418 research outputs found
Automated detection of premature atrial contractions in non-invasive fetal heart rate recordings : a case report
Automated detection of premature atrial contractions in non-invasive fetal heart rate recordings : a case report
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
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
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
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
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