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- ItemConvergence bounds for empirical nonlinear least-squares(Les Ulis : EDP Sciences, 2022) Eigel, Martin; Schneider, Reinhold; Trunschke, PhilippWe consider best approximation problems in a nonlinear subset ℳ of a Banach space of functions (𝒱,∥•∥). The norm is assumed to be a generalization of the L 2-norm for which only a weighted Monte Carlo estimate ∥•∥n can be computed. The objective is to obtain an approximation v ∈ ℳ of an unknown function u ∈ 𝒱 by minimizing the empirical norm ∥u − v∥n. We consider this problem for general nonlinear subsets and establish error bounds for the empirical best approximation error. Our results are based on a restricted isometry property (RIP) which holds in probability and is independent of the specified nonlinear least squares setting. Several model classes are examined and the analytical statements about the RIP are compared to existing sample complexity bounds from the literature. We find that for well-studied model classes our general bound is weaker but exhibits many of the same properties as these specialized bounds. Notably, we demonstrate the advantage of an optimal sampling density (as known for linear spaces) for sets of functions with sparse representations.
- ItemDynamical studies on the generation of periodic surface structures by femtosecond laser pulses(Les Ulis : EDP Sciences, 2013) Rosenfeld, A.; Höhm, S.; Bonse, J.; Krüger, J.The dynamics of the formation of laser-induced periodic surface structures (LIPSS) on fused silica upon irradiation with linearly polarized fs-laser pulses (50 fs pulse duration, 800 nm center wavelength) is studied experimentally using a double pulse experiment with cross polarized pulse sequences and a trans illumination femtosecond time-resolved (0.1 ps - 1 ns) pump-probe diffraction approach. The results in both experiments confirm the importance of the ultrafast energy deposition and the laser-induced free-electron plasma in the conduction band of the solids for the formation of LIPSS.
- ItemOn the fundamental relation of laser schlieren deflectometry for temperature measurements in filamentary plasmas(Les Ulis : EDP Sciences, 2015) Schäfer, Jan; Bonaventura, Zdeněk; Foest, RüdigerRecently, laser schlieren deflectometry (LSD) had been successfully employed as a temperature measurement method to reveal the heat convection generated by micro filaments of a self-organized non-thermal atmospheric plasma jet. Based on the theory of the temperature measurements using LSD, in this work, three approaches for an application of the method are introduced: (i) a hyperbolic-like model of refractive index is applied which allows an analytical theory for the evaluation of the deflection angle to be developed, (ii) a Gaussian shape model for the filament temperature is implemented which is analyzed numerically and (iii) an experimental calibration of the laser deflection with a gas mixture of helium and argon is performed. Thus, these approaches demonstrate that a universal relation between the relative maximum temperature of the filament core (T1/T0) and a the maximum deflection angle δ1 of the laser beam can be written as T1/T0=(1 − δ1/δ0)−1, where δ0 is a parameter that is defined by the configuration of the experiment and by the assumed model for the shape of the temperature profile.
- ItemDisentangling nonlinear geomagnetic variability during magnetic storms and quiescence by timescale dependent recurrence properties(Les Ulis : EDP Sciences, 2020) Alberti, Tommaso; Lekscha, Jaqueline; Consolini, Giuseppe; De Michelis, Paola; Donner, Reik V.Understanding the complex behavior of the near-Earth electromagnetic environment is one of the main challenges of Space Weather studies. This includes both the correct characterization of the different physical mechanisms responsible for its configuration and dynamics as well as the efforts which are needed for a correct forecasting of several phenomena. By using a nonlinear multi-scale dynamical systems approach, we provide here new insights into the scale-to-scale dynamical behavior of both quiet and disturbed periods of geomagnetic activity. The results show that a scale-dependent dynamical transition occurs when moving from short to long timescales, i.e., from fast to slow dynamical processes, the latter being characterized by a more regular behavior, while more dynamical anomalies are found in the behavior of the fast component. This suggests that different physical processes are typical for both dynamical regimes: the fast component, being characterized by a more chaotic and less predictable behavior, can be related to the internal dynamical state of the near-Earth electromagnetic environment, while the slow component seems to be less chaotic and associated with the directly driven processes related to the interplanetary medium variability. Moreover, a clear difference has been found between quiet and disturbed periods, the former being more complex than the latter. These findings support the view that, for a correct forecasting in the framework of Space Weather studies, more attention needs to be devoted to the identification of proxies describing the internal dynamical state of the near-Earth electromagnetic environment. © T. Alberti et al., Published by EDP Sciences 2020.
