Computational geometry.

We report the evolution of magnetic field and its energy in NOAA active region 11158 over 5 days based on a vector magnetogram series from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO). Fast flux emergence and strong shearing motion led to a quadrupolar sunspot complex that produced several major eruptions, including the first X-class flare of Solar Cycle 24. Extrapolated non-linear force-free coronal fields show substantial electric current and free energy increase during early flux emergence near a low-lying sigmoidal filament with sheared kilogauss field in the filament channel. The computed magnetic free energy reaches a maximum of ∼2.6 × 10 32 erg, about 50% of which is stored below 6 Mm. It decreases by ∼0.3 × 10 32 erg within 1 hour of the X-class flare, which is likely an underestimation of the actual energy loss. During the flare, the photospheric field changed rapidly: horizontal field was enhanced by 28% in the core region, becoming more inclined and more parallel to the polarity inversion line. Such change is consistent with the conjectured coronal field “implosion”, and is supported by the coronal loop retraction observed by the Atmospheric Imaging Assembly (AIA). The extrapolated field becomes more “compact” after the flare, with shorter loops in the core region, probably because of reconnection. The coronal field becomes slightly more sheared in the lowest layer, relaxes faster with height, and is overall less energetic.

Evolution of Magnetic Field and Energy in A Major Eruptive Active Region Based on SDO/HMI Observation

Thiacalixarenes, a subclass of "third generation" calixarenes, exhibit many interesting features such as enlarged ring size, facile chemical modification, and metal complexation due to the presence of bridging sulfur atoms. The thiacalixarene scaffold is a unique host with vast possibilities for functionalization not only at the upper and lower rim but also at the bridging sulfide groups. Modified thiacalixarenes have been used for many applications such as the detection and separation of biologically important cations, anions, and bio-analytes, mimicking molecular logic gates and devices, and synthesis of self-assembled coordination cages, multinuclear complexes, magnetic materials and luminescent materials. This review article summarizes recent developments in the derivatization methods of thiacalixarenes and their utilization in various applications.

Recent developments of thiacalixarene based molecular motifs

Recently, cloud point extraction (CPE) has been an attractive subject as an alternative to liquid-liquid extraction. The technique is based on the property of most non-ionic surfactants in aqueous solutions to form micelles and become turbid when heated to the cloud point temperature. This review covers a selection of the literature published on applications of CPE in determination of metal ions over the period between 2004 and 2008.

Separation and preconcentration by a cloud point extraction procedure for determination of metals: an overview.

Applied Methods of the Theory of Random Functions. By A. A. Sveshnikov. Pp. ix, 321. 1966. (Pergamon.)

Cloud point extraction of lanthanide(III) ions via use of Triton X-100 without and with water-soluble calixarenes as added chelating agents.

A topological method for detecting the new emergence of magnetic flux using SOHO/MDI magnetograms of the full solar disk is proposed. This method uses the number of pixels in the image that can be distinguished from a specified value to within a predetermined threshold (the number of disconnected components). We study more than ten very powerful active regions (ARs) with very high flare activity and show that the number of disconnected components increases directly before the development of a series of M and X flares, or accompanies this process. This behaviour is evident not only when there is an explicit emergence of a new flux and a series of fast flares, such as in AR 9236 (November 2000), but also in groups with many non-stationary processes developing along a neutral line of the large-scale magnetic field. We also discuss the possibility of using the obtained results for flare prediction.

Detection of new emerging magnetic flux from the topology of SOHO/MDI magnetograms

A quantitative description of the geometry and topology of the magnetic field of the Sun is given in terms of Minkowski functionals: the Euler characteristic and the perimeter of excursion sets for specified levels. Methods of mathematical morphology are applied to background fragments of magnetograms for the entire solar disk. The results obtained show that the topological characteristics of the background field are stable in time and correspond to log-normal, intermittent random fields.

Topology of magnetic fields from MDI data: Background field

The aim of this work is to diagnose pre-flare dynamics of magnetic fields in the active regions of the Sun on the HMI SDO magnetograms. We use a tool based on the methods of the geometry of random fields and computational topology. The results show that the proposed formalism allows one to find some precursors of major flares for practically significant time slots.

Methods of Computational Topology for the Analysis of Dynamics of Active Regions of the Sun

This work analyzes the temporal evolution for three active regions (ARs) (AR 2034, AR 2035, and AR 2036). In terms of complexity, these are objects with high a priori probability of flares. However, their actual flare scenarios proved to be very different. The temporal evolution of ARs is analyzed with modern prognostic parameters and descriptors obtained by methods of computational topology. We show that these methods are more suitable for describing the actual situation. We note that the change in complexity descriptors for prognostic problems is more important than the set of characteristics themselves.

I. S. Knyazeva

Papers

Cloud point extraction of lanthanide(III) ions via use of Triton X-100 without and with water-soluble calixarenes as added chelating agents.

Detection of new emerging magnetic flux from the topology of SOHO/MDI magnetograms

Topology of magnetic fields from MDI data: Background field

Methods of Computational Topology for the Analysis of Dynamics of Active Regions of the Sun

Comparison of the dynamics of active regions by methods of computational topology