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- Institut für Physik und Astronomie (1480) (remove)
Subject of this work is the investigation of universal scaling laws which are observed in coupled chaotic systems. Progress is made by replacing the chaotic fluctuations in the perturbation dynamics by stochastic processes. First, a continuous-time stochastic model for weakly coupled chaotic systems is introduced to study the scaling of the Lyapunov exponents with the coupling strength (coupling sensitivity of chaos). By means of the the Fokker-Planck equation scaling relations are derived, which are confirmed by results of numerical simulations. Next, the new effect of avoided crossing of Lyapunov exponents of weakly coupled disordered chaotic systems is described, which is qualitatively similar to the energy level repulsion in quantum systems. Using the scaling relations obtained for the coupling sensitivity of chaos, an asymptotic expression for the distribution function of small spacings between Lyapunov exponents is derived and compared with results of numerical simulations. Finally, the synchronization transition in strongly coupled spatially extended chaotic systems is shown to resemble a continuous phase transition, with the coupling strength and the synchronization error as control and order parameter, respectively. Using results of numerical simulations and theoretical considerations in terms of a multiplicative noise partial differential equation, the universality classes of the observed two types of transition are determined (Kardar-Parisi-Zhang equation with saturating term, directed percolation).
Various mathematical Black-Scholes-Merton-like models of option pricing employ the paradigmatic stochastic process of geometric Brownian motion (GBM). The innate property of such models and of real stock-market prices is the roughly exponential growth of prices with time [on average, in crisis-free times]. We here explore the ensemble- and time averages of a multiplicative-noise stochastic process with power-law-like time-dependent volatility, sigma(t) similar to t(alpha), named scaled GBM (SGBM). For SGBM, the mean-squared displacement (MSD) computed for an ensemble of statistically equivalent trajectories can grow faster than exponentially in time, while the time-averaged MSD (TAMSD)-based on a sliding-window averaging along a single trajectory-is always linear at short lag times Delta. The proportionality factor between these the two averages of the time series is Delta/T at short lag times, where T is the trajectory length, similarly to GBM. This discrepancy of the scaling relations and pronounced nonequivalence of the MSD and TAMSD at Delta/T << 1 is a manifestation of weak ergodicity breaking for standard GBM and for SGBM with s (t)-modulation, the main focus of our analysis. The analytical predictions for the MSD and mean TAMSD for SGBM are in quantitative agreement with the results of stochastic computer simulations.
Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.
Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.
We investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion coefficient D(t)∼tα−1 with α>0 (scaled Brownian motion) is stochastically reset to its initial position, and starts anew. In the present work we discuss the situation in which the memory on the value of the diffusion coefficient at a resetting time is erased, so that the whole process is a fully renewal one. The situation when the resetting of the coordinate does not affect the diffusion coefficient's time dependence is considered in the other work of this series [A. S. Bodrova et al., Phys. Rev. E 100, 012119 (2019)]. We show that the properties of the probability densities in such processes (erasing or retaining the memory on the diffusion coefficient) are vastly different. In addition we discuss the first-passage properties of the scaled Brownian motion with renewal resetting and consider the dependence of the efficiency of search on the parameters of the process.
Samarium hexaboride
(2018)
Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface.
Context:
Gyrochronology allows the derivation of ages for cool main sequence stars based on their observed rotation periods and masses, or a suitable proxy thereof. It is increasingly well-explored for FGK stars, but requires further measurements for older ages and K - M-type stars.
Aims:
We study the 2.7 Gyr-old open cluster Ruprecht 147 to compare it with the previously-studied, but far more distant, NGC 6819 cluster, and especially to measure cooler stars than was previously possible there.
Methods:
We constructed an inclusive list of 102 cluster members from prior work, including Gaia DR2, and for which light curves were also obtained during Campaign 7 of the Kepler/K2 space mission. We placed them in the cluster color-magnitude diagram and checked the related information against appropriate isochrones. The light curves were then corrected for data systematics using Principal Component Analysis on all observed K2 C07 stars and subsequently subjected to periodicity analysis.
Results:
Periodic signals are found for 32 stars, 21 of which are considered to be both highly reliable and to represent single, or effectively single, Ru 147 stars. These stars cover the spectral types from late-F to mid-M stars, and they have periods ranging from 6 d - 33 d, allowing for a comparison of Ruprecht 147 to both other open clusters and to models of rotational spindown. The derived rotation periods connect reasonably to, overlap with, and extend to lower masses the known rotation period distribution of the 2.5 Gyr-old cluster NGC 6819.
