Torsional Alfven waves in stratified and expanding magnetic flux tubes

The effects of both density stratification and magnetic field expansion on torsional Alfven waves in magnetic flux tubes are studied. The frequencies, the period ratio P1/P2 of the fundamental and its first-overtone, and eigenfunctions of torsional Alfven modes are obtained. Our numerical results show that the density stratification and magnetic field expansion have opposite effects on the oscillating properties of torsional Alfven waves.Comment: 13 pages, 7 figures, Accepted for publication in Astrophysics and Space Scienc

A novel flexible model for lot sizing and scheduling with non-triangular, period overlapping and carryover setups in different machine configurations

© 2017, Springer Science+Business Media New York. This paper develops and tests an efficient mixed integer programming model for capacitated lot sizing and scheduling with non-triangular and sequence-dependent setup times and costs incorporating all necessary features of setup carryover and overlapping on different machine configurations. The model’s formulation is based on the asymmetric travelling salesman problem and allows multiple lots of a product within a period. The model conserves the setup state when no product is being processed over successive periods, allows starting a setup in a period and ending it in the next period, permits ending a setup in a period and starting production in the next period(s), and enforces a minimum lot size over multiple periods. This new comprehensive model thus relaxes all limitations of physical separation between the periods. The model is first developed for a single machine and then extended to other machine configurations, including parallel machines and flexible flow lines. Computational tests demonstrate the flexibility and comprehensiveness of the proposed models

Torsional Alfvén waves in small scale current threads of the solar corona

Context. The magnetic field structuring in the solar corona occurs on large scales (loops and funnels), but also on small scales. For instance, coronal loops are made up of thin strands with different densities and magnetic fields across the loop. Aims. We consider a thin current thread and model it as a magnetic flux tube with twisted magnetic field inside the tube and straight field outside. We prove the existence of trapped Alfvén modes in twisted magnetic flux tubes (current threads) and we calculate the wave profile in the radial direction for two different magnetic twist models. Methods. We used the Hall MHD equations that we linearized in order to derive and solve the eigenmode equation for the torsional Alfvén waves. Results. We show that the trapped Alfv én eigenmodes do exist and are localized in thin current threads where the magnetic field is twisted. The wave spectrum is discrete in phase velocity, and the number of modes is finite and depends on the amount of the magnetic field twist. The phase speeds of the modes are between the minimum of the Alfvén speed in the interior and the exterior Alfén speed. Conclusions. Torsional Alfvén waves can be guided by thin twisted magnetic flux-tubes (current threads) in the solar corona. We suggest that the current threads guiding torsional Alfvén waves, are subject to enhanced plasma heating due to wave dissipation

Torsional Alfvén waves in small scale density threads of the solar corona

The density structuring of the solar corona is observed at large scales (loops and funnels), but also at small scales (sub-structures of loops and funnels). Coronal loops consist of thin density threads with sizes down to (and most probably below) the resolution limit. We study properties of torsional Alfvén waves propagating in inhomogeneous cylindrical density threads using the two-fluid magnetohydrodynamic equations. The eigenmode solutions supported by such a structure are obtained and analysed. It is shown that the dispersive and dissipative effects become important for the waves localised in thin threads. In this case, the Alfvén wave continuum is replaced with a discrete spectrum of Alfvén waves. This mathematical model is applied to the waves propagating in coronal structures. In particular, we consider ~1 Hz Alfvén waves propagating along density threads with a relatively smooth radial profile, where a density contrast of about 1.1 is attained at radial distances of about 0.1 km. We found that the dissipation distance of these waves is less than the typical length of hot coronal loops, 50 Mm. Torsional Alfvén waves are localised in thin density threads and produce localised heating. Therefore, these waves can be responsible for coronal heating and for maintenance of small-scale coronal structuring

Damping of phase-mixed slow magneto-acoustic waves: Real or apparent?

The propagation of slow magnetoacoustic waves along a multithreaded coronal loop is modelled analytically by means of a ray tracing method. It is shown how cross field gradients build up due to phase mixing. The cross field gradients can enhance shear viscosity so that it dominates over compressive viscosity. Nevertheless the short dissipation distances (~107 m) observed for slow waves in coronal loops require very small cross field length scales which imply a filamentary structure on scales at least three orders of magnitude below the current detection limit of TRACE and close to the limit where magnetohydrodynamic (MHD) theory breaks down. The observed dissipation distances can alternatively be explained by phase mixing in its ideal regime, where the apparent damping is due to the spatial integration of the phase mixed amplitudes by the observation