Related papers: Closed Colored Models and Demazure Crystals
We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositions of these ideals and, for certain subclasses of models,…
This article present the double-periodical lattice made of infinite elastic fibers that withstand bending and tension. The model describes the elastic properties of flat periodic structure. With this model the behavior of a two-dimensional…
The internal structure of adhesive tapes determines the effective mechanical properties. This holds true especially for blended systems, here consisting of acrylate and rubber phases. In this note, we propose a lattice-based model to study…
A real-space approach for the calculation of the Moir\'e lattice parameters for superstructures formed by a set of rotated hexagonal 2D crystals such as graphene or transition-metal dichalcogenides, is presented. Apparent Moir\'e lattices…
We present a computer simulation study on crystal nucleation and growth in supersaturated suspensions of mono-disperse hard spheres induced by a triangular lattice substrate. The main result is that compressed substrates are wet by the…
We describe how to design a large class of always on spin-1 interactions between polar molecules trapped in an optical lattice. The spin degrees of freedom correspond to the hyperfine levels of a ro-vibrational ground state molecule.…
In this paper we primarily study monomial ideals and their minimal free resolutions by studying their associated LCM lattices. In particular, we formally define the notion of coordinatizing a finite atomic lattice P to produce a monomial…
This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…
Topological crystalline insulator (TCI) is one of the symmetry-protected topological states. Any TCI can be deformed into a simple product state of several decoupled two-dimensional (2D) topologically nontrivial layers in its lattice…
A data driven computational model that accounts for more than two material states has been presented in this work. Presented model can account for multiple state variables, such as stresses, strains, strain rates and failure stress, as…
The world of two-dimensional crystals is of great significance for the design and study of structural and functional materials with novel properties. The world of two-dimensional crystals is of great significance for the design and study of…
The ability to manipulate polar entities with multiple external fields opens exciting possibilities for emerging functionalities and novel applications in spin systems, photonics, metamaterials, and soft matter. Liquid crystals (LCs),…
We consider the affine Lie algebra $\widehat{\mathfrak{sl}_2}$ and the Kostant-Kumar submodules of tensor products of its level 1 highest weight integrable representations. We construct crystals for these submodules in terms of the charged…
We predict the existence of a new defect-lattice phase near the nematic - smectic-C (NC) transition. This tilt- analogue of the blue phase is a lattice of double-tilt cylinders. We discuss the structure and stability of the cone phase. We…
We analyze the possibility of heavy-light tetraquark bound states by means of a chiral constituent quark model. The study is done in a variational approach. Special attention is paid to the contribution given by the different terms of the…
We investigate the pairing and crystalline instabilities of bosonic and fermionic polar molecules confined to a ladder geometry. By means of analytical and quasi-exact numerical techniques, we show that gases of composite molecular dimers…
Phase diagram of a two-dimensional system with a potential which stabilizes Kagome lattice is calculated. It is shown that this system demonstrate a set of crystalline and the regions of stability of these phases are calculated. The…
We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry protected topological states can be…
This is a review of the authors' recent results on an integrable structure of the melting crystal model with external potentials. The partition function of this model is a sum over all plane partitions (3D Young diagrams). By the method of…
A lattice model with soft repulsion followed by attraction is developed for a monolayer of hybrid core-shell particles self-assembling at an interface. The model is solved exactly in one dimension. One, two or three periodic structures and…