Institut für Physik und Astronomie
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We prove that quantum many-body systems on a one-dimensional lattice locally relax to Gaussian states under non- equilibrium dynamics generated by a bosonic quadratic Hamiltonian. This is true for a large class of initial states-pure or mixed-which have to satisfy merely weak conditions concerning the decay of correlations. The considered setting is a proven instance of a situation where dynamically evolving closed quantum systems locally appear as if they had truly relaxed, to maximum entropy states for fixed second moments. This furthers the understanding of relaxation in suddenly quenched quantum many-body systems. The proof features a non-commutative central limit theorem for non-i.i.d. random variables, showing convergence to Gaussian characteristic functions, giving rise to trace-norm closeness. We briefly link our findings to the ideas of typicality and concentration of measure.
The influence of the solvent-evaporation rate on the formation of of. and P crystalline phases in solution-cast poly(vinylidene fluoride) (PVDF) films was systematically investigated. Films were crystallized from PVDF/N,N- dimethylformamide solutions with concentrations of 2.5, 5.0, 10, and 20 wt % at different temperatures. During crystallization, the solvent evaporation rate was monitored in situ by means of a semianalytic balance. With this system, it was possible to determine the evaporation rate for different concentrations and temperatures of the solution under specific ambient conditions (pressure, temperature, and humidity). Fourier-Transform InfraRed spectroscopy with Attenuated Total Reflectance revealed the P-phase content in the PVDF films and its dependence on previous evaporation rates. Based on the relation between the evaporation rate and the PVDF phase composition, a consistent explanation for the different amounts of P phase observed at the upper and lower sample surfaces is achieved. Furthermore, the role of the sample thickness has also been studied. The experimental results show that not only the temperature but also the evaporation rate have to be controlled to obtain the desired crystalline phases in solution-cast PVDF films.
Despite many previous Studies on the association between hyperthyroidism and the hyperadrenergic state, controversies still exist. Detrended fluctuation analysis (DFA) is a well recognized method in the nonlinear analysis of heart rate variability (HRV), and it has physiological significance related to the autonomic nervous system. In particular, an increased short-term scaling exponent alpha 1 calculated from DFA is associated with both increased sympathetic activity and decreased vagal activity. No study has investigated the DFA of HRV in hyperthyroidism. This study was designed to assess the sympathovagal balance in hyperthyroidism. We performed the DFA along with the linear analysis of HRV in 36 hyperthyroid Graves' disease patients (32 females and 4 males; age 30 +/- 1 years, means +/- SE) and 36 normal controls matched by sex, age and body mass index. Compared with the normal controls, the hyperthyroid patients revealed a significant increase (P < 0.001) in alpha 1 (hyperthyroid 1.28 +/- 0.04 versus control 0.91 +/- 0.02), long-term scaling exponent alpha 2 (1.05 +/- 0.02 versus 0.90 +/- 0.01), overall scaling exponent alpha (1.11 +/- 0.02 versus 0.89 +/- 0.01), low frequency power in normalized units (LF%) and the ratio of low frequency power to high frequency power (LF/HF); and a significant decrease (P < 0.001) in the standard deviation of the R-R intervals (SDNN) and high frequency power (HF). In conclusion, hyperthyroidism is characterized by concurrent sympathetic activation and vagal withdrawal. This sympathovagal imbalance state in hyperthyroidism helps to explain the higher prevalence of atrial fibrillation and exercise intolerance among hyperthyroid patients.
