@article{AbdallaAharonianBenkhalietal.2019,
  author    = {Abdalla, Hassan E. and Aharonian, Felix A. and Benkhali, F. Ait and Ang{\"u}ner, Ekrem Oǧuzhan and Arakawa, M. and Arcaro, C. and Armand, C. and Arrieta, M. and Backes, M. and Barnard, M. and Becherini, Y. and Tjus, J. Becker and Berge, D. and Bernloehr, K. and Blackwell, R. and Bottcher, M. and Boisson, C. and Bolmont, J. and Bonnefoy, S. and Bordas, Pol and Bregeon, J. and Brun, F. and Brun, P. and Bryan, M. and Buechele, M. and Bulik, T. and Bylund, T. and Capasso, M. and Caroff, S. and Carosi, A. and Casanova, Sabrina and Cerruti, M. and Chakraborty, N. and Chand, T. and Chandra, S. and Chaves, R. C. G. and Chen, A. and Colafrancesco, S. and Condon, B. and Davids, I. D. and Deil, C. and Devin, J. and deWilt, P. and Dirson, L. and Djannati-Atai, A. and Dmytriiev, A. and Donath, A. and Doroshenko, V and Dyks, J. and Egberts, Kathrin and Emery, G. and Ernenwein, J-P and Eschbach, S. and Fegan, S. and Fiasson, A. and Fontaine, G. and Funk, S. and Fuessling, M. and Gabici, S. and Gallant, Y. A. and Gate, F. and Giavitto, G. and Glawion, D. and Glicenstein, J. F. and Gottschall, D. and Grondin, M-H and Hahn, J. and Haupt, M. and Heinzelmann, G. and Henri, G. and Hermann, G. and Hinton, James Anthony and Hofmann, W. and Hoischen, Clemens and Holch, Tim Lukas and Holler, M. and Horns, D. and Huber, D. and Iwasaki, H. and Jacholkowska, A. and Jamrozy, M. and Jankowsky, D. and Jankowsky, F. and Jouvin, L. and Jung-Richardt, I and Kastendieck, M. A. and Katarzynski, K. and Katsuragawa, M. and Katz, U. and Kerszberg, D. and Khangulyan, D. and Khelifi, B. and King, J. and Klepser, S. and Kluzniak, W. and Komin, Nu and Kosack, K. and Kraus, M. and Lamanna, G. and Lau, J. and Lefaucheur, J. and Lemiere, A. and Lemoine-Goumard, M. and Lenain, J-P and Leser, Eva and Lohse, T. and Lopez-Coto, R. and Lypova, I and Malyshev, D. and Marandon, V and Marcowith, Alexandre and Mariaud, C. and Marti-Devesa, G. and Marx, R. and Maurin, G. and Meintjes, P. J. and Mitchell, A. M. W. and Moderski, R. and Mohamed, M. and Mohrmann, L. and Moore, C. and Moulin, Emmanuel and Murach, T. and Nakashima, S. and de Naurois, M. and Ndiyavala, H. and Niederwanger, F. and Niemiec, J. and Oakes, L. and Odaka, H. and Ohm, S. and Ostrowski, M. and Oya, I and Panter, M. and Parsons, R. D. and Perennes, C. and Petrucci, P-O and Peyaud, B. and Piel, Q. and Pita, S. and Poireau, V and Noel, A. Priyana and Prokhorov, D. A. and Prokoph, H. and Puehlhofer, G. and Punch, M. and Quirrenbach, A. and Raab, S. and Rauth, R. and Reimer, A. and Reimer, O. and Renaud, M. and Rieger, F. and Rinchiuso, L. and Romoli, C. and Rowell, G. and Rudak, B. and Ruiz-Velasco, E. and Sahakian, V and Saito, S. and Sanchez, David M. and Santangelo, A. and Sasaki, M. and Schlickeiser, R. and Schussler, F. and Schulz, A. and Schutte, H. and Schwanke, U. and Schwemmer, S. and Seglar-Arroyo, M. and Senniappan, M. and Seyffert, A. S. and Shafi, N. and Shilon, I and Shiningayamwe, K. and Simoni, R. and Sinha, A. and Sol, H. and Specovius, A. and Spir-Jacob, M. and Stawarz, L. and Steenkamp, R. and Stegmann, Christian and Steppa, Constantin Beverly and Takahashi, T. and Tavernet, J-P and Tavernier, T. and Taylor, A. M. and Terrier, R. and Tibaldo, L. and Tiziani, D. and Tluczykont, M. and Trichard, C. and Tsirou, M. and Tsuji, N. and Tuffs, R. and Uchiyama, Y. and van der Walt, D. J. and van Eldik, C. and van Rensburg, C. and van Soelen, B. and Vasileiadis, G. and Veh, J. and Venter, C. and Vincent, P. and Vink, J. and Voisin, F. and Voelk, H. J. and Vuillaume, T. and Wadiasingh, Z. and Wagner, S. J. and Wagner, R. M. and White, R. and Wierzcholska, A. and Yang, R. and Yoneda, H. and Zaborov, D. and Zacharias, M. and Zanin, R. and Zdziarski, A. A. and Zech, Alraune and Zefi, F. and Ziegler, A. and Zorn, J. and Zywucka, N.},
  title     = {Particle transport within the pulsar wind nebula HESS J1825-137},
  series = {Astronomy and astrophysics : an international weekly journal},
  volume    = {621},
  journal   = {Astronomy and astrophysics : an international weekly journal},
  publisher = {EDP Sciences},
  address   = {Les Ulis},
  organization    = {HESS Collaboration},
  issn      = {1432-0746},
  doi       = {10.1051/0004-6361/201834335},
  pages     = {18},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@article{Beta2016,
  author    = {Beta, Carsten},
  title     = {To turn or not to turn?},
  series = {NEW JOURNAL OF PHYSICS},
  volume    = {18},
  journal   = {NEW JOURNAL OF PHYSICS},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/18/5/051003},
  pages     = {1 -- 17},
  year      = {2016},
  abstract  = {Bacteria typically swim in straight runs, interruped by sudden turning events. In particular, some species are limited to a reversal in the swimming direction as the only turning maneuver at their disposal. In a recent article, Grossmann et al (2016 New J. Phys. 18 043009) introduce a theoretical framework to analyze the diffusive properties of active particles following this type of run-and-reverse pattern. Based on a stochastic clock model to mimic the regulatory pathway that triggers reversal events, they show that a run-and-reverse swimmer can optimize its diffusive spreading by tuning the reversal rate according to the level of rotational noise. With their approach, they open up promising new perspectives of how to incorporate the dynamics of intracellular signaling into coarse-grained active particle descriptions.},
