Institut für Physik und Astronomie
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Institute
We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law ∼T−h with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.
The electrical conductivity of organic semiconductors can be enhanced by orders of magnitude via doping with strong molecular electron acceptors or donors. Ground-state integer charge transfer and charge-transfer complex formation between organic semiconductors and molecular dopants have been suggested as the microscopic mechanisms causing these profound changes in electrical materials properties. Here, we study charge-transfer interactions between the common molecular p-dopant 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane and a systematic series of thiophene-based copolymers by a combination of spectroscopic techniques and electrical measurements. Subtle variations in chemical structure are seen to significantly impact the nature of the charge-transfer species and the efficiency of the doping process, underlining the need for a more detailed understanding of the microscopic doping mechanism in organic semiconductors to reliably guide targeted chemical design.
We study the diffusion of a tracer particle, which moves in continuum space between a lattice of excluded volume, immobile non-inert obstacles. In particular, we analyse how the strength of the tracer-obstacle interactions and the volume occupancy of the crowders alter the diffusive motion of the tracer. From the details of partitioning of the tracer diffusion modes between trapping states when bound to obstacles and bulk diffusion, we examine the degree of localisation of the tracer in the lattice of crowders. We study the properties of the tracer diffusion in terms of the ensemble and time averaged mean squared displacements, the trapping time distributions, the amplitude variation of the time averaged mean squared displacements, and the non-Gaussianity parameter of the diffusing tracer. We conclude that tracer-obstacle adsorption and binding triggers a transient anomalous diffusion. From a very narrow spread of recorded individual time averaged trajectories we exclude continuous type random walk processes as the underlying physical model of the tracer diffusion in our system. For moderate tracer-crowder attraction the motion is found to be fully ergodic, while at stronger attraction strength a transient disparity between ensemble and time averaged mean squared displacements occurs. We also put our results into perspective with findings from experimental single-particle tracking and simulations of the diffusion of tagged tracers in dense crowded suspensions. Our results have implications for the diffusion, transport, and spreading of chemical components in highly crowded environments inside living cells and other structured liquids.
The looping of polymers such as DNA is a fundamental process in the molecular biology of living cells, whose interior is characterised by a high degree of molecular crowding. We here investigate in detail the looping dynamics of flexible polymer chains in the presence of different degrees of crowding. From the analysis of the looping-unlooping rates and the looping probabilities of the chain ends we show that the presence of small crowders typically slows down the chain dynamics but larger crowders may in fact facilitate the looping. We rationalise these non-trivial and often counterintuitive effects of the crowder size on the looping kinetics in terms of an effective solution viscosity and standard excluded volume. It is shown that for small crowders the effect of an increased viscosity dominates, while for big crowders we argue that confinement effects (caging) prevail. The tradeoff between both trends can thus result in the impediment or facilitation of polymer looping, depending on the crowder size. We also examine how the crowding volume fraction, chain length, and the attraction strength of the contact groups of the polymer chain affect the looping kinetics and hairpin formation dynamics. Our results are relevant for DNA looping in the absence and presence of protein mediation, DNA hairpin formation, RNA folding, and the folding of polypeptide chains under biologically relevant high-crowding conditions.
Mixing layer manipulation experiment from open-loop forcing to closed-loop machine learning control
(2015)
Context. Blazars are variable sources on various timescales over a broad energy range spanning from radio to very high energy (>100 GeV, hereafter VHE). Mrk 501 is one of the brightest blazars at TeV energies and has been extensively studied since its first VHE detection in 1996. However, most of the gamma-ray studies performed on Mrk 501 during the past years relate to flaring activity, when the source detection and characterization with the available gamma-ray instrumentation was easier to perform.
Aims. Our goal is to characterize the source gamma-ray emission in detail, together with the radio-to-X-ray emission, during the non-flaring (low) activity, which is less often studied than the occasional flaring (high) activity.