The 8.2 ka event : abrupt transition of the subpolar gyre toward a modern North Atlantic circulation
(2010)
Climate model simulations of the 8.2 ka event show an abrupt strengthening of the Atlantic subpolar gyre that allows us to connect two major but apparently contradictory climate events of the early Holocene: the freshwater outburst from proglacial lakes and the onset of Labrador Sea water formation. The 8.2 ka event is the largest climatic signal of our present interglacial with a widespread cooling in the North Atlantic region about 8200 years before present. It coincides with a meltwater outburst from North American proglacial lakes that is believed to have weakened the Atlantic meridional overturning circulation and northward heat transport, followed by a recovery of the deep ocean circulation and rising temperatures after a few centuries. Marine proxy data, however, date the onset of deep water formation in Labrador Sea to the same time. The subsequent strengthening of the slope current system created a regional signal recorded as an abrupt and persistent surface temperature decrease. Although similarities in timing are compelling, a mechanism to reconcile these apparently contradictory events was missing. Our simulations show that an abrupt and persistent strengthening of the Atlantic subpolar gyre provides a plausible explanation. The intense freshwater pulse triggered a transition of the gyre circulation into a different mode of operation, stabilized by internal feedbacks and persistent after the cessation of the perturbation. As a direct consequence, deep water formation around its center intensifies. This corresponds to the modern flow regime and stabilizes the meridional overturning circulation, possibly contributing to the Holocene's climatic stability.
We report on a self-emerging chimera state in a homogeneous chain of nonlocally and nonlinearly coupled oscillators. This chimera, i.e., a state with coexisting regions of complete and partial synchrony, emerges via a supercritical bifurcation from a homogeneous state. We develop a theory of chimera based on the Ott-Antonsen equations for the local complex order parameter. Applying a numerical linear stability analysis, we also describe the instability of the chimera and transition to phase turbulence with persistent patches of synchrony.
We report results on dispersion relations and instabilities of traveling waves in excitable systems. Experiments employ solutions of the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction confined to thin capillary tubes which create a pseudo-one-dimensional system. Theoretical analyses focus on a three-variable reaction-diffusion model that is known to reproduce qualitatively many of the experimentally observed dynamics. Using continuation methods, we show that the transition from normal, monotonic to anomalous, single-overshoot dispersion curves is due to an orbit flip bifurcation of the solitary pulse homoclinics. In the case of "wave stacking", this anomaly induces attractive pulse interaction, slow solitary pulses, and faster wave trains. For "wave merging", wave trains break up in the wake of the slow solitary pulse due to an instability of wave trains at small wavelength. A third case, "wave tracking" is characterized by the non-existence of solitary waves but existence of periodic wave trains. The corresponding dispersion curve is a closed curve covering a finite band of wavelengths.
We quantify random migration of the social ameba Dictyostelium discoideum. We demonstrate that the statistics of cell motion can be described by an underlying Langevin-type stochastic differential equation. An analytic expression for the velocity distribution function is derived. The separation into deterministic and stochastic parts of the movement shows that the cells undergo a damped motion with multiplicative noise. Both contributions to the dynamics display a distinct response to external physiological stimuli. The deterministic component depends on the developmental state and ambient levels of signaling substances, while the stochastic part does not.
We have used space-charge limited current measurements to study the mobility of holes and electrons in two fluorene-based copolymers for temperatures from 100 to 300 K. Interpreting the results using the standard analytical model produced an Arrhenius-type temperature dependence for a limited temperature range only and mobility was found to be apparently dependent on the thickness of the polymer film. To improve on this, we have interpreted our data using a numerical model that takes into account the effects of the carrier concentration and energetic disorder on transport. This accounted for the thickness dependence and gave a more consistent temperature dependence across the full range of temperatures, giving support to the extended Gaussian disorder model for transport in disordered polymers. Furthermore, we find that the same model adequately describes both electron and hole transport without the need to explicitly include a distribution of electron traps. Room-temperature mobilities were found to be in the region of 4 x 10(-8) and 2 x 10(- 8) cm(2) V-1 s(-1) in the limit of zero field and zero carrier density with disorders of 110+/-10 and 100+/-10 meV for polymers poly{9,9-dioctylfluorene-co-bis[N,N'-(4-butylphenyl)]bis(N, N'-phenyl-1,4-phenylene)diamine} and poly(9,9-dioctylfluorene-co-benzothiadiazole), respectively.