Conclusions:
The data confirm that cool stars lie on a single surface in rotation period-mass-age space, and they simultaneously challenge its commonly assumed shape. The shape at the low mass region of the color-period diagram at the age of Ru 147 favors a recently-proposed model which requires a third mass-dependent timescale in addition to the two timescales required by a former model, suggesting that a third physical process is required to model rotating stars effectively.
Extreme weather events like heatwaves and floods severely affect societies with impacts ranging from economic damages to losses in human lifes. Global warming caused by anthropogenic greenhouse gas emissions is expected to increase their frequency and intensity, particularly in the warm season. Next to these thermodynamic changes, climate change might also impact the large scale atmospheric circulation.Such dynamic changes might additionally act on the occurence of extreme weather events, but involved mechanisms are often highly non-linear. Therefore, large uncertainty exists on the exact nature of these changes and the related risks to society. Particularly in the densely populated mid-latitudes weather patterns are governed by the large scale circulation like the jet-streams and storm tracks. Extreme weather in this region is often related to persistent weather systems associated with a strongly meandering jet-stream. Such meanders are called Rossby waves. Under specific conditions they can become slow moving, stretched around the entire hemisphere and generate simultaneaous heat- and rainfall extremes in far-away regions.
This thesis aims at enhancing the understanding of synoptic-scale, circumglobal Rossby waves and the associated risks of dynamical changes to society. More specific, the analyses investigate their relation to extreme weather, regions at risk, under which conditions they are generated, and the influence of anthropogenic climate change on those conditions now, in the past and in the future.
I find that circumglobal Rossby waves promoted simultaneous occuring weather extremes across the northern hemisphere in several recent summers. Further, I present evidence that they are often linked to quasiresonant-amplification of planetary waves. These events include the 2003 European heatwave and the Moscow heatwave of 2010. This non-linear mechanism acts on the upper level flow through trapping and amplification of stationary synoptic scale waves. I show that this resonance mechanism acts in both hemispheres and is related to extreme weather. A main finding is that circumglobal Rossby waves primarily occur as two specific teleconnection patterns associated with a wave 5 and wave 7 pattern in the northern hemisphere, likely due to the favourable longitudinal distance of prominent mountain ridges here. Furthermore, I identify those regions which are particularly at risk: The central United States, western Europe and the Ukraine/Russian region. Moreover, I present evidence that the wave 7 pattern has and extreme weather in these regions. My results suggest that the increase in frequency can be linked to favourable changes in large scale temperature gradients, which I show to be largely underestimated by model simulations. Using surface temperature fingerprint as proxy for investigating historic and future model ensembles, evidence is presented that anthropogenic warming has likely increased the probability for the occurence of circumglobal Rossby waves. Further it is shown that this might lead to a doubling of such events until the end of the century under a high-emission scenario.
Overall, this thesis establishes several atmosphere-dynamical pathways by which changes in large scale temperature gradients might link to persistent boreal summer weather. It highlights the societal risks associated with the increasing occurence of a newly discovered Rossby wave teleconnection pattern, which has the potential to cause simultaneaous heat-extremes in the mid-latitudinal bread-basket regions. In addition, it provides further evidence that the traditional picture by which quasi-stationary Rossby waves occur only in the low wavenumber regime, should be reconsidered.
In the soil bacterium Pseudomonas putida, the motor torque for flagellar rotation is generated by the two stators MotAB and MotCD.
Here, we construct mutant strains in which one or both stators are knocked out and investigate their swimming motility in fluids of different viscosity and in heterogeneous structured environments (semisolid agar).
Besides phase-contrast imaging of single-cell trajectories and spreading cultures, dual-color fluorescence microscopy allows us to quantify the role of the stators in enabling P. putida's three different swimming modes, where the flagellar bundle pushes, pulls, or wraps around the cell body.
The MotAB stator is essential for swimming motility in liquids, while spreading in semisolid agar is not affected. Moreover, if the MotAB stator is knocked out, wrapped mode formation under low-viscosity conditions is strongly impaired and only partly restored for increased viscosity and in semisolid agar.
In contrast, when the MotCD stator is missing, cells are indistinguishable from the wild type in fluid experiments but spread much more slowly in semisolid agar.
Analysis of the microscopic trajectories reveals that the MotCD knockout strain forms sessile clusters, thereby reducing the number of motile cells, while the swimming speed is unaffected. Together, both stators ensure a robust wild type that swims efficiently under different environmental conditions.
IMPORTANCE
Because of its heterogeneous habitat, the soil bacterium Pseudomonas putida needs to swim efficiently under very different environmental conditions. In this paper, we knocked out the stators MotAB and MotCD to investigate their impact on the swimming motility of P. putida.
