@article{GrebenkovMetzlerOshanin2022, author = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb}, title = {Search efficiency in the Adam-Delbruck reduction-of-dimensionality scenario versus direct diffusive search}, series = {New journal of physics : the open-access journal for physics}, volume = {24}, journal = {New journal of physics : the open-access journal for physics}, number = {8}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/ac8824}, pages = {32}, year = {2022}, abstract = {The time instant-the first-passage time (FPT)-when a diffusive particle (e.g., a ligand such as oxygen or a signalling protein) for the first time reaches an immobile target located on the surface of a bounded three-dimensional domain (e.g., a hemoglobin molecule or the cellular nucleus) is a decisive characteristic time-scale in diverse biophysical and biochemical processes, as well as in intermediate stages of various inter- and intra-cellular signal transduction pathways. Adam and Delbruck put forth the reduction-of-dimensionality concept, according to which a ligand first binds non-specifically to any point of the surface on which the target is placed and then diffuses along this surface until it locates the target. In this work, we analyse the efficiency of such a scenario and confront it with the efficiency of a direct search process, in which the target is approached directly from the bulk and not aided by surface diffusion. We consider two situations: (i) a single ligand is launched from a fixed or a random position and searches for the target, and (ii) the case of 'amplified' signals when N ligands start either from the same point or from random positions, and the search terminates when the fastest of them arrives to the target. For such settings, we go beyond the conventional analyses, which compare only the mean values of the corresponding FPTs. Instead, we calculate the full probability density function of FPTs for both scenarios and study its integral characteristic-the 'survival' probability of a target up to time t. On this basis, we examine how the efficiencies of both scenarios are controlled by a variety of parameters and single out realistic conditions in which the reduction-of-dimensionality scenario outperforms the direct search.}, language = {en} } @article{CherstvyWangMetzleretal.2021, author = {Cherstvy, Andrey G. and Wang, Wei and Metzler, Ralf and Sokolov, Igor M.}, title = {Inertia triggers nonergodicity of fractional Brownian motion}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {104}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {2}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.104.024115}, pages = {12}, year = {2021}, abstract = {How related are the ergodic properties of the over- and underdamped Langevin equations driven by fractional Gaussian noise? We here find that for massive particles performing fractional Brownian motion (FBM) inertial effects not only destroy the stylized fact of the equivalence of the ensemble-averaged mean-squared displacement (MSD) to the time-averaged MSD (TAMSD) of overdamped or massless FBM, but also dramatically alter the values of the ergodicity-breaking parameter (EB). Our theoretical results for the behavior of EB for underdamped or massive FBM for varying particle mass m, Hurst exponent H, and trace length T are in excellent agreement with the findings of stochastic computer simulations. The current results can be of interest for the experimental community employing various single-particle-tracking techniques and aiming at assessing the degree of nonergodicity for the recorded time series (studying, e.g., the behavior of EB versus lag time). To infer FBM as a realizable model of anomalous diffusion for a set single-particle-tracking data when massive particles are being tracked, the EBs from the data should be compared to EBs of massive (rather than massless) FBM.}, language = {en} } @article{KlettCherstvyShinetal.2021, author = {Klett, Kolja and Cherstvy, Andrey G. and Shin, Jaeoh and Sokolov, Igor M. and Metzler, Ralf}, title = {Non-Gaussian, transiently anomalous, and ergodic self-diffusion of flexible dumbbells in crowded two-dimensional environments}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {104}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {6}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.104.064603}, pages = {18}, year = {2021}, abstract = {We employ Langevin-dynamics simulations to unveil non-Brownian and non-Gaussian center-of-mass self-diffusion of massive flexible dumbbell-shaped particles in crowded two-dimensional solutions. We study the intradumbbell dynamics of the relative motion of the two constituent elastically coupled disks. Our main focus is on effects of the crowding fraction phi and of the particle structure on the diffusion characteristics. We evaluate the time-averaged mean-squared displacement (TAMSD), the displacement probability-density function (PDF), and the displacement autocorrelation function (ACF) of the dimers. For the TAMSD at highly crowded conditions of dumbbells, e.g., we