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- Institut für Physik und Astronomie (1486) (remove)
In this chapter we review the basic principles of photocurrent generation in bulk heterojunction organic solar cells, discuss the loss channels limiting their efficiency, and present case studies of several polymer-fullerene blends. Using steady-state and transient, optical, and electrooptical techniques, we create a precise picture of the fundamental processes that ultimately govern solar cell efficiency.
This thesis discusses heat and charge transport phenomena in single-crystalline Silicon penetrated by nanometer-sized pores, known as mesoporous Silicon (pSi). Despite the extensive attention given to it as a thermoelectric material of interest, studies on microscopic thermal and electronic transport beyond its macroscopic characterizations are rarely reported. In contrast, this work reports the interplay of both.
PSi samples synthesized by electrochemical anodization display a temperature dependence of specific heat 𝐶𝑝 that deviates from the characteristic 𝑇^3 behaviour (at 𝑇<50𝐾). A thorough analysis reveals that both 3D and 2D Einstein and Debye modes contribute to this specific heat. Additional 2D Einstein modes (~3 𝑚𝑒𝑉) agree reasonably well with the boson peak of SiO2 in pSi pore walls. 2D Debye modes are proposed to account for surface acoustic modes causing a significant deviation from the well-known 𝑇^3 dependence of 𝐶𝑝 at 𝑇<50𝐾.
A novel theoretical model gives insights into the thermal conductivity of pSi in terms of porosity and phonon scattering on the nanoscale. The thermal conductivity analysis utilizes the peculiarities of the pSi phonon dispersion probed by the inelastic neutron scattering experiments. A phonon mean-free path of around 10 𝑛𝑚 extracted from the presented model is proposed to cause the reduced thermal conductivity of pSi by two orders of magnitude compared to p-doped bulk Silicon. Detailed analysis indicates that compound averaging may cause a further 10-50% reduction. The percolation threshold of 65% for thermal conductivity of pSi samples is subsequently determined by employing theoretical effective medium models.
Temperature-dependent electrical conductivity measurements reveal a thermally activated transport process. A detailed analysis of the activation energy 𝐸𝐴𝜎 in the thermally activated transport exhibits a Meyer Neldel compensation rule between different samples that originates in multi-phonon absorption upon carrier transport. Activation energies 𝐸𝐴𝑆 obtained from temperature-dependent thermopower measurements provide further evidence for multi-phonon assisted hopping between localized states as a dominant charge transport mechanism in pSi, as they systematically differ from the determined 𝐸𝐴𝜎 values.
Auf der Grundlage von Sonnenphotometermessungen an drei Messstationen (AWIPEV/ Koldewey in Ny-Ålesund (78.923 °N, 11.923 °O) 1995–2008, 35. Nordpol Driftstation – NP-35 (84.3–85.5 °N, 41.7–56.6 °O) März/April 2008, Sodankylä (67.37 °N, 26.65 °O) 2004–2007) wird die Aerosolvariabilität in der europäischen Arktis und deren Ursachen untersucht. Der Schwerpunkt liegt dabei auf der Frage des Zusammenhanges zwischen den an den Stationen gemessenen Aerosolparametern (Aerosol optische Dicke, Angström Koeffizient, usw.) und dem Transport des Aerosols sowohl auf kurzen Zeitskalen (Tagen) als auch auf langen Zeitskalen (Monate, Jahre). Um diesen Zusammenhang herzustellen, werden für die kurzen Zeitskalen mit dem Trajektorienmodell PEP-Tracer 5-Tage Rückwärtstrajektorien in drei Starthöhen (850 hPa, 700 hPa, 500 hPa) für die Uhrzeiten 00, 06, 12 und 18 Uhr berechnet. Mit Hilfe der nicht-hierarchischen Clustermethode k-means werden die berechneten Rückwärtstrajektorien dann zu Gruppen zusammengefasst und bestimmten Quellgebieten und den gemessenen Aerosol optischen Dicken zugeordnet. Die Zuordnung von Aerosol optischer Dicke und Quellregion ergibt keinen eindeutigen Zusammenhang zwischen dem Transport verschmutzter