TY - JOUR A1 - Stojkoski, Viktor A1 - Sandev, Trifce A1 - Kocarev, Ljupco A1 - Pal, Arnab T1 - Autocorrelation functions and ergodicity in diffusion with stochastic resetting JF - Journal of physics : A, Mathematical and theoretical N2 - 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. KW - autocorrelations KW - ergodicity KW - diffusion KW - stochastic resetting Y1 - 2022 U6 - https://doi.org/10.1088/1751-8121/ac4ce9 SN - 1751-8113 SN - 1751-8121 VL - 55 IS - 10 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Spallanzani, Roberta A1 - Koga, Kenneth T. A1 - Cichy, Sarah B. A1 - Wiedenbeck, Michael A1 - Schmidt, Burkhard C. A1 - Oelze, Marcus A1 - Wilke, Max T1 - Lithium and boron diffusivity and isotopic fractionation in hydrated rhyolitic melts JF - Contributions to mineralogy and petrology N2 - 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. KW - stable isotopes KW - diffusion KW - isotopic fractionation KW - hydrated silicate KW - melts Y1 - 2022 U6 - https://doi.org/10.1007/s00410-022-01937-2 SN - 0010-7999 SN - 1432-0967 VL - 177 IS - 8 PB - Springer CY - New York ER - TY - JOUR A1 - Vilk, Ohad A1 - Aghion, Erez A1 - Nathan, Ran A1 - Toledo, Sivan A1 - Metzler, Ralf A1 - Assaf, Michael T1 - Classification of anomalous diffusion in animal movement data using power spectral analysis JF - Journal of physics : A, Mathematical and theoretical N2 - 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. KW - diffusion KW - anomalous diffusion KW - power spectral analysis KW - ecological KW - movement data Y1 - 2022 U6 - https://doi.org/10.1088/1751-8121/ac7e8f SN - 1751-8113 SN - 1751-8121 VL - 55 IS - 33 PB - IOP Publishing CY - Bristol ER - TY - JOUR A1 - Cai, Gaochao A1 - Tötzke, Christian A1 - Kaestner, Anders A1 - Ahmed, Mutez Ali T1 - Quantification of root water uptake and redistribution using neutron imaging: a review and future directions JF - The plant journal N2 - 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. KW - attenuation coefficient KW - convection KW - diffusion KW - radiography KW - root hydraulics KW - root water uptake KW - tomography Y1 - 2022 U6 - https://doi.org/10.1111/tpj.15839 SN - 0960-7412 SN - 1365-313X VL - 111 IS - 2 SP - 348 EP - 359 PB - Wiley-Blackwell CY - Oxford [u.a.] ER - TY - JOUR A1 - Guggenberger, Tobias A1 - Chechkin, Aleksei A1 - Metzler, Ralf T1 - Absence of stationary states and non-Boltzmann distributions of fractional Brownian motion in shallow external potentials JF - New journal of physics : the open-access journal for physics N2 - 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. KW - diffusion KW - Boltzmann distribution KW - fractional Brownian motion Y1 - 2022 U6 - https://doi.org/10.1088/1367-2630/ac7b3c SN - 1367-2630 VL - 24 IS - 7 PB - Dt. Physikalische Ges. CY - [Bad Honnef] ER - TY - JOUR A1 - Hennig, Theresa A1 - Kühn, Michael T1 - Potential uranium migration within the geochemical gradient of the opalinus clay system at the Mont Terri JF - Minerals N2 - Transport properties of potential host rocks for nuclear waste disposal are typically determined in laboratory or in-situ experiments under geochemically controlled and constant conditions. Such a homogeneous assumption is no longer applicable on the host rock scale as can be seen from the pore water profiles of the potential host rock Opalinus Clay at Mont Terri (Switzerland). The embedding aquifers are the hydro-geological boundaries, that established gradients in the 210 m thick low permeable section through diffusive exchange over millions of years. Present-day pore water profiles were confirmed by a data-driven as well as by a conceptual scenario. Based on the modelled profiles, the influence of the geochemical gradient on uranium migration was quantified by comparing the distances after one million years with results of common homogeneous models. Considering the heterogeneous system, uranium migrated up to 24 m farther through the formation depending on the source term position within the gradient and on the partial pressure of carbon dioxide pCO2 of the system. Migration lengths were almost equal for single- and multicomponent diffusion. Differences can predominantly be attributed to changes in the sorption capacity, whereby pCO2 governs how strong uranium migration is affected by the geochemical gradient. Thus, the governing parameters for uranium migration in the Opalinus Clay can be ordered in descending priority: pCO2, geochemical gradients, mineralogical heterogeneity.

