Institut für Physik und Astronomie
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In this study, we present an empirical model of the equatorial electron pitch angle distributions (PADs) in the outer radiation belt based on the full data set collected by the Magnetic Electron Ion Spectrometer (MagEIS) instrument onboard the Van Allen Probes in 2012-2019. The PADs are fitted with a combination of the first, third and fifth sine harmonics. The resulting equation resolves all PAD types found in the outer radiation belt (pancake, flat-top, butterfly and cap PADs) and can be analytically integrated to derive omnidirectional flux. We introduce a two-step modeling procedure that for the first time ensures a continuous dependence on L, magnetic local time and activity, parametrized by the solar wind dynamic pressure. We propose two methods to reconstruct equatorial electron flux using the model. The first approach requires two uni-directional flux observations and is applicable to low-PA data. The second method can be used to reconstruct the full equatorial PADs from a single uni- or omnidirectional measurement at off-equatorial latitudes. The model can be used for converting the long-term data sets of electron fluxes to phase space density in terms of adiabatic invariants, for physics-based modeling in the form of boundary conditions, and for data assimilation purposes.
We study populations of globally coupled noisy rotators (oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the model is reduced to the Kuramoto model of coupled noise oscillators. These approaches provide also analytical criteria distinguishing supercritical and subcritical transitions to the desynchronized state and indicate the universality of such transitions in rotator ensembles. All the obtained analytical results are confirmed by the numerical ones, both by direct simulations of the large ensembles and by solution of the associated Fokker-Planck equation. We also propose generalizations of the developed approaches for setups where different rotators parameters (natural frequencies, masses, noise intensities, strengths and phase shifts in coupling) are dispersed.
Nonstationary coherence-incoherence patterns in nonlocally coupled heterogeneous phase oscillators
(2020)
We consider a large ring of nonlocally coupled phase oscillators and show that apart from stationary chimera states, this system also supports nonstationary coherence-incoherence patterns (CIPs). For identical oscillators, these CIPs behave as breathing chimera states and are found in a relatively small parameter region only. It turns out that the stability region of these states enlarges dramatically if a certain amount of spatially uniform heterogeneity (e.g., Lorentzian distribution of natural frequencies) is introduced in the system. In this case, nonstationary CIPs can be studied as stable quasiperiodic solutions of a corresponding mean-field equation, formally describing the infinite system limit. Carrying out direct numerical simulations of the mean-field equation, we find different types of nonstationary CIPs with pulsing and/or alternating chimera-like behavior. Moreover, we reveal a complex bifurcation scenario underlying the transformation of these CIPs into each other. These theoretical predictions are confirmed by numerical simulations of the original coupled oscillator system.
After the United Kingdom has left the European Union it remains unclear whether the two parties can successfully negotiate and sign a trade agreement within the transition period. Ongoing negotiations, practical obstacles and resulting uncertainties make it highly unlikely that economic actors would be fully prepared to a “no-trade-deal” situation. Here we provide an economic shock simulation of the immediate aftermath of such a post-Brexit no-trade-deal scenario by computing the time evolution of more than 1.8 million interactions between more than 6,600 economic actors in the global trade network. We find an abrupt decline in the number of goods produced in the UK and the EU. This sudden output reduction is caused by drops in demand as customers on the respective other side of the Channel incorporate the new trade restriction into their decision-making. As a response, producers reduce prices in order to stimulate demand elsewhere. In the short term consumers benefit from lower prices but production value decreases with potentially severe socio-economic consequences in the longer term.
After the United Kingdom has left the European Union it remains unclear whether the two parties can successfully negotiate and sign a trade agreement within the transition period. Ongoing negotiations, practical obstacles and resulting uncertainties make it highly unlikely that economic actors would be fully prepared to a “no-trade-deal” situation. Here we provide an economic shock simulation of the immediate aftermath of such a post-Brexit no-trade-deal scenario by computing the time evolution of more than 1.8 million interactions between more than 6,600 economic actors in the global trade network. We find an abrupt decline in the number of goods produced in the UK and the EU. This sudden output reduction is caused by drops in demand as customers on the respective other side of the Channel incorporate the new trade restriction into their decision-making. As a response, producers reduce prices in order to stimulate demand elsewhere. In the short term consumers benefit from lower prices but production value decreases with potentially severe socio-economic consequences in the longer term.
The Cluster mission has produced a large data set of electron flux measurements in the Earth's magnetosphere since its launch in late 2000. Electron fluxes are measured using Research with Adaptive Particle Imaging Detector (RAPID)/Imaging Electron Spectrometer (IES) detector as a function of energy, pitch angle, spacecraft position, and time. However, no adiabatic invariants have been calculated for Cluster so far. In this paper we present a step-by-step guide to calculations of adiabatic invariants and conversion of the electron flux to phase space density (PSD) in these coordinates. The electron flux is measured in two RAPID/IES energy channels providing pitch angle distribution at energies 39.2-50.5 and 68.1-94.5 keV in nominal mode since 2004. A fitting method allows to expand the conversion of the differential fluxes to the range from 40 to 150 keV. Best data coverage for phase space density in adiabatic invariant coordinates can be obtained for values of second adiabatic invariant, K, similar to 10(2), and values of the first adiabatic invariant mu in the range approximate to 5-20 MeV/G. Furthermore, we describe the production of a new data product "LSTAR," equivalent to the third adiabatic invariant, available through the Cluster Science Archive for years 2001-2018 with 1-min resolution. The produced data set adds to the availability of observations in Earth's radiation belts region and can be used for long-term statistical purposes.