- ItemLensing from small-scale travelling ionospheric disturbances observed using LOFAR(Les Ulis : EDP Sciences, 2022) Boyde, Ben; Wood, Alan; Dorrian, Gareth; Fallows, Richard A.; Themens, David; Mielich, Jens; Elvidge, Sean; Mevius, Maaijke; Zucca, Pietro; Dabrowski, Bartosz; Krankowski, Andrzej; Vocks, Christian; Bisi, MarioObservations made using the LOw-Frequency ARray (LOFAR) between 10:15 and 11:48 UT on the 15th of September 2018 over a bandwidth of approximately 25-65 MHz contain discrete pseudo-periodic features of ionospheric origin. These features occur within a period of approximately 10 min and collectively last roughly an hour. They are strongly frequency dependent, broadening significantly in time towards the lower frequencies, and show an overlaid pattern of diffraction fringes. By modelling the ionosphere as a thin phase screen containing a wave-like disturbance, we are able to replicate the observations, suggesting that they are associated with small-scale travelling ionospheric disturbances (TIDs). This modelling indicates that the features observed here require a compact radio source at a low elevation and that the TID or TIDs in question have a wavelength <~30 km. Several features suggest the presence of deviations from an idealised sinusoidal wave form. These results demonstrate LOFAR-s capability to identify and characterise small-scale ionospheric structures.
- ItemAerosol absorption profiling from the synergy of lidar and sun-photometry: The ACTRIS-2 campaigns in Germany, Greece and Cyprus(Les Ulis : EDP Sciences, 2018) Tsekeri, Alexandra; Amiridis, Vassilis; Lopatin, Anton; Marinou, Eleni; Giannakaki, Eleni; Pikridas, Michael; Sciare, Jean; Liakakou, Eleni; Gerasopoulos, Evangelos; Duesing, Sebastian; Corbin, Joel C.; Gysel, Martin; Bukowiecki, Nicolas; Baars, Holger; Engelmann, Ronny; Wehner, Birgit; Kottas, Michael; Mamali, Dimitra; Kokkalis, Panagiotis; Raptis, Panagiotis I.; Stavroulas, Iasonas; Keleshis, Christos; Müller, Detlef; Solomos, Stavros; Binietoglou, Ioannis; Mihalopoulos, Nikolaos; Papayannis, Alexandros; Stachlewska, Iwona S.; Igloffstein, Julia; Wandinger, Ulla; Ansmann, Albert; Dubovik, Oleg; Goloub, Philippe; Nicolae, D.; Makoto, A.; Vassilis, A.; Balis, D.; Behrendt, A.; Comeron, A.; Gibert, F.; Landulfo, E.; McCormick, M.P.; Senff, C.; Veselovskii, I.; Wandinger, U.Aerosol absorption profiling is crucial for radiative transfer calculations and climate modelling. Here, we utilize the synergy of lidar with sun-photometer measurements to derive the absorption coefficient and single scattering albedo profiles during the ACTRIS-2 campaigns held in Germany, Greece and Cyprus. The remote sensing techniques are compared with in situ measurements in order to harmonize and validate the different methodologies and reduce the absorption profiling uncertainties.
- ItemThe PAC2MAN mission: A new tool to understand and predict solar energetic events(Les Ulis : EDP Sciences, 2015) Amaya, Jorge; Musset, Sophie; Andersson, Viktor; Diercke, Andrea; Höller, Christian; Iliev, Sergiu; Juhász, Lilla; Kiefer, René; Lasagni, Riccardo; Lejosne, Solène; Madi, Mohammad; Rummelhagen, Mirko; Scheucher, Markus; Sorba, Arianna; Thonhofer, StefanAn accurate forecast of flare and coronal mass ejection (CME) initiation requires precise measurements of the magnetic energy buildup and release in the active regions of the solar atmosphere. We designed a new space weather mission that performs such measurements using new optical instruments based on the Hanle and Zeeman effects. The mission consists of two satellites, one orbiting the L1 Lagrangian point (Spacecraft Earth, SCE) and the second in heliocentric orbit at 1AU trailing the Earth by 80° (Spacecraft 80, SC80). Optical instruments measure the vector magnetic field in multiple layers of the solar atmosphere. The orbits of the spacecraft allow for a continuous imaging of nearly 73% of the total solar surface. In-situ plasma instruments detect solar wind conditions at 1AU and ahead of our planet. Earth-directed CMEs can be tracked using the stereoscopic view of the spacecraft and the strategic placement of the SC80 satellite. Forecasting of geoeffective space weather events is possible thanks to an accurate surveillance of the magnetic energy buildup in the Sun, an optical tracking through the interplanetary space, and in-situ measurements of the near-Earth environment.