observe a transition from the short-time ballistic behavior, via an intermediate subdiffusive regime, to long-time Brownian-like spreading dynamics. The crowded system of dimers exhibits two distinct diffusion regimes distinguished by the scaling exponent of the TAMSD, the dependence of the diffusivity on phi, and the features of the displacement-ACF. We attribute these regimes to a crowding-induced transition from viscous to viscoelastic diffusion upon growing phi. We also analyze the relative motion in the dimers, finding that larger phi suppress their vibrations and yield strongly non-Gaussian PDFs of rotational displacements. For the diffusion coefficients D(phi) of translational and rotational motion of the dumbbells an exponential decay with phi for weak and a power-law variation D(phi) proportional to (phi - phi(star))(2.4) for strong crowding is found. A comparison of simulation results with theoretical predictions for D(phi) is discussed and some relevant experimental systems are overviewed.}, language = {en} } @article{BolotovSmirnovBubnovaetal.2021, author = {Bolotov, Maxim I. and Smirnov, Lev A. and Bubnova, E. S. and Osipov, Grigory V. and Pikovskij, Arkadij}, title = {Spatiotemporal regimes in the Kuramoto-Battogtokh system of nonidentical oscillators}, series = {Journal of experimental and theoretical physics}, volume = {132}, journal = {Journal of experimental and theoretical physics}, number = {1}, publisher = {Springer}, address = {Heidelberg [u.a.]}, issn = {1063-7761}, doi = {10.1134/S1063776121010106}, pages = {127 -- 147}, year = {2021}, abstract = {We consider the spatiotemporal states of an ensemble of nonlocally coupled nonidentical phase oscillators, which correspond to different regimes of the long-term evolution of such a system. We have obtained homogeneous, twisted, and nonhomogeneous stationary solutions to the Ott-Antonsen equations corresponding to key variants of the realized collective rotational motion of elements of the medium in question with nonzero mesoscopic characteristics determining the degree of coherence of the dynamics of neighboring particles. We have described the procedures of the search for the class of nonhomogeneous solutions as stationary points of the auxiliary point map and of determining the stability based on analysis of the eigenvalue spectrum of the composite operator. Static and breather cluster regimes have been demonstrated and described, as well as the regimes with an irregular behavior of averaged complex fields including, in particular, the local order parameter.}, language = {en} } @article{VilkAghionNathanetal.2022, author = {Vilk, Ohad and Aghion, Erez and Nathan, Ran and Toledo, Sivan and Metzler, Ralf and Assaf, Michael}, title = {Classification of anomalous diffusion in animal movement data using power spectral analysis}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {55}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {33}, publisher = {IOP Publishing}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/ac7e8f}, pages = {16}, year = {2022}, abstract = {The field of movement ecology has seen a rapid increase in high-resolution data in recent years, leading to the development of numerous statistical and numerical methods to analyse relocation trajectories. Data are often collected at the level of the individual and for long periods that may encompass a range of behaviours. Here, we use the power spectral density (PSD) to characterise the random movement patterns of a black-winged kite (Elanus caeruleus) and a white stork (Ciconia ciconia). The tracks are first segmented and clustered into different behaviours (movement modes), and for each mode we measure the PSD and the ageing properties of the process. For the foraging kite we find 1/f noise, previously reported in ecological systems mainly in the context of population dynamics, but not for movement data. We further suggest plausible models for each of the behavioural modes by comparing both the measured PSD exponents and the distribution of the single-trajectory PSD to known theoretical results and simulations.}, language = {en} } @article{SposiniChechkinSokolovetal.2022, author = {Sposini, Vittoria and Chechkin, Aleksei and Sokolov, Igor M. and Roldan-Vargas, Sandalo}, title = {Detecting temporal correlations in hopping dynamics in Lennard-Jones liquids}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {55}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {32}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/ac7e0a}, pages = {15}, year = {2022}, abstract = {Lennard-Jones mixtures represent one of the popular systems for the study of glass-forming liquids. Spatio/temporal heterogeneity and rare (activated) events are at the heart of the slow dynamics typical of these systems. Such slow dynamics is characterised by the development of a plateau in the mean-squared displacement (MSD) at intermediate times, accompanied by a non-Gaussianity in the displacement distribution identified by exponential tails. As pointed out by some recent works, the non-Gaussianity persists at times beyond the MSD plateau, leading to a Brownian yet non-Gaussian regime and thus highlighting once again the relevance of rare events in such systems. Single-particle motion of glass-forming liquids is usually interpreted as an alternation of rattling within the local cage and cage-escape motion and therefore can be described as a sequence of waiting times and jumps. In this work, by using a simple yet robust algorithm, we extract jumps and waiting times from single-particle trajectories obtained via molecular dynamics simulations. We investigate the presence of correlations between waiting times and find negative correlations, which becomes more and more pronounced when lowering the temperature.