While the MotAB stator is crucial for swimming in fluids, in semisolid agar, both stators are sufficient to sustain a fast-swimming phenotype and increased frequencies of the wrapped mode, which is known to be beneficial for escaping mechanical traps. However, in contrast to the MotAB knockout, a culture of MotCD knockout cells spreads much more slowly in the agar, as it forms nonmotile clusters that reduce the number of motile cells.
Because of its heterogeneous habitat, the soil bacterium Pseudomonas putida needs to swim efficiently under very different environmental conditions. In this paper, we knocked out the stators MotAB and MotCD to investigate their impact on the swimming motility of P. putida.
In this Letter, we propose that the x-ray and the TeV observations in the vicinity of Geminga can be understood in the framework of anisotropic diffusion of injected electrons or positrons. This interpretation only requires the turbulence in the vicinity of Geminga to be sub-Alfvenic with the local mean magnetic field direction approximately aligned with our line of sight towards Geminga, without invoking extreme conditions for the environment, such as an extremely small diffusion coefficient and a weak magnetic field of submicrogauss as suggested in previous literature.
The Dirac point of a topological surface state (TSS) is protected against gapping by time-reversal symmetry. Conventional wisdom stipulates, therefore, that only through magnetisation may a TSS become gapped. However, non-magnetic gaps have now been demonstrated in Bi2Se3 systems doped with Mn or In, explained by hybridisation of the Dirac cone with induced impurity resonances. Recent photoemission experiments suggest that an analogous mechanism applies even when Bi2Se3 is surface dosed with Au. Here, we perform a systematic spin- and angle-resolved photoemission study of Au-dosed Bi2Se3. Although there are experimental conditions wherein the TSS appears gapped due to unfavourable photoemission matrix elements, our photon-energy-dependent spectra unambiguously demonstrate the robustness of the Dirac cone against high Au coverage. We further show how the spin textures of the TSS and its accompanying surface resonances remain qualitatively unchanged following Au deposition, and discuss the mechanism underlying the suppression of the spectral weight.
Robotic telescopes & Doppler imaging : measuring differential rotation on long-period active stars
(2004)
The sun shows a wide variety of magnetic-activity related phenomena. The magnetic field responsible for this is generated by a dynamo process which is believed to operate in the tachocline, which is located at the bottom of the convection zone. This dynamo is driven in part by differential rotation and in part by magnetic turbulences in the convection zone. The surface differential rotation, one key ingredient of dynamo theory, can be measured by tracing sunspot positions.To extend the parameter space for dynamo theories, one can extend these measurements to other stars than the sun. The primary obstacle in this endeavor is the lack of resolved surface images on other stars. This can be overcome by the Doppler imaging technique, which uses the rotation-induced Doppler-broadening of spectral lines to compute the surface distribution of a physical parameter like temperature. To obtain the surface image of a star, high-resolution spectroscopic observations, evenly distributed over one stellar rotation period are needed. This turns out to be quite complicated for long period stars. The upcoming robotic observatory STELLA addresses this problem with a dedicated scheduling routine, which is tailored for Doppler imaging targets. This will make observations for Doppler imaging not only easier, but also more efficient.As a preview of what can be done with STELLA, we present results of a Doppler imaging study of seven stars, all of which show evidence for differential rotation, but unfortunately the errors are of the same order of magnitude as the measurements due to unsatisfactory data quality, something that will not happen on STELLA. Both, cross-correlation analysis and the sheared image technique where used to double check the results if possible. For four of these stars, weak anti-solar differential rotation was found in a sense that the pole rotates faster than the equator, for the other three stars weak differential rotation in the same direction as on the sun was found.Finally, these new measurements along with other published measurements of differential rotation using Doppler imaging, were analyzed for correlations with stellar evolution, binarity, and rotation period. The total sample of stars show a significant correlation with rotation period, but if separated into antisolar and solar type behavior, only the subsample showing anti-solar differential rotation shows this correlation. Additionally, there is evidence for binary stars showing less differential rotation as single stars, as is suggested by theory. All other parameter combinations fail to deliver any results due to the still small sample of stars available.
