TY  - JOUR
A1  - Cherstvy, Andrey G.
A1  - Vinod, Deepak
A1  - Aghion, Erez
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Time averaging, ageing and delay analysis of financial time series
JF  - New journal of physics
N2  - We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black–Scholes–Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.
KW  - time averaging
KW  - diffusion
KW  - geometric Brownian motion
KW  - financial time series
Y1  - 2017
U6  - https://doi.org/10.1088/1367-2630/aa7199
SN  - 1367-2630
VL  - 19
SP  - 1
EP  - 11
PB  - IOP
CY  - London
ER  - 
TY  - JOUR
A1  - Sposini, Vittoria
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - First passage statistics for diffusing diffusivity
JF  - Journal of physics : A, Mathematical and theoretical
N2  - A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law < r(2)(t)> similar or equal to Dt yet the distribution of particle displacements is strongly non-Gaussian. A central approach to describe this effect is the diffusing diffusivity (DD) model in which the diffusion coefficient itself is a stochastic quantity, mimicking heterogeneities of the environment encountered by the tracer particle on its path. We here quantify in terms of analytical and numerical approaches the first passage behaviour of the DD model. We observe significant modifications compared to Brownian-Gaussian diffusion, in particular that the DD model may have a faster first passage dynamics. Moreover we find a universal crossover point of the survival probability independent of the initial condition.
KW  - diffusion
KW  - superstatistics
KW  - first passage
Y1  - 2018
U6  - https://doi.org/10.1088/1751-8121/aaf6ff
SN  - 1751-8113
SN  - 1751-8121
VL  - 52
IS  - 4
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Grätz, Fabio M.
A1  - Seiss, Martin
A1  - Spahn, Frank
T1  - Formation of moon-induced gaps in dense planetary rings
BT  - application to the rings of saturn
JF  - The astrophysical journal : an international review of spectroscopy and astronomical physics
N2  - We develop an axisymmetric diffusion model to describe radial density profiles in the vicinity of tiny moons embedded in planetary rings. Our diffusion model accounts for the gravitational scattering of the ring particles by an embedded moon and for the viscous diffusion of the ring matter back into the gap. With test particle simulations, we show that the scattering of the ring particles passing the moon is larger for small impact parameters than estimated by Goldreich & Tremaine and Namouni. This is significant for modeling the Keeler gap. We apply our model to the gaps of the moons Pan and Daphnis embedded in the outer A ring of Saturn with the aim to estimate the shear viscosity of the ring in the vicinity of the Encke and Keeler gap. In addition, we analyze whether tiny icy moons whose dimensions lie below Cassini's resolution capabilities would be able to explain the gap structure of the C ring and the Cassini division.
KW  - diffusion
KW  - planets and satellites: rings
KW  - scattering
Y1  - 2018
U6  - https://doi.org/10.3847/1538-4357/aace00
SN  - 0004-637X
SN  - 1538-4357
VL  - 862
IS  - 2
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Ślęzak, Jakub
A1  - Metzler, Ralf
A1  - Magdziarz, Marcin
T1  - Codifference can detect ergodicity breaking and non-Gaussianity
JF  - New Journal of Physics
N2  - We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.
KW  - diffusion
KW  - stochastic time series
KW  - anomalous diffusion
Y1  - 2019
U6  - https://doi.org/10.1088/1367-2630/ab13f3
SN  - 1367-2630
VL  - 21
PB  - Deutsche Physikalische Gesellschaft
CY  - Bad Honnef
ER  - 
TY  - JOUR
A1  - Sposini, Vittoria
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - Single-trajectory spectral analysis of scaled Brownian motion
JF  - New Journal of Physics
N2  - 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.
KW  - diffusion
KW  - anomalous diffusion
KW  - power spectral analysis
KW  - single trajectory analysis
Y1  - 2019
U6  - https://doi.org/10.1088/1367-2630/ab2f52
SN  - 1367-2630
VL  - 21
PB  - Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics
CY  - Bad Honnef und London
ER  - 
TY  - JOUR
A1  - Ślęzak, Jakub
A1  - Burnecki, Krzysztof
A1  - Metzler, Ralf
T1  - Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems
JF  - New Journal of Physics
N2  - 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.
