@misc{SposiniMetzlerOshanin2019, author = {Sposini, Vittoria and Metzler, Ralf and Oshanin, Gleb}, title = {Single-trajectory spectral analysis of scaled Brownian motion}, series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, number = {753}, issn = {1866-8372}, doi = {10.25932/publishup-43652}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436522}, pages = {16}, year = {2019}, abstract = {Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.}, language = {en} } @misc{GuggenbergerPagniniVojtaetal.2019, author = {Guggenberger, Tobias and Pagnini, Gianni and Vojta, Thomas and Metzler, Ralf}, title = {Fractional Brownian motion in a finite interval}, series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, number = {755}, issn = {1866-8372}, doi = {10.25932/publishup-43666}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436665}, pages = {13}, year = {2019}, abstract = {Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite interval with reflecting boundary conditions. The probability density function of this reflected FBM at long times converges to a stationary distribution showing distinct deviations from the fully flat distribution of amplitude 1/L in an interval of length L found for reflected normal Brownian motion. While for superdiffusion, corresponding to a mean squared displacement (MSD) 〈X² (t)〉 ⋍ tᵅ with 1 < α < 2, the probability density function is lowered in the centre of the interval and rises towards the boundaries, for subdiffusion (0 < α < 1) this behaviour is reversed and the particle density is depleted close to the boundaries. The MSD in these cases at long times converges to a stationary value, which is, remarkably, monotonically increasing with the anomalous diffusion exponent α. Our a priori surprising results may have interesting consequences for the application of FBM for processes such as molecule or tracer diffusion in the confines of living biological cells or organelles, or other viscoelastic environments such as dense liquids in microfluidic chambers.}, language = {en} } @misc{ŚlęzakBurneckiMetzler2019, author = {Ślęzak, Jakub and Burnecki, Krzysztof and Metzler, Ralf}, title = {Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems}, series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, number = {765}, issn = {1866-8372}, doi = {10.25932/publishup-43792}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-437923}, pages = {18}, year = {2019}, abstract = {Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as 'superstatistics' or 'diffusing diffusivity'. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.}, language = {en} } @article{Omelʹchenko2020, author = {Omelʹchenko, Oleh E.}, title = {Nonstationary coherence-incoherence patterns in nonlocally coupled heterogeneous phase oscillators}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {30}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {4}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.5145259}, pages = {8}, year = {2020}, abstract = {We consider a large ring of nonlocally coupled phase oscillators and show that apart from stationary chimera states, this system also supports nonstationary coherence-incoherence patterns (CIPs). For identical oscillators, these CIPs behave as breathing chimera states and are found in a relatively small parameter region only. It turns out that the stability region of these states enlarges dramatically if a certain amount of spatially uniform heterogeneity (e.g., Lorentzian distribution of natural frequencies) is introduced in the system. In this case, nonstationary CIPs can be studied as stable quasiperiodic solutions of a corresponding mean-field equation, formally describing the infinite system limit. Carrying out direct numerical simulations of the mean-field equation, we find different types of nonstationary CIPs with pulsing and/or alternating chimera-like behavior. Moreover, we reveal a complex bifurcation scenario underlying the transformation of these CIPs into each other. These theoretical predictions are confirmed by numerical simulations of the original coupled oscillator system.}, language = {en} } @article{WangCherstvyChechkinetal.2020, author = {Wang, Wei and Cherstvy, Andrey G. and Chechkin, Aleksei V. and Thapa, Samudrajit and Seno, Flavio and Liu, Xianbin and Metzler, Ralf}, title = {Fractional Brownian motion with random diffusivity}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {53}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {47}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/aba467}, pages = {34}, year = {2020}, abstract = {Numerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments. Here, we address the case of non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise. We study the ergodic properties of this model via examining the ensemble- and time-averaged mean-squared displacements as well as the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the latter. For long measurement times, interesting crossover behaviour is found as function of the correlation time tau characterising the diffusivity dynamics. We unveil that at short lag times the EB parameter reaches a universal plateau. The corresponding residual value of EB is shown to depend only on tau and the trajectory length. The EB parameter at long lag times, however, follows the same power-law scaling as for fractional Brownian motion. We also determine a corresponding plateau at short lag times for the discrete representation of fractional Brownian motion, absent in the continuous-time formulation. These analytical predictions are in excellent agreement with results of computer simulations of the underlying stochastic processes. Our findings can help distinguishing and categorising certain nonergodic and non-Gaussian features of particle displacements, as observed in recent single-particle tracking experiments.