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How related are the ergodic properties of the over- and underdamped Langevin equations driven by fractional Gaussian noise? We here find that for massive particles performing fractional Brownian motion (FBM) inertial effects not only destroy the stylized fact of the equivalence of the ensemble-averaged mean-squared displacement (MSD) to the time-averaged MSD (TAMSD) of overdamped or massless FBM, but also dramatically alter the values of the ergodicity-breaking parameter (EB). Our theoretical results for the behavior of EB for underdamped or massive FBM for varying particle mass m, Hurst exponent H, and trace length T are in excellent agreement with the findings of stochastic computer simulations. The current results can be of interest for the experimental community employing various single-particle-tracking techniques and aiming at assessing the degree of nonergodicity for the recorded time series (studying, e.g., the behavior of EB versus lag time). To infer FBM as a realizable model of anomalous diffusion for a set single-particle-tracking data when massive particles are being tracked, the EBs from the data should be compared to EBs of massive (rather than massless) FBM.
Marine sedimentary archives are routinely used to reconstruct past environmental changes. In many cases, bioturbation and sedimentary mixing affect the proxy time-series and the age-depth relationship. While idealized models of bioturbation exist, they usually assume homogeneous mixing, thus that a single sample is representative for the sediment layer it is sampled from.
However, it is largely unknown to which extent this assumption holds for sediments used for paleoclimate reconstructions.
To shed light on
1) the age-depth relationship and its full uncertainty,
2) the magnitude of mixing processes affecting the downcore proxy variations, and
3) the representativity of the discrete sample for the sediment layer, we designed and performed a case study on South China Sea sediment material which was collected using a box corer and which covers the last glacial cycle.
Using the radiocarbon content of foraminiferal tests as a tracer of time, we characterize the spatial age-heterogeneity of sediments in a three-dimensional setup. In total, 118 radiocarbon measurements were performed on defined small- and large-volume bulk samples ( similar to 200 specimens each) to investigate the horizontal heterogeneity of the sediment. Additionally, replicated measurements on small numbers of specimens (10 x 5 specimens) were performed to assess the heterogeneity within a sample volume. Visual assessment of X-ray images and a quantitative assessment of the mixing strength show typical mixing from bioturbation corresponding to around 10 cm mixing depth.
Notably, our 3D radiocarbon distribution reveals that the horizontal heterogeneity (up to 1,250 years), contributing to the age uncertainty, is several times larger than the typically assumed radiocarbon based age-model error (single errors up to 250 years). Furthermore, the assumption of a perfectly bioturbated layer with no mixing underneath is not met.
Our analysis further demonstrates that the age-heterogeneity might be a function of sample size; smaller samples might contain single features from the incomplete mixing and are thus less representative than larger samples.
We provide suggestions for future studies, optimal sampling strategies for quantitative paleoclimate reconstructions and realistic uncertainty in age models, as well as discuss possible implications for the interpretation of paleoclimate records.
In this study, the kinetics of the adsorption of 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F(4)TCNQ) on the surface of Ag nanoparticles (Ag NPs) in chloroform has been intensively investigated, as molecular doping is known to play a crucial role in organic electronic devices. Based on the results obtained from UV-visible (vis)-near-infrared (NIR) absorption spectroscopy, cryogenic transmission electron microscopy, scanning nanobeam electron diffraction, and electron energy loss spectroscopy, a two-step interaction kinetics has been proposed for the Ag NPs and F(4)TCNQ molecules, which includes the first step of electron transfer from Ag NPs to F(4)TCNQ indicated by the ionization of F(4)TCNQ and the second step of the formation of a Ag-F(4)TCNQ complex. The whole process has been followed via UV-vis-NIR absorption spectroscopy, which reveals distinct kinetics at two stages: the instantaneous ionization and the long-term complex formation. The kinetics and the influence of the molar ratio of Ag NPs/F(4)TCNQ molecules on the interaction between Ag NPs and F(4)TCNQ molecules in an organic solution are reported herein for the first time. Furthermore, the control experiment with silica-coated Ag NPs manifests that the charge transfer at the surface between Ag NPs and F(4)TCNQ molecules is prohibited by a silica layer of 18 nm.
The within-site variability in site response is the randomness in site response at a given site from different earthquakes and is treated as aleatory variability in current seismic hazard/risk analyses.
In this study, we investigate the single-station variability in linear site response at K-NET and KiK-net stations in Japan using a large number of earthquake recordings.
We found that the standard deviation of the horizontal-to-vertical Fourier spectral ratio at individual sites, that is single-station horizontal-to-vertical spectral ratio (HVSR) sigma sigma(HV,s), approximates the within-site variability in site response quantified using surface-to-borehole spectral ratios (for oscillator frequencies higher than the site fundamental frequency) or empirical ground-motion models.
Based on this finding, we then utilize the single-station HVSR sigma as a convenient tool to study the site-response variability at 697 KiK-net and 1169 K-NET sites.
Our results show that at certain frequencies, stiff, rough and shallow sites, as well as small and local events tend to have a higher sigma(HV,s).
However, when being averaged over different sites, the single-station HVSR sigma, that is sigma(HV), increases gradually with decreasing frequency. In the frequency range of 0.25-25 Hz, sigma(HV) is centred at 0.23-0.43 in ln scales (a linear scale factor of 1.26-1.54) with one standard deviation of less than 0.1. sigma(HV) is quite stable across different tectonic regions, and we present a constant, as well as earthquake magnitude- and distance-dependent sigma(HV) models.