  language  = {en}
}
@article{ChechkinLenzKlages2012,
  author    = {Chechkin, Aleksei V. and Lenz, F. and Klages, Rainer},
  title     = {Normal and anomalous fluctuation relations for gaussian stochastic dynamics},
  series = {Journal of statistical mechanics: theory and experiment},
  journal   = {Journal of statistical mechanics: theory and experiment},
  number    = {4},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1742-5468},
  doi       = {10.1088/1742-5468/2012/11/L11001},
  pages     = {12},
  year      = {2012},
  abstract  = {We study transient work fluctuation relations (FRs) for Gaussian stochastic systems generating anomalous diffusion. For this purpose we use a Langevin approach by employing two different types of additive noise: (i) internal noise where the fluctuation dissipation relation of the second kind (FDR II) holds, and (ii) external noise without FDR II. For internal noise we demonstrate that the existence of FDR II implies the existence of the fluctuation dissipation relation of the first kind (FDR I), which in turn leads to conventional (normal) forms of transient work FRs. For systems driven by external noise we obtain violations of normal FRs, which we call anomalous FRs. We derive them in the long-time limit and demonstrate the existence of logarithmic factors in FRs for intermediate times. We also outline possible experimental verifications.},
  language  = {en}
}
@article{ChenPohlBottcheretal.2016,
  author    = {Chen, Xuhui and Pohl, Martin and Bottcher, Markus and Gao, Shan},
  title     = {Particle diffusion and localized acceleration in inhomogeneous AGN jets - II. Stochastic variation},
  series = {Monthly notices of the Royal Astronomical Society},
  volume    = {458},
  journal   = {Monthly notices of the Royal Astronomical Society},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0035-8711},
  doi       = {10.1093/mnras/stw528},
  pages     = {3260 -- 3271},
  year      = {2016},
  abstract  = {We study the stochastic variation of blazar emission under a 2D spatially resolved leptonic jet model we previously developed. Random events of particle acceleration and injection in small zones within the emission region are assumed to be responsible for flux variations. In addition to producing spectral energy distributions that describe the observed flux of Mrk 421, we further analyse the timing properties of the simulated light curves, such as the power spectral density (PSD) at different bands, flux-flux correlations, aswell as the cross-correlation function between X-rays and TeV gamma-rays. We find spectral breaks in the PSD at a time-scale comparable to the dominant characteristic time-scale in the system, which is usually the predefined decay time-scale of an acceleration event. Cooling imposes a delay, and so PSDs taken at lower energy bands in each emission component (synchrotron or inverse Compton) generally break at longer time-scales. The flux-flux correlation between X-rays and TeV gamma-rays can be either quadratic or linear, depending on whether or not there are large variation of the injection into the particle acceleration process. When the relationship is quadratic, the TeV flares lag the X-ray flares, and the optical and GeV flares are large enough to be comparable to the ones in X-ray. When the relationship is linear, the lags are insignificant, and the optical and GeV flares are small.},
  language  = {en}
}
@article{ChenPohlBoettcher2015,
  author    = {Chen, Xuhui and Pohl, Martin and B{\"o}ttcher, Markus},
  title     = {Particle diffusion and localized acceleration in inhomogeneous AGN jets - I. Steady-state spectra},
  series = {Monthly notices of the Royal Astronomical Society},
  volume    = {447},
  journal   = {Monthly notices of the Royal Astronomical Society},
  number    = {1},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0035-8711},
  doi       = {10.1093/mnras/stu2438},
  pages     = {530 -- 544},
  year      = {2015},
  abstract  = {We study the acceleration, transport, and emission of particles in relativistic jets. Localized stochastic particle acceleration, spatial diffusion, and synchrotron as well as synchrotron self-Compton (SSC) emission are considered in a leptonic model. To account for inhomogeneity, we use a 2D axisymmetric cylindrical geometry for both relativistic electrons and magnetic field. In this first phase of our work, we focus on steady-state spectra that develop from a time-dependent model. We demonstrate that small isolated acceleration region in a much larger emission volume are sufficient to accelerate particles to high energy. Diffusive escape from these small regions provides a natural explanation for the spectral form of the jet emission. The location of the acceleration regions within the jet is found to affect the cooling break of the spectrum in this diffusive model. Diffusion-caused energy-dependent inhomogeneity in the jets predicts that the SSC spectrum is harder than the synchrotron spectrum. There can also be a spectral hardening towards the high-energy section of the synchrotron spectrum, if particle escape is relatively slow. These two spectral hardening effects indicate that the jet inhomogeneity might be a natural explanation for the unexpected hard. gamma-ray spectra observed in some blazars.},
