TY - JOUR A1 - Awad, Emad A1 - Metzler, Ralf T1 - Closed-form multi-dimensional solutions and asymptotic behaviours for subdiffusive processes with crossovers: II. Accelerating case JF - Journal of physics : A, Mathematical and theoretical N2 - Anomalous diffusion with a power-law time dependence vertical bar R vertical bar(2)(t) similar or equal to t(alpha i) of the mean squared displacement occurs quite ubiquitously in numerous complex systems. Often, this anomalous diffusion is characterised by crossovers between regimes with different anomalous diffusion exponents alpha(i). Here we consider the case when such a crossover occurs from a first regime with alpha(1) to a second regime with alpha(2) such that alpha(2) > alpha(1), i.e., accelerating anomalous diffusion. A widely used framework to describe such crossovers in a one-dimensional setting is the bi-fractional diffusion equation of the so-called modified type, involving two time-fractional derivatives defined in the Riemann-Liouville sense. We here generalise this bi-fractional diffusion equation to higher dimensions and derive its multidimensional propagator (Green's function) for the general case when also a space fractional derivative is present, taking into consideration long-ranged jumps (Levy flights). We derive the asymptotic behaviours for this propagator in both the short- and long-time as well the short- and long-distance regimes. Finally, we also calculate the mean squared displacement, skewness and kurtosis in all dimensions, demonstrating that in the general case the non-Gaussian shape of the probability density function changes. KW - multidimensional fractional diffusion equation KW - continuous time random KW - walks KW - crossover anomalous diffusion dynamics KW - non-Gaussian probability KW - density Y1 - 2022 U6 - https://doi.org/10.1088/1751-8121/ac5a90 SN - 1751-8113 SN - 1751-8121 VL - 55 IS - 20 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Cervantes Villa, Juan Sebastian A1 - Shprits, Yuri Y. A1 - Aseev, Nikita A1 - Drozdov, Alexander A1 - Castillo Tibocha, Angelica Maria A1 - Stolle, Claudia T1 - Identifying radiation belt electron source and loss processes by assimilating spacecraft data in a three-dimensional diffusion model JF - Journal of geophysical research : Space physics N2 - Data assimilation aims to blend incomplete and inaccurate data with physics-based dynamical models. In the Earth's radiation belts, it is used to reconstruct electron phase space density, and it has become an increasingly important tool in validating our current understanding of radiation belt dynamics, identifying new physical processes, and predicting the near-Earth hazardous radiation environment. In this study, we perform reanalysis of the sparse measurements from four spacecraft using the three-dimensional Versatile Electron Radiation Belt diffusion model and a split-operator Kalman filter over a 6-month period from 1 October 2012 to 1 April 2013. In comparison to previous works, our 3-D model accounts for more physical processes, namely, mixed pitch angle-energy diffusion, scattering by Electromagnetic Ion Cyclotron waves, and magnetopause shadowing. We describe how data assimilation, by means of the innovation vector, can be used to account for missing physics in the model. We use this method to identify the radial distances from the Earth and the geomagnetic conditions where our model is inconsistent with the measured phase space density for different values of the invariants mu and K. As a result, the Kalman filter adjusts the predictions in order to match the observations, and we interpret this as evidence of where and when additional source or loss processes are active. The current work demonstrates that 3-D data assimilation provides a comprehensive picture of the radiation belt electrons and is a crucial step toward performing reanalysis using measurements from ongoing and future missions. KW - acceleration KW - code KW - density KW - emic waves KW - energetic particle KW - mechanisms KW - reanalysis KW - ultrarelativistic electrons KW - weather Y1 - 2019 U6 - https://doi.org/10.1029/2019JA027514 SN - 2169-9380 SN - 2169-9402 VL - 125 IS - 1 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Jay, Raphael M. A1 - Vaz da Cruz, Vinicius A1 - Eckert, Sebastian A1 - Fondell, Mattis A1 - Mitzner, Rolf A1 - Föhlisch, Alexander T1 - Probing solute-solvent interactions of transition metal complexes using L-edge absorption spectroscopy JF - The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces & biophysical chemistry N2 - In order to tailor solution-phase chemical reactions involving transition metal complexes, it is critical to understand how their valence electronic charge distributions are affected by the solution environment. Here, solute-solvent interactions of a solvatochromic mixed-ligand iron complex were investigated using X-ray absorption spectroscopy at the transition metal L-2,L-3-edge. Due to the selectivity of the corresponding core excitations to the iron 3d orbitals, the method grants direct access to the valence electronic structure around the iron center and its response to interactions with the solvent environment. A linear increase of the total L-2,L-3-edge absorption cross section as a function of the solvent Lewis acidity is revealed. The effect is caused by relative changes in different metal-ligand-bonding channels, which preserve local charge densities while increasing the density of unoccupied states around the iron center. These conclusions are corroborated by a combination of molecular dynamics and spectrum simulations based on time-dependent density functional theory. The simulations reproduce the spectral trends observed in the X-ray but also optical absorption experiments. Our results underscore the importance of solute-solvent interactions when aiming for an accurate description of the valence electronic structure of solvated transition metal complexes and demonstrate how L-2,L-3-edge absorption spectroscopy can aid in understanding the impact of the solution environment on intramolecular covalency and the electronic charge distribution. KW - basis-sets KW - charge-transfer KW - density KW - dynamics KW - electron localization KW - iron KW - solvation KW - spin-crossover KW - tranfer excited-state KW - x-ray-absorption Y1 - 2020 U6 - https://doi.org/10.1021/acs.jpcb.0c00638 SN - 1520-6106 SN - 1520-5207 VL - 124 IS - 27 SP - 5636 EP - 5645 PB - American Chemical Society CY - Washington ER -