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The stability of the recently discovered compacton solutions is studied by means of both linear stability analysis as well as Lyapunov stability criteria. From the results obtained it follows that, unlike solitons, all the allowed compacton…
Quantitative stability for crystalline anisotropic perimeters, with control on the oscillation of the boundary with respect to the corresponding Wulff shape, is proven for $n\geq 3$. This extends a result of [Neu16] in $n=2$.
We find computable criteria for stability of symplectic leaves of Poisson manifolds. Using Poisson geometry as an inspiration, we also give a general criterion for stability of leaves of Lie algebroids, including singular ones. This not…
We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.
We construct a subset of the space of stability conditions for any projective threefold with an ample polarization that satisfies a certain Bogomolov-Gieseker inequality to refine the result in arXiv:1410.1585. Then, we demonstrate that the…
We investigate the dynamics of cellular solidification patterns using three-dimensional phase-field simulations. The cells can organize into stable hexagonal patterns or exhibit unsteady evolutions. We identify the relevant secondary…
We present a one dimensional model for the nonlinear response of a colloidal crystal to intense light illumination along a high symmetry direction. The strong coupling between light and the colloidal lattice, via the electric gradient force…
Crystalline solids with extreme insulation often exhibit a plateau or even an upward-sloping tail in thermal conductivity above room temperature. Herein, we synthesized a crystalline material AgTl$_2$I$_3$ with an exceptionally low thermal…
In this work stability of polygonal configurations on a plane and sphere is investigated. The conditions of linear stability are obtained. A nonlinear analysis of the problem is made with the help of Birkhoff normalization. Some problems…
We demonstrate a robust, stable, mobile, two-dimensional (2D) spatial and three-dimensional (3D) spatiotemporal optical soliton in the core of an optical vortex, while all nonlinearities are of the cubic (Kerr) type. The 3D soliton can…
We follow a polynomial approach to analyse strong stability of linear difference equations with rationally independent delays. Upon application of the Hermite stability criterion on the discrete-time homogeneous characteristic polynomial,…
The existing experiments and simulations suggest that the molecular symmetry is always transmitted to homogeneous phases in liquid crystals. It has been proved for rod-like molecules. We conjecture that it holds for three other symmetries,…
We study the stability of switched systems where the dynamic modes are described by systems of higher-order linear differential equations not necessarily sharing the same state space. Concatenability of trajectories at the switching…
For each lattice complex hyperbolic triangle group, we study the Fuchsian stabilizer of a reprentative of each group orbit of mirrors of complex reflections. We give explicit generators for the stabilizers, and compute their signature in…
Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states which are either circular or straight are investigated analytically and illustrated by…
Symmetry of the crystal lattice can be a determining factor for the structure of Cooper pairs in unconventional superconductors. In this study we extend the discussion of superconductivity in non-centrosymmetric materials to the case when…
We obtain sharp criteria for transverse stability and instability of line solitons in the discrete nonlinear Schr\"{o}dinger equations on one- and two-dimensional lattices near the anti-continuum limit. On a two-dimensional lattice, the…
Extensively evaluating the capabilities of (large) language models is difficult. Rapid development of state-of-the-art models induce benchmark saturation, while creating more challenging datasets is labor-intensive. Inspired by the recent…
The stability and the critical properties of the three-dimensional vortex-glass order in random type-II superconductors with point disorder is investigated in the unscreened limit based on a lattice {\it XY} model with a uniform field. By…
We make use of the previously developed formalism for a monomer ensemble and include angular dependence of the segments of the polymer chains thus described. In particular we show how to deal with stiffness when the polymer chain is…