Luftmassen aus Europa oder Russland bzw. Asien und erhöhter Aerosol optischer Dicke. Dennoch ist für einen konkreten Einzelfall (März 2008) ein direkter Zusammenhang von Aerosoltransport und hohen Aerosol optischen Dicken nachweisbar. In diesem Fall gelangte Waldbrandaerosol aus Südwestrussland in die Arktis und konnte sowohl auf der NP-35 als auch in Ny-Ålesund beobachtet werden. In einem weiteren Schritt wird mit Hilfe der EOF-Analyse untersucht, inwieweit großskalige atmosphärische Zirkulationsmuster für die Aerosolvariabilität in der europäischen Arktis verantwortlich sind. Ähnlich wie bei der Trajektorienanalyse ist auch die Verbindung der atmosphärischen Zirkulation zu den Photometermessungen an den Stationen in der Regel nur schwach ausgeprägt. Eine Ausnahme findet sich bei der Betrachtung des Jahresganges des Bodendruckes und der Aerosol optischen Dicke. Hohe Aerosol optische Dicken treten im Frühjahr zum einen dann auf, wenn durch das Islandtief und das sibirische Hochdruckgebiet Luftmassen aus Europa oder Russland/Asien in die Arktis gelangen, und zum anderen, wenn sich ein kräftiges Hochdruckgebiet über Grönland und weiten Teilen der Arktis befindet. Ebenso zeigt sich, dass der Übergang zwischen Frühjahr und Sommer zumindest teilweise bedingt ist durch denWechsel vom stabilen Polarhoch im Winter und Frühjahr zu einer stärker von Tiefdruckgebieten bestimmten arktischen Atmosphäre im Sommer. Die geringere Aerosolkonzentration im Sommer kann zum Teil mit einer Zunahme der nassen Deposition als Aerosolsenke begründet werden. Für Ny-Ålesund wird neben den Transportmustern auch die chemische Zusammensetzung des Aerosols mit Hilfe von Impaktormessungen an der Zeppelinstation auf dem Zeppelinberg (474m ü.NN) nahe Ny-Ålesund abgeleitet. Dabei ist die positive Korrelation der Aerosoloptischen Dicke mit der Konzentration von Sulfationen und Ruß sehr deutlich. Beide Stoffe gelangen zu einem Großteil durch anthropogene Emissionen in die Atmosphäre. Die damit nachweisbar anthropogen geprägte Zusammensetzung des arktischen Aerosols steht im Widerspruch zum nicht eindeutig herstellbaren Zusammenhang mit dem Transport des Aerosols aus Industrieregionen. Dies kann nur durch einen oder mehrere gleichzeitig stattfindende Transformationsprozesse (z. B. Nukleation von Schwefelsäurepartikeln) während des Transportes aus den Quellregionen (Europa, Russland) erklärt werden.
Over the past decades, there has been a growing interest in ‘extreme events’ owing to the increasing threats that climate-related extremes such as floods, heatwaves, droughts, etc., pose to society. While extreme events have diverse definitions across various disciplines, ranging from earth science to neuroscience, they are characterized mainly as dynamic occurrences within a limited time frame that impedes the normal functioning of a system. Although extreme events are rare in occurrence, it has been found in various hydro-meteorological and physiological time series (e.g., river flows, temperatures, heartbeat intervals) that they may exhibit recurrent behavior, i.e., do not end the lifetime of the system. The aim of this thesis to develop some
sophisticated methods to study various properties of extreme events.
One of the main challenges in analyzing such extreme event-like time series is that they have large temporal gaps due to the paucity of the number of observations of extreme events. As a result, existing time series analysis tools are usually not helpful to decode the underlying
information. I use the edit distance (ED) method to analyze extreme event-like time series in their unaltered form. ED is a specific distance metric, mainly designed to measure the similarity/dissimilarity between point process-like data. I combine ED with recurrence plot techniques to identify the recurrence property of flood events in the Mississippi River in the United States. I also use recurrence quantification analysis to show the deterministic properties
and serial dependency in flood events.