KW - PHREEQC KW - reactive transport KW - sorption KW - diffusion KW - repository far-field KW - hydro-geological system Y1 - 2021 U6 - https://doi.org/10.3390/min11101087 SN - 2075-163X VL - 11 IS - 10 PB - MDPI CY - Basel ER - TY - JOUR A1 - Doerries, Timo J. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Apparent anomalous diffusion and non-Gaussian distributions in a simple mobile-immobile transport model with Poissonian switching JF - Interface : journal of the Royal Society N2 - 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. KW - diffusion KW - mobile-immobile model KW - tau proteins Y1 - 2022 U6 - https://doi.org/10.1098/rsif.2022.0233 SN - 1742-5689 SN - 1742-5662 VL - 19 IS - 192 PB - Royal Society CY - London ER - TY - JOUR A1 - Mutothya, Nicholas Mwilu A1 - Xu, Yong A1 - Li, Yongge A1 - Metzler, Ralf A1 - Mutua, Nicholas Muthama T1 - First passage dynamics of stochastic motion in heterogeneous media driven by correlated white Gaussian and coloured non-Gaussian noises JF - Journal of physics. Complexity N2 - We study the first passage dynamics for a diffusing particle experiencing a spatially varying diffusion coefficient while driven by correlated additive Gaussian white noise and multiplicative coloured non-Gaussian noise. We consider three functional forms for position dependence of the diffusion coefficient: power-law, exponential, and logarithmic. The coloured non-Gaussian noise is distributed according to Tsallis' q-distribution. Tracks of the non-Markovian systems are numerically simulated by using the fourth-order Runge-Kutta algorithm and the first passage times (FPTs) are recorded. The FPT density is determined along with the mean FPT (MFPT). Effects of the noise intensity and self-correlation of the multiplicative noise, the intensity of the additive noise, the cross-correlation strength, and the non-extensivity parameter on the MFPT are discussed. KW - first passage KW - diffusion KW - non-Gaussian KW - correlated noise Y1 - 2021 U6 - https://doi.org/10.1088/2632-072X/ac35b5 SN - 2632-072X VL - 2 PB - IOP Publishing CY - Bristol ER - TY - JOUR A1 - Mutothya, Nicholas Mwilu A1 - Xu, Yong A1 - Li, Yongge A1 - Metzler, Ralf T1 - Characterising stochastic motion in heterogeneous media driven by coloured non-Gaussian noise JF - Journal of physics : A, Mathematical and theoretical N2 - We study the stochastic motion of a test particle in a heterogeneous medium in terms of a position dependent diffusion coefficient mimicking measured deterministic diffusivity gradients in biological cells or the inherent heterogeneity of geophysical systems. Compared to previous studies we here investigate the effect of the interplay of anomalous diffusion effected by position dependent diffusion coefficients and coloured non-Gaussian noise. The latter is chosen to be distributed according to Tsallis' q-distribution, representing a popular example for a non-extensive statistic. We obtain the ensemble and time averaged mean squared displacements for this generalised process and establish its non-ergodic properties as well as analyse the non-Gaussian nature of the associated displacement distribution. We consider both non-stratified and stratified environments. KW - diffusion KW - anomalous diffusion KW - non-extensive statistics KW - coloured KW - noise KW - heterogeneous diffusion process Y1 - 2021 U6 - https://doi.org/10.1088/1751-8121/abfba6 SN - 1751-8113 SN - 1751-8121 VL - 54 IS - 29 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Shoaee, Safa A1 - Sanna, Anna Laura A1 - Sforazzini, Giuseppe T1 - Elucidating charge generation in green-solvent processed organic solar cells JF - Molecules : a journal of synthetic chemistry and natural product chemistry / Molecular Diversity Preservation International N2 - Organic solar cells have the potential to become the cheapest form of electricity. Rapid increase in the power conversion efficiency of organic solar cells (OSCs) has been achieved with the development of non-fullerene small-molecule acceptors. Next generation photovoltaics based upon environmentally benign "green solvent" processing of organic semiconductors promise a step-change in the adaptability and versatility of solar technologies and promote sustainable development. However, high-performing OSCs are still processed by halogenated (non-environmentally friendly) solvents, so hindering their large-scale manufacture. In this perspective, we discuss the recent progress in developing highly efficient OSCs processed from eco-compatible solvents, and highlight research challenges that should be addressed for the future development of high power conversion efficiencies devices. KW - organic solar cells KW - green solvents KW - non-halogenated solvents KW - exaction KW - diffusion KW - photoluminescence quenching Y1 - 2021 U6 - https://doi.org/10.3390/molecules26247439 SN - 1420-3049 VL - 26 IS - 24 PB - MDPI CY - Basel ER -