- ItemConsistency and convergence for a family of finite volume discretizations of the Fokker–Planck operator(Les Ulis : EDP Sciences, 2021) Heida, Martin; Kantner, Markus; Stephan, ArturWe introduce a family of various finite volume discretization schemes for the Fokker–Planck operator, which are characterized by different Stolarsky weight functions on the edges. This family particularly includes the well-established Scharfetter–Gummel discretization as well as the recently developed square-root approximation (SQRA) scheme. We motivate this family of discretizations both from the numerical and the modeling point of view and provide a uniform consistency and error analysis. Our main results state that the convergence order primarily depends on the quality of the mesh and in second place on the choice of the Stolarsky weights. We show that the Scharfetter–Gummel scheme has the analytically best convergence properties but also that there exists a whole branch of Stolarsky means with the same convergence quality. We show by numerical experiments that for small convection the choice of the optimal representative of the discretization family is highly non-trivial, while for large gradients the Scharfetter–Gummel scheme stands out compared to the others.
- ItemA LOFAR observation of ionospheric scintillation from two simultaneous travelling ionospheric disturbances(Les Ulis : EDP Sciences, 2020) Fallows, Richard A.; Forte, Biagio; Astin, Ivan; Allbrook, Tom; Arnold, Alex; Wood, Alan; Dorrian, Gareth; Mevius, Maaijke; Rothkaeh, Hanna; Matyjasiak, Barbara; Krankowski, Andrzej; Anderson, James M.; Asgekar, Ashish; Avruch, I. Max; Bentum, Mark; Bisi, Mario M.; Butcher, Harvey R; Ciardi, Benedetta; Dabrowski, Bartosz; Damstra, Sieds; de Gasperin, Francesco; Duscha, Sven; Eislöffel, Jochen; Franzen, Thomas M.O.; Garrett, Michael A.; Griessmeier, Jean-Matthias; Gunst, Andre W.; Hoeft, Matthias; Horandel, Jorg R.; Iacobelli, Marco; Intema, Huib T.; Koopmans, Leon V.E.; Maat, Peter; Mann, Gottfried; Nelles, Anna; Paas, Harm; Pandey, Vishambhar N.; Reich, Wolfgang; Rowlinson, Antonia; Ruiter, Mark; Schwarz, Dominik J.; Serylak, Maciej; Shulevski, Aleksander; Smirnov, Oleg M.; Soida, Marian; Steinmetz, Matthias; Thoudam, Satyendra; Toribio, M. Carmen; van Ardenne, Arnold; van Bemmel, Ilse M.; van der Wiel, Matthijs H.D.; van Haarlem, Michiel P.; Vermeulen, Rene C.; Vocks, Christian; Wijers, Ralph A.M.J.; Wucknitz, Olaf; Zarka, Philippe; Zucca, PietroThis paper presents the results from one of the first observations of ionospheric scintillation taken using the Low-Frequency Array (LOFAR). The observation was of the strong natural radio source Cassiopeia A, taken overnight on 18–19 August 2013, and exhibited moderately strong scattering effects in dynamic spectra of intensity received across an observing bandwidth of 10–80 MHz. Delay-Doppler spectra (the 2-D FFT of the dynamic spectrum) from the first hour of observation showed two discrete parabolic arcs, one with a steep curvature and the other shallow, which can be used to provide estimates of the distance to, and velocity of, the scattering plasma. A cross-correlation analysis of data received by the dense array of stations in the LOFAR “core” reveals two different velocities in the scintillation pattern: a primary velocity of ~20–40 ms−1 with a north-west to south-east direction, associated with the steep parabolic arc and a scattering altitude in the F-region or higher, and a secondary velocity of ~110 ms−1 with a north-east to south-west direction, associated with the shallow arc and a scattering altitude in the D-region. Geomagnetic activity was low in the mid-latitudes at the time, but a weak sub-storm at high latitudes reached its peak at the start of the observation. An analysis of Global Navigation Satellite Systems (GNSS) and ionosonde data from the time reveals a larger-scale travelling ionospheric disturbance (TID), possibly the result of the high-latitude activity, travelling in the north-west to south-east direction, and, simultaneously, a smaller-scale TID travelling in a north-east to south-west direction, which could be associated with atmospheric gravity wave activity. The LOFAR observation shows scattering from both TIDs, at different altitudes and propagating in different directions. To the best of our knowledge this is the first time that such a phenomenon has been reported.
- ItemOn forward and inverse uncertainty quantification for models involving hysteresis operators(Les Ulis : EDP Sciences, 2020) Klein, Olaf; Davino, Daniele; Visone, CiroParameters within hysteresis operators modeling real world objects have to be identified from measurements and are therefore subject to corresponding errors. To investigate the influence of these errors, the methods of Uncertainty Quantification (UQ) are applied. Results of forward UQ for a play operator with a stochastic yield limit are presented. Moreover, inverse UQ is performed to identify the parameters in the weight function in a Prandtl-Ishlinskiĭ operator and the uncertainties of these parameters.