Related papers: Framing Lattices and Flow Polytopes
We present a hybrid lattice Boltzmann algorithm for the simulation of flow glass-forming fluids, characterized by slow structural relaxation, at the level of the Navier-Stokes equation. The fluid is described in terms of a nonlinear…
This is the first contribution of a sequence of papers introducing the notions of $s$-weak order and $s$-permutahedra, certain discrete objects that are indexed by a sequence of non-negative integers $s$. In this first paper, we concentrate…
We study the phase diagram of the Bose-Hubbard model on the kagome lattice with a broken sublattice symmetry. Such a superlattice structure can naturally be created and tuned by changing the potential offset of one sublattice in the optical…
We investigate equilibrium flux lattice structures in superconductors with unconventional order parameters, such as high-$T_c$ cuprates, using a generalized London model with non-local electrodynamics derived from a simple microscopic…
Covering a graph or a lattice with non-overlapping dimers is a problem that has received considerable interest in areas such as discrete mathematics, statistical physics, chemistry and materials science. Yet, the problem of percolation on…
This article aims to propose a novel analytical model for anisotropic multi-layer elliptical structures incorporating graphene layers. The multi-layer structure is formed of various magnetic materials. An external magnetic bias has been…
In topological photonics, artificial photonic structures are constructed for realizing nontrivial unidirectional propagation of photonic information. On the other hand, moir\'e superlattices are emerging as an important avenue for…
We introduce a new class of partial actions of free groups on totally disconnected compact Hausdorff spaces, which we call convex subshifts. These serve as an abstract framework for the partial actions associated with finite separated…
A non-perturbative algebraic theory of lattice Boltzmann method is developed based on a symmetry of a product. It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which…
This is the first paper in a series on intrinsic Donaldson-Thomas theory, where we develop a new framework for enumerative geometry that allows the generalization of constructions and results from linear moduli stacks to general non-linear…
We compute the dynamical polarization function for a graphene antidot lattice in the random-phase approximation. The computed polarization functions display a much more complicated structure than what is found for pristine graphene (even…
We study algebras encoding stable range branching rules for the pairs of complex classical groups of the same type in the context of toric degenerations of spherical varieties. By lifting affine semigroup algebras constructed from…
Optical lattices offer the possibility to investigate the superfluid properties of both Bose condensates and Fermionic superfluid gases. When a population imbalance is present in a Fermi mixture, this leads to frustration of the pairing,…
Rowmotion is a simple cyclic action on the distributive lattice of order ideals of a poset: it sends the order ideal x to the order ideal generated by the minimal elements not in x. It can also be computed in "slow motion" as a sequence of…
It is well known by analysts that a concept lattice has an exponential size in the data. Thus, as soon as he works with real data, the size of the concept lattice is a fundamental problem. In this chapter, we propose to investigate factor…
Stacking two layers of graphene with a relative twist angle gives rise to moir\'e patterns, which can strongly modify electronic behavior and may lead to unconventional superconductivity. A synthetic version of twisted bilayers can be…
Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symmetric edge polytopes for various models of random graphs.…
We study superfluidity of strongly repulsive fermionic atoms in optical lattices. The atoms are paired up through a correlated tunneling mechanism