@phdthesis{Spallanzani2022,
  author    = {Spallanzani, Roberta},
  title     = {Li and B in ascending magmas: an experimental study on their mobility and isotopic fractionation},
  doi       = {10.25932/publishup-56061},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-560619},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xiv, 131},
  year      = {2022},
  abstract  = {This research study focuses on the behaviour of Li and B during magmatic ascent, and decompression-driven degassing related to volcanic systems. The main objective of this dissertation is to determine whether it is possible to use the diffusion properties of the two trace elements as a tool to trace magmatic ascent rate. With this objective, diffusion-couple and decompression experiments have been performed in order to study Li and B mobility in intra-melt conditions first, and then in an evolving system during decompression-driven degassing. Synthetic glasses were prepared with rhyolitic composition and an initial water content of 4.2 wt\%, and all the experiments were performed using an internally heated pressure vessel, in order to ensure a precise control on the experimental parameters such as temperature and pressure. Diffusion-couple experiments were performed with a fix pressure 300 MPa. The temperature was varied in the range of 700-1250 °C with durations between 0 seconds and 24 hours. The diffusion-couple results show that Li diffusivity is very fast and starts already at very low temperature. Significant isotopic fractionation occurs due to the faster mobility of 6Li compared to 7Li. Boron diffusion is also accelerated by the presence of water, but the results of the isotopic ratios are unclear, and further investigation would be necessary to well constrain the isotopic fractionation process of boron in hydrous silicate melts. The isotopic ratios results show that boron isotopic fractionation might be affected by the speciation of boron in the silicate melt structure, as 10B and 11B tend to have tetrahedral and trigonal coordination, respectively. Several decompression experiments were performed at 900 °C and 1000 °C, with pressures going from 300 MPa to 71-77 MPa and durations of 30 minutes, two, five and ten hours, in order to trigger water exsolution and the formation of vesicles in the sample. Textural observations and the calculation of the bubble number density confirmed that the bubble size and distribution after decompression is directly proportional to the decompression rate. The overall SIMS results of Li and B show that the two trace elements tend to progressively decrease their concentration with decreasing decompression rates. This is explained because for longer decompression times, the diffusion of Li and B into the bubbles has more time to progress and the melt continuously loses volatiles as the bubbles expand their volumes. For fast decompression, Li and B results show a concentration increase with a δ7Li and δ11B decrease close to the bubble interface, related to the sudden formation of the gas bubble, and the occurrence of a diffusion process in the opposite direction, from the bubble meniscus to the unaltered melt. When the bubble growth becomes dominant and Li and B start to exsolve into the gas phase, the silicate melt close to the bubble gets depleted in Li and B, because of a stronger diffusion of the trace elements into the bubble. Our data are being applied to different models, aiming to combine the dynamics of bubble nucleation and growth with the evolution of trace elements concentration and isotopic ratios. Here, first considerations on these models will be presented, giving concluding remarks on this research study. All in all, the final remarks constitute a good starting point for further investigations. These results are a promising base to continue to study this process, and Li and B can indeed show clear dependences on decompression-related magma ascent rates in volcanic systems.},
  language  = {en}
}
@misc{XuZhouMetzleretal.2022,
  author    = {Xu, Pengbo and Zhou, Tian and Metzler, Ralf and Deng, Weihua},
  title     = {Stochastic harmonic trapping of a L{\´e}vy walk: transport and first-passage dynamics under soft resetting strategies},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-56040},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-560402},
  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}
}
@phdthesis{Hennig2022,
  author    = {Hennig, Theresa},
  title     = {Uranium migration in the Opalinus Clay quantified on the host rock scale with reactive transport simulations},
  doi       = {10.25932/publishup-55270},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-552700},
  school      = {Universit{\"a}t Potsdam},
  pages     = {161},
  year      = {2022},