}, language = {en} } @article{KraemerGelbrechtPavithranetal.2022, author = {Kr{\"a}mer, Hauke Kai and Gelbrecht, Maximilian and Pavithran, Induja and Sujith, Ravindran and Marwan, Norbert}, title = {Optimal state space reconstruction via Monte Carlo decision tree search}, series = {Nonlinear Dynamics}, volume = {108}, journal = {Nonlinear Dynamics}, number = {2}, publisher = {Springer}, address = {Dordrecht}, issn = {0924-090X}, doi = {10.1007/s11071-022-07280-2}, pages = {1525 -- 1545}, year = {2022}, abstract = {A novel idea for an optimal time delay state space reconstruction from uni- and multivariate time series is presented. The entire embedding process is considered as a game, in which each move corresponds to an embedding cycle and is subject to an evaluation through an objective function. This way the embedding procedure can be modeled as a tree, in which each leaf holds a specific value of the objective function. By using a Monte Carlo ansatz, the proposed algorithm populates the tree with many leafs by computing different possible embedding paths and the final embedding is chosen as that particular path, which ends at the leaf with the lowest achieved value of the objective function. The method aims to prevent getting stuck in a local minimum of the objective function and can be used in a modular way, enabling practitioners to choose a statistic for possible delays in each embedding cycle as well as a suitable objective function themselves. The proposed method guarantees the optimization of the chosen objective function over the parameter space of the delay embedding as long as the tree is sampled sufficiently. As a proof of concept, we demonstrate the superiority of the proposed method over the classical time delay embedding methods using a variety of application examples. We compare recurrence plot-based statistics inferred from reconstructions of a Lorenz-96 system and highlight an improved forecast accuracy for map-like model data as well as for palaeoclimate isotope time series. Finally, we utilize state space reconstruction for the detection of causality and its strength between observables of a gas turbine type thermoacoustic combustor.}, language = {en} } @article{YuanZhangQiuetal.2022, author = {Yuan, Jun and Zhang, Chujun and Qiu, Beibei and Liu, Wei and So, Shu Kong and Mainville, Mathieu and Leclerc, Mario and Shoaee, Safa and Neher, Dieter and Zou, Yingping}, title = {Effects of energetic disorder in bulk heterojunction organic solar cells}, series = {Energy \& environmental science}, volume = {15}, journal = {Energy \& environmental science}, number = {7}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1754-5692}, doi = {10.1039/d2ee00271j}, pages = {2806 -- 2818}, year = {2022}, abstract = {Organic solar cells (OSCs) have progressed rapidly in recent years through the development of novel organic photoactive materials, especially non-fullerene acceptors (NFAs). Consequently, OSCs based on state-of-the-art NFAs have reached significant milestones, such as similar to 19\% power conversion efficiencies (PCEs) and small energy losses (less than 0.5 eV). Despite these significant advances, understanding of the interplay between molecular structure and optoelectronic properties lags significantly behind. For example, despite the theoretical framework for describing the energetic disorder being well developed for the case of inorganic semiconductors, the question of the applicability of classical semiconductor theories in analyzing organic semiconductors is still under debate. A general observation in the inorganic field is that inorganic photovoltaic materials possessing a polycrystalline microstructure exhibit suppressed disorder properties and better charge carrier transport compared to their amorphous analogs. Accordingly, this principle extends to the organic semiconductor field as many organic photovoltaic materials are synthesized to pursue polycrystalline-like features. Yet, there appears to be sporadic examples that exhibit an opposite trend. However, full studies decoupling energetic disorder from aggregation effects have largely been left out. Hence, the potential role of the energetic disorder in OSCs has received little attention. Interestingly, recently reported state-of-the-art NFA-based devices could achieve a small energetic disorder and high PCE at the same time; and interest in this investigation related to the disorder properties in OSCs was revived. In this contribution, progress in terms of the correlation between molecular design and energetic disorder is reviewed together with their effects on the optoelectronic mechanism and photovoltaic performance. Finally, the specific challenges and possible solutions in reducing the energetic disorder of OSCs from the viewpoint of materials and devices are proposed.