Related papers: Mechanical stability conditions for 3D and 2D crys…
Two-dimensional (2D) materials can roll up, forming stable scrolls under suitable conditions. However, the great diversity of materials and fabrication techniques has resulted in a huge parameter space significantly complicating the…
We study some examples of Bridgeland-Douglas stability conditions on triangulated categories. From one side we give a complete description of the stability manifolds for smooth projective curves of positive genus. From the other side we…
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…
We study avenues to shape multistability and shape-morphing in flexible crystalline membranes of cylindrical topology, enabled by glide mobility of dislocations. Using computational modeling, we obtain states of mechanical equilibrium…
A new Chebyshev-type family of stabilized explicit methods for solving mildly stiff ODEs is presented. Besides conventional conditions of order and stability we impose an additional restriction on the methods: their stability function must…
The stable and unstable solutions of a square 2D extreme type-II superconductor are studied in the field of a magnetic disc. We use a preconditioned Newton-Krylov solver to find the solutions and use numerical continuation to track the…
We continue our study on variable order Arnold-Falk-Winther elements for 2D elasticity in context of both affine and parametric curvilinear elements. We present an $h$-stability result for affine elements, and an asymptotic stability result…
We study the bounded derived category $\mathcal{D}$ of an Euclidean quiver, or equivalently, that of coherent sheaves on a tame weighted projective line. We give a description of the moduli space $\mathrm{ToSS}$ of the total semi-stability…
Radial mode stability is a necessary condition for the astrophysical viability of compact objects. In recent years, astrophysical models with two fluids have gain popularity, especially in their ability to model dark matter admixed neutron…
In this paper we investigate the behavior of the condition number of the stiffness matrix resulting from the approximation of a 2D Poisson problem by means of the Virtual Element Method. It turns out that ill-conditioning appears when…
We consider the hydrodynamics for the biaxial nematic phase characterized by a field of orthonormal frame, which can be derived from a molecular-theory-based tensor model. In dimension two and three, we establish the local well-posedness…
Let $f\colon X\to\mathrm{Spec}\, R$ be a 3-fold flopping contraction, where $X$ has at worst Gorenstein terminal singularities and $R$ is complete local. We describe the space of Bridgeland stability conditions on the null subcategory…
We have previously introduced the parameter `alpha' as an indicator of stability to m=2 nonaxisymmetric modes in rotating, self-gravitating, axisymmetric, gaseous and stellar systems. This parameter can be written as a function of the total…
In this work we conduct a numerical search of non-trivial mechanisms, leading to new tendencies towards long-range ferromagnetic ordering in two-dimensional materials. For this purpose we employ an original variant of pairwise infinitesimal…
In this work, we consider the stability of solitons for the KdV equation below the energy space, using spatially-exponentially-weighted norms. Using a combination of the $I$-method and spectral analysis following Pego and Weinstein, we are…
In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…
The dynamical stability of three-dimensional (3D) Lennard-Jones (LJ) crystals has been studied for many years. The face-centered-cubic and hexagonal close packed structures are dynamically stable, while the body-centered cubic structure is…
Motivated by experiments in electroconvection in nematic liquid crystals with homeotropic alignment we study the coupled amplitude equations describing the formation of a stationary roll pattern in the presence of a weakly-damped mode that…
A three-level system with partially broken SU(3) symmetry immersed in a metal, comprised of a unique non-interacting ground state and two-fold degenerate excited states, exhibits a stable two-channel Kondo fixed point within a wide range of…
Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is,…