Related papers: Evolution of safety factor profiles in sawteeth
We extend latent representation methods for safety control design to set-valued states. Recent work has shown that barrier functions designed in a learned latent space can transfer safety guarantees back to the original system, but these…
Shrunk sample covariance matrix is a factor model of a special form combining some (typically, style) risk factor(s) and principal components with a (block-)diagonal factor covariance matrix. As such, shrinkage, which essentially inherits…
Stability properties of magnetic-field configurations containing the toroidal and axial field are considered. The stability is treated by making use of linear analysis. It is shown that the conditions required for the onset of instability…
Reinforcement learning algorithms typically necessitate extensive exploration of the state space to find optimal policies. However, in safety-critical applications, the risks associated with such exploration can lead to catastrophic…
In their thought-provoking paper [1], Belkin et al. illustrate and discuss the shape of risk curves in the context of modern high-complexity learners. Given a fixed training sample size $n$, such curves show the risk of a learner as a…
An evolution of a magnetic reconnection in a collisionless accretion disk is investigated using a 2.5 dimensional hybrid code simulation. In astrophysical disks, magnetorotational instability (MRI) is considered to play an important role by…
High levels of horizontal magnetic flux have been reported in the quiet-Sun internetwork, often based on Stokes profile inversions. Here we introduce a new method for deducing the inclination of magnetic elements and use it to test magnetic…
This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics…
Results from 2.5D and 3D studies of the onset and development of the tearing instability are presented, using high fidelity resistive MHD simulations. A limited parameter study of the strength of the reconnecting field (or shear angle) was…
We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points invariant under the permutational symmetry $S_q$ in two dimensions, and show how one of these scattering solutions describes the…
Context. Analyses of magnetic properties on umbrae boundaries led to the Jurcak criterion, which states that umbra-penumbra boundaries in stable sunspots are equally defined by a constant value of the vertical magnetic field, Bver_crit, and…
We model the non-linear ideal magnetohydrodynamics of poloidal magnetic fields in neutron stars in general relativity assuming a polytropic equation of state. We identify familiar hydromagnetic modes, in particular the 'sausage/varicose'…
The magnetic fields observed in Ap-stars, white dwarfs, and neutron stars are known to be stable for long times. However, the physical conditions inside the stellar interiors that allow these states are still a matter of research. It has…
The accuracy of Milne-Eddington (ME) inversions, used to retrieve the magnetic field vector, depends upon the signal-to-noise ratio (SNR) of the spectro-polarimetric observations. The SNR in real observations varies from pixel to pixel,…
In previous simulations of collisionless 2D magnetic reconnection it was consistently found that the term in the generalised Ohm's law that breaks the frozen-in condition is the divergence of the electron pressure tensor's non-gyrotropic…
Rather weak fossil magnetic fields in the radiative core can produce the solar tachocline if the field is poloidal and almost horizontal in the tachocline region, i.e. if the field is confined within the core. This particular field geometry…
In addition to buoyancy- and magnetic tension-driven instabilities, magnetic flux rings are also susceptible to an instability induced by the hydrodynamic drag force. We investigate the influence of the toroidal shape and equilibrium…
Solar flares may be the best-known examples of the explosive conversion of magnetic energy into bulk motion, plasma heating, and particle acceleration via magnetic reconnection. The energy source for all flares is the highly sheared…
The possibility that the magnetic shear-flow instability (MRI, Balbus-Hawley instability) might give rise to turbulence in a cylindric Couette flow is investigated through numerical simulations. The study is linear and the fluid flow is…
Many solar filaments and prominences show short-lived horizontal threads lying parallel to the photosphere. In this work the possible link between Rayleigh-Taylor instabilities and thread lifetimes is investigated. This is done by…