X-ray free-electron lasers (XFELs) and table-top sources of x-rays based upon high harmonic generation (HHG) have revolutionized the field of ultrafast x-ray atomic and molecular physics, largely due to an explosive growth in capabilities in the past decade. XFELs now provide unprecedented intensity (10(20) W cm(-2)) of x-rays at wavelengths down to similar to 1 Angstrom, and HHG provides unprecedented time resolution (similar to 50 attoseconds) and a correspondingly large coherent bandwidth at longer wavelengths. For context, timescales can be referenced to the Bohr orbital period in hydrogen atom of 150 attoseconds and the hydrogen-molecule vibrational period of 8 femtoseconds; wavelength scales can be referenced to the chemically significant carbon K-edge at a photon energy of similar to 280 eV (44 Angstroms) and the bond length in methane of similar to 1 Angstrom. With these modern x-ray sources one now has the ability to focus on individual atoms, even when embedded in a complex molecule, and view electronic and nuclear motion on their intrinsic scales (attoseconds and Angstroms). These sources have enabled coherent diffractive imaging, where one can image non-crystalline objects in three dimensions on ultrafast timescales, potentially with atomic resolution. The unprecedented intensity available with XFELs has opened new fields of multiphoton and nonlinear x-ray physics where behavior of matter under extreme conditions can be explored. The unprecedented time resolution and pulse synchronization provided by HHG sources has kindled fundamental investigations of time delays in photoionization, charge migration in molecules, and dynamics near conical intersections that are foundational to AMO physics and chemistry. This roadmap coincides with the year when three new XFEL facilities, operating at Angstrom wavelengths, opened for users (European XFEL, Swiss-FEL and PAL-FEL in Korea) almost doubling the present worldwide number of XFELs, and documents the remarkable progress in HHG capabilities since its discovery roughly 30 years ago, showcasing experiments in AMO physics and other applications. Here we capture the perspectives of 17 leading groups and organize the contributions into four categories: ultrafast molecular dynamics, multidimensional x-ray spectroscopies; high-intensity x-ray phenomena; attosecond x-ray science.
The results of the theoretical consideration of stochastic resonance in overdamped bistable oscillators are given. These results are founded not on the model of two states as in [McNamara B, Wiesenfeld K. Theory of stochastic resonance. Phys Rev A 1989;39:4854-69], but on splitting of motion into regular and random and the rigorous solution of the Fokker-Planck equation for the random component. We show that this resonance is caused by a change, under the influence of noise, of the system's effective stiffness and damping factor contained in the equation for the regular component. For a certain value of the noise intensity the effective stiffness is minimal, and this fact causes non-monotonic change of the output signal amplitude as the noise intensity changes. It is important that the location of the minimum and its value depend essentially on the signal frequency.
Traditional inorganic semiconductors can be electronically doped with high precision. Conversely, there is still conjecture regarding the assessment of the electronic doping density in metal-halide perovskites, not to mention of a control thereof. This paper presents a multifaceted approach to determine the electronic doping density for a range of different lead-halide perovskite systems. Optical and electrical characterization techniques, comprising intensity-dependent and transient photoluminescence, AC Hall effect, transfer-length-methods, and charge extraction measurements were instrumental in quantifying an upper limit for the doping density. The obtained values are subsequently compared to the electrode charge per cell volume under short-circuit conditions ( CUbi/eV), which amounts to roughly 10(16) cm(-3). This figure of merit represents the critical limit below which doping-induced charges do not influence the device performance. The experimental results consistently demonstrate that the doping density is below this critical threshold 10(12) cm(-3), which means << CUbi / e V) for all common lead-based metal-halide perovskites. Nevertheless, although the density of doping-induced charges is too low to redistribute the built-in voltage in the perovskite active layer, mobile ions are present in sufficient quantities to create space-charge-regions in the active layer, reminiscent of doped pn-junctions. These results are well supported by drift-diffusion simulations, which confirm that the device performance is not affected by such low doping densities.
How do different reset protocols affect ergodicity of a diffusion process in single-particle-tracking experiments? We here address the problem of resetting of an arbitrary stochastic anomalous-diffusion process (ADP) from the general mathematical points of view and assess ergodicity of such reset ADPs for an arbitrary resetting protocol. The process of stochastic resetting describes the events of the instantaneous restart of a particle’s motion via randomly distributed returns to a preset initial position (or a set of those). The waiting times of such resetting events obey the Poissonian, Gamma, or more generic distributions with specified conditions regarding the existence of moments. Within these general approaches, we derive general analytical results and support them by computer simulations for the behavior of the reset mean-squared displacement (MSD), the new reset increment-MSD (iMSD), and the mean reset time-averaged MSD (TAMSD). For parental nonreset ADPs with the MSD(t)∝ tμ we find a generic behavior and a switch of the short-time growth of the reset iMSD and mean reset TAMSDs from ∝ _μ for subdiffusive to ∝ _1 for superdiffusive reset ADPs. The critical condition for a reset ADP that recovers its ergodicity is found to be more general than that for the nonequilibrium stationary state, where obviously the iMSD and the mean TAMSD are equal. The consideration of the new statistical quantifier, the iMSD—as compared to the standard MSD—restores the ergodicity of an arbitrary reset ADP in all situations when the μth moment of the waiting-time distribution of resetting events is finite. Potential applications of these new resetting results are, inter alia, in the area of biophysical and soft-matter systems.