  abstract  = {Humankind and their environment need to be protected from the harmful effects of spent nuclear fuel, and therefore disposal in deep geological formations is favoured worldwide. Suitability of potential host rocks is evaluated, among others, by the retention capacity with respect to radionuclides. Safety assessments are based on the quantification of radionuclide migration lengths with numerical simulations as experiments cannot cover the required temporal (1 Ma) and spatial scales (>100 m). Aim of the present thesis is to assess the migration of uranium, a geochemically complex radionuclide, in the potential host rock Opalinus Clay. Radionuclide migration in clay formations is governed by diffusion due to their low permeability and retarded by sorption. Both processes highly depend on pore water geochemistry and mineralogy that vary between different facies. Diffusion is quantified with the single-component (SC) approach using one diffusion coefficient for all species and the process-based multi-component (MC) option. With this, each species is assigned its own diffusion coefficient and the interaction with the diffuse double layer is taken into account. Sorption is integrated via a bottom-up approach using mechanistic surface complexation models and cation exchange. Therefore, reactive transport simulations are conducted with the geochemical code PHREEQC to quantify uranium migration, i.e. diffusion and sorption, as a function of mineralogical and geochemical heterogeneities on the host rock scale. Sorption processes are facies dependent. Migration lengths vary between the Opalinus Clay facies by up to 10 m. Thereby, the geochemistry of the pore water, in particular the partial pressure of carbon dioxide (pCO2), is more decisive for the sorption capacity than the amount of clay minerals. Nevertheless, higher clay mineral quantities compensate geochemical variations. Consequently, sorption processes must be quantified as a function of pore water geochemistry in contact with the mineral assemblage. Uranium diffusion in the Opalinus Clay is facies independent. Speciation is dominated by aqueous ternary complexes of U(VI) with calcium and carbonate. Differences in the migration lengths between SC and MC diffusion are with +/-5 m negligible. Further, the application of the MC approach highly depends on the quality and availability of the underlying data. Therefore, diffusion processes can be adequately quantified with the SC approach using experimentally determined diffusion coefficients. The hydrogeological system governs pore water geochemistry within the formation rather than the mineralogy. Diffusive exchange with the adjacent aquifers established geochemical gradients over geological time scales that can enhance migration by up to 25 m. Consequently, uranium sorption processes must be quantified following the identified priority: pCO2 > hydrogeology > mineralogy. The presented research provides a workflow and orientation for other potential disposal sites with similar pore water geochemistry due to the identified mechanisms and dependencies. With a maximum migration length of 70 m, the retention capacity of the Opalinus Clay with respect to uranium is sufficient to fulfill the German legal minimum requirement of a thickness of at least 100 m.},
  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{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}
}
@article{GuggenbergerChechkinMetzler2022,
  author    = {Guggenberger, Tobias and Chechkin, Aleksei and Metzler, Ralf},
  title     = {Absence of stationary states and non-Boltzmann distributions of fractional Brownian motion in shallow external potentials},
  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    = {7},
  publisher = {Dt. Physikalische Ges.},
  address   = {[Bad Honnef]},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ac7b3c},
  pages     = {18},
  year      = {2022},
  abstract  = {We study the diffusive motion of a particle in a subharmonic potential of the form U(x) = |x|( c ) (0 < c < 2) driven by long-range correlated, stationary fractional Gaussian noise xi ( alpha )(t) with 0 < alpha <= 2. In the absence of the potential the particle exhibits free fractional Brownian motion with anomalous diffusion exponent alpha. While for an harmonic external potential the dynamics converges to a Gaussian stationary state, from extensive numerical analysis we here demonstrate that stationary states for shallower than harmonic potentials exist only as long as the relation c > 2(1 - 1/alpha) holds. We analyse the motion in terms of the mean squared displacement and (when it exists) the stationary probability density function. Moreover we discuss analogies of non-stationarity of Levy flights in shallow external potentials.},
  language  = {en}
}
@article{CaiToetzkeKaestneretal.2022,
  author    = {Cai, Gaochao and T{\"o}tzke, Christian and Kaestner, Anders and Ahmed, Mutez Ali},
  title     = {Quantification of root water uptake and redistribution using neutron imaging: a review and future directions},
  series = {The plant journal},
  volume    = {111},
  journal   = {The plant journal},
  number    = {2},
  publisher = {Wiley-Blackwell},
  address   = {Oxford [u.a.]},
  issn      = {0960-7412},
  doi       = {10.1111/tpj.15839},
  pages     = {348 -- 359},
  year      = {2022},