Methods. We organized a multiwavelength (MW) campaign on Mrk 501 between March and May 2008. This multi-instrument effort included the most sensitive VHE gamma-ray instruments in the northern hemisphere, namely the imaging atmospheric Cherenkov telescopes MAGIC and VERITAS, as well as Swift, RXTE, the F-GAMMA, GASP-WEBT, and other collaborations and instruments. This provided extensive energy and temporal coverage of Mrk 501 throughout the entire campaign.
Results. Mrk 501 was found to be in a low state of activity during the campaign, with a VHE flux in the range of 10%-20% of the Crab nebula flux. Nevertheless, significant flux variations were detected with various instruments, with a trend of increasing variability with energy and a tentative correlation between the X-ray and VHE fluxes. The broadband spectral energy distribution during the two different emission states of the campaign can be adequately described within the homogeneous one-zone synchrotron self-Compton model, with the (slightly) higher state described by an increase in the electron number density.
Conclusions. The one-zone SSC model can adequately describe the broadband spectral energy distribution of the source during the two months covered by the MW campaign. This agrees with previous studies of the broadband emission of this source during flaring and non-flaring states. We report for the first time a tentative X-ray-to-VHE correlation during such a low VHE activity. Although marginally significant, this positive correlation between X-ray and VHE, which has been reported many times during flaring activity, suggests that the mechanisms that dominate the X-ray/VHE emission during non-flaring-activity are not substantially different from those that are responsible for the emission during flaring activity.
The gamma-ray spectrum of the low-frequency-peaked BL Lac (LBL) object AP Librae is studied, following the discovery of very-high-energy (VHE; E > 100 GeV) gamma-ray emission up to the TeV range by the H.E.S.S. experiment. Thismakes AP Librae one of the few VHE emitters of the LBL type. The measured spectrum yields a flux of (8.8 +/- 1.5(stat) +/- 1.8(sys)) x 10(-12) cm(-2) s(-1) above 130 GeV and a spectral index of Gamma = 2.65 +/- 0.19(stat) +/- 0.20(sys). This study also makes use of Fermi-LAT observations in the high energy (HE, E > 100 MeV) range, providing the longest continuous light curve (5 years) ever published on this source. The source underwent a flaring event between MJD 56 306-56 376 in the HE range, with a flux increase of a factor of 3.5 in the 14 day bin light curve and no significant variation in spectral shape with respect to the low-flux state. While the H.E.S.S. and (low state) Fermi-LAT fluxes are in good agreement where they overlap, a spectral curvature between the steep VHE spectrum and the Fermi-LAT spectrum is observed. The maximum of the gamma-ray emission in the spectral energy distribution is located below the GeV energy range.
We used microfluidic tools and high-speed time-lapse microscopy to record trajectories of the soil bacterium Pseudomonas putida in a confined environment with cells swimming in close proximity to a glass-liquid interface. While the general swimming pattern is preserved, when compared to swimming in the bulk fluid, our results show that cells in the presence of two solid boundaries display more frequent reversals in swimming direction and swim faster. Additionally, we observe that run segments are no longer straight and that cells swim on circular trajectories, which can be attributed to the hydrodynamic wall effect. Using the experimentally observed parameters together with a recently presented analytic model for a run-reverse random walker, we obtained additional insight on how the spreading behavior of a cell population is affected under confinement. While on short time scales, the mean square displacement of confined swimmers grows faster as compared to the bulk fluid case, our model predicts that for large times the situation reverses due to the strong increase in effective rotational diffusion.
