Regions of positivity for polyharmonic Green functions in arbitrary domains

The Green function for the biharmonic operator on bounded domains with zero Dirichlet boundary conditions is in general not of fixed sign. However, by extending an idea of Z. Nehari, we are able to identify regions of positivity for Green functions of polyharmonic operators. In particular, the biharmonic Green function is considered in all space dimensions. As a consequence we see that the negative part of any such Green function is somehow small compared with the singular positive part.

     

Magnetic antivortex-core reversal by circular-rotational spin currents

Topological singularities occur as antivortices in ferromagnetic thin-film microstructures. Antivortices behave as two-dimensional oscillators with a gyrotropic eigenmode which can be excited resonantly by spin currents and magnetic fields. We show that the two excitation types couple in an opposing sense of rotation in the case of resonant antivortex excitation with circular-rotational currents. If the sense of rotation of the current coincides with the intrinsic sense of gyration of the antivortex, the coupling to the Oersted fields is suppressed and only the spin-torque contribution locks into the gyrotropic eigenmode. We report on the experimental observation of purely spin-torque induced antivortex-core reversal. The dynamic response of an isolated antivortex is imaged by time-resolved scanning transmission x-ray microscopy on its genuine time and length scale.     

Electric field effect on low temperature nanoscale oxidation

The influence of electric fields on the low temperature oxidation of individual nanoscale tungsten wires was investigated. In the experiments at room temperature, the nanowires were biased as anode opposite to a macroscopic cathode and H₂O-vapor with a pressure of 10^?7–10¹ mbar was provided as oxygen source. Under the influence of an electric field, a dramatic change of the oxidation behavior is observed with the formation of several 10 nm thick oxide layers for electric fields exceeding a threshold. The chemical composition of the layers formed is determined with laser-assisted atom probe tomography to be slightly understoichiometric WO₃. After an initial period of fast growth, the oxidation rate later rapidly decreases to immeasurable low values. Evaluation of the electric field distribution in the vicinity of the sample by the finite element method reveals that oxide formation only proceeds if a critical field in the range of 0.7–5.0 V/nm, depending on the H₂O-pressure, is present. This critical field is attributed to a field-activated reaction of H₂O at the oxide–vapor interface. Besides for tungsten, field-induced oxidation is also observed for aluminum and p-doped silicon and thus apparently is a widely material independent phenomenon.     

Normal forms of dispersive scalar Poisson brackets with two independent variables

We classify the dispersive Poisson brackets with one dependent variable and two independent variables, with leading order of hydrodynamic type, up to Miura transformations. We show that, in contrast to the case of a single independent variable for which a well-known triviality result exists, the Miura equivalence classes are parametrised by an infinite number of constants, which we call numerical invariants of the brackets. We obtain explicit formulas for the first few numerical invariants.     

Lower bound for electron spin entanglement from beam splitter current correlations

We determine a lower bound for the entanglement of formation of pairs of electron spins injected into a mesoscopic conductor. The bound can be expressed in terms of experimentally accessible quantities, the zero-frequency current correlators (shot noise power or cross correlators) after transmission through an electronic beam splitter and can be used to gain information about the entanglement from experiment. Spin relaxation (T1 processes) and decoherence (T2) during the ballistic coherent transmission of carriers are taken into account within Bloch theory. A variable inhomogeneous magnetic field gives rise to a useful lower bound for the entanglement of arbitrary states. The decrease in entanglement due to thermally mixed states is studied. Both the entanglement of the output of a source (entangler) and T(1,2) can be determined from current correlators.     

Bootstrapping Topological Properties and Systemic Risk of Complex Networks Using the Fitness Model

In this paper we present a novel method to reconstruct global topological properties of a complex network starting from limited information. We assume to know for all the nodes a non-topological quantity that we interpret as fitness. In contrast, we assume to know the degree, i.e. the number of connections, only for a subset of the nodes in the network. We then use a fitness model, calibrated on the subset of nodes for which degrees are known, in order to generate ensembles of networks. Here, we focus on topological properties that are relevant for processes of contagion and distress propagation in networks, i.e. network density and k-core structure, and we study how well these properties can be estimated as a function of the size of the subset of nodes utilized for the calibration. Finally, we also study how well the resilience to distress propagation in the network can be estimated using our method. We perform a first test on ensembles of synthetic networks generated with the Exponential Random Graph model, which allows to apply common tools from statistical mechanics. We then perform a second test on empirical networks taken from economic and financial contexts. In both cases, we find that a subset as small as 10 % of nodes can be enough to estimate the properties of the network along with its resilience with an error of 5 %.     

Rashba spin-orbit interaction and shot noise for spin-polarized and entangled electrons

We study shot noise for spin-polarized currents and entangled electron pairs in a four-probe (beam-splitter) geometry with a local Rashba spin-orbit (s-o) interaction in the incoming leads. Within the scattering formalism we find that shot noise exhibits Rashba-induced oscillations with continuous bunching and antibunching. We show that entangled states and triplet states can be identified via their Rashba phase in noise measurements. For two-channel leads, we find an additional spin rotation due to s-o induced interband coupling which enhances spin control. We show that the s-o interaction deter-mines the Fano factor, which provides a direct way to measure the Rashba coupling constant via noise.     

Magnetic soft x-ray microscopy of the domain wall depinning process in permalloy magnetic nanowires

Full-field magnetic transmission x-ray microscopy at high spatial resolution down to 20 nm is used to directly observe field-driven domain wall motion in notch-patterned permalloy nanowires. The depinning process of a domain wall around a notch exhibits a stochastic nature in most nanowires. The stochasticity of the domain wall depinning sensitively depends on the geometry of the nanowire such as the wire thickness, the wire width, and the notch depth. We propose an optimized design of the nanowire for deterministic domain wall depinning field at a notch.     

Short-term carbon dynamics in a temperate grassland and heathland ecosystem exposed to 104 days of drought followed by irrigation

Temperate ecosystems are susceptible to drought events. The effect of a severe drought (104 days) followed by irrigation on the plant C uptake, its assimilation and input of C in soil were examined using a triple ¹³CO₂ pulse-chase labelling experiment in model grassland and heathland ecosystems. First ¹³CO₂ pulse at day 0 of the experiment revealed much higher ¹³C tracer uptake for shoots, roots and soil compared to the second pulse (day 44), where all plants showed significantly lower ¹³C tracer uptake. After the third ¹³CO₂ pulse (day 70), very low ¹³C uptake in shoots led to a negligible allocation of ¹³C into roots and soil. During irrigation after the severe drought, the ¹³C tracer that was allocated in plant tissues during the second and third pulse labelling was re-allocated in roots and soil, as soon as the irrigation started. This re-allocation was higher and longer lasting in heathland compared to grassland ecosystems.