After that, I use this non-linear similarity measure (ED) to compute the pairwise dependency in extreme precipitation event series. I incorporate the similarity measure within the framework of complex network theory to study the collective behavior of climate extremes. Under this architecture, the nodes are defined by the spatial grid points of the given spatio-temporal climate dataset. Each node is associated with a time series corresponding to the temporal evolution
of the climate observation at that grid point. Finally, the network links are functions of the pairwise statistical interdependence between the nodes. Various network measures, such as degree, betweenness centrality, clustering coefficient, etc., can be used to quantify the network’s topology. We apply the methodology mentioned above to study the spatio-temporal coherence pattern of extreme rainfall events in the United States and the Ganga River basin, which reveals its relation to various climate processes and the orography of the region.
The identification of precursors associated with the occurrence of extreme events in the near future is extremely important to prepare the masses for an upcoming disaster and mitigate the potential risks associated with such events. Under this motivation, I propose an in-data prediction recipe for predicting the data structures that typically occur prior to extreme events using the Echo state network, a type of Recurrent Neural Network which is a part of the reservoir
computing framework. However, unlike previous works that identify precursory structures in the same variable in which extreme events are manifested (active variable), I try to predict these structures by using data from another dynamic variable (passive variable) which does not show large excursions from the nominal condition but carries imprints of these extreme events. Furthermore, my results demonstrate that the quality of prediction depends on the magnitude
of events, i.e., the higher the magnitude of the extreme, the better is its predictability skill. I show quantitatively that this is because the input signals collectively form a more coherent pattern for an extreme event of higher magnitude, which enhances the efficiency of the machine to predict the forthcoming extreme events.
The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum.
Strange nonchaotic attractors typically appear in quasiperiodically driven nonlinear systems. Two methods of their characterization are proposed. The first one is based on the bifurcation analysis of the systems, resulting from periodic approximations of the quasiperiodic forcing. Secondly, we propose th characterize their strangeness by calculating a phase sensitivity exponent, that measures the sensitivity with respect to changes of the phase of the external force. It is shown, that phase sensitivity appears if there is a non-zero probability for positive local Lyapunov exponents to occur.
This paper presents a study of the galactic environment of a chemically pristine (<0.6 per cent solar metallicity) Lyman Limit system (LLS) discovered along the sightline towards QSO SDSSJ 135726.27+043541.4 (Z(QSO) = 1.233) at projected distance d = 126 physical kpc (pkpc) from a luminous red galaxy (LRG) at z = 0.33. Combining deep Hubble Space Telescope images, MUSE integral field spectroscopic data, and wide-field redshift survey data has enabled an unprecedented, ultradeep view of the environment around this LRG-LLS pair. A total of 12 galaxies, including the LRG, are found at d less than or similar to 400 pkpc and line-of-sight velocity Delta v < 600 km S-1 of the LLS, with intrinsic luminosity ranging from 0.001 L-* to 2 L-* and a corresponding stellar mass range of M-star approximate to 10(7-11) M-circle dot. All 12 galaxies contribute to a total mass of M-star = 1.6 x 10(11) M-circle dot with approximate to 80 per cent contained in the LRG. The line-of-sight velocity dispersion of these galaxies is found to be sigma (group) = 230 km s(-1) with the centre of mass at d(group) = 118 pkpc and line-of-sight velocity offset of Delta v(group) = 181 km s(-1) from the LLS. Three of these are located at d less than or similar to 100 pkpc from the LLS, and they are all faint with intrinsic luminosity less than or similar to 0.02 L-* and gas-phase metallicity of approximate to 10 per cent solar in their interstellar medium. The disparity in the chemical enrichment level between the LLS and the group members suggests that the LLS originates in infalling intergalactic medium and that parts of the intergalactic gas near old and massive galaxies can still remain chemically pristine through the not too distant past.