We employ Langevin-dynamics simulations to unveil non-Brownian and non-Gaussian center-of-mass self-diffusion of massive flexible dumbbell-shaped particles in crowded two-dimensional solutions. We study the intradumbbell dynamics of the relative motion of the two constituent elastically coupled disks. Our main focus is on effects of the crowding fraction phi and of the particle structure on the diffusion characteristics. We evaluate the time-averaged mean-squared displacement (TAMSD), the displacement probability-density function (PDF), and the displacement autocorrelation function (ACF) of the dimers. For the TAMSD at highly crowded conditions of dumbbells, e.g., we observe a transition from the short-time ballistic behavior, via an intermediate subdiffusive regime, to long-time Brownian-like spreading dynamics. The crowded system of dimers exhibits two distinct diffusion regimes distinguished by the scaling exponent of the TAMSD, the dependence of the diffusivity on phi, and the features of the displacement-ACF. We attribute these regimes to a crowding-induced transition from viscous to viscoelastic diffusion upon growing phi. We also analyze the relative motion in the dimers, finding that larger phi suppress their vibrations and yield strongly non-Gaussian PDFs of rotational displacements. For the diffusion coefficients D(phi) of translational and rotational motion of the dumbbells an exponential decay with phi for weak and a power-law variation D(phi) proportional to (phi - phi(star))(2.4) for strong crowding is found. A comparison of simulation results with theoretical predictions for D(phi) is discussed and some relevant experimental systems are overviewed.
In this study we present a novel method for the automatic detection of minerals and elements using hyperspectral transmittance imaging microscopy measurements of complete thin sections (HyperTIM).
This is accomplished by using a hyperspectral camera system that operates in the visible and near-infrared (VNIR) range with a specifically designed sample holder, scanning setup, and a microscope lens.
We utilize this method on a monazite ore thin section from Steenkampskraal (South Africa), which we analyzed for the rare earth element (REE)-bearing mineral monazite ((Ce,Nd,La)PO4), with high concentrations of Nd. The transmittance analyses with the hyperspectral VNIR camera can be used to identify REE minerals and Nd in thin sections.
We propose a three-point band depth index, the Nd feature depth index (NdFD), and its related product the Nd band depth index (NdBDI), which enables automatic mineral detection and classification for the Nd-bearing monazites in thin sections. In combination with the average concentration of the relative Nd content, it permits a destruction-free, total concentration calculation for Nd across the entire thin section.
We consider the spatiotemporal states of an ensemble of nonlocally coupled nonidentical phase oscillators, which correspond to different regimes of the long-term evolution of such a system. We have obtained homogeneous, twisted, and nonhomogeneous stationary solutions to the Ott-Antonsen equations corresponding to key variants of the realized collective rotational motion of elements of the medium in question with nonzero mesoscopic characteristics determining the degree of coherence of the dynamics of neighboring particles. We have described the procedures of the search for the class of nonhomogeneous solutions as stationary points of the auxiliary point map and of determining the stability based on analysis of the eigenvalue spectrum of the composite operator. Static and breather cluster regimes have been demonstrated and described, as well as the regimes with an irregular behavior of averaged complex fields including, in particular, the local order parameter.
Groundwater recharge (GWR) is one of the most challenging water fluxes to estimate, as it relies on observed data that are often limited in many developing countries.
This study developed an innovative water budget method using satellite products for estimating the spatially distributed GWR at monthly and annual scales in tropical wet sedimentary regions despite cloudy conditions.
The distinctive features proposed in this study include the capacity to address 1) evapotranspiration estimations in tropical wet regions frequently overlaid by substantial cloud cover; and 2) seasonal root-zone water storage estimations in sedimentary regions prone to monthly variations.
The method also utilises satellite-based information of the precipitation and surface runoff. The GWR was estimated and validated for the hydrologically contrasting years 2016 and 2017 over a tropical wet sedimentary region located in North-eastern Brazil, which has substantial potential for groundwater abstraction.
This study showed that applying a cloud-cleaning procedure based on monthly compositions of biophysical data enables the production of a reasonable proxy for evapotranspiration able to estimate groundwater by the water budget method.
The resulting GWR rates were 219 (2016) and 302 (2017) mm yr(-1), showing good correlations (CC = 0.68 to 0.83) and slight underestimations (PBIAS =-13 to-9%) when compared with the referenced estimates obtained by the water table fluctuation method for 23 monitoring wells. Sensitivity analysis shows that water storage changes account for +19% to-22% of our monthly evaluation.
The satellite-based approach consistently demonstrated that the consideration of cloud-cleaned evapotranspiration and root-zone soil water storage changes are essential for a proper estimation of spatially distributed GWR in tropical wet sedimentary regions because of their weather seasonality and cloudy conditions.
The Levenberg–Marquardt regularization for the backward heat equation with fractional derivative
(2022)
The backward heat problem with time-fractional derivative in Caputo's sense is studied. The inverse problem is severely ill-posed in the case when the fractional order is close to unity. A Levenberg-Marquardt method with a new a posteriori stopping rule is investigated. We show that optimal order can be obtained for the proposed method under a Hölder-type source condition. Numerical examples for one and two dimensions are provided.