The Cluster mission has produced a large data set of electron flux measurements in the Earth's magnetosphere since its launch in late 2000. Electron fluxes are measured using Research with Adaptive Particle Imaging Detector (RAPID)/Imaging Electron Spectrometer (IES) detector as a function of energy, pitch angle, spacecraft position, and time. However, no adiabatic invariants have been calculated for Cluster so far. In this paper we present a step-by-step guide to calculations of adiabatic invariants and conversion of the electron flux to phase space density (PSD) in these coordinates. The electron flux is measured in two RAPID/IES energy channels providing pitch angle distribution at energies 39.2-50.5 and 68.1-94.5 keV in nominal mode since 2004. A fitting method allows to expand the conversion of the differential fluxes to the range from 40 to 150 keV. Best data coverage for phase space density in adiabatic invariant coordinates can be obtained for values of second adiabatic invariant, K, similar to 10(2), and values of the first adiabatic invariant mu in the range approximate to 5-20 MeV/G. Furthermore, we describe the production of a new data product "LSTAR," equivalent to the third adiabatic invariant, available through the Cluster Science Archive for years 2001-2018 with 1-min resolution. The produced data set adds to the availability of observations in Earth's radiation belts region and can be used for long-term statistical purposes.
The Sea-level Response to Ice Sheet Evolution (SeaRISE) effort explores the sensitivity of the current generation of ice sheet models to external forcing to gain insight into the potential future contribution to sea level from the Greenland and Antarctic ice sheets. All participating models simulated the ice sheet response to three types of external forcings: a change in oceanic condition, a warmer atmospheric environment, and enhanced basal lubrication. Here an analysis of the spatial response of the Greenland ice sheet is presented, and the impact of model physics and spin-up on the projections is explored. Although the modeled responses are not always homogeneous, consistent spatial trends emerge from the ensemble analysis, indicating distinct vulnerabilities of the Greenland ice sheet. There are clear response patterns associated with each forcing, and a similar mass loss at the full ice sheet scale will result in different mass losses at the regional scale, as well as distinct thickness changes over the ice sheet. All forcings lead to an increased mass loss for the coming centuries, with increased basal lubrication and warmer ocean conditions affecting mainly outlet glaciers, while the impacts of atmospheric forcings affect the whole ice sheet.
In dieser Arbeit werden nichtlineare Kopplungsmechanismen von akustischen Oszillatoren untersucht, die zu Synchronisation führen können. Aufbauend auf die Fragestellungen vorangegangener Arbeiten werden mit Hilfe theoretischer und experimenteller Studien sowie mit Hilfe numerischer Simulationen die Elemente der Tonentstehung in der Orgelpfeife und die Mechanismen der gegenseitigen Wechselwirkung von Orgelpfeifen identifiziert. Daraus wird erstmalig ein vollständig auf den aeroakustischen und fluiddynamischen Grundprinzipien basierendes nichtlinear gekoppeltes Modell selbst-erregter Oszillatoren für die Beschreibung des Verhaltens zweier wechselwirkender Orgelpfeifen entwickelt. Die durchgeführten Modellrechnungen werden mit den experimentellen Befunden verglichen. Es zeigt sich, dass die Tonentstehung und die Kopplungsmechanismen von Orgelpfeifen durch das entwickelte Oszillatormodell in weiten Teilen richtig beschrieben werden. Insbesondere kann damit die Ursache für den nichtlinearen Zusammenhang von Kopplungsstärke und Synchronisation des gekoppelten Zwei-Pfeifen Systems, welcher sich in einem nichtlinearen Verlauf der Arnoldzunge darstellt, geklärt werden. Mit den gewonnenen Erkenntnissen wird der Einfluss des Raumes auf die Tonentstehung bei Orgelpfeifen betrachtet. Dafür werden numerische Simulationen der Wechselwirkung einer Orgelpfeife mit verschiedenen Raumgeometrien, wie z. B. ebene, konvexe, konkave, und gezahnte Geometrien, exemplarisch untersucht. Auch der Einfluss von Schwellkästen auf die Tonentstehung und die Klangbildung der Orgelpfeife wird studiert. In weiteren, neuartigen Synchronisationsexperimenten mit identisch gestimmten Orgelpfeifen, sowie mit Mixturen wird die Synchronisation für verschiedene, horizontale und vertikale Pfeifenabstände in der Ebene der Schallabstrahlung, untersucht. Die dabei erstmalig beobachteten räumlich isotropen Unstetigkeiten im Schwingungsverhalten der gekoppelten Pfeifensysteme, deuten auf abstandsabhängige Wechsel zwischen gegen- und gleichphasigen Sychronisationsregimen hin. Abschließend wird die Möglichkeit dokumentiert, das Phänomen der Synchronisation zweier Orgelpfeifen durch numerische Simulationen, also der Behandlung der kompressiblen Navier-Stokes Gleichungen mit entsprechenden Rand- und Anfangsbedingungen, realitätsnah abzubilden. Auch dies stellt ein Novum dar.