We investigate properties of quantum mechanical systems in the light of quantum information theory. We put an emphasize on systems with infinite-dimensional Hilbert spaces, so-called continuous-variable systems'', which are needed to describe quantum optics beyond the single photon regime and other Bosonic quantum systems. We present methods to obtain a description of such systems from a series of measurements in an efficient manner and demonstrate the performance in realistic situations by means of numerical simulations. We consider both unconditional quantum state tomography, which is applicable to arbitrary systems, and tomography of matrix product states. The latter allows for the tomography of many-body systems because the necessary number of measurements scales merely polynomially with the particle number, compared to an exponential scaling in the generic case. We also present a method to realize such a tomography scheme for a system of ultra-cold atoms in optical lattices. Furthermore, we discuss in detail the possibilities and limitations of using continuous-variable systems for measurement-based quantum computing. We will see that the distinction between Gaussian and non-Gaussian quantum states and measurements plays an crucial role. We also provide an algorithm to solve the large and interesting class of naturally occurring Hamiltonians, namely frustration free ones, efficiently and use this insight to obtain a simple approximation method for slightly frustrated systems. To achieve this goals, we make use of, among various other techniques, the well developed theory of matrix product states, tensor networks, semi-definite programming, and matrix analysis.
The contamination of barley by molds on the field or in storage leads to the spoilage of grain and the production of mycotoxins, which causes major economic losses in malting facilities and breweries. Therefore, on-site detection of hidden fungus contaminations in grain storages based on the detection of volatile marker compounds is of high interest. In this work, the volatile metabolites of 10 different fungus species are identified by gas chromatography (GC) combined with two complementary mass spectrometric methods, namely, electron impact (EI) and chemical ionization at atmospheric pressure (APCI)-mass spectrometry (MS). The APCI source utilizes soft X-radiation, which enables the selective protonation of the volatile metabolites largely without side reactions. Nearly 80 volatile or semivolatile compounds from different substance classes, namely, alcohols, aldehydes, ketones, carboxylic acids, esters, substituted aromatic compounds, alkenes, terpenes, oxidized terpenes, sesquiterpenes, and oxidized sesquiterpenes, could be identified. The profiles of volatile and semivolatile metabolites of the different fungus species are characteristic of them and allow their safe differentiation. The application of the same GC parameters and APCI source allows a simple method transfer from MS to ion mobility spectrometry (IMS), which permits on-site analyses of grain stores. Characterization of IMS yields limits of detection very similar to those of APCI-MS. Accordingly, more than 90% of the volatile metabolites found by APCI-MS were also detected in IMS. In addition to different fungus genera, different species of one fungus genus could also be differentiated by GC-IMS.
The performance of the recently commissioned spectrometer PEAXIS for resonant inelastic soft X-ray scattering (RIXS) and X-ray photoelectron spectroscopy and its hosting beamline U41-PEAXIS at the BESSY II synchrotron are characterized. The beamline provides linearly polarized light from 180 eV to 1600 eV allowing for RIXS measurements in the range 200-1200 eV. The monochromator optics can be operated in different configurations to provide either high flux with up to 10(12) photons s(-1) within the focal spot at the sample or high energy resolution with a full width at half maximum of <40 meV at an incident photon energy of similar to 400 eV. The measured total energy resolution of the RIXS spectrometer is in very good agreement with theoretically predicted values obtained by ray-tracing simulations. PEAXIS features a 5 m-long RIXS spectrometer arm that can be continuously rotated about the sample position by 106 degrees within the horizontal photon scattering plane, thus enabling the study of momentum-transfer-dependent excitations. Selected scientific examples are presented to demonstrate the instrument capabilities, including measurements of excitations in single-crystalline NiO and in liquid acetone employing a fluid cell sample manipulator. Planned upgrades of the beamline and the RIXS spectrometer to further increase the energy resolution to similar to 100 meV at 1000 eV incident photon energy are discussed.