KW  - diffusion
KW  - Langevin equation
KW  - Brownian yet non-Gaussian diffusion
KW  - diffusing diffusivity
KW  - superstatistics
KW  - autoregressive models
KW  - time series analysis
KW  - codifference
Y1  - 2019
U6  - https://doi.org/10.1088/1367-2630/ab3366
SN  - 1367-2630
VL  - 21
PB  - Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics
CY  - Bad Honnef und London
ER  - 
TY  - JOUR
A1  - Weber, Ariane
A1  - Bahrs, Marco
A1  - Alirezaeizanjani, Zahra
A1  - Zhang, Xingyu
A1  - Beta, Carsten
A1  - Zaburdaev, Vasily
T1  - Rectification of Bacterial Diffusion in Microfluidic Labyrinths
JF  - Frontiers in Physics
N2  - In nature as well as in the context of infection and medical applications, bacteria often have to move in highly complex environments such as soil or tissues. Previous studies have shown that bacteria strongly interact with their surroundings and are often guided by confinements. Here, we investigate theoretically how the dispersal of swimming bacteria can be augmented by microfluidic environments and validate our theoretical predictions experimentally. We consider a system of bacteria performing the prototypical run-and-tumble motion inside a labyrinth with square lattice geometry. Narrow channels between the square obstacles limit the possibility of bacteria to reorient during tumbling events to an area where channels cross. Thus, by varying the geometry of the lattice it might be possible to control the dispersal of cells. We present a theoretical model quantifying diffusive spreading of a run-and-tumble random walker in a square lattice. Numerical simulations validate our theoretical predictions for the dependence of the diffusion coefficient on the lattice geometry. We show that bacteria moving in square labyrinths exhibit enhanced dispersal as compared to unconfined cells. Importantly, confinement significantly extends the duration of the phase with strongly non-Gaussian diffusion, when the geometry of channels is imprinted in the density profiles of spreading cells. Finally, in good agreement with our theoretical findings, we observe the predicted behaviors in experiments with E. coli bacteria swimming in a square lattice labyrinth created in amicrofluidic device. Altogether, our comprehensive understanding of bacterial dispersal in a simple two-dimensional labyrinth makes the first step toward the analysis of more complex geometries relevant for real world applications.
KW  - diffusion
KW  - rectification
KW  - random walk
KW  - bacteria
KW  - confinement
Y1  - 2019
U6  - https://doi.org/10.3389/fphy.2019.00148
SN  - 2296-424X
SN  - 0429-7725
VL  - 7
PB  - Frontiers Media
CY  - Lausanne
ER  - 
TY  - JOUR
A1  - Abdalla, Hassan E.
A1  - Aharonian, Felix A.
A1  - Benkhali, F. Ait
A1  - Angüner, Ekrem Oǧuzhan
A1  - Arakawa, M.
A1  - Arcaro, C.
A1  - Armand, C.
A1  - Arrieta, M.
A1  - Backes, M.
A1  - Barnard, M.
A1  - Becherini, Y.
A1  - Tjus, J. Becker
A1  - Berge, D.
A1  - Bernloehr, K.
A1  - Blackwell, R.
A1  - Bottcher, M.
A1  - Boisson, C.
A1  - Bolmont, J.
A1  - Bonnefoy, S.
A1  - Bordas, Pol
A1  - Bregeon, J.
A1  - Brun, F.
A1  - Brun, P.
A1  - Bryan, M.
A1  - Buechele, M.
A1  - Bulik, T.
A1  - Bylund, T.
A1  - Capasso, M.
A1  - Caroff, S.
A1  - Carosi, A.
A1  - Casanova, Sabrina
A1  - Cerruti, M.
A1  - Chakraborty, N.
A1  - Chand, T.
A1  - Chandra, S.
A1  - Chaves, R. C. G.
A1  - Chen, A.
A1  - Colafrancesco, S.
A1  - Condon, B.
A1  - Davids, I. D.
A1  - Deil, C.
A1  - Devin, J.
A1  - deWilt, P.
A1  - Dirson, L.
A1  - Djannati-Atai, A.
A1  - Dmytriiev, A.
A1  - Donath, A.
A1  - Doroshenko, V
A1  - Dyks, J.
A1  - Egberts, Kathrin
A1  - Emery, G.
A1  - Ernenwein, J-P
A1  - Eschbach, S.
A1  - Fegan, S.
A1  - Fiasson, A.
A1  - Fontaine, G.
A1  - Funk, S.
A1  - Fuessling, M.
A1  - Gabici, S.
A1  - Gallant, Y. A.
A1  - Gate, F.
A1  - Giavitto, G.
A1  - Glawion, D.
A1  - Glicenstein, J. F.
A1  - Gottschall, D.
A1  - Grondin, M-H
A1  - Hahn, J.
A1  - Haupt, M.
A1  - Heinzelmann, G.
A1  - Henri, G.
A1  - Hermann, G.
A1  - Hinton, James Anthony
A1  - Hofmann, W.
A1  - Hoischen, Clemens
A1  - Holch, Tim Lukas
A1  - Holler, M.
A1  - Horns, D.
A1  - Huber, D.
A1  - Iwasaki, H.
A1  - Jacholkowska, A.
A1  - Jamrozy, M.
A1  - Jankowsky, D.
