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Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.
Near-ambient pressure x-ray photoelectron spectroscopy (NAP-XPS) is a less traditional form of XPS that allows samples to be analyzed at relatively high pressures, i. e., at greater than 2500 Pa. In this study, poly(.- benzyl L- glutamate) (PBLG) with a molar mass of 11.3 kg/mol was analyzed by NAP-XPS; here, we show the survey, C 1s, N 1s, and O 1s narrow scans of PBLG. The C 1s peak envelope was fitted in three different ways, to five, six, or seven synthetic peaks. In each fit, there was also a shake-up signal. The O 1s narrow scan was well fit with three peaks: CZO and CvO in a 1:2 ratio from the polymer, and a higher energy signal from water vapor. Hartree-Fock orbital energies of a model monomer served as a guide to an additional fit of the C 1s envelope.
Germanium oxide is a prototype network-forming oxide with pressure-induced structural changes similar to those found in crystals and amorphous silicate oxides at high pressure. Studying density and coordination changes in amorphous GeO2 allows for insight into structural changes in silicate oxides at very high pressure, with implications for the properties of planetary magmas. Here, we report the density of germanium oxide glass up to 133 GPa using the x-ray absorption technique, with very good agreement with previous experimental data at pressure below 40 GPa and recent calculation up to 140 GPa. Our data highlight four distinct compressibility domains, corresponding to changes of the local structure of GeO2. Above 80 GPa, our density data show a compressibility and bulk modulus similar to the counterpart crystal phase, and we propose that a compact distorted sixfold coordination, similar to the structural motif of the pyritelike crystalline GeO2 polymorph, is likely to be stable in that pressure range. Our density data point to a smooth continuous evolution of the average coordination for pressure above 20 GPa with persistent sixfold coordination, without sharp density or density slope discontinuities. These observations are in very good agreement with theoretical calculations and spectroscopic measurements, and our results indicate that glasses and melts may behave similarly to their high-pressure solid counterparts with comparable densities, compressibility, and possibly average coordination.
Border effect corrections for diagonal line based recurrence quantification analysis measures
(2019)
Recurrence Quantification Analysis (RQA) defines a number of quantifiers, which base upon diagonal line structures in the recurrence plot (RP). Due to the finite size of an RP, these lines can be cut by the borders of the RP and, thus, bias the length distribution of diagonal lines and, consequently, the line based RQA measures. In this letter we investigate the impact of the mentioned border effects and of the thickening of diagonal lines in an RP (caused by tangential motion) on the estimation of the diagonal line length distribution, quantified by its entropy. Although a relation to the Lyapunov spectrum is theoretically expected, the mentioned entropy yields contradictory results in many studies. Here we summarize correction schemes for both, the border effects and the tangential motion and systematically compare them to methods from the literature. We show that these corrections lead to the expected behavior of the diagonal line length entropy, in particular meaning zero values in case of a regular motion and positive values for chaotic motion. Moreover, we test these methods under noisy conditions, in order to supply practical tools for applied statistical research.
We investigate the ultrafast magnetization dynamics of FePt in the L1(0) phase after an optical heating pulse, as used in heat-assisted magnetic recording. We compare continuous and nano-granular thin films and emphasize the impact of the finite size on the remagnetization dynamics. The remagnetization speeds up significantly with increasing external magnetic field only for the continuous film, where domain-wall motion governs the dynamics. The ultrafast remagnetization dynamics in the continuous film are only dominated by heat transport in the regime of high magnetic fields, whereas the timescale required for cooling is prevalent in the granular film for all magnetic field strengths. These findings highlight the necessary conditions for studying the intrinsic heat transport properties in magnetic materials.
In this paper we investigate the magneto-optical (MO) and magnetic properties of bismuth iron garnet Bi3Fe5O12 thin films over a wide range of photon energies (1.6-3.5 eV) and temperatures (5-740 K). Depending on the photon energy range, the Faraday rotation (Theta(F)) and ellipticity (epsilon(F)) vary nonmonotonously with temperature. This behavior cannot be explained by a magnetization variation that can only decrease with increasing temperature. Theta(F) and epsilon(F) spectra have therefore been analyzed using a model based on two optical transitions of a diamagnetic nature, representing the tetrahedral and octahedral iron sites. Thus, the contribution of each magnetic sublattice has been extracted from the global macroscopic MO response and investigated as a function of temperature. The magnetic properties of octahedral and tetrahedral sublattices depend differently on temperature, suggesting a different anisotropy due to oxygen coordination. We have demonstrated that this relatively simple macroscopic measurement with a subsequent analysis can grant access to the information on the properties at a microscopic level. These results can advance the fundamental understanding of MO properties in multisublattice magnetic materials.
Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here, we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the periodically forced Stuart-Landau oscillator as the paradigmatic model, we determine and numerically analyse the coupling functions up to the fourth order in the force strength. We show that the found nonlinear phase coupling functions can be used for predicting synchronization regions of the forced oscillator.
We introduce a versatile mechanism of light-driven self-propelled motion applied to porous Janus-type particles. The mechanism is based on the generation of local light-driven diffusio-osmotic (l-LDDO) flow around each single porous particle subjected to suitable irradiation conditions. The photosensitivity is introduced by a cationic azobenzene containing surfactant, which undergoes a photoisomerization reaction from a more hydrophobic trans-state to a rather hydrophilic cis-state under illumination with light. The negatively charged porous silica particles are dispersed in a corresponding aqueous solution and absorb molecules in their trans-state but expel them in their cis-state. During illumination with blue light triggering both trans-cis and cis-trans isomerization at the same time, the colloids start to move due to the generation of a steady-state diffusive flow of cis-isomers out of and trans-isomers into the particle. This is because a hemi-spherical metal cap partially sealing the colloid breaks the symmetry of the otherwise radially directed local flow around the particle, leading to self-propelled motion. Janus particles exhibit superdiffusive motion with a velocity of similar to 0.5 mu m/s and a persistence length of ca. 50 mu m, confined to microchannels the direction can be maintained up to 300 mu m before rotational diffusion reverts it. Particles forming dimers of different shapes can be made to travel along circular trajectories. The unique feature of this mechanism is that the strength of self-propulsion can be tuned by convenient external optical stimuli (intensity and irradiation wavelength) such that a broad variety of experimental situations can be realized in a spatiotemporal way and in situ.
In July 2004 the Cassini–Huygens mission reached the Saturnian system and started its orbital tour. A total of 75 orbits will be carried out during the primary mission until August 2008. In these four years Cassini crosses the ring plane 150 times and spends approx. 400 h within Titan's orbit. The Cosmic Dust Analyser (CDA) onboard Cassini characterises the dust environment with its extended E ring and embedded moons. Here, we focus on the CDA results of the first year and we present the Dust Analyser (DA) data within Titan's orbit. This paper does investigate High Rate Detector data and dust composition measurements. The authors focus on the analysis of impact rates, which were strongly variable primarily due to changes of the spacecraft pointing. An overview is given about the ring plane crossings and the DA counter measurements. The DA dust impact rates are compared with the DA boresight configuration around all ring plane crossings between June 2004 and July 2005. Dust impacts were registered at altitudes as high as 100 000 km above the ring plane at distances from Saturn between 4 and 10 Saturn radii. In those regions the dust density of particles bigger than 0.5 can reach values of 0.001m-3.
In this study, we detect high percentile rainfall events in the eastern central Andes, based on Tropical Rainfall Measuring Mission (TRMM) with a spatial resolution of 0.25 × 0.25°, a temporal resolution of 3 h, and for the duration from 2001 to 2018. We identify three areas with high mean accumulated rainfall and analyze their atmospheric behaviour and rainfall characteristics with specific focus on extreme events. Extreme events are defined by events above the 95th percentile of their daily mean accumulated rainfall. Austral summer (DJF) is the period of the year presenting the most frequent extreme events over these three regions. Daily statistics show that the spatial maxima, as well as their associated extreme events, are produced during the night. For the considered period, ERA-Interim reanalysis data, provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) with 0.75° x0.75° spatial and 6-hourly temporal resolutions, were used for the analysis of the meso- and synoptic-scale atmospheric patterns. Night- and day-time differences indicate a nocturnal overload of northerly and northeasterly low-level humidity flows arriving from tropical South America. Under these conditions, cooling descending air from the mountains may find unstable air at the surface, giving place to the development of strong local convection. Another possible mechanism is presented here: a forced ascent of the low-level flow due to the mountains, disrupting the atmospheric stratification and generating vertical displacement of air trajectories. A Principal Component Analysis (PCA) in T-mode is applied to day- and night-time data during the maximum and extreme events. The results show strong correlation areas over each subregion under study during night-time, whereas during day-time no defined patterns are found. This confirms the observed nocturnal behavior of rainfall within these three hotspots.