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Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as ‘superstatistics’ or ‘diffusing diffusivity’. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.

New wave frequency and amplitude models for the nightside and dayside chorus waves are built based on measurements from the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrument onboard the Van Allen Probes. The corresponding 3D diffusion coefficients are systematically obtained. Compared with previous commonly-used (typical) parameterizations, the new parameterizations result in differences in diffusion rates that depend on the energy and pitch angle. Furthermore, one-year 3D diffusive simulations are performed using the Versatile Electron Radiation Belt (VERB) code. Both typical and new wave parameterizations simulation results are in a good agreement with observations at 0.9 MeV. However, the new parameterizations for nightside chorus better reproduce the observed electron fluxes. These parameterizations will be incorporated into future modeling efforts.

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 nature as well as in the context of infection and medical applications, bacteria often have to move in highly complex environments such as soil or tissues. Previous studies have shown that bacteria strongly interact with their surroundings and are often guided by confinements. Here, we investigate theoretically how the dispersal of swimming bacteria can be augmented by microfluidic environments and validate our theoretical predictions experimentally. We consider a system of bacteria performing the prototypical run-and-tumble motion inside a labyrinth with square lattice geometry. Narrow channels between the square obstacles limit the possibility of bacteria to reorient during tumbling events to an area where channels cross. Thus, by varying the geometry of the lattice it might be possible to control the dispersal of cells. We present a theoretical model quantifying diffusive spreading of a run-and-tumble random walker in a square lattice. Numerical simulations validate our theoretical predictions for the dependence of the diffusion coefficient on the lattice geometry. We show that bacteria moving in square labyrinths exhibit enhanced dispersal as compared to unconfined cells. Importantly, confinement significantly extends the duration of the phase with strongly non-Gaussian diffusion, when the geometry of channels is imprinted in the density profiles of spreading cells. Finally, in good agreement with our theoretical findings, we observe the predicted behaviors in experiments with E. coli bacteria swimming in a square lattice labyrinth created in amicrofluidic device. Altogether, our comprehensive understanding of bacterial dispersal in a simple two-dimensional labyrinth makes the first step toward the analysis of more complex geometries relevant for real world applications.

We investigate anomalous diffusion processes governed by the fractional Langevin equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As the random and damping forces in the fractional Langevin equation fulfill the appropriate fluctuation-dissipation relation, the probability density on a finite interval converges for long times towards the expected uniform distribution prescribed by thermal equilibrium. In contrast, on a semi-infinite interval with a reflecting wall at the origin, the probability density shows pronounced deviations from the Gaussian behavior observed for normal diffusion. If the correlations of the random force are persistent (positive), particles accumulate at the reflecting wall while antipersistent (negative) correlations lead to a depletion of particles near the wall. We compare and contrast these results with the strong accumulation and depletion effects recently observed for nonthermal fractional Brownian motion with reflecting walls, and we discuss broader implications.

Dielectric Relaxation Spectroscopy (DRS) and Thermally Stimulated Depolarization Current (TSDC) measurements were employed to study dielectric-relaxation processes, structural transitions and electric-polarization phenomena in poly(vinylidenefluoride-trifluoroethylene-chlorofluoroethylene) (P(VDF-TrFE-CFE)) terpolymer films. Results from DRS confirm the existence of two separate dispersion regions related to a para-to-ferroelectric phase transition and to the glass transition. The dipolar TSDC peak correlates with the loss peak of the ? relaxation that represents the glass transition. The electric polarization calculated from the dipolar TSDC peak (glass transition) shows a non-linear electric-field dependence and saturates at high electric poling fields. As the observed behaviour is essentially the same as that of the electric polarization obtained from direct polarization-versus-electric-field hysteresis measurements, TSDC experiments are also suitable for studying the polarization in relaxor-ferroelectric polymers. A saturation polarization of 44 mC m(?2) was found for an electric field of 190 MV m(?1).

Both climate-change damages and climate-change mitigation will incur economic costs. While the risk of severe damages increases with the level of global warming (Dell et al., 2014; IPCC, 2014b, 2018; Lenton et al., 2008), mitigating costs increase steeply with more stringent warming limits (IPCC, 2014a; Luderer et al., 2013; Rogelj et al., 2015). Here, we show that the global warming limit that minimizes this century's total economic costs of climate change lies between 1.9 and 2 ∘C, if temperature changes continue to impact national economic growth rates as observed in the past and if instantaneous growth effects are neither compensated nor amplified by additional growth effects in the following years. The result is robust across a wide range of normative assumptions on the valuation of future welfare and inequality aversion. We combine estimates of climate-change impacts on economic growth for 186 countries (applying an empirical damage function from Burke et al., 2015) with mitigation costs derived from a state-of-the-art energy–economy–climate model with a wide range of highly resolved mitigation options (Kriegler et al., 2017; Luderer et al., 2013, 2015). Our purely economic assessment, even though it omits non-market damages, provides support for the international Paris Agreement on climate change. The political goal of limiting global warming to “well below 2 degrees” is thus also an economically optimal goal given above assumptions on adaptation and damage persistence.

We consider a simple model for active random walk with general temporal correlations, and investigate the shape of the probability distribution function of the displacement during a short time interval. We find that under certain conditions the distribution exhibits multiple peaks and we show analytically and numerically that the existence of these peaks is governed by the walker?s tendency to move forward, while the correlations between the timing of its active motion control the magnitude and shape of the peaks. In particular, we find that in a homogeneous system such peaks can occur only if the persistence is strong enough.