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The max-min and min-max of matrices arise prevalently in science and engineering. However, in many real-world situations the computation of the max-min and min-max is challenging as matrices are large and full information about their entries is lacking. Here we take a statistical-physics approach and establish limit laws—akin to the central limit theorem—for the max-min and min-max of large random matrices. The limit laws intertwine random-matrix theory and extreme-value theory, couple the matrix dimensions geometrically, and assert that Gumbel statistics emerge irrespective of the matrix entries' distribution. Due to their generality and universality, as well as their practicality, these results are expected to have a host of applications in the physical sciences and beyond.
High-density polyethylene becomes optically transparent during tensile drawing when previously saturated with diesel fuel. This unusual phenomenon is investigated as it might allow conclusions with respect to the material behavior. Microscopy, differential scanning calorimetry, density measurements are applied together with two scanning X-ray scattering techniques: wide angle X-ray scattering (WAXS) and X-ray refraction, able to extract the spatially resolved crystal orientation and internal surface, respectively. The sorbed diesel softens the material and significantly alters the yielding characteristics. Although the crystallinity among stretched regions is similar, a virgin reference sample exhibits strain whitening during stretching, while the diesel-saturated sample becomes transparent. The WAXS results reveal a pronounced fiber texture in the tensile direction in the stretched region and an isotropic orientation in the unstretched region. This texture implies the formation of fibrils in the stretched region, while spherulites remain intact in the unstretched parts of the specimens. X-ray refraction reveals a preferred orientation of internal surfaces along the tensile direction in the stretched region of virgin samples, while the sample stretched in the diesel-saturated state shows no internal surfaces at all. Besides from stretching saturated samples, optical transparency is also obtained from sorbing samples in diesel after stretching.
We numerically and analytically analyze transitions between different synchronous states in a network of globally coupled phase oscillators with attractive and repulsive interactions. The elements within the attractive or repulsive group are identical, but natural frequencies of the groups differ. In addition to a synchronous two-cluster state, the system exhibits a solitary state, when a single oscillator leaves the cluster of repulsive elements, as well as partially synchronous quasiperiodic dynamics. We demonstrate how the transitions between these states occur when the repulsion starts to prevail over attraction.
Aims. In this study, we analyzed a filament system, which expanded between moving magnetic features (MMFs) of a decaying sunspot and opposite flux outside of the active region from the nearby quiet-Sun network. This configuration deviated from a classical arch filament system (AFS), which typically connects two pores in an emerging flux region. Thus, we called this system an extended AFS. We contrasted classical and extended AFSs with an emphasis on the complex magnetic structure of the latter. Furthermore, we examined the physical properties of the extended AFS and described its dynamics and connectivity. Methods. The extended AFS was observed with two instruments at the Dunn Solar Telescope (DST). The Rapid Oscillations in the Solar Atmosphere (ROSA) imager provided images in three different wavelength regions, which covered the dynamics of the extended AFS at different atmospheric heights. The Interferometric Bidimensional Spectropolarimeter (IBIS) provided spectroscopic Ha data and spectropolarimetric data that was obtained in the near-infrared (NIR) Call lambda 8542 angstrom line. We derived the corresponding line-of-sight (LOS) velocities and used He II lambda 304 angstrom extreme ultraviolet (EUV) images of the Atmospheric Imaging Assembly (AIA) and LOS magnetograms of the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) as context data. Results. The NIR Call Stokes-V maps are not suitable to definitively define a clear polarity inversion line and to classify this chromospheric structure. Nevertheless, this unusual AFS connects the MMFs of a decaying sunspot with the network field. At the southern footpoint, we measured that the flux decreases over time. We find strong downflow velocities at the footpoints of the extended AFS, which increase in a time period of 30 min. The velocities are asymmetric at both footpoints with higher velocities at the southern footpoint. An EUV brigthening appears in one of the arch filaments, which migrates from the northern footpoint toward the southern one. This activation likely influences the increasing redshift at the southern footpoint. Conclusions. The extended AFS exhibits a similar morphology as classical AFSs, for example, threaded filaments of comparable length and width. Major differences concern the connection from MMFs around the sunspot with the flux of the neighboring quietSun network, converging footpoint motions, and longer lifetimes of individual arch filaments of about one hour, while the extended AFS is still very dynamic.
The in-depth understanding of charge carrier photogeneration and recombination mechanisms in organic solar cells is still an ongoing effort. In donor:acceptor (bulk) heterojunction organic solar cells, charge photogeneration and recombination are inter-related via the kinetics of charge transfer states-being singlet or triplet states. Although high-charge-photogeneration quantum yields are achieved in many donor:acceptor systems, only very few systems show significantly reduced bimolecular recombination relative to the rate of free carrier encounters, in low-mobility systems. This is a serious limitation for the industrialization of organic solar cells, in particular when aiming at thick active layers. Herein, a meta-analysis of the device performance of numerous bulk heterojunction organic solar cells is presented for which field-dependent photogeneration, charge carrier mobility, and fill factor are determined. Herein, a "spin-related factor" that is dependent on the ratio of back electron transfer of the triplet charge transfer (CT) states to the decay rate of the singlet CT states is introduced. It is shown that this factor links the recombination reduction factor to charge-generation efficiency. As a consequence, it is only in the systems with very efficient charge generation and very fast CT dissociation that free carrier recombination is strongly suppressed, regardless of the spin-related factor.