How do different reset protocols affect ergodicity of a diffusion process in single-particle-tracking experiments? We here address the problem of resetting of an arbitrary stochastic anomalous-diffusion process (ADP) from the general mathematical points of view and assess ergodicity of such reset ADPs for an arbitrary resetting protocol. The process of stochastic resetting describes the events of the instantaneous restart of a particle’s motion via randomly distributed returns to a preset initial position (or a set of those). The waiting times of such resetting events obey the Poissonian, Gamma, or more generic distributions with specified conditions regarding the existence of moments. Within these general approaches, we derive general analytical results and support them by computer simulations for the behavior of the reset mean-squared displacement (MSD), the new reset increment-MSD (iMSD), and the mean reset time-averaged MSD (TAMSD). For parental nonreset ADPs with the MSD(t)∝ tμ we find a generic behavior and a switch of the short-time growth of the reset iMSD and mean reset TAMSDs from ∝ _μ for subdiffusive to ∝ _1 for superdiffusive reset ADPs. The critical condition for a reset ADP that recovers its ergodicity is found to be more general than that for the nonequilibrium stationary state, where obviously the iMSD and the mean TAMSD are equal. The consideration of the new statistical quantifier, the iMSD—as compared to the standard MSD—restores the ergodicity of an arbitrary reset ADP in all situations when the μth moment of the waiting-time distribution of resetting events is finite. Potential applications of these new resetting results are, inter alia, in the area of biophysical and soft-matter systems.
Most image restoration methods in astronomy rely upon probabilistic tools that infer the best solution for a deconvolution problem. They achieve good performances when the point spread function (PSF) is spatially invariant in the image plane.
However, this condition is not always satisfied in real optical systems. We propose a new method for the restoration of images affected by static and anisotropic aberrations using Deep Neural Networks that can be directly applied to sky images.
The network is trained using simulated sky images corresponding to the T80-S Telescope optical model, a 80-cm survey imager at Cerro Tololo (Chile), which are synthesized using a Zernike polynomial representation of the optical system.
Once trained, the network can be used directly on sky images, outputting a corrected version of the image that has a constant and known PSF across its field of view. The method is to be tested on the T80-S Telescope.
We present the method and results on synthetic data.
LCST-type synthetic thermoresponsive polymers can reversibly respond to certain stimuli in aqueous media with a massive change of their physical state. When fluorophores, that are sensitive to such changes, are incorporated into the polymeric structure, the response can be translated into a fluorescence signal. Based on this idea, this thesis presents sensing schemes which transduce the stimuli-induced variations in the solubility of polymer chains with covalently-bound fluorophores into a well-detectable fluorescence output. Benefiting from the principles of different photophysical phenomena, i.e. of fluorescence resonance energy transfer and solvatochromism, such fluorescent copolymers enabled monitoring of stimuli such as the solution temperature and ionic strength, but also of association/disassociation mechanisms with other macromolecules or of biochemical binding events through remarkable changes in their fluorescence properties. For instance, an aqueous ratiometric dual sensor for temperature and salts was developed, relying on the delicate supramolecular assembly of a thermoresponsive copolymer with a thiophene-based conjugated polyelectrolyte. Alternatively, by taking advantage of the sensitivity of solvatochromic fluorophores, an increase in solution temperature or the presence of analytes was signaled as an enhancement of the fluorescence intensity. A simultaneous use of the sensitivity of chains towards the temperature and a specific antibody allowed monitoring of more complex phenomena such as competitive binding of analytes. The use of different thermoresponsive polymers, namely poly(N-isopropylacrylamide) and poly(meth)acrylates bearing oligo(ethylene glycol) side chains, revealed that the responsive polymers differed widely in their ability to perform a particular sensing function. In order to address questions regarding the impact of the chemical structure of the host polymer on the sensing performance, the macromolecular assembly behavior below and above the phase transition temperature was evaluated by a combination of fluorescence and light scattering methods. It was found that although the temperature-triggered changes in the macroscopic absorption characteristics were similar for these polymers, properties such as the degree of hydration or the extent of interchain aggregations differed substantially. Therefore, in addition to the demonstration of strategies for fluorescence-based sensing with thermoresponsive polymers, this work highlights the role of the chemical structure of the two popular thermoresponsive polymers on the fluorescence response. The results are fundamentally important for the rational choice of polymeric materials for a specific sensing strategy.