Related papers: Stability under lamination and polycrystalline eff…
We formulate a notion of stability for maps between polarised varieties which generalises Kontsevich's definition when the domain is a curve and Tian-Donaldson's definition of K-stability when the target is a point. We give some examples,…
The well-posedness of the three dimensional Prandtl equation is an outstanding open problem due to the appearance of the secondary flow even though there are studies on analytic and Gevrey function spaces. This problem is raised as the…
The quest to improve transparent conductors balances two key goals: increasing electrical conductivity and increasing optical transparency. To improve both simultaneously is hindered by the physical limitation that good metals with high…
In this paper, we study the positive stability of $P$-matrices. We prove that a $P$-matrix A is positively stable if A is a $Q^2$-matrix and there is at least one nested sequence of principal submatrices of A each of which is also a…
Stable embedded solitons are discovered in the generalized third-order nonlinear Schroedinger equation. When this equation can be reduced to a perturbed complex modified KdV equation, we developed a soliton perturbation theory which shows…
Trigonometric formulas for eigenvalues of $3 \times 3$ matrices that build on Cardano's and Vi\`ete's work on algebraic solutions of the cubic are numerically unstable for matrices with repeated eigenvalues. This work presents numerically…
We investigate the stability of an attractive Bose-Einstein condensate in a moving 1D optical lattice in the presence of transverse confinement. By means of a Bogoliubov linear stability analysis we find that the system is dynamically…
Most of hydrocarbons are either molecular structures or linear polymeric chains. Discovery of graphene and manufacturing of its monohydride -- graphane incite interest in search for three-dimensional hydrocarbon polymers. However up to now…
Persistent spin textures (PSTs) in solid-state materials arise from a unidirectional spin-orbit field in momentum space and offer a route to deliver long carrier spin lifetimes sought for future quantum microelectronic devices. Nonetheless,…
In this paper we study the problem of classifying pencils of curves of degree $d$ in $\mathbb{P}^2$ using geometric invariant theory. We consider the action of $SL(3)$ and we relate the stability of a pencil to the stability of its…
Let $S$ be an oriented closed surface of genus at least two, and let $M = S \times (0,1)$. Suppose that $h$ is a Riemannian metric on $S$ with curvature strictly greater than $-1$, $h^{*}$ is a Riemannian metric on $S$ with curvature…
The global static stability of a Starling Resistor conveying non-Newtonian fluid is considered. The Starling Resistor consists of two rigid circular tubes and axisymmetric collapsible tube mounted between them. Upstream and downstream…
Stable ring vortex solitons, featuring a bright-shape, appear to be very rare in nature. However, here we show that they exist and can be made dynamically stable in defocusing cubic nonlinear media with an imprinted Bessel optical lattice.…
This article contains a self-contained proof of the stability under convolution of the space of resurgent functions associated with a closed discrete subset of the complex plane (the set of possible singularities), under the assumption that…
Two-dimensional phononic crystals (PnCs) formed by a periodic array of holes in a suspended membrane have previously been used to coherently control thermal conductance at low temperatures by modifying the phonon dispersion, thereby…
While the Born elastic stability criteria are well-known for cubic crystals, there is some confusion in the literature about the form it should take for lower symmetry crystal classes. We present here closed form necessary and sufficient…
We investigate positive definiteness, Hurwitz stability and Schur stability of parametric interval matrices. We give a verifiable sufficient condition for positive definiteness of parametric interval matrices with non-linear dependencies.…
Ultra-thin tri-color (tri-layer) titanate superlattices ([3u.c. LaTiO3/2u.c. SrTiO3/3u.c. YTiO3], u.c. = unit cells) were grown in a layer-by-layer way on single crystal TbScO3 (110) substrates by pulsed laser deposition. High sample…
We study three methods that prove the positivity of a natural numerical invariant associated to $1-$parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a…
Strong inter-particle interactions between polaritons have traditionally stemmed from their exciton component. In this work, we impart a strong photonic nonlinearity to a polaritonic mode by embedding a nonlinear polymethine dye within a…