Starting from expressions in Connor et al. (1988) [1], we derive a one-dimensional tearing equation similar to the approximate equation obtained by Hegna and Callen (1984) [2] and by Nishimura et al (1998) [3], but for more realistic toroidal equilib...
Alright, I'll cut to the chase. First of all, I want to preface that I like the stable. I do. But, there are some flaws that I would want to change out. 1. Make them far, far more brutal. And I'm ...
We address the question of perturbative consistency in the scalar fishnet models presented by Caetano, Gurdogan and Kazakov\cite{Gurdogan:2015csr, Caetano:2016ydc}. We argue that their 3-dimensional $φ^{6}$ fishnet model becomes perturbatively stabl...
This note is a supplement to our paper `Proof of spherical flocking based on quantitative rearrangement inequalities'. Recently, M. Christ has derived a deep result concerning stability of the Riesz rearrangement inequality. We are interested in the...
Perturbations in a non-normal system can grow transiently even if the system is linearly stable. If this transient growth is sufficiently large, it can trigger self-sustained oscillations from small initial disturbances. This has important practical...
We consider odd symmetric (1+1)-scalar field models with one internal mode. Under natural and robust assumptions, including the Fermi golden rule, we prove the asymptotic stability of the kink by odd perturbations in the energy space. For example, th...
We prove that the linearised operator around any sufficiently small solitary wave of the one-dimensional Zakharov system has no internal mode. This spectral result, along with its proof, is expected to play a role in the study of the asymptotic stabi...
A wide variety of nonmonotonic semantics can be expressed as approximators defined under AFT (Approximation Fixpoint Theory). Using traditional AFT theory, it is not possible to define approximators that rely on information computed in previous itera...
I came to this revelation as I entered my late 20s, once my own financial situation was stablized and improved. I originally grew up in Los Angeles, but my parents lost their jobs and houses during th...
We propose an end-to-end trained neural networkarchitecture to robustly predict the complex dynamics of fluid flows with high temporal stability. We focus on single-phase smoke simulations in 2D and 3D based on the incompressible Navier-Stokes (NS) e...
Maxwell's investigations into the stability of Saturn's rings provide one of the earliest analyses of the dynamics of astrophysical discs. Current research in planetary rings extends Maxwell's kinetic theory to treat dense granular gases of particl...
We prove that optimal traffic plans for the mailing problem in $\mathbb{R}^d$ are stable with respect to variations of the given coupling, above the critical exponent $α=1-1/d$, thus solving an open problem stated in the book "Optimal transportation...
We present a systematic approach for calculating higher-order derivatives of smooth functions on a uniform grid using Padé approximants. We illustrate our findings by deriving higher-order approximations using traditional second-order finite-differ...
The file contains PhD Dissertation by Oskar Jakub Szymański. This work ends his study at Doctoral School of Exact and Natural Sciences at Jagiellonian University where the Author has attended in years 2019-2024. The subject of the Thesis is the stab...
The investigation of twist engineering in easy-axis magnetic systems has revealed the remarkable potential for generating topological spin textures, such as magnetic skyrmions. Here, by implementing twist engineering in easy-plane magnets, we introdu...
As a fundamental type of topological spin textures in two-dimensional (2D) magnets, a magnetic meron carries half-integer topological charge and forms a pair with its antithesis to keep the stability in materials. However, it is challenging to quanti...
In bistable systems, the stability of front structures often influences the dynamics of extended patterns. We show how the combined effect of an instability to curvature modulations and proximity to a pitchfork front bifurcation leads to spontaneou...
The stability of statistical analysis is an important indicator for reproducibility, which is one main principle of scientific method. It entails that similar statistical conclusions can be reached based on independent samples from the same underlyin...
We explore the idea of accidental dark matter (aDM) stability in the scale invariant local $U(1)_{B-L}$ model, which is a theory for neutrino and at the same time radiatively breaks scale invariance via quantum mechanical dynamics in the $U(1)_{B-L}$...
On 5 March 2009, his killer, 40-year-old Vince Li, was found not criminally responsible for murder, after it was determined that he was [schizophrenic](https://en.wikipedia.org/wiki/Schizophrenia). L...