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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.
The surface morphology of icy moons is affected by several processes implicating exchanges between their subsurfaces and atmospheres (if any). The possible exchange of material between the subsurface and the surface is mainly determined by the mechanical properties of the lithosphere, which isolates the deep, warm and ductile ice material from the cold surface conditions. Exchanges through this layer occur only if it is sufficiently thin and/or if it is fractured owing to tectonic stresses, melt intrusion or impact cratering. If such conditions are met, cryomagma can be released, erupting fresh volatile-rich materials onto the surface. For a very few icy moons (Titan, Triton, Enceladus), the emission of gas associated with cryovolcanic activity is sufficiently large to generate an atmosphere, either long- lived or transient. For those moons, atmosphere-driven processes such as cryovolcanic plume deposition, phase transitions of condensable materials and wind interactions continuously re-shape their surfaces, and are able to transport cryovolcanically generated materials on a global scale. In this chapter, we discuss the physics of these different exchange processes and how they affect the evolution of the satellites' surfaces.
We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. We have confirmed these results by estimating instantaneous phases including phase difference, average phase, average frequency, frequency ratio, and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non-phase-coherent attractors. The results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non-phase-coherent attractors directly without explicitly introducing the measure of phase.
Time delays are ubiquitous in real world and are often sources of complex behaviors of dynamical systems. This paper addresses the problem of parameters identification and synchronization of uncertain chaotic delayed systems subject to time-varying delay. Firstly, a novel and systematic adaptive scheme of synchronization is proposed for delayed dynamical systems containing uncertainties based on Razumikhin condition and extended invariance principle for functional differential equations. Then, the proposed adaptive scheme is used to estimate the unknown parameters of nonlinear delayed systems from time series, and a sufficient condition is given by virtue of this scheme. The delayed system under consideration is a very generic one that includes almost all well-known delayed systems (neural network, complex networks, etc.). Two classical examples are used to demonstrate the effectiveness of the proposed adaptive scheme.
Actuators based on soft dielectric elastomers deform due to electric field induced Maxwell's stress, interacting with the mechanical properties of the material. The relatively high operating voltages of such actuators can be reduced by increasing the permittivity of the active material, while maintaining the mechanical properties and high electrical breakdown strength. Approaches relying on the use of highly polarizable molecules or conjugated polymers have so far provided the best results, however it has been difficult to maintain high breakdown strengths. In this work, a new approach for increasing the electrostatic energy density of a soft polymer based on molecular composites is presented, relying on chemically grafting soft gel-state pi-conjugated conducting macromolecules (polyaniline (PANI)) to a flexible elastomer backbone SEBS-g-MA (poly-styrene-co-ethylene-co-butylene-co-styrene-g-maleic anhydride). The approach was found to result in composites of increased permittivity (470% over the elastomer matrix) with hardly any reduction in breakdown strength (from 140 to 120 V mu m(-1)), resulting in a large increase in stored electrostatic energy. This led to an improvement in the measured electromechanical response as well as in the maximum actuation strain. A transition was observed when amounts of PANI exceeded 2 vol%, which was ascribed to the exhaustion of the MA- functionality of the SEBS-g-MA. The transition led to drastic increases in permittivity and conductivity, and a sharp drop in electrical breakdown strength. Although the transition caused further improvement of the electromechanical response, the reduction in electrical breakdown strength caused a limitation of the maximum achievable actuation strain.
We consider the suppression of spatiotemporal chaos in the complex Ginzburg-Landau equation by a combined global and local time-delay feedback. Feedback terms are implemented as a control scheme, i.e., they are proportional to the difference between the time-delayed state of the system and its current state. We perform a linear stability analysis of uniform oscillations with respect to space-dependent perturbations and compare with numerical simulations. Similarly, for the fixed-point solution that corresponds to amplitude death in the spatially extended system, a linear stability analysis with respect to space-dependent perturbations is performed and complemented by numerical simulations.
Bulk electron transport and charge injection in a high mobility n-type semiconducting polymer
(2010)
Bulk electron transport in a high mobility n-type polymer is studied by time-of-flight photocurrent measurements and electron-only devices. Bulk electron mobilities of similar to 5 x 10(-3) cm(2)/Vs are obtained. The analysis of the electron currents suggests the presence of an injection barrier for all conventionally used low workfunction cathodes.