We present an efficient expression for the analytic continuation to arbitrary complex frequencies of the complex optical and ac conductivity of a homogeneous superconductor with an arbitrary mean free path. Knowledge of this quantity is fundamental in the calculation of thermodynamic potentials and dispersion energies involving type-I superconducting bodies. When considered for imaginary frequencies, our formula evaluates faster than previous schemes involving Kramers-Kronig transforms. A number of applications illustrate its efficiency: a simplified low-frequency expansion of the conductivity, the electromagnetic bulk self-energy due to longitudinal plasma oscillations, and the Casimir free energy of a superconducting cavity.
Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multiscale entanglement renormalization Ansatz (MERA). It is shown that, with the exception of one spatial dimension, MERA states are actually states with finite correlations, i.e., projected entangled pair states (PEPS) with a bond dimension independent of the system size. Hence, real-space renormalization generates states which can be encoded with local effective degrees of freedom, and MERA states form an efficiently contractible class of PEPS that obey the area law for the entanglement entropy. It is further pointed out that there exist other efficiently contractible schemes violating the area law.
The method of current extraction under linear increasing voltages (CELIV) allows for the simultaneous determination of charge mobilities and charge densities directly in thin-film geometries as used in organic photovoltaic (OPV) cells. It has been specifically applied to investigate the interrelation of microstructure and charge-transport properties in such systems. Numerical and analytical calculations presented in this work show that the evaluation of CELIV transients with the commonly used analysis scheme is error prone once charge recombination and, possibly, field- dependent charge mobilities are taken into account. The most important effects are an apparent time dependence of charge mobilities and errors in the determined field dependencies. Our results implicate that reports on time-dependent mobility relaxation in OPV materials obtained by the CELIV technique should be carefully revisited and confirmed by other measurement methods.
A recently developed efficient recursive approach for analytically calculating the short-time evolution of the one-particle propagator to extremely high orders is applied here for numerically studying the thermodynamical and dynamical properties of a rotating ideal Bose gas of Rb-87 atoms in an anharmonic trap. At first, the one-particle energy spectrum of the system is obtained by diagonalizing the discretized short-time propagator. Using this, many-boson properties such as the condensation temperature, the ground-state occupancy, density profiles, and time-of-flight absorption pictures are calculated for varying rotation frequencies. The obtained results improve previous semiclassical calculations, in particular for smaller particle numbers. Furthermore, we find that typical time scales for a free expansion are increased by an order of magnitude for the delicate regime of both critical and overcritical rotation.
We consider large populations of phase oscillators with global nonlinear coupling. For identical oscillators such populations are known to demonstrate a transition from completely synchronized state to the state of self-organized quasiperiodicity. In this state phases of all units differ, yet the population is not completely incoherent but produces a nonzero mean field; the frequency of the latter differs from the frequency of individual units. Here we analyze the dynamics of such populations in case of uniformly distributed natural frequencies. We demonstrate numerically and describe theoretically (i) states of complete synchrony, (ii) regimes with coexistence of a synchronous cluster and a drifting subpopulation, and (iii) self-organized quasiperiodic states with nonzero mean field and all oscillators drifting with respect to it. We analyze transitions between different states with the increase of the coupling strength; in particular we show that the mean field arises via a discontinuous transition. For a further illustration we compare the results for the nonlinear model with those for the Kuramoto-Sakaguchi model.
