Related papers: Virtual Crystals and Nakajima Monomials
The evolution of skyrmion crystal encapsulates skyrmion critical behaviors, such as nucleation, deformation and annihilation. Here, we achieve a tunable evolution of artificial skyrmion crystal in nanostructured synthetic antiferromagnet…
Modeling the atomic structure of amorphous materials has long been a critical challenge in materials science. Recent advances in monolayer amorphous materials enable direct observation of their atomic structures, paving the way for a better…
This paper presents a matrix of 206 snow crystal growth observations as a function of temperature and water vapor supersaturation in air, each illustrating the morphology and size of a crystal forming on the tip of an isolated c-axis ice…
The model presented in this research predicts ideal chiral crystal and propose a new direction of designing chiral crystals. Skyrmions are topologically protected and structurally assymetric materials with an exotic spin composition. This…
In this paper, we introduce the notion of abstract crystals for quantum generalized Kac-Moody algebras and study their fundamental properties. We then prove the crystal embedding theorem and give a characterization of the crystals…
We use Kashiwara's theory of crystal bases to study the plactic monoid for type C. Then we describe the correponding sliding and bumping algorithms.
The crystal base of the modified quantized enveloping algebras of type $A_{+\infty}$ or $A_\infty$ is realized as a set of integral bimatrices. It is obtained by describing the decomposition of the tensor product of a highest weight crystal…
Modern three-dimensional nanofabrication methods make it possible to generate arbitrarily shaped nanomagnets, including periodic networks of interconnected magnetic nanowires. Structurally similar to optical or acoustic metamaterials, these…
We develop a relativistic variational model for a nematic liquid crystal interacting with an electro- magnetic field. The constitutive relation for a general anisotropic uniaxial diamagnetic and dielectric medium is analyzed. We discuss…
We present a geometric construction of highest weight crystals for quantum generalized Kac-Moody algebras. It is given in terms of the irreducible components of certain Lagrangian subvarieties of Nakajima's quiver varieties associated to…
The room temperature structure of aluminum, copper and gold infinite nanowires is studied. The molecular dynamics simulation method and the same type of the embedded atom potentials made by Voter and coworkers are used. It was found that…
We construct an explicit basis for the coordinate ring of the Bott-Samelson variety Z_i associated to G = GL(n) and an arbitrary sequence of simple reflections i. Our basis is parametrized by certain standard tableaux and generalizes the…
We discuss Cauchy type decompositions of crystal graphs for general linear Lie superalgebras. More precisely, we consider bicrystal graph structures on various sets of matrices of non-negative integers, and obtain their decompositions with…
We define new crystal maps on $B(\infty)$ using its polyhedral realization, and show that the crystal $B(\infty)$ equipped with the new crystal maps is isomorphic to Kashiwara's $B(\infty)$ as bicrystals. In addition, we combinatorially…
We investigate one-dimensional periodic chains of alternate type of particles interacting through mirror symmetric potentials. The optimality of the equidistant configuration at fixed density -- also called crystallization -- is shown in…
Truncated shifted Yangians are a family of algebras which are natural quantizations of slices in the affine Grassmannian. We study the highest weight representations of these algebras. In particular, we conjecture that the possible highest…
Through extensive molecular simulations we determine a phase diagram of attractive, flexible polymer chains in two and three dimensions. A surprisingly rich collection of distinct crystal morphologies appear, which can be finely tuned…
We discuss Vassiliev invariants for virtual knots, expanding upon the theory of quantum virtual knot invariants developed in arXiv:1509.00578. In particular, following the theory of quantum invariants we work with 'rotational' virtual…
We give a new algorithm for merging sorted lists of monomials. Together with a projection technique we obtain a new complexity bound for the BM-algorithm.
We study modules with 1-dimensional socle for preprojective algebras for type A quivers. In particular, we classify such modules, determine all homomorphisms between them, and then explain how they may be used to describe the components of…