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We extend exploration of potential vorticity instabilities in cold astrophysical disks whose mean states are baroclinic. In particular, we seek to demonstrate the potential existence of traditional baroclinic instabilities of meteorological…
In this article we prove that for a diffeomorphism on a compact Riemannian manifold, if there is a nontrival homoclinic class that is not uniformly hyperbolic or the diffeomorphism is a $C^{1+\alpha}$ and there is a hyperbolic ergodic…
We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on $\mathbb{R}^{d}$. Under standard spectral stability assumptions, we establish Lyapunov stability of the front against fully…
Anomaly detection is a critical task in industrial manufacturing, aiming to identify defective parts of products. Most industrial anomaly detection methods assume the availability of sufficient normal data for training. This assumption may…
In the Gaia era, understanding the effects of the perturbations of the Galactic disc is of major importance in the context of dynamical modelling. In this theoretical paper we extend previous work in which, making use of the epicyclic…
Ambipolar diffusion is a physical mechanism related to the drift between charged and neutral particles in a partially ionized plasma that is key in many different astrophysical systems. However, understanding its effects is challenging due…
Recent investigations of the pseudospectrum in black hole spacetimes have shown that quasinormal mode frequencies suffer from spectral instabilities. This phenomenon may severely affect gravitational-wave spectroscopy and limit precision…
We consider a scalar diffusion equation with a sign-changing coefficient in its principle part. The well-posedness of such problems has already been studied extensively provided that the contrast of the coefficient is non-critical.…
Global stability of differentially rotating plasma is investigated using a generalized effective potential. We first, for a current-free system, obtain a general form of an effective potential in terms of the free energies of global…
The coupling of the high-lying dipole mode to the low-lying quadrupole modes for the case of deformed gamma-unstable nuclei is studied. Results from the geometrical model are compared to those obtained within the dipole boson model.…
The aim of this work is to improve understanding of the resonant spectra of black holes under perturbations arising from e.g. compact objects or accretion disks in their vicinity. It is known that adding a weak perturbation to the radial…
Analytical treatment of black hole accretion generally presumes the stability of the stationary configuration. Various authors in the past several decades demonstrated the validity of such an assumption for inviscid hydrodynamic flow.…
This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for biharmonic equations with built-in stabilizers. Unlike existing stabilizer-free WG methods limited to convex elements in finite element partitions, our…
A general inversion technique for the recovery of the underlying distribution function for observed galactic disks is presented and illustrated. Under the assumption that these disks are axi-symmetric and thin, the proposed method yields…
This paper continues a series reporting different aspects of the behaviour of disc galaxy simulations that support spiral instabilities. The focus in this paper is to demonstrate how linear spiral instabilities saturate and decay, and how…
We construct aligned and unaligned stationary perturbation configurations in a composite system of stellar and coplanarly magnetized gaseous singular isothermal discs (SIDs) coupled by gravity. In comparison with SID problems studied…
Recent numerical simulations indicate the presence of dynamical instabilities of the f-mode in differentially rotating stars even at very low values of $T/|W|$, the ratio of kinetic to potential energy. In this Letter we argue that these…
A recently developed Eulerian finite element method is applied to solve advection-diffusion equations posed on hypersurfaces. When transport processes on a surface dominate over diffusion, finite element methods tend to be unstable unless…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
Diffusion models (DMs) are capable of generating remarkably high-quality samples by iteratively denoising a random vector, a process that corresponds to moving along the probability flow ordinary differential equation (PF ODE).…