Weak index pairs and the Conley index for discrete multivalued dynamical systems

Motivated by the problem of reconstructing dynamics from samples we revisit the Conley index theory for discrete multivalued dynamical systems. We introduce a new, less restrictive definition of the isolating neighbourhood. It turns out that then the main tool for the construction of the index, i.e. the index pair, is no longer useful. In order to overcome this obstacle we use the concept of weak index pairs

Discretization strategies for computing Conley indices and Morse decompositions of flows

Conley indices and Morse decompositions of flows can be found by using algorithms which rigorously analyze discrete dynamical systems. This usually involves integrating a time discretization of the flow using interval arithmetic. We compare the old idea of fixing a time step as a parameters to a time step continuously varying in phase space. We present an example where this second strategy necessarily yields better numerical outputs and prove that our outputs yield a valid Morse decomposition of the given flow

EUV and HXR Signatures of Electron Acceleration During the Failed Eruption of a Filament

We search for EUV brightenings in TRACE 171 {\AA} images and HXR bursts observed during failed eruptions. We expect that if an eruption is confined due to interaction with overlying magnetic structures then we should observe effects connected with reconnection between magnetic structures and acceleration of particles. We utilized TRACE observations of three well observed failed eruptions. EUV images were compared to HXR spatial distribution reconstructed from Yohkoh/HXT and RHESSI data. The EUV light curves of a selected area were compared to height profiles of eruption, HXR emission and HXR photon spectral index of power-law fit to HXR data. We have found that EUV brightenings are closely related to the eruption velocity decrease, to HXR bursts and to episodes of hardening of HXR spectra. The EUV brightened areas are observed far from the flaring structure, in footpoints of large systems of loops observed 30-60 minutes after the maximum of a flare. These are not `post-flare' loops that are also observed but at significantly lower heights. The high lying systems of loops are observed at heights equal to height, at which eruption was observed to stop. We observed HXR source spatially correlated with EUV brightening only once. For other EUV brightened areas we estimated the expected brightness of HXR sources. We find that EUV brightenings are produced due to interaction between the erupting structure with overlying loops. The interaction is strong enough to heat the system of high loops. These loops cool down and are visible in EUV range about 30-60 minutes later. The estimated brightness of HXR sources associated with EUV brightenings shows that they are too weak to be detected with present instruments. However, next generation instruments will have enough dynamic range and sensitivity to enable such observations.Comment: A&A accepte

Coronal Mass Ejections Associated with Slow Long Duration Flares

It is well known that there is temporal relationship between coronal mass ejections (CMEs) and associated flares. The duration of the acceleration phase is related to the duration of the rise phase of a flare. We investigate CMEs associated with slow long duration events (LDEs), i.e. flares with the long rising phase. We determined the relationships between flares and CMEs and analyzed the CME kinematics in detail. The parameters of the flares (GOES flux, duration of the rising phase) show strong correlations with the CME parameters (velocity, acceleration during main acceleration phase and duration of the CME acceleration phase). These correlations confirm the strong relation between slow LDEs and CMEs. We also analyzed the relation between the parameters of the CMEs, i.e. a velocity, an acceleration during the main acceleration phase, a duration of the acceleration phase, and a height of a CME at the end of the acceleration phase. The CMEs associated with the slow LDEs are characterized by high velocity during the propagation phase, with the median equal 1423 km/s. In half of the analyzed cases, the main acceleration was low (a<300 m/s^2), which suggests that the high velocity is caused by the prolongated acceleration phase (the median for the duration of the acceleration phase is equal 90 minutes). The CMEs were accelerated up to several solar radii (with the median 7 Rsun), which is much higher than in typical impulsive CMEs. Therefore, slow LDEs may potentially precede extremely strong geomagnetic storms. The analysis of slow LDEs and associated CMEs may give important information for developing more accurate space weather forecasts, especially for extreme events.Comment: Solar Physics, accepte

\v{C}ech-Delaunay gradient flow and homology inference for self-maps

We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspace of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for \v{C}ech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive \v{C}ech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems.Comment: 22 pages, 8 figure

Anisotropic-cyclicgraphene: A new two-dimensional semiconducting carbon allotrope

Potentially new, single-atom thick semiconducting 2D-graphene-like material, called Anisotropic-cyclicgraphene, have been generated by the two stage searching strategy linking molecular and ab initio approach. The candidate derived from the evolutionary based algorithm and molecular simulations was then profoundly analysed using first-principles density functional theory from the structural, mechanical, phonon, and electronic properties point of view. The proposed polymorph of graphene (rP16-P1m1) is mechanically, dynamically, and thermally stable and can be semiconducting with a direct band gap of 0.829 eV.Comment: 15 pages, 14 figure