Supercritical Kuramoto oscillators with distributed frequencies can be separated into two disjoint groups: an ordered one locked to the mean field, and a disordered one consisting of effectively decoupled oscillators-at least so in the thermodynamic limit. In finite ensembles, in contrast, such clear separation fails: The mean field fluctuates due to finite-size effects and thereby induces order in the disordered group. This publication demonstrates this effect, similar to noise-induced synchronization, in a purely deterministic system. We start by modeling the situation as a stationary mean field with additional white noise acting on a pair of unlocked Kuramoto oscillators. An analytical expression shows that the cross-correlation between the two increases with decreasing ratio of natural frequency difference and noise intensity. In a deterministic finite Kuramoto model, the strength of the mean-field fluctuations is inextricably linked to the typical natural frequency difference. Therefore, we let a fluctuating mean field, generated by a finite ensemble of active oscillators, act on pairs of passive oscillators with a microscopic natural frequency difference between which we then measure the cross-correlation, at both super- and subcritical coupling.
The purity of the analysed samples (e.g. quartz) with respect to chemical composition and radionuclide contamination is essential for geomorphologic applications using so-called terrestrial cosmogenic nuclides (TCNs). To guarantee this, numerous cleaning and dissolution procedures have been developed. At the DREsden Accelerator Mass Spectrometry (DREAMS) facility, we also work on enhancing the chemical quartz-enrichment methodology from bulk rock and dissolution of quartz. Repeated exposure of the bulk material to acid mixtures (HCl/H2SiF6) at room temperature for cleaning and its monitoring by optical microscopy works for most quartz-rich samples. The quartz dissolution in HF under rather mild conditions (at room temperature on a shaker-table) has the advantage to leave difficult-to-dissolve minerals (e.g., tourmaline, zircon, rutile, sillimanite, kyanite, chromite, corundum), not separated by other physical methods before, as residue. Our comparison with a high-temperature dissolution method (in a microwave) indicates an additional amount of interfering elements, such as in average about 3 mg of Ti, more than 7 mg of Al, and about 22 mu g of Be (for 50 g SiO2), is added to the sample, hence showing the superiority of our mild method. This way, we reduce problems for chemistry and AMS, but also ensure better comparability to production rates of cleaner stoichiometric quartz from calibration sites.
Simulations of the inner magnetospheric energetic electrons using the IMPTAM-VERB coupled model
(2019)
In this study, we present initial results of the coupling between the Inner Magnetospheric Particle Transport and Acceleration Model (IMPTAM) and the Versatile Electron Radiation Belt (VERB-3D) code. IMPTAM traces electrons of 10-100 keV energies from the plasma sheet (L = 9 Re) to inner L-shell regions. The flux evolution modeled by IMPTAM is used at the low energy and outer L* computational boundaries of the VERB code (assuming a dipole approximation) to perform radiation belt simulations of energetic electrons. The model was tested on the March 17th, 2013 storm, for a six-day period. Four different simulations were performed and their results compared to satellites observations from Van Allen probes and GOES. The coupled IMPTAM-VERB model reproduces evolution and storm-time features of electron fluxes throughout the studied storm in agreement with the satellite data (within similar to 0.5 orders of magnitude). Including dynamics of the low energy population at L* = 6.6 increases fluxes closer to the heart of the belt and has a strong impact in the VERB simulations at all energies. However, inclusion of magnetopause losses leads to drastic flux decreases even below L* = 3. The dynamics of low energy electrons (max. 10s of keV) do not affect electron fluxes at energies >= 900 keV. Since the IMPTAM-VERB coupled model is only driven by solar wind parameters and the Dst and Kp indexes, it is suitable as a forecasting tool. In this study, we demonstrate that the estimation of electron dynamics with satellite-data-independent models is possible and very accurate.
Holocene glacial chronostratigraphies in glaciated valleys spread throughout the Himalayan-Tibetan orogen, including the Himalaya, Tibet, Pamir, and Tian Shan, are developed using a landsystems approach, detailed geomorphic mapping, and new and published Be-10 surface exposure dating. New studies in the Kulti valley of Lahul and the Parkachik valley of the Nun Kun massif of the Himalaya of northern India define three glacier advances at similar to 14.7, 12.2, 0.5 ka, in addition to one historically dated late 19th Century advance in the Kulti valley, and one Late Holocene advance at similar to 0.2 ka in the Parkachik valley. Three major climatic groups (subdivided into five climatic zones) are defined across the orogen using Cluster Analysis (CA) and Principal Component Analysis (PCA) to identify glaciated regions with comparable climatic characteristics to evaluate the timing, and extent of Holocene glacier advances across these regions. Our regional analyses across the Himalayan-Tibetan orogen suggest at least one Lateglacial (similar to 15.3-11.8 ka) and five Himalayan-Tibetan Holocene glacial stages (HTHS) at similar to 11.5-9.5, similar to 8.8-7.7, similar to 7.0-3.2, similar to 2.3-1.0, and <1 ka. The extent (amplitude) of glacier advances in 77 glaciated valleys is reconstructed and defined using equilibrium-line altitudes (ELAs). Modern glacier hypsometries are also assessed to help explain the intra-regional variations in glacier amplitudes during each regional glacier advance. A linear inverse glacier flow model is used to decipher the net changes in temperature (Delta T) between periods of reconstructed regional glacier advances in 66 glaciated valleys across different climatic regions throughout the orogen. The Be-10, ELAs, and Delta T data suggest enhanced monsoonal and increased precipitation during the Early Holocene, followed by relative cooling and increased aridity during the Mid- and Late Holocene that influenced glaciation. The sublimation-dominated cold-based glaciers in the northern regions of Himalayan-Tibetan orogen are more affected during these shifts in climate than the temperate glaciers in the south. (C) 2019 Elsevier Ltd. All rights reserved.