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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.
If not oriented perfectly isotropically, the strong dipole moment of polar organic semiconductor materials such as tris-(8-hydroxyquinolate)aluminum (Alq3) will lead to the buildup of a giant surface potential (GSP) and thus to a macroscopic dielectric polarization of the organic film. Despite this having been a known fact for years, the implications of such high potentials within an organic layer stack have only been studied recently. In this work, the influence of the GSP on hole injection into organic layers is investigated. Therefore, we apply a concept called dipolar doping to devices consisting of the prototypical organic materials N,N′-Di(1-naphthyl)-N,N′-diphenyl-(1,1′-biphenyl)-4,4′-diamine (NPB) as nonpolar host and Alq3 as dipolar dopant with different mixing ratios to tune the GSP. The mixtures are investigated in single-layer monopolar devices as well as bilayer metal/insulator/semiconductor structures. Characterization is done electrically using current-voltage (I-V) characteristics, impedance spectroscopy, and charge extraction by linearly increasing voltage and time of flight, as well as with ultraviolet photoelectron spectroscopy. We find a maximum in device performance for moderate to low doping concentrations of the polar species in the host. The observed behavior can be described on the basis of the Schottky effect for image-force barrier lowering, if the changes in the interface dipole, the carrier mobility, and the GSP induced by dipolar doping are taken into account.
The possibility to manufacture perovskite solar cells (PSCs) at low temperatures paves the way to flexible and lightweight photovoltaic (PV) devices manufactured via high-throughput roll-to-roll processes. In order to achieve higher power conversion efficiencies, it is necessary to approach the radiative limit via suppression of non-radiative recombination losses. Herein, we performed a systematic voltage loss analysis for a typical low-temperature processed, flexible PSC in n-i-p configuration using vacuum deposited C-60 as electron transport layer (ETL) and two-step hybrid vacuum-solution deposition for CH3NH3PbI3 perovskite absorber. We identified the ETL/absorber interface as a bottleneck in relation to non-radiative recombination losses, the quasi-Fermi level splitting (QFLS) decreases from similar to 1.23 eV for the bare absorber, just similar to 90 meV below the radiative limit, to similar to 1.10 eV when C-60 is used as ETL. To effectively mitigate these voltage losses, we investigated different interfacial modifications via vacuum deposited interlayers (BCP, B4PyMPM, 3TPYMB, and LiF). An improvement in QFLS of similar to 30-40 meV is observed after interlayer deposition and confirmed by comparable improvements in the open-circuit voltage after implementation of these interfacial modifications in flexible PSCs. Further investigations on absorber/hole transport layer (HTL) interface point out the detrimental role of dopants in Spiro-OMeTAD film (widely employed HTL in the community) as recombination centers upon oxidation and light exposure. [GRAPHICS] .
In the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small 'escape window' in the otherwise impermeable boundary, once it arrives to this window and crosses an entropic barrier at the entrance to it. This generic problem is mathematically identical to that of a diffusion-mediated reaction with a partially-reactive site on the container's boundary. Considerable knowledge is available on the dependence of the mean first-reaction time (FRT) on the pertinent parameters. We here go a distinct step further and derive the full FRT distribution for the NEP. We demonstrate that typical FRTs may be orders of magnitude shorter than the mean one, thus resulting in a strong defocusing of characteristic temporal scales. We unveil the geometry-control of the typical times, emphasising the role of the initial distance to the target as a decisive parameter. A crucial finding is the further FRT defocusing due to the barrier, necessitating repeated escape or reaction attempts interspersed with bulk excursions. These results add new perspectives and offer a broad comprehension of various features of the by-now classical NEP that are relevant for numerous biological and technological systems.
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.
For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.