In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support ...functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It turns out that to do so one has to calculate the support function of the uncertainty set and the concave conjugate of the nonlinear constraint function. Conveniently, these two computations are completely independent. This approach has several advantages. First, it provides an easy structured way to construct the robust counterpart both for linear and nonlinear inequalities. Second, it shows that for new classes of uncertainty regions and for new classes of nonlinear optimization problems tractable counterparts can be derived. We also study some cases where the inequality is nonconcave in the uncertain parameters.
Abstract
Observations of the Sun’s off-limb white-light (WL) flares offer rare opportunities to study the energy release and transport mechanisms in flare loops. One of the best such events was ...SOL2017-09-10, an X8.2 flare that occurred near the Sun’s west limb on 2017 September 10 and produced a WL loop system lasting more than 60 minutes and reaching an altitude higher than 30 Mm. The event was well observed by a suite of ground- and space-based instruments, including the Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) that captured its off-limb loops in WL continuum near Fe
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6173 Å, and the Atmospheric Imager Assembly (SDO/AIA) that observed its ultraviolet (UV) and extreme-ultraviolet (EUV) counterparts. We found quasi-periodic pulsations in the WL and UV emissions at the flare loop-top with a period around 8.0 minutes. Each pulsation appears to have an EUV counterpart that occurs earlier in time and higher in altitude. Despite many similarities in the WL and UV images and light curves, the WL flux at the loop-top continues to grow for about 16 minutes while the UV fluxes gradually decay. We discuss the implication of these unprecedented observations on the understanding of the enigmatic off-limb WL flare emission mechanisms.
We report a novel optical resolution photoacoustic microscopy concept to obtain an axial resolution only by optical methods. The photoacoustic signal is generated through a non-radiative relaxation ...from a level that is populated by excited state absorption. This two-step excitation process of a single laser enables to achieve an optical sectioning without any acoustic selectivity, whereby a full optical resolution photoacoustic microscopy is obtained. We bring a proof of this concept using Rhodamine and Zinc Tetraphenylporphyrin dyes known for their efficient excited state absorption process.
Interior Point Methods for Linear Optimization is a comprehensive, thorough textbook on interior point methods (IPMs). The era of IPMs was initiated by N. Karmarkar's 1984 paper, which triggered ...turbulent research and reshaped almost all areas of optimization theory and computational practice. This book gives a comprehensive review of the main results of more than a decade of IPM research. Numerous exercises are provided to aid in understanding the material.
Interfaces provide the structural basis of essential bone functions. In the hierarchical structure of bone tissue, heterogeneities such as porosity or boundaries are found at scales ranging from ...nanometers to millimeters, all of which contributing to macroscopic properties. To date, however, the complexity or limitations of currently used imaging methods restrict our understanding of this functional integration. Here we address this issue using label-free third-harmonic generation (THG) microscopy. We find that the porous lacuno-canalicular network (LCN), revealing the geometry of osteocytes in the bone matrix, can be directly visualized in 3D with submicron precision over millimetric fields of view compatible with histology. THG also reveals interfaces delineating volumes formed at successive remodeling stages. Finally, we show that the structure of the LCN can be analyzed in relation with that of the extracellular matrix and larger-scale structures by simultaneously recording THG and second-harmonic generation (SHG) signals relating to the collagen organization.
We report the development of a stimulated emission depletion (STED) selective plane illumination (SPIM) microscope based on a single diode-pumped solid state (DPSS) laser that simultaneously delivers ...nanosecond-pulses at two wavelengths. The two wavelengths, 355 nm and 532 nm, are generated by harmonic conversion and they are used to induce respectively excitation and stimulated emission depletion. This source should allow a low-cost, compact, very efficient and simplified STED scheme since the two beams are intrinsically aligned and synchronized. Using a chromatic beam shaping device which leaves the excitation beam unaffected and produces a donut-shaped STED beam, we demonstrate a 300% reduction of the light sheet thickness, together with an enhancement of the sheet uniformity over larger field of view, at low STED power, in Coumarin dye solution.
This paper addresses the improved science resulting from joint observations performed by the different instruments onboard the Advanced Space-based Solar Observatory (ASO-S) mission along with ...ancillary instruments on missions flying at the same time. It first describes the three major instruments along with their stated objectives. Then it presents some basic science issues concerning jointly observed flares, coronal mass ejections (CMEs) and eruptive prominences (EPs). Each physical candidate (magnetic reconnection, instability, hard X-ray emission and magnetic coronal field topology) is discussed in terms of its signature and identification with ASO-S instrumentation. The importance of Lyα detection and non-LTE modeling is stressed. Some instrumental and science challenges are briefly discussed.
Abstract
We reexamine a 50+ yr old problem of deep central reversals predicted for strong solar spectral lines, in contrast to the smaller reversals seen in observations. We examine data and ...calculations for the resonance lines of H
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, Mg
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, and Ca
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, the self-reversed cores of which form in the upper chromosphere. Based on 3D simulations, as well as data for the Mg
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lines from the Interface Region Imaging Spectrograph (IRIS), we argue that the resolution lies not in velocity fields on scales in either of the micro- or macroturbulent limits. Macroturbulence is ruled out using observations of optically thin lines formed in the upper chromosphere, and by showing that it would need to have unreasonably special properties to account for critical observations of the Mg
ii
resonance lines from the IRIS mission. The power in “turbulence” in the upper chromosphere may therefore be substantially lower than earlier analyses have inferred. Instead, in 3D calculations horizontal radiative transfer produces smoother source functions, smoothing out intensity gradients in wavelength and in space. These effects increase in stronger lines. Our work will have consequences for understanding the onset of the transition region, for understanding the energy in motions available for heating the corona, and for the interpretation of polarization data in terms of the Hanle effect applied to resonance line profiles.
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