Lyapunov spectra of billiards with cylindrical scatterers: comparison with many-particle systems

The dynamics of a system consisting of many spherical hard particles can be described as a single point particle moving in a high-dimensional space with fixed hypercylindrical scatterers with specific orientations and positions. In this paper, the similarities in the Lyapunov exponents are investigated between systems of many particles and high-dimensional billiards with cylindrical scatterers which have isotropically distributed orientations and homogeneously distributed positions. The dynamics of the isotropic billiard are calculated using a Monte-Carlo simulation, and a reorthogonalization process is used to find the Lyapunov exponents. The results are compared to numerical results for systems of many hard particles as well as the analytical results for the high-dimensional Lorentz gas. The smallest three-quarters of the positive exponents behave more like the exponents of hard-disk systems than the exponents of the Lorentz gas. This similarity shows that the hard-disk systems may be approximated by a spatially homogeneous and isotropic system of scatterers for a calculation of the smaller Lyapunov exponents, apart from the exponent associated with localization. The method of the partial stretching factor is used to calculate these exponents analytically, with results that compare well with simulation results of hard disks and hard spheres.Comment: Submitted to PR

Derivation of Instrument Requirements for Polarimetry using Mg, Fe, and Mn lines between 250 and 290 nm

Judge et al. (2021) recently argued that a region of the solar spectrum in the near-UV between about 250 and 290 nm is optimal for studying magnetism in the solar chromosphere due to an abundance of Mg II, Fe II, and Fe I lines that sample various heights in the solar atmosphere. In this paper we derive requirements for spectropolarimetric instruments to observe these lines. We derive a relationship between the desired sensitivity to magnetic field and the signal-to-noise of the measurement from the weak-field approximation of the Zeeman effect. We find that many lines will exhibit observable polarization signals for both longitudinal and transverse magnetic field with reasonable amplitudes

The Lyapunov spectrum of the many-dimensional dilute random Lorentz gas

For a better understanding of the chaotic behavior of systems of many moving particles it is useful to look at other systems with many degrees of freedom. An interesting example is the high-dimensional Lorentz gas, which, just like a system of moving hard spheres, may be interpreted as a dynamical system consisting of a point particle in a high-dimensional phase space, moving among fixed scatterers. In this paper, we calculate the full spectrum of Lyapunov exponents for the dilute random Lorentz gas in an arbitrary number of dimensions. We find that the spectrum becomes flatter with increasing dimensionality. Furthermore, for fixed collision frequency the separation between the largest Lyapunov exponent and the second largest one increases logarithmically with dimensionality, whereas the separations between Lyapunov exponents of given indices not involving the largest one, go to fixed limits.Comment: 8 pages, revtex, 6 figures, submitted to Physical Review

Dynamic Ly alpha jets

The solar chromosphere and transition region are highly structured and complex regimes. A recent breakthrough has been the identification of dynamic fibrils observed in H alpha as caused by field-aligned magnetoacoustic shocks. We seek to find whether such dynamic fibrils are also observed in Ly alpha. We used a brief sequence of four high-resolution Ly alpha images of the solar limb taken by the Very high Angular resolution ULtraviolet Telescope (VAULT), which displays many extending and retracting Ly alpha jets. We measured their top trajectories and fitted parabolas to the 30 best-defined ones. Most jet tops move supersonically. Half of them decelerate, sometimes superballistically, the others accelerate. This bifurcation may arise from incomplete sampling of recurrent jets. The similarities between dynamic Ly alpha jets and H alpha fibrils suggest that the magnetoacoustic shocks causing dynamic H alpha fibrils also affect dynamic Ly alpha jets.Comment: 5 pages, 7 figures; changed title and content; accepted in Astronomy and Astrophysics; eps figures in full resolution are available at http://www.astro.sk/~koza/publications/vault/figs

Dynamics of isolated magnetic bright points derived from Hinode/SOT G-band observations

Small-scale magnetic fields in the solar photosphere can be identified in high-resolution magnetograms or in the G-band as magnetic bright points (MBPs). Rapid motions of these fields can cause magneto-hydrodynamical waves and can also lead to nanoflares by magnetic field braiding and twisting. The MBP velocity distribution is a crucial parameter for estimating the amplitudes of those waves and the amount of energy they can contribute to coronal heating. The velocity and lifetime distributions of MBPs are derived from solar G-band images of a quiet sun region acquired by the Hinode/SOT instrument with different temporal and spatial sampling rates. We developed an automatic segmentation, identification and tracking algorithm to analyse G-Band image sequences to obtain the lifetime and velocity distributions of MBPs. The influence of temporal/spatial sampling rates on these distributions is studied and used to correct the obtained lifetimes and velocity distributions for these digitalisation effects. After the correction of algorithm effects, we obtained a mean MBP lifetime of (2.50 +- 0.05) min and mean MBP velocities, depending on smoothing processes, in the range of (1 - 2) km/s. Corrected for temporal sampling effects, we obtained for the effective velocity distribution a Rayleigh function with a coefficient of (1.62 +- 0.05) km/s. The x- and y- components of the velocity distributions are Gaussians. The lifetime distribution can be fitted by an exponential function.Comment: Astronomy and Astrophysics (in press

Transport of magnetic flux from the canopy to the internetwork

Recent observations have revealed that 8% of linear polarization patches in the internetwork quiet Sun are fully embedded in downflows. These are not easily explained with the typical scenarios for the source of internetwork fields which rely on flux emergence from below. We explore using radiative MHD simulations a scenario where magnetic flux is transported from the magnetic canopy overlying the internetwork into the photosphere by means of downward plumes associated with convective overshoot. We find that if a canopy-like magnetic field is present in the simulation, the transport of flux from the canopy is an important process for seeding the photospheric layers of the internetwork with magnetic field. We propose that this mechanism is relevant for the Sun as well, and it could naturally explain the observed internetwork linear polarization patches entirely embedded in downflows.Comment: Accepted to Ap