The initiation of a marine ice-sheet instability (MISI) is generally discussed from the ocean side of the ice sheet. It has been shown that the reduction in ice-shelf buttressing and softening of the coastal ice can destabilize a marine ice sheet if the bedrock is sloping upward towards the ocean. Using a conceptional flow-line geometry, we investigate the possibility of whether a MISI can be triggered from the direction of the ice divide as opposed to coastal forcing and explore the interaction between connected basins. We find that the initiation of a MISI in one basin can induce a destabilization in the other. The underlying mechanism of basin interaction is based on dynamic thinning and a consecutive motion of the ice divide which induces a thinning in the adjacent basin and a successive initiation of the instability. Our simplified and symmetric topographic setup allows scaling both the geometry and the transition time between both instabilities. We find that the ice profile follows a universal shape that is scaled with the horizontal extent of the ice sheet and that the same exponent of 1/2 applies for the scaling relation between central surface elevation and horizontal extent as in the pure shallow ice approximation (Vialov profile). Altering the central bed elevation, we find that the extent of grounding-line retreat in one basin determines the degree of interaction with the other. Different scenarios of basin interaction are discussed based on our modeling results as well as on a conceptual flux-balance analysis. We conclude that for the three-dimensional case, the possibility of drainage basin interaction on timescales on the order of 1 kyr or larger cannot be excluded and hence needs further investigation.
Paper-based microfluidics provide an inexpensive, easy to use technology for point-of-care diagnostics in developing countries. Here, we combine paper-based microfluidic devices with responsive hydrogels to add an entire new class of functions to these versatile low-cost fluidic systems. The hydrogels serve as fluid reservoirs. In response to an external stimulus, e.g. an increase in temperature, the hydrogels collapse and release fluid into the structured paper substrate. In this way, chemicals that are either stored on the paper substrate or inside the hydrogel pads can be dissolved, premixed, and brought to reaction to fulfill specific analytic tasks. We demonstrate that multi-step sequences of chemical reactions can be implemented in a paper-based system and operated without the need for external precision pumps. We exemplify this technology by integrating an antibody-based E. coli test on a small and easy to use paper device.
What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density sigma(c)-defining the adsorption-desorption transition-are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of sigma(c) for the concave interfaces versus the Debye screening length 1/kappa and the extent of confinement a for these three interfaces for small kappa a values. For large kappa a the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/kappa. We also rationalize how sigma(c)(kappa) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption-the effect often hard to tackle theoretically-putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids.
Brownian motion is ergodic in the Boltzmann-Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann-Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat-depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions-both a constant and a velocity-dependent (viscoelastic) restitution coefficient epsilon. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of epsilon on the impact velocity of particles.
X-ray spectroscopy is a powerful tool to study the local charge distribution of chemical systems. Together with the liquid jet it becomes possible to probe chemical systems in their natural environment, the liquid phase. In this work, we present X-ray absorption (XA), X-ray emission (XE) and resonant inelastic X-ray scattering (RIXS) data of pure water and various salt solutions and show the possibilities these methods offer to elucidate the nature of ion-water interaction.
We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law similar to T-h with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.
The plasmon resonance of metal nanoparticles determines their optical response in the visible spectral range. Many details such as the electronic properties of gold near the particle surface and the local environment of the particles influence the spectra. We show how the cheap but highly precise fabrication of composite nanolayers by spin-assisted layer-by-layer deposition of polyelectrolytes can be used to investigate the spectral response of gold nanospheres (GNS) and gold nanorods (GNR) in a self-consistent way, using the established Maxwell-Garnett effective medium (MGEM) theory beyond the limit of homogeneous media. We show that the dielectric function of gold nanoparticles differs from the bulk value and experimentally characterize the shape and the surrounding of the particles thoroughly by SEM, AFM and ellipsometry. Averaging the dielectric functions of the layered surrounding by an appropriate weighting with the electric field intensity yields excellent agreement for the spectra of several nanoparticles and nanorods with various cover-layer thicknesses.
The electrophoretic deposition process was used to produce multi-layered ceramics consisting of alternating layers of fully stabilized cubic zirconia and partially stabilized tetragonal zirconia to make use of their different mechanical behaviour, investigating the possibility to deflect advancing cracks at the interfaces of the different layers. This crack deflection is apparently impacted by a toughening mechanism only found in the tetragonal stabilized zirconia polymorph and is characterized by the stress induced transformation of the metastable tetragonal phase into the monoclinic one, which is accompanied by a volume increase resulting in a closing mechanism for advancing cracks.