}, language = {en} } @article{KurilovichMantsevichStevensonetal.2020, author = {Kurilovich, Aleksandr A. and Mantsevich, Vladimir and Stevenson, Keith J. and Chechkin, Aleksei V. and Palyulin, V. V.}, title = {Complex diffusion-based kinetics of photoluminescence in semiconductor nanoplatelets}, series = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, volume = {22}, journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, number = {42}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/d0cp03744c}, pages = {24686 -- 24696}, year = {2020}, abstract = {We present a diffusion-based simulation and theoretical models for explanation of the photoluminescence (PL) emission intensity in semiconductor nanoplatelets. It is shown that the shape of the PL intensity curves can be reproduced by the interplay of recombination, diffusion and trapping of excitons. The emission intensity at short times is purely exponential and is defined by recombination. At long times, it is governed by the release of excitons from surface traps and is characterized by a power-law tail. We show that the crossover from one limit to another is controlled by diffusion properties. This intermediate region exhibits a rich behaviour depending on the value of diffusivity. The proposed approach reproduces all the features of experimental curves measured for different nanoplatelet systems.}, language = {en} } @article{SteppaEgberts2020, author = {Steppa, Constantin and Egberts, Kathrin}, title = {Modelling the Galactic very-high-energy gamma-ray source population}, series = {Astronomy and astrophysics : an international weekly journal}, volume = {643}, journal = {Astronomy and astrophysics : an international weekly journal}, publisher = {EDP Sciences}, address = {Les Ulis}, issn = {0004-6361}, doi = {10.1051/0004-6361/202038172}, pages = {11}, year = {2020}, abstract = {Context. The High Energy Stereoscopic System Galactic plane survey (HGPS) is to date the most comprehensive census of Galactic gamma -ray sources at very high energies (VHE; 100 GeV <= E <= 100 TeV). As a consequence of the limited sensitivity of this survey, the 78 detected gamma -ray sources comprise only a small and biased subsample of the overall population. The larger part consists of currently unresolved sources, which contribute to large-scale diffuse emission to a still uncertain amount.Aims. We study the VHE gamma -ray source population in the Milky Way. For this purpose population-synthesis models are derived based on the distributions of source positions, extents, and luminosities.Methods. Several azimuth-symmetric and spiral-arm models are compared for spatial source distribution. The luminosity and radius function of the population are derived from the source properties of the HGPS data set and are corrected for the sensitivity bias of the HGPS. Based on these models, VHE source populations are simulated and the subsets of sources detectable according to the HGPS are compared with HGPS sources.Results. The power-law indices of luminosity and radius functions are determined to range between -1.6 and -1.9 for luminosity and -1.1 and -1.6 for radius. A two-arm spiral structure with central bar is discarded as spatial distribution of VHE sources, while azimuth-symmetric distributions and a distribution following a four-arm spiral structure without bar describe the HGPS data reasonably well. The total number of Galactic VHE sources is predicted to be in the range from 800 to 7000 with a total luminosity and flux of (1.6-6.3) x 10(36) ph s(-1) and (3-15) x 10(-10) ph cm(-2) s(-1), respectively.Conclusions. Depending on the model, the HGPS sample accounts for (68-87)\% of the emission of the population in the scanned region. This suggests that unresolved sources represent a critical component of the diffuse emission measurable in the HGPS. With the foreseen jump in sensitivity of the Cherenkov Telescope Array, the number of detectable sources is predicted to increase by a factor between 5 and 9.}, 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{KietheHeuerJechow2017, author = {Kiethe, Jan and Heuer, Axel and Jechow, Andreas}, title = {Second-order coherence properties of amplified spontaneous emission from a high-power tapered superluminescent diode}, series = {Laser physics letters}, volume = {14}, journal = {Laser physics letters}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1612-2011}, doi = {10.1088/1612-202X/aa772c}, pages = {4}, year = {2017}, abstract = {We study the degree of second-order coherence of the emission of a high-power multi-quantum well superluminescent diode with a lateral tapered amplifier section with and without optical feedback. When operated in an external cavity, the degree of second-order coherence changed from the almost thermal case of g((2))(0)approximate to 1.9 towards the mostly coherent case of g((2)) (0) approximate to 1.2 when the injection current at the tapered section was increased. We found good agreement with semi-classical laser theory near and below threshold while above laser threshold a slightly higher g((2))(0) was observed. As a free running device, the superluminescent diode yielded more than 400 mW of optical output power with good spatial beam quality of M-slow(2) < 1.6. In this case, the degree of second-order coherence dropped only slightly from 1.9 at low powers to 1.6 at the maximum output power. To our knowledge, this is the first investigation of a high-power tapered superluminescent diode concerning the degree of second-order coherence. Such a device might be useful for real-world applications probing the second order coherence function, such as ghost imaging.}, language = {en} } @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} }