The performance of the recently commissioned spectrometer PEAXIS for resonant inelastic soft X-ray scattering (RIXS) and X-ray photoelectron spectroscopy and its hosting beamline U41-PEAXIS at the BESSY II synchrotron are characterized. The beamline provides linearly polarized light from 180 eV to 1600 eV allowing for RIXS measurements in the range 200-1200 eV. The monochromator optics can be operated in different configurations to provide either high flux with up to 10(12) photons s(-1) within the focal spot at the sample or high energy resolution with a full width at half maximum of <40 meV at an incident photon energy of similar to 400 eV. The measured total energy resolution of the RIXS spectrometer is in very good agreement with theoretically predicted values obtained by ray-tracing simulations. PEAXIS features a 5 m-long RIXS spectrometer arm that can be continuously rotated about the sample position by 106 degrees within the horizontal photon scattering plane, thus enabling the study of momentum-transfer-dependent excitations. Selected scientific examples are presented to demonstrate the instrument capabilities, including measurements of excitations in single-crystalline NiO and in liquid acetone employing a fluid cell sample manipulator. Planned upgrades of the beamline and the RIXS spectrometer to further increase the energy resolution to similar to 100 meV at 1000 eV incident photon energy are discussed.
The strong chromospheric absorption lines Ca ii H & K are tightly connected to stellar surface magnetic fields. Only for the Sun, spectral activity indices can be related to evolving magnetic features on the solar disk. The Solar Disk-Integrated (SDI) telescope feeds the Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI) of the Large Binocular Telescope (LBT) at Mt. Graham International Observatory, Arizona, U.S.A. We present high-resolution, high-fidelity spectra that were recorded on 184 & 82 days in 2018 & 2019 and derive the Ca ii H & K emission ratio, that is, the S-index. In addition, we compile excess brightness and area indices based on full-disk Ca ii K-line-core filtergrams of the Chromospheric Telescope (ChroTel) at Observatorio del Teide, Tenerife, Spain and full-disk ultraviolet (UV) 1600 angstrom images of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). Thus, Sun-as-a-star spectral indices are related to their counterparts derived from resolved images of the solar chromosphere. All indices display signatures of rotational modulation, even during the very low magnetic activity in the minimum of Solar Cycle 24. Bringing together different types of activity indices has the potential to join disparate chromospheric datasets yielding a comprehensive description of chromospheric activity across many solar cycles.
In this work, binding interactions between biomolecules were analyzed by a technique that is based on electrically controllable DNA nanolevers. The technique was applied to virus-receptor interactions for the first time. As receptors, primarily peptides on DNA nanostructures and antibodies were utilized. The DNA nanostructures were integrated into the measurement technique and enabled the presentation of the peptides in a controllable geometrical order. The number of peptides could be varied to be compatible to the binding sites of the viral surface proteins.
Influenza A virus served as a model system, on which the general measurability was demonstrated. Variations of the receptor peptide, the surface ligand density, the measurement temperature and the virus subtypes showed the sensitivity and applicability of the technology. Additionally, the immobilization of virus particles enabled the measurement of differences in oligovalent binding of DNA-peptide nanostructures to the viral proteins in their native environment.
When the coronavirus pandemic broke out in 2020, work on binding interactions of a peptide from the hACE2 receptor and the spike protein of the SARS-CoV-2 virus revealed that oligovalent binding can be quantified in the switchSENSE technology. It could also be shown that small changes in the amino acid sequence of the spike protein resulted in complete loss of binding. Interactions of the peptide and inactivated virus material as well as pseudo virus particles could be measured. Additionally, the switchSENSE technology was utilized to rank six antibodies for their binding affinity towards the nucleocapsid protein of SARS-CoV-2 for the development of a rapid antigen test device.
The technique was furthermore employed to show binding of a non-enveloped virus (adenovirus) and a virus-like particle (norovirus-like particle) to antibodies. Apart from binding interactions, the use of DNA origami levers with a length of around 50 nm enabled the switching of virus material. This proved that the technology is also able to size objects with a hydrodynamic diameter larger than 14 nm.
A theoretical work on diffusion and reaction-limited binding interactions revealed that the technique and the chosen parameters enable the determination of binding rate constants in the reaction-limited regime.