beta-phase poly(vinylidene fluoride-hexafluoropropylene) (P(VDF-HFP)) copolymer films were prepared by uniaxially stretching solution-cast or melt-quenched samples. Different preparation routes lead to different amounts of the crystalline alpha and beta phases in the films, as detected by means of Fourier-transform infrared spectroscopy and X-ray diffractometry. The beta phase is significantly enhanced in melt-quenched and stretched films in comparison to solution-cast and stretched films. This is particularly true for copolymer samples with higher HFP content. The beta- phase enhancement is also observed in ferroelectric-hysteresis experiments where a rather high polarization of 58 mC/ m(2) was found on melt-quenched and stretched samples after poling at electric fields of 140 MV/m. After poling at 160 MV/m, one of these samples exhibited a piezoelectric d(33) coefficient as high as 21 pC/N. An electric-field-induced partial transition from the alpha to the beta phase was also observed on the melt-quenched and stretched samples. This effect leads to a further increase in the applications-relevant dipole polarization. Uniaxially stretched ferroelectric- polymer films are highly anisotropic. Dielectric resonance spectroscopy reveals a strong increase of the transverse piezoelectric d(32) coefficient and a strong decrease of the transverse elastic modulus c(32) upon heating from 20 to 50 degrees C.
Stellar wind from hot subdwarf stars is mainly accelerated by the interaction of ultraviolet photospheric radiation with metals, mainly oxygen. Absorbing ions share momentum through Coulombic collisions with the remaining passive part of the plasma (namely protons). We found that in the case of the winds from hot subdwarfs, interactions could be so small that they stop the momentum transfer between the passive bulk of plasma and absorbing ions. As a result wind decouples at a certain point.
The present study shows that small admixtures of one chlorophyll a (Chla) molecule per several hundred lipid molecules have strong destabilizing effect on lipid bilayers. This effect is clearly displayed in the properties of the L-alpha-H-II transformations and results from a Chla preference for the H-II relative to the L-alpha phase. Chla disfavors the lamellar liquid crystalline phase L-alpha and induces its replacement with inverted hexagonal phase H-II, as is consistently demonstrated by DSC and X-ray diffraction measurements on phosphatidylethanolamine (PE) dispersions. Chla lowers the L-alpha-H-II transition temperature (42 degrees C) of the fully hydrated dipalmitoleoyl PE (DPoPE) by similar to 8 degrees C and similar to 17 degrees C at Chla/DPoPE molar ratios of 1:500 and 1:100, respectively. Similar Chla effect was recorded also for dielaidoyl PE dispersions. The lowering of the transition temperature and the accompanying significant loss of transition cooperativity reflect the Chla repartitioning and preference for the H-II phase. The reduction of the H-II phase lattice constant in the presence of Chla is an indication that Chla favors v phase formation by decreasing the radius of spontaneous monolayer curvature, and not by filling up the interstitial spaces between the H-II phase cylinders. The observed Chla preference for H-II phase and the substantial bilayer destabilization in the vicinity of a bilayer-to-nonbilayer phase transformation caused by low Chla concentrations can be of interest as a potential regulatory or membrane-damaging factor.
Entanglement entropy obeys area law scaling for typical physical quantum systems. This may naively be argued to follow from the locality of interactions. We show that this is not the case by constructing an explicit simple spin chain Hamiltonian with nearest-neighbor interactions that presents an entanglement volume scaling law. This non- translational model is contrived to have couplings that force the accumulation of singlet bonds across the half-chain. This configuration of the couplings is suggested by real-space renormalization group arguments. Computation of the entanglement entropy is performed by mapping the system to free fermions and diagonalizing numerically its correlation matrix. An analytical relationship between the entanglement entropy and the Frobenius norm of the correlation matrix is also established. Our result is complementary to the known relationship between non-translational invariant, nearest- neighbor interacting Hamiltonians and quantum Merlin-Arthur (QMA)complete problems.