A1  - Jankowsky, F.
A1  - Jouvin, L.
A1  - Jung-Richardt, I
A1  - Kastendieck, M. A.
A1  - Katarzynski, K.
A1  - Katsuragawa, M.
A1  - Katz, U.
A1  - Kerszberg, D.
A1  - Khangulyan, D.
A1  - Khelifi, B.
A1  - King, J.
A1  - Klepser, S.
A1  - Kluzniak, W.
A1  - Komin, Nu
A1  - Kosack, K.
A1  - Kraus, M.
A1  - Lamanna, G.
A1  - Lau, J.
A1  - Lefaucheur, J.
A1  - Lemiere, A.
A1  - Lemoine-Goumard, M.
A1  - Lenain, J-P
A1  - Leser, Eva
A1  - Lohse, T.
A1  - Lopez-Coto, R.
A1  - Lypova, I
A1  - Malyshev, D.
A1  - Marandon, V
A1  - Marcowith, Alexandre
A1  - Mariaud, C.
A1  - Marti-Devesa, G.
A1  - Marx, R.
A1  - Maurin, G.
A1  - Meintjes, P. J.
A1  - Mitchell, A. M. W.
A1  - Moderski, R.
A1  - Mohamed, M.
A1  - Mohrmann, L.
A1  - Moore, C.
A1  - Moulin, Emmanuel
A1  - Murach, T.
A1  - Nakashima, S.
A1  - de Naurois, M.
A1  - Ndiyavala, H.
A1  - Niederwanger, F.
A1  - Niemiec, J.
A1  - Oakes, L.
A1  - Odaka, H.
A1  - Ohm, S.
A1  - Ostrowski, M.
A1  - Oya, I
A1  - Panter, M.
A1  - Parsons, R. D.
A1  - Perennes, C.
A1  - Petrucci, P-O
A1  - Peyaud, B.
A1  - Piel, Q.
A1  - Pita, S.
A1  - Poireau, V
A1  - Noel, A. Priyana
A1  - Prokhorov, D. A.
A1  - Prokoph, H.
A1  - Puehlhofer, G.
A1  - Punch, M.
A1  - Quirrenbach, A.
A1  - Raab, S.
A1  - Rauth, R.
A1  - Reimer, A.
A1  - Reimer, O.
A1  - Renaud, M.
A1  - Rieger, F.
A1  - Rinchiuso, L.
A1  - Romoli, C.
A1  - Rowell, G.
A1  - Rudak, B.
A1  - Ruiz-Velasco, E.
A1  - Sahakian, V
A1  - Saito, S.
A1  - Sanchez, David M.
A1  - Santangelo, A.
A1  - Sasaki, M.
A1  - Schlickeiser, R.
A1  - Schussler, F.
A1  - Schulz, A.
A1  - Schutte, H.
A1  - Schwanke, U.
A1  - Schwemmer, S.
A1  - Seglar-Arroyo, M.
A1  - Senniappan, M.
A1  - Seyffert, A. S.
A1  - Shafi, N.
A1  - Shilon, I
A1  - Shiningayamwe, K.
A1  - Simoni, R.
A1  - Sinha, A.
A1  - Sol, H.
A1  - Specovius, A.
A1  - Spir-Jacob, M.
A1  - Stawarz, L.
A1  - Steenkamp, R.
A1  - Stegmann, Christian
A1  - Steppa, Constantin Beverly
A1  - Takahashi, T.
A1  - Tavernet, J-P
A1  - Tavernier, T.
A1  - Taylor, A. M.
A1  - Terrier, R.
A1  - Tibaldo, L.
A1  - Tiziani, D.
A1  - Tluczykont, M.
A1  - Trichard, C.
A1  - Tsirou, M.
A1  - Tsuji, N.
A1  - Tuffs, R.
A1  - Uchiyama, Y.
A1  - van der Walt, D. J.
A1  - van Eldik, C.
A1  - van Rensburg, C.
A1  - van Soelen, B.
A1  - Vasileiadis, G.
A1  - Veh, J.
A1  - Venter, C.
A1  - Vincent, P.
A1  - Vink, J.
A1  - Voisin, F.
A1  - Voelk, H. J.
A1  - Vuillaume, T.
A1  - Wadiasingh, Z.
A1  - Wagner, S. J.
A1  - Wagner, R. M.
A1  - White, R.
A1  - Wierzcholska, A.
A1  - Yang, R.
A1  - Yoneda, H.
A1  - Zaborov, D.
A1  - Zacharias, M.
A1  - Zanin, R.
A1  - Zdziarski, A. A.
A1  - Zech, Alraune
A1  - Zefi, F.
A1  - Ziegler, A.
A1  - Zorn, J.
A1  - Zywucka, N.
