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– Using numerical simulations, we investigate the evolution of the structure of force networks in slowly compressed model granular materials in two spatial dimensions. We quantify the global properties of the force networks using the zeroth Betti number B0, which is a topological invariant. We find that B0 can distinguish among force networks in systems(More)
We utilize the tools of persistent homology to analyze features of force networks in dense granular matter, modeled as a collection of circular, inelastic frictional particles. The proposed approach describes these networks in a precise and tractable manner, allowing us to identify features that are difficult or impossible to characterize by other means. In(More)
Hanle-effect observations of forbidden coronal line transitions and recently also longitudinal Zeeman-effect measurements of coronal lines show quantitative signatures of the weak coronal magnetic field. The interpretation of these observations is, however, complicated by the fact that they are the result of line-of-sight integrations through the optically(More)
The force network of a granular assembly, defined by the contact network and the corresponding contact forces, carries valuable information about the state of the packing. Simple analysis of these networks based on the distribution of force strengths is rather insensitive to the changes in preparation protocols or to the types of particles. In this and the(More)
Coronal Mass ejections (CMEs) are enormous eruptions of magnetized plasma expelled from the Sun into the interplanetary space, over the course of hours to days. They can create major disturbances in the interplanetary medium and trigger severe magnetic storms when they collide with the Earth's magnetosphere. It is important to know their real speed,(More)
In second order Lagrangian systems bifurcation branches of periodic solutions preserve certain topological invariants. These invariants are based on the observation that periodic orbits of second order Lagrangian lie on 3-dimensional (non-compact) energy manifolds and the periodic orbits may have various linking and knotting properties. The main ingredients(More)
Clear-sky brightness temperatures (BT) in five bands of the Advanced Himawari Imager and IR12, respectively) are used in the NOAA Advanced Clear-Sky Processor for Oceans (ACSPO) sea surface temperature (SST) retrieval system. Here, AHI BTs are preliminarily evaluated for stability and consistency with the corresponding VIIRS and MODIS BTs, using the sensor(More)
We combine functional analytical and graph theoretical methods in order to study flows in networks. We show that these flows can be described by a strongly continuous operator semigroup on a Banach space. Using Perron-Frobenius spectral theory we then prove that this semigroup behaves asymptotically periodic.
In this paper we investigate periodic solutions of second order Lagrangian systems which oscillate around equilibrium points of center type. The main ingredients are the discretization of second order Lagrangian systems that satisfy the twist property and the theory of discrete braid invariants developed in [5]. The problem with applying this topological(More)
In order to analize the influence of a Coronal Mass Ejection (CME) on the coronal streamer belt, we made 3-D reconstructions of the electron density in the corona at he-liospheric distances from 1.5 to 4 R for periods before and after a CME occured. The reconstructions were performed using a tomography technique. We studied two CME cases: (i) a slow CME on(More)
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