Related papers: Virtual Crystals and Nakajima Monomials
In this paper, local monomialization theorems are proven for analytic morphisms of complex and real analytic spaces. This gives the generalization of the local monomialization theorem for morphisms of algebraic varieties over a field of…
We consider the moduli spaces of quasimaps to zero-dimensional $A_{\infty}$ Nakajima quiver varieties. An explicit combinatorial formula for the equivariant Euler characteristic of these moduli spaces is obtained and applications to…
The new class of integrable mappings and chains is introduced. Corresponding (1+2) integrable systems invariant with respect to such discrete transformations are represented in explicit form. Soliton like solutions of them are represented…
Quasiperiodic magnonic crystals, in contrast to their periodic counterparts, lack strict periodicity which gives rise to complex and localised spin wave spectra characterized by numerous band gaps and fractal features. Despite their…
A new type of magnonic crystals, curvature induced ones, is realized in ferromagnetic nanowires with periodically deformed shape. A magnon band structure of such crystal is fully determined by its curvature: the developed theory is well…
Symmetry considerations are used in presenting a model of the electronic structure and the associated dynamics of the nitrogen-vacancy center in diamond. The model accounts for the occurrence of optically induced spin polarization, for the…
Following the recent discussion on the puzzling nature of the interactions in the nanotubular system Na2V3O7, we present a detailed ab-initio microscopic analysis of its electronic and magnetic properties. By means of a non-trivial…
This paper reviews the status of molecular dynamics as a method in describing solid-solid phase transitions, and its relationship to continuum approaches. Simulation work done in NiTi and Zr using first principles and semi-empirical…
A mutation operation for $\tau$-exceptional sequences of modules over any finite-dimensional algebra was recently introduced, generalising the mutation for exceptional sequences of modules over hereditary algebras. We interpret this…
The Cluster Variation Method (CVM) is applied to the Ishibashi model for ammonium dihydrogen phosphate ($\rm NH_{4}H_{2}PO_{4}$) of a typical hydrogen bonded anti-ferroelectric crystal. The staggered and the uniform susceptibility without…
The set of finite binary matrices of a given size is known to carry a finite type A bicrystal structure. We first review this classical construction, explain how it yields a short proof of the equality between Kostka polynomials and…
Computer simulations of simple model systems for liquid crystals are briefly reviewed, with special emphasis on systems of ellipsoids. First, we give an overview over some of the most commonly studied systems (ellipsoids, Gay-Berne…
In this paper we discuss algebraic, combinatorial and topological properties of singular virtual braids. On the algebraic side we state the relations between classical and virtual singular objects, in addition we discuss a Birman-like…
Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions, developing models for interface and grain boundary structures. In…
We give a description of the Namikawa-Weyl group of affinizations of smooth Nakajima quiver varieties using combinatorial data of the underlying quiver, and compute some explicit examples. This extends a result of McGerty and Nevins for…
In this article, we present a numerical study of the optical properties of a metal nanowire interacting with a localized cavity in a two dimensional photonic crystal. The nature of the modes, their wavelength and width are investigated as a…
In type A we find equivalences of geometries arising in three settings: Nakajima's (``framed'') quiver varieties, conjugacy classes of matrices and loop Grassmannians. These are now all given by explicit formulas. In particular, we embedd…
The exploration of solid-solid phase transition suffers from the uncertainty of how atoms in two crystal structures match. We devised a theoretical framework to describe and classify crystal-structure matches (CSM). Such description fully…
The dimensions of certain varieties defined by monomials are computed using only high school algebra.
This is a review of recent results on the integrable structure of the ordinary and modified melting crystal models. When deformed by special external potentials, the partition function of the ordinary melting crystal model is known to…