While improving the electrophoretic deposition process, we investigated the transformation toughening mechanism at the layer interfaces and their effect on crack propagation. Investigations involved a combination of different imaging methods, including light microscopy, white light interferometry, atomic force microscopy, scanning electron microscopy, energy dispersive X-ray spectroscopy and Raman spectroscopy.
We present the XMM-Newton discovery of X-ray emission from the planetary nebula (PN) A78, the second born-again PN detected in X-rays apart from A30. These two PNe share similar spectral and morphological characteristics: they harbor diffuse soft X-ray emission associated with the interaction between the H-poor ejecta and the current fast stellar wind and a point-like source at the position of the central star (CSPN). We present the spectral analysis of the CSPN, using for the first time an NLTE code for expanding atmospheres that takes line blanketing into account for the UV and optical spectra. The wind abundances are used for the X-ray spectral analysis of the CSPN and the diffuse emission. The X-ray emission from the CSPN in A78 can be modeled by a single C VI emission line, while the X-ray emission from its diffuse component is better described by an optically thin plasma emission model with a temperature of kT = 0.088 keV (T approximate to 1.0 x 10(6) K). We estimate X-ray luminosities in the 0.2-2.0 keV energy band of L-X,L-CSPN =(1.2 +/- 0.3) x 10(31) erg s(-1) and L-X,L-DIFF =(9.2 +/- 2.3) x 10(30) erg s(-1) for the CSPN and diffuse components, respectively.
We present the results of a broadband X-ray study of the enigmatic Be star Gamma Cassiopeiae (herein gamma Cas) based on observations made with both the Suzaku and INTEGRAL observatories.. Cas has long been recognized as the prototypical example of a small subclass of Be stars with moderately strong X-ray emission dominated by a hot thermal component in the 0.5-12 keV energy range (L-x approximate to 10(32)-10(33) erg s(-1)). This places them at the high end of the known luminosity distribution for stellar emission, but several orders of magnitude below typical accretion-powered Be X-ray binaries. The INTEGRAL observations spanned an eight-year baseline and represent the deepest measurement to date at energies above similar to 50 keV. We find that the INTEGRAL data are consistent within statistics to a constant intensity source above 20 keV, with emission extending up to similar to 100 keV, and that searches for all of the previously reported periodicities of the system at lower energies led to null results. We further find that our combined Suzaku and INTEGRAL spectrum, which we suggest is the most accurate broadband X-ray measurement of gamma Cas to date, is fitted extremely well with a thermal plasma emission model with a single absorption component. We found no compelling need for an additional non-thermal high-energy component. We discuss these results in the context of a currently favored models for gamma Cas and its analogs.
Magnetic reconnection in the partially ionized solar chromosphere is studied in 2.5 dimensional magnetohydrodynamic simulations including radiative cooling and ambipolar diffusion. A Harris current sheet with and without a guide field is considered. Characteristic values of the parameters in the middle chromosphere imply a high magnetic Reynolds number of similar to 10(6)-10(7) in the present simulations. Fast magnetic reconnection then develops as a consequence of the plasmoid instability without the need to invoke anomalous resistivity enhancements. Multiple levels of the instability are followed as it cascades to smaller scales, which approach the ion inertial length. The reconnection rate, normalized to the asymptotic values of magnetic field and Alfven velocity in the inflow region, reaches values in the range similar to 0.01-0.03 throughout the cascading plasmoid formation and for zero as well as for strong guide field. The outflow velocity reaches approximate to 40 km s(-1). Slow-mode shocks extend from the X-points, heating the plasmoids up to similar to 8 x 10(4) K. In the case of zero guide field, the inclusion of both ambipolar diffusion and radiative cooling causes a rapid thinning of the current sheet (down to similar to 30 m) and early formation of secondary islands. Both of these processes have very little effect on the plasmoid instability for a strong guide field. The reconnection rates, temperature enhancements, and upward outflow velocities from the vertical current sheet correspond well to their characteristic values in chromospheric jets.