Testing magnetofrictional extrapolation with the Titov-Demoulin model of solar active regions
(2010)
We examine the nonlinear magnetofrictional extrapolation scheme using the solar active region model by Titov and Demoulin as test field. This model consists of an arched, line-tied current channel held in force-free equilibrium by the potential field of a bipolar flux distribution in the bottom boundary. A modified version with a parabolic current density profile is employed here. We find that the equilibrium is reconstructed with very high accuracy in a representative range of parameter space, using only the vector field in the bottom boundary as input. Structural features formed in the interface between the flux rope and the surrounding arcade - "hyperbolic flux tube" and "bald patch separatrix surface" - are reliably reproduced, as are the flux rope twist and the energy and helicity of the configuration. This demonstrates that force-free fields containing these basic structural elements of solar active regions can be obtained by extrapolation. The influence of the chosen initial condition on the accuracy of reconstruction is also addressed, confirming that the initial field that best matches the external potential field of the model quite naturally leads to the best reconstruction. Extrapolating the magnetogram of a Titov-Demoulin equilibrium in the unstable range of parameter space yields a sequence of two opposing evolutionary phases, which clearly indicate the unstable nature of the configuration: a partial buildup of the flux rope with rising free energy is followed by destruction of the rope, losing most of the free energy.
Context. Helicity is a fundamental property of magnetic fields, conserved in ideal MHD. In flux rope geometry, it consists of twist and writhe helicity. Despite the common occurrence of helical structures in the solar atmosphere, little is known about how their shape relates to the writhe, which fraction of helicity is contained in writhe, and how much helicity is exchanged between twist and writhe when they erupt. Aims. Here we perform a quantitative investigation of these questions relevant for coronal flux ropes. Methods. The decomposition of the writhe of a curve into local and nonlocal components greatly facilitates its computation. We use it to study the relation between writhe and projected S shape of helical curves and to measure writhe and twist in numerical simulations of flux rope instabilities. The results are discussed with regard to filament eruptions and coronal mass ejections (CMEs). Results. (1) We demonstrate that the relation between writhe and projected S shape is not unique in principle, but that the ambiguity does not affect low- lying structures, thus supporting the established empirical rule which associates stable forward (reverse) S shaped structures low in the corona with positive (negative) helicity. (2) Kink-unstable erupting flux ropes are found to transform a far smaller fraction of their twist helicity into writhe helicity than often assumed. (3) Confined flux rope eruptions tend to show stronger writhe at low heights than ejective eruptions (CMEs). This argues against suggestions that the writhing facilitates the rise of the rope through the overlying field. (4) Erupting filaments which are S shaped already before the eruption and keep the sign of their axis writhe (which is expected if field of one chirality dominates the source volume of the eruption), must reverse their S shape in the course of the rise. Implications for the occurrence of the helical kink instability in such events are discussed. (5) The writhe of rising loops can easily be estimated from the angle of rotation about the direction of ascent, once the apex height exceeds the footpoint separation significantly. Conclusions. Writhe can straightforwardly be computed for numerical data and can often be estimated from observations. It is useful in interpreting S shaped coronal structures and in constraining models of eruptions.
A considerable fraction of the central stars of planetary nebulae (CSPNe) are hydrogen-deficient. As a rule, these CSPNe exhibit a chemical composition of helium, carbon, and oxygen with the majority showing Wolf-Rayet-like emission line spectra. These stars are classified as CSPNe of a spectral type [WC]. We perform a spectral analysis of CSPN PB 8 with the Potsdam Wolf-Rayet (PoWR) models for expanding atmospheres. The source PB8 displays wind-broadened emission lines from strong mass loss. Most strikingly, we find that its surface composition is hydrogen-deficient, but not carbon-rich. With mass fractions of 55% helium, 40% hydrogen, 1.3% carbon, 2% nitrogen, and 1.3% oxygen, it differs greatly from the 30-50% of carbon which are typically seen in [WC]-type central stars. The atmospheric mixture in PB8 has an analogy in the WN/WC transition type among the massive Wolf-Rayet stars. Therefore we suggest to introduce a new spectral type [WN/WC] for CSPNe, with PB8 as its first member. The central star of PB8 has a relatively low temperature of T-* = 52 kK, as expected for central stars in their early evolutionary stages. Its surrounding nebula is less than 3000 years old, i.e. relatively young. Existing calculations for the post-AGB evolution can produce hydrogen-deficient stars of the [WC] type, but do not predict the composition found in PB8. We discuss various scenarios that might explain the origin of this unique object.