonic trapping of a L{\´e}vy walk}, series = {New journal of physics : the open-access journal for physics / Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics}, volume = {24}, journal = {New journal of physics : the open-access journal for physics / Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics}, number = {3}, publisher = {Deutsche Physikalische Gesellschaft}, address = {Bad Honnef}, issn = {1367-2630}, doi = {10.1088/1367-2630/ac5282}, pages = {1 -- 28}, year = {2022}, abstract = {We introduce and study a L{\´e}vy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic.}, language = {en} } @article{WangCherstvyMetzleretal.2022, author = {Wang, Wei and Cherstvy, Andrey G. and Metzler, Ralf and Sokolov, Igor M.}, title = {Restoring ergodicity of stochastically reset anomalous-diffusion processes}, series = {Physical Review Research}, volume = {4}, journal = {Physical Review Research}, edition = {1}, publisher = {American Physical Society}, address = {College Park, Maryland, United States}, issn = {2643-1564}, doi = {10.1103/PhysRevResearch.4.013161}, pages = {013161-1 -- 013161-13}, year = {2022}, abstract = {How do different reset protocols affect ergodicity of a diffusion process in single-particle-tracking experiments? We here address the problem of resetting of an arbitrary stochastic anomalous-diffusion process (ADP) from the general mathematical points of view and assess ergodicity of such reset ADPs for an arbitrary resetting protocol. The process of stochastic resetting describes the events of the instantaneous restart of a particle's motion via randomly distributed returns to a preset initial position (or a set of those). The waiting times of such resetting events obey the Poissonian, Gamma, or more generic distributions with specified conditions regarding the existence of moments. Within these general approaches, we derive general analytical results and support them by computer simulations for the behavior of the reset mean-squared displacement (MSD), the new reset increment-MSD (iMSD), and the mean reset time-averaged MSD (TAMSD). For parental nonreset ADPs with the MSD(t)∝ tμ we find a generic behavior and a switch of the short-time growth of the reset iMSD and mean reset TAMSDs from ∝ _μ for subdiffusive to ∝ _1 for superdiffusive reset ADPs. The critical condition for a reset ADP that recovers its ergodicity is found to be more general than that for the nonequilibrium stationary state, where obviously the iMSD and the mean TAMSD are equal. The consideration of the new statistical quantifier, the iMSD—as compared to the standard MSD—restores the ergodicity of an arbitrary reset ADP in all situations when the μth moment of the waiting-time distribution of resetting events is finite. Potential applications of these new resetting results are, inter alia, in the area of biophysical and soft-matter systems.}, language = {en} } @article{SarabadaniMetzlerAlaNissila2022, author = {Sarabadani, Jalal and Metzler, Ralf and Ala-Nissila, Tapio}, title = {Driven polymer translocation into a channel: Isoflux tension propagation theory and Langevin dynamics simulations}, series = {Physical Review Research}, volume = {4}, journal = {Physical Review Research}, edition = {3}, publisher = {American Physical Society}, address = {College Park, Maryland, USA}, issn = {2643-1564}, doi = {10.1103/PhysRevResearch.4.033003}, pages = {033003-1 -- 033003-14}, year = {2022}, abstract = {Isoflux tension propagation (IFTP) theory and Langevin dynamics (LD) simulations are employed to study the dynamics of channel-driven polymer translocation in which a polymer translocates into a narrow channel and the monomers in the channel experience a driving force fc. In the high driving force limit, regardless of the channel width, IFTP theory predicts τ ∝ f βc for the translocation time, where β = -1 is the force scaling exponent. Moreover, LD data show that for a very narrow channel fitting only a single file of monomers, the entropic force due to the subchain inside the channel does not play a significant role in the translocation dynamics and the force exponent β = -1 regardless of the force magnitude. As the channel width increases the number of possible spatial configurations of the subchain inside the channel becomes significant and the resulting entropic force causes the force exponent to drop below unity.}, language = {en} } @article{GrebenkovMetzlerOshanin2021, author = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb}, title = {Distribution of first-reaction times with target regions on boundaries of shell-like domains}, series = {New Journal of Physics (NJP)}, volume = {2021}, journal = {New Journal of Physics (NJP)}, edition = {23}, publisher = {IOP Publishing}, address = {London}, issn = {1367-2630}, doi = {10.1088/1367-2630/ac4282}, pages = {1 -- 23}, year = {2021}, abstract = {We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted 'onion-shell' geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.}, language = {en} }