T1  - Particle transport within the pulsar wind nebula HESS J1825-137
JF  - Astronomy and astrophysics : an international weekly journal
N2  - Context. We present a detailed view of the pulsar wind nebula (PWN) HESS J1825-137. We aim to constrain the mechanisms dominating the particle transport within the nebula, accounting for its anomalously large size and spectral characteristics. Aims. The nebula was studied using a deep exposure from over 12 years of H.E.S.S. I operation, together with data from H.E.S.S. II that improve the low-energy sensitivity. Enhanced energy-dependent morphological and spatially resolved spectral analyses probe the very high energy (VHE, E > 0.1 TeV) gamma-ray properties of the nebula. Methods. The nebula emission is revealed to extend out to 1.5 degrees from the pulsar, similar to 1.5 times farther than previously seen, making HESS J1825-137, with an intrinsic diameter of similar to 100 pc, potentially the largest gamma-ray PWN currently known. Characterising the strongly energy-dependent morphology of the nebula enables us to constrain the particle transport mechanisms. A dependence of the nebula extent with energy of R proportional to E alpha with alpha = -0.29 +/- 0.04(stat) +/- 0.05(sys) disfavours a pure diffusion scenario for particle transport within the nebula. The total gamma-ray flux of the nebula above 1 TeV is found to be (1.12 +/- 0.03(stat) +/- 0.25(sys)) +/- 10(-11) cm(-2) s(-1), corresponding to similar to 64% of the flux of the Crab nebula. Results. HESS J1825-137 is a PWN with clearly energy-dependent morphology at VHE gamma-ray energies. This source is used as a laboratory to investigate particle transport within intermediate-age PWNe. Based on deep observations of this highly spatially extended PWN, we produce a spectral map of the region that provides insights into the spectral variation within the nebula.
KW  - gamma rays: general
KW  - acceleration of particles
KW  - convection
KW  - diffusion
KW  - pulsars: general
Y1  - 2019
U6  - https://doi.org/10.1051/0004-6361/201834335
SN  - 1432-0746
VL  - 621
PB  - EDP Sciences
CY  - Les Ulis
ER  - 
TY  - JOUR
A1  - Granado, Felipe Le Vot
A1  - Abad, Enrique
A1  - Metzler, Ralf
A1  - Yuste, Santos B.
T1  - Continuous time random walk in a velocity field
BT  - role of domain growth, Galilei-invariant advection-diffusion, and kinetics of particle mixing
JF  - New Journal of Physics
N2  - We consider the emerging dynamics of a separable continuous time random walk (CTRW) in the case when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid vesicles, biofilms and tissues, but also macroscopic systems such as expanding aquifers during rainy periods, or the expanding Universe. The CTRW in this study can be subdiffusive, normal diffusive or superdiffusive, including the particular case of a Lévy flight. We first consider the case when the velocity field is absent. In the subdiffusive case, we reveal an interesting time dependence of the kurtosis of the particle probability density function. In particular, for a suitable parameter choice, we find that the propagator, which is fat tailed at short times, may cross over to a Gaussian-like propagator. We subsequently incorporate the effect of the velocity field and derive a bi-fractional diffusion-advection equation encoding the time evolution of the particle distribution. We apply this equation to study the mixing kinetics of two diffusing pulses, whose peaks move towards each other under the action of velocity fields acting in opposite directions. This deterministic motion of the peaks, together with the diffusive spreading of each pulse, tends to increase particle mixing, thereby counteracting the peak separation induced by the domain growth. As a result of this competition, different regimes of mixing arise. In the case of Lévy flights, apart from the non-mixing regime, one has two different mixing regimes in the long-time limit, depending on the exact parameter choice: in one of these regimes, mixing is mainly driven by diffusive spreading, while in the other mixing is controlled by the velocity fields acting on each pulse. Possible implications for encounter–controlled reactions in real systems are discussed.
KW  - diffusion
KW  - expanding medium
KW  - continuous time random walk
Y1  - 2020
U6  - https://doi.org/10.1088/1367-2630/ab9ae2
SN  - 1367-2630
VL  - 22
PB  - Dt. Physikalische Ges.
CY  - Bad Honnef
ER  - 
TY  - JOUR
A1  - Li, Yongge
A1  - Mei, Ruoxing
A1  - Xu, Yong
A1  - Kurths, Jürgen
A1  - Duan, Jinqiao
A1  - Metzler, Ralf
T1  - Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity
JF  - New Journal of Physics
N2  - This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.
KW  - diffusion
KW  - channel
KW  - space-dependent diffusivity
Y1  - 2020
U6  - https://doi.org/10.1088/1367-2630/ab81b9
SN  - 1367-2630
VL  - 22
PB  - Dt. Physikalische Ges.
CY  - Bad Honnef
ER  -