Overall, the applicability of the switchSENSE technique to virus-receptor binding interactions could be demonstrated on multiple examples. While there are challenges that remain, the setup enables the determination of affinities between viruses and receptors in their native environment. Especially the possibilities regarding the quantification of oligo- and multivalent binding interactions could be presented.
Nanostructured silicon and silicon-aluminum compounds are synthesized by a novel synthesis strategy based on spark plasma sintering (SPS) of silicon nanopowder, mesoporous silicon (pSi), and aluminum nanopowder. The interplay of metal-assisted crystallization and inherent porosity is exploited to largely suppress thermal conductivity. Morphology and temperature-dependent thermal conductivity studies allow us to elucidate the impact of porosity and nanostructure on the macroscopic heat transport. Analytic electron microscopy along with quantitative image analysis is applied to characterize the sample morphology in terms of domain size and interpore distance distributions. We demonstrate that nanostructured domains and high porosity can be maintained in densified mesoporous silicon samples. In contrast, strong grain growth is observed for sintered nanopowders under similar sintering conditions. We observe that aluminum agglomerations induce local grain growth, while aluminum diffusion is observed in porous silicon and dispersed nanoparticles. A detailed analysis of the measured thermal conductivity between 300 and 773 K allows us to distinguish the effect of reduced thermal conductivity caused by porosity from the reduction induced by phonon scattering at nanosized domains. With a modified Landauer/Lundstrom approach the relative thermal conductivity and the scattering length are extracted. The relative thermal conductivity confirms the applicability of Kirkpatrick's effective medium theory. The extracted scattering lengths are in excellent agreement with the harmonic mean of log-normal distributed domain sizes and the interpore distances combined by Matthiessen's rule.
The diffuse very high-energy (VHE; > 100 GeV) gamma-ray emission observed in the central 200 pc of the Milky Way by H.E.S.S. was found to follow dense matter distribution in the central molecular zone (CMZ) up to a longitudinal distance of about 130 pc to the Galactic centre (GC), where the flux rapidly decreases. This was initially interpreted as the result of a burst-like injection of energetic particles 104 yr ago, but a recent more sensitive H.E.S.S. analysis revealed that the cosmic-ray (CR) density profile drops with the distance to the centre, making data compatible with a steady cosmic PeVatron at the GC. In this paper, we extend this analysis to obtain, for the first time, a detailed characterisation of the correlation with matter and to search for additional features and individual gamma-ray sources in the inner 200 pc. Taking advantage of 250 h of H.E.S.S. data and improved analysis techniques, we perform a detailed morphology study of the diffuse VHE emission observed from the GC ridge and reconstruct its total spectrum. To test the various contributions to the total gamma-ray emission, we used an iterative 2D maximum-likelihood approach that allows us to build a phenomenological model of the emission by summing a number of different spatial components. We show that the emission correlated with dense matter covers the full CMZ and that its flux is about half the total diffuse emission flux. We also detect some emission at higher latitude that is likely produced by hadronic collisions of CRs in less dense regions of the GC interstellar medium. We detect an additional emission component centred on the GC and extending over about 15 pc that is consistent with the existence of a strong CR density gradient and confirms the presence of a CR accelerator at the very centre of our Galaxy. We show that the spectrum of full ridge diffuse emission is compatible with that previously derived from the central regions, suggesting that a single population of particles fills the entire CMZ. Finally, we report the discovery of a VHE gamma-ray source near the GC radio arc and argue that it is produced by the pulsar wind nebula candidate G0.13-0.11.
Characterising stochastic motion in heterogeneous media driven by coloured non-Gaussian noise
(2021)
We study the stochastic motion of a test particle in a heterogeneous medium in terms of a position dependent diffusion coefficient mimicking measured deterministic diffusivity gradients in biological cells or the inherent heterogeneity of geophysical systems. Compared to previous studies we here investigate the effect of the interplay of anomalous diffusion effected by position dependent diffusion coefficients and coloured non-Gaussian noise. The latter is chosen to be distributed according to Tsallis' q-distribution, representing a popular example for a non-extensive statistic. We obtain the ensemble and time averaged mean squared displacements for this generalised process and establish its non-ergodic properties as well as analyse the non-Gaussian nature of the associated displacement distribution. We consider both non-stratified and stratified environments.