  language  = {en}
}
@article{CherstvyMetzler2015,
  author    = {Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Ergodicity breaking, ageing, and confinement in generalized diffusion processes with position and time dependent diffusivity},
  series = {Journal of statistical mechanics: theory and experiment},
  journal   = {Journal of statistical mechanics: theory and experiment},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1742-5468},
  doi       = {10.1088/1742-5468/2015/05/P05010},
  pages     = {20},
  year      = {2015},
  abstract  = {We study generalized anomalous diffusion processes whose diffusion coefficient D(x, t) similar to D-0x(alpha)t(beta) depends on both the position x of the test particle and the process time t. This process thus combines the features of scaled Brownian motion and heterogeneous diffusion parent processes. We compute the ensemble and time averaged mean squared displacements of this generalized diffusion process. The scaling exponent of the ensemble averaged mean squared displacement is shown to be the product of the critical exponents of the parent processes, and describes both subdiffusive and superdiffusive systems. We quantify the amplitude fluctuations of the time averaged mean squared displacement as function of the length of the time series and the lag time. In particular, we observe a weak ergodicity breaking of this generalized diffusion process: even in the long time limit the ensemble and time averaged mean squared displacements are strictly disparate. When we start to observe this process some time after its initiation we observe distinct features of ageing. We derive a universal ageing factor for the time averaged mean squared displacement containing all information on the ageing time and the measurement time. External confinement is shown to alter the magnitudes and statistics of the ensemble and time averaged mean squared displacements.},
  language  = {en}
}
@article{CherstvyVinodAghionetal.2017,
  author    = {Cherstvy, Andrey G. and Vinod, Deepak and Aghion, Erez and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Time averaging, ageing and delay analysis of financial time series},
  series = {New journal of physics},
  volume    = {19},
  journal   = {New journal of physics},
  publisher = {IOP},
  address   = {London},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/aa7199},
  pages     = {1 -- 11},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@misc{CherstvyVinodAghionetal.2017,
  author    = {Cherstvy, Andrey G. and Vinod, Deepak and Aghion, Erez and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Time averaging, ageing and delay analysis of financial time series},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-400541},
  pages     = {11},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@article{CherstvyVinodAghionetal.2017,
  author    = {Cherstvy, Andrey G. and Vinod, Deepak and Aghion, Erez and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Time averaging, ageing and delay analysis of financial time series},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {19},
  journal   = {New journal of physics : the open-access journal for physics},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/aa7199},
  pages     = {135 -- 147},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@article{DoerriesChechkinMetzler2022,
  author    = {Doerries, Timo J. and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Apparent anomalous diffusion and non-Gaussian distributions in a simple mobile-immobile transport model with Poissonian switching},
  series = {Interface : journal of the Royal Society},
  volume    = {19},
  journal   = {Interface : journal of the Royal Society},
  number    = {192},
  publisher = {Royal Society},
  address   = {London},
  issn      = {1742-5689},
  doi       = {10.1098/rsif.2022.0233},
  pages     = {14},
  year      = {2022},
  abstract  = {We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching, we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. Our discussion is based on experimental parameters for tau proteins in neuronal cells, but the results obtained here are expected to be of relevance for a broad class of processes in complex systems. Specifically, we obtain that, when the mean binding time is significantly longer than the mean mobile time, transient anomalous diffusion is observed at short and intermediate time scales, with a strong dependence on the fraction of initially mobile and immobile particles. We unveil a Laplace distribution of particle displacements at relevant intermediate time scales. For any initial fraction of mobile particles, the respective mean squared displacement (MSD) displays a plateau. Moreover, we demonstrate a short-time cubic time dependence of the MSD for immobile tracers when initially all particles are immobile.},
  language  = {en}
}