31 research outputs found
Transient chaos and resonant phase mixing in violent relaxation
This paper explores how orbits in a galactic potential can be impacted by
large amplitude time-dependences of the form that one might associate with
galaxy or halo formation or strong encounters between pairs of galaxies. A
period of time-dependence with a strong, possibly damped, oscillatory component
can give rise to large amounts of transient chaos, and it is argued that
chaotic phase mixing associated with this transient chaos could play a major
role in accounting for the speed and efficiency of violent relaxation. Analysis
of simple toy models involving time-dependent perturbations of an integrable
Plummer potential indicates that this chaos results from a broad, possibly
generic, resonance between the frequencies of the orbits and harmonics thereof
and the frequencies of the time-dependent perturbation. Numerical computations
of orbits in potentials exhibiting damped oscillations suggest that, within a
period of 10 dynamical times t_D or so, one could achieve simultaneously both
`near-complete' chaotic phase mixing and a nearly time-independent, integrable
end state.Comment: 11 pages and 12 figures: an extended version of the original
manuscript, containing a modified title, one new figure, and approximately
one page of additional text, to appear in Monthly Notices of the Royal
Astronomical Societ
Thunderstorm nowcasting with deep learning: a multi-hazard data fusion model
Predictions of thunderstorm-related hazards are needed in several sectors,
including first responders, infrastructure management and aviation. To address
this need, we present a deep learning model that can be adapted to different
hazard types. The model can utilize multiple data sources; we use data from
weather radar, lightning detection, satellite visible/infrared imagery,
numerical weather prediction and digital elevation models. It can be trained to
operate with any combination of these sources, such that predictions can still
be provided if one or more of the sources become unavailable. We demonstrate
the ability of the model to predict lightning, hail and heavy precipitation
probabilistically on a 1 km resolution grid, with a time resolution of 5 min
and lead times up to 60 min. Shapley values quantify the importance of the
different data sources, showing that the weather radar products are the most
important predictors for all three hazard types.Comment: 15 pages, 3 figures. Submitted to Geophysical Research Letter
Dynamics of Cuspy Triaxial Galaxies with a Supermassive Black Hole
This talk provides a progress report on an extended collaboration which has
aimed to address two basic questions, namely: Should one expect to see cuspy,
triaxial galaxies in nature? And can one construct realistic cuspy, triaxial
equilibrium models that are robust? Three technical results are described: (1)
Unperturbed chaotic orbits in cuspy triaxial potentials can be extraordinarily
sticky, much more so than orbits in many other three-dimensional potentials.
(2) Even very weak perturbations can be important by drastically reducing,
albeit not completely eliminating, this stickiness. (3) A simple toy model
facilitates a simple understanding of why black holes and cusps can serve as an
effective source of chaos. These results suggest that, when constructing models
of galaxies using Schwarzschild's method or any analogue thereof, astronomers
would be well advised to use orbital building blocks that have been perturbed
by `noise' or other weak irregularities, since such building blocks are likely
to be more nearly time-independent than orbits evolved in the absence of all
perturbations.Comment: a contributed talk at The International Conference on Stellar
Dynamics: From Classical to Modern, Sobolev Astronomical Institute, St.
Petersburg State University, August 200
Fluctuations Do Matter: Large Noise-Enhanced Halos in Charged-Particle Beams
The formation of beam halos has customarily been described in terms of a
particle-core model in which the space-charge field of the oscillating core
drives particles to large amplitudes. This model involves parametric resonance
and predicts a hard upper bound to the orbital amplitude of the halo particles.
We show that the presence of colored noise due to space-charge fluctuations
and/or machine imperfections can eject particles to much larger amplitudes than
would be inferred from parametric resonance alone.Comment: 13 pages total, including 5 figure
Smooth potential chaos and N-body simulations
Integrations in fixed N-body realisations of smooth density distributions
corresponding to a chaotic galactic potential can be used to derive reliable
estimates of the largest (finite time) Lyapunov exponent X_S associated with an
orbit in the smooth potential generated from the same initial condition, even
though the N-body orbit is typically characterised by an N-body exponent X_N >>
X_S. This can be accomplished either by comparing initially nearby orbits in a
single N-body system or by tracking orbits with the same initial condition
evolved in two different N-body realisations of the same smooth density.Comment: 9 pages plus 7 figures, expanded version to appear in Astrophysical
Journa