}, language = {en} } @article{KrohEllerSchoetzetal.2022, author = {Kroh, Daniel and Eller, Fabian and Sch{\"o}tz, Konstantin and Wedler, Stefan and Perdig{\´o}n-Toro, Lorena and Freychet, Guillaume and Wei, Qingya and D{\"o}rr, Maximilian and Jones, David and Zou, Yingping and Herzig, Eva M. and Neher, Dieter and K{\"o}hler, Anna}, title = {Identifying the signatures of intermolecular interactions in blends of PM6 with Y6 and N4 using absorption spectroscopy}, series = {Advanced functional materials}, volume = {32}, journal = {Advanced functional materials}, number = {44}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {1616-301X}, doi = {10.1002/adfm.202205711}, pages = {14}, year = {2022}, abstract = {In organic solar cells, the resulting device efficiency depends strongly on the local morphology and intermolecular interactions of the blend film. Optical spectroscopy was used to identify the spectral signatures of interacting chromophores in blend films of the donor polymer PM6 with two state-of-the-art nonfullerene acceptors, Y6 and N4, which differ merely in the branching point of the side chain. From temperature-dependent absorption and luminescence spectroscopy in solution, it is inferred that both acceptor materials form two types of aggregates that differ in their interaction energy. Y6 forms an aggregate with a predominant J-type character in solution, while for N4 molecules the interaction is predominantly in a H-like manner in solution and freshly spin-cast film, yet the molecules reorient with respect to each other with time or thermal annealing to adopt a more J-type interaction. The different aggregation behavior of the acceptor materials is also reflected in the blend films and accounts for the different solar cell efficiencies reported with the two blends.}, language = {en} } @phdthesis{Doerries2024, author = {D{\"o}rries, Timo Julian}, title = {Anomalous transport and non-Gaussian dynamics in mobile-immobile models}, doi = {10.25932/publishup-63495}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-634959}, school = {Universit{\"a}t Potsdam}, pages = {ii, 177}, year = {2024}, abstract = {The mobile-immobile model (MIM) has been established in geoscience in the context of contaminant transport in groundwater. Here the tracer particles effectively immobilise, e.g., due to diffusion into dead-end pores or sorption. The main idea of the MIM is to split the total particle density into a mobile and an immobile density. Individual tracers switch between the mobile and immobile state following a two-state telegraph process, i.e., the residence times in each state are distributed exponentially. In geoscience the focus lies on the breakthrough curve (BTC), which is the concentration at a fixed location over time. We apply the MIM to biological experiments with a special focus on anomalous scaling regimes of the mean squared displacement (MSD) and non-Gaussian displacement distributions. As an exemplary system, we have analysed the motion of tau proteins, that diffuse freely inside axons of neurons. Their free diffusion thereby corresponds to the mobile state of the MIM. Tau proteins stochastically bind to microtubules, which effectively immobilises the tau proteins until they unbind and continue diffusing. Long immobilisation durations compared to the mobile durations give rise to distinct non-Gaussian Laplace shaped distributions. It is accompanied by a plateau in the MSD for initially mobile tracer particles at relevant intermediate timescales. An equilibrium fraction of initially mobile tracers gives rise to non-Gaussian displacements at intermediate timescales, while the MSD remains linear at all times. In another setting bio molecules diffuse in a biosensor and transiently bind to specific receptors, where advection becomes relevant in the mobile state. The plateau in the MSD observed for the advection-free setting and long immobilisation durations persists also for the case with advection. We find a new clear regime of anomalous diffusion with non-Gaussian distributions and a cubic scaling of the MSD. This regime emerges for initially mobile and for initially immobile tracers. For an equilibrium fraction of initially mobile tracers we observe an intermittent ballistic scaling of the MSD. The long-time effective diffusion coefficient is enhanced by advection, which we physically explain with the variance of mobile durations. Finally, we generalize the MIM to incorporate arbitrary immobilisation time distributions and focus on a Mittag-Leffler immobilisation time distribution with power-law tail ~ t^(-1-mu) with 0