This work investigates diffusion in nonlinear Hamiltonian systems. The diffusion, more precisely subdiffusion, in such systems is induced by the intrinsic chaotic behavior of trajectories and thus is called chaotic diffusion''. Its properties are studied on the example of one- or two-dimensional lattices of harmonic or nonlinear oscillators with nearest neighbor couplings. The fundamental observation is the spreading of energy for localized initial conditions. Methods of quantifying this spreading behavior are presented, including a new quantity called excitation time. This new quantity allows for a more precise analysis of the spreading than traditional methods. Furthermore, the nonlinear diffusion equation is introduced as a phenomenologic description of the spreading process and a number of predictions on the density dependence of the spreading are drawn from this equation. Two mathematical techniques for analyzing nonlinear Hamiltonian systems are introduced. The first one is based on a scaling analysis of the Hamiltonian equations and the results are related to similar scaling properties of the NDE. From this relation, exact spreading predictions are deduced. Secondly, the microscopic dynamics at the edge of spreading states are thoroughly analyzed, which again suggests a scaling behavior that can be related to the NDE. Such a microscopic treatment of chaotically spreading states in nonlinear Hamiltonian systems has not been done before and the results present a new technique of connecting microscopic dynamics with macroscopic descriptions like the nonlinear diffusion equation. All theoretical results are supported by heavy numerical simulations, partly obtained on one of Europe's fastest supercomputers located in Bologna, Italy. In the end, the highly interesting case of harmonic oscillators with random frequencies and nonlinear coupling is studied, which resembles to some extent the famous Discrete Anderson Nonlinear Schroedinger Equation. For this model, a deviation from the widely believed power-law spreading is observed in numerical experiments. Some ideas on a theoretical explanation for this deviation are presented, but a conclusive theory could not be found due to the complicated phase space structure in this case. Nevertheless, it is hoped that the techniques and results presented in this work will help to eventually understand this controversely discussed case as well.
We study synchronization properties of three nonlinearly coupled chaotic maps. Coupling is introduced in such a way, that it cannot be reduced to pairwise terms, but includes combined action of all interacting units. For two models of nonlinear coupling we characterize the transition to complete synchrony, as well as partially synchronized states. Relation to hypernetworks of chaotic units is also discussed.
Changes in extratropical storm track activity and their implications for extreme weather events
(2016)
Polymer foams are in industrial use for several decades. More recently, non-polar polymer foams were found to be piezoelectric (so-called piezoelectrets) after internal electrical charging of the cavities. So far, few studies have been carried out on the electrical-insulation properties of polymer foams. Here, we compare the piezoelectric and the DC-voltage electrical-insulation properties of cellular polypropylene (PP) foams. Their cavity microstructure can be adjusted via inflation in high-pressure nitrogen gas in combination with a subsequent thermal treatment. While inflation is effective for improving the piezoelectricity, it is detrimental for the electrical-insulation properties. The original cellular PP foam shows a breakdown strength of approximately 230 MV/m, within the same range as that of solid PP. The breakdown strength decreases with increasing degree of inflation, and the dependence on the foam thickness follows an inverse power law with an exponent of 1.2. Nevertheless, up to a thickness of 140 mu m (3.5 times the original thickness), the breakdown strength of cellular-foam PP films is at least 7 times that of an air gap with the same thickness. In addition, the influence of high temperatures and high humidities on the piezoelectricity and the breakdown strength of cellular PP was studied. It was found that the piezoelectric d(33) coefficient decays rapidly already at 70 degrees C, while the breakdown strength slightly increases during storage at 70 or 90 degrees C. Under a relative humidity of 95%, the breakdown strength increases with storage time, while the piezoelectric d(33) coefficient slightly decreases.