Related papers: Strict Periodic Extreme Lattices
Understanding the dynamics of climate extreme is important in its prediction and modeling. In this study, linear trends in percentile, threshold, absolute, and duration based temperature and precipitation extremes indicator were obtained…
The response of precipitation extremes to climate change is considered using results from theory, modeling, and observations, with a focus on the physical factors that control the response. Observations and simulations with climate models…
Exceptional points (EPs) are spectral defects displayed by non-Hermitian systems in which multiple degenerate eigenvalues share a single eigenvector. This distinctive feature makes systems exhibiting EPs more sensitive to external…
We consider a family of periodic tight-binding models (combinatorial graphs) that have the minimal number of links between copies of the fundamental domain. For this family we establish a local condition of second derivative type under…
The set of all subracks $\mathcal{R}(X)$ of a finite rack $X$ form a lattice under inclusion. We prove that if a rack $X$ satisfies a certain condition then the homotopy type of the order complex of $\mathcal{R}(X)$ is a $(m-2)$-sphere,…
Stability of off-site vortex solitons in a photorefractive optical lattice is analyzed. It is shown that such solitons are linearly unstable in both the high and low intensity limits. In the high-intensity limit, the vortex looks like a…
Optical lattices are considered loaded by atoms or molecules that can exhibit strong interactions between different lattice sites. The strength of these interactions can be sufficient for generating collective phonon excitations above the…
Lattices and periodic point sets are well known objects from discrete geometry. They are also used in crystallography as one of the models of atomic structure of periodic crystals. In this paper we study the embedding properties of spaces…
A unifying description of lattice potentials generated by aperiodic one-dimensional sequences is proposed in terms of their local reflection or parity symmetry properties. We demonstrate that the ranges and axes of local reflection symmetry…
We define the notion of $\varepsilon$-flexible periodic point: it is a periodic point with stable index equal to two whose dynamics restricted to the stable direction admits $\varepsilon$-perturbations both to a homothety and a saddle…
A discrete set $A$ in the Euclidian space is almost periodic if the measure with the unite masses at points of the set is almost periodic in the weak sense. We investigate properties of such sets in the case when $A-A$ is discrete. In…
We propose a methodology for the homogenization of periodic elastic lattices that covers the case of unstable lattices, having affine (macroscopic) or periodic (microscopic) mechanisms. The singular cell problems that are encountered when a…
Higher-order exceptional points (EPs), which appear as multifold degeneracies in the spectra of non-Hermitian systems, are garnering extensive attention in various multidisciplinary fields. However, constructing higher-order EPs still…
The spatiotemporal complexity induced by perturbed initial excitations through the development of modulational instability in nonlinear lattices with or without disorder, may lead to the formation of very high amplitude, localized transient…
A periodic lattice in Euclidean space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by infinitely many different bases. This ambiguity was only partially resolved, but standard…
We address edge states and rich localization regimes available in the one-dimensional (1D) dynamically modulated superlattices, both theoretically and numerically. In contrast to conventional lattices with straight waveguides, the…
In the current paper we study extremal semilattices with respect to their equational properties. In the class $\mathbf{S}_n$ of all semilattices of order $n$ we find semilattices which have maximal (minimal) number of consistent equations.…
A lattice $\Lambda$ is said to be an extension of a sublattice $L$ of smaller rank if $L$ is equal to the intersection of $\Lambda$ with the subspace spanned by $L$. The goal of this paper is to initiate a systematic study of the geometry…
We study theoretically and numerically the microscopic cause of the mechanical stability of hard sphere glasses near their maximum packing. We show that, after coarse-graining over time, the hard sphere interaction can be described by an…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…