  abstract  = {Quantifying root water uptake is essential to understanding plant water use and responses to different environmental conditions. However, non-destructive measurement of water transport and related hydraulics in the soil-root system remains a challenge. Neutron imaging, with its high sensitivity to hydrogen, has become an unparalleled tool to visualize and quantify root water uptake in vivo. In combination with isotopes (e.g., deuterated water) and a diffusion-convection model, root water uptake and hydraulic redistribution in root and soil can be quantified. Here, we review recent advances in utilizing neutron imaging to visualize and quantify root water uptake, hydraulic redistribution in roots and soil, and root hydraulic properties of different plant species. Under uniform soil moisture distributions, neutron radiographic studies have shown that water uptake was not uniform along the root and depended on both root type and age. For both tap (e.g., lupine [Lupinus albus L.]) and fibrous (e.g., maize [Zea mays L.]) root systems, water was mainly taken up through lateral roots. In mature maize, the location of water uptake shifted from seminal roots and their laterals to crown/nodal roots and their laterals. Under non-uniform soil moisture distributions, part of the water taken up during the daytime maintained the growth of crown/nodal roots in the upper, drier soil layers. Ultra-fast neutron tomography provides new insights into 3D water movement in soil and roots. We discuss the limitations of using neutron imaging and propose future directions to utilize neutron imaging to advance our understanding of root water uptake and soil-root interactions.},
  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{SpallanzaniKogaCichyetal.2022,
  author    = {Spallanzani, Roberta and Koga, Kenneth T. and Cichy, Sarah B. and Wiedenbeck, Michael and Schmidt, Burkhard C. and Oelze, Marcus and Wilke, Max},
  title     = {Lithium and boron diffusivity and isotopic fractionation in hydrated rhyolitic melts},
  series = {Contributions to mineralogy and petrology},
  volume    = {177},
  journal   = {Contributions to mineralogy and petrology},
  number    = {8},
  publisher = {Springer},
  address   = {New York},
  issn      = {0010-7999},
  doi       = {10.1007/s00410-022-01937-2},
  pages     = {17},
  year      = {2022},
  abstract  = {Lithium and boron are trace components of magmas, released during exsolution of a gas phase during volcanic activity. In this study, we determine the diffusivity and isotopic fractionation of Li and B in hydrous silicate melts. Two glasses were synthesized with the same rhyolitic composition (4.2 wt\% water), having different Li and B contents; these were studied in diffusion-couple experiments that were performed using an internally heated pressure vessel, operated at 300 MPa in the temperature range 700-1250 degrees C for durations from 0 s to 24 h. From this we determined activation energies for Li and B diffusion of 57 +/- 4 kJ/mol and 152 +/- 15 kJ/mol with pre-exponential factors of 1.53 x 10(-7) m(2)/s and 3.80 x 10(-8) m(2)/s, respectively. Lithium isotopic fractionation during diffusion gave beta values between 0.15 and 0.20, whereas B showed no clear isotopic fractionation. Our Li diffusivities and isotopic fractionation results differ somewhat from earlier published values, but overall confirm that Li diffusivity increases with water content. Our results on B diffusion show that similarly to Li, B mobility increases in the presence of water. By applying the Eyring relation, we confirm that B diffusivity is limited by viscous flow in silicate melts. Our results on Li and B diffusion present a new tool for understanding degassing-related processes, offering a potential geospeedometer to measure volcanic ascent rates.},
  language  = {en}
}
@article{StojkoskiSandevKocarevetal.2022,
  author    = {Stojkoski, Viktor and Sandev, Trifce and Kocarev, Ljupco and Pal, Arnab},
  title     = {Autocorrelation functions and ergodicity in diffusion with stochastic resetting},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {55},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {10},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/ac4ce9},
  pages     = {22},
  year      = {2022},
  abstract  = {Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc. What remains less explored is the two time point correlation functions whose evaluation is often daunting since it requires the implementation of the exact time dependent probability density functions of the resetting processes which are unknown for most of the problems. We adopt a different approach that allows us to write a stochastic solution for a single trajectory undergoing resetting. Moments and the autocorrelation functions between any two times along the trajectory can then be computed directly using the laws of total expectation. Estimation of autocorrelation functions turns out to be pivotal for investigating the ergodic properties of various observables for this canonical model. In particular, we investigate two observables (i) sample mean which is widely used in economics and (ii) time-averaged-mean-squared-displacement (TAMSD) which is of acute interest in physics. We find that both diffusion and drift-diffusion processes with resetting are ergodic at the mean level unlike their reset-free counterparts. In contrast, resetting renders ergodicity breaking in the TAMSD while both the stochastic processes are ergodic when resetting is absent. We quantify these behaviors with detailed analytical study and corroborate with extensive numerical simulations. Our results can be verified in experimental set-ups that can track single particle trajectories and thus have strong implications in understanding the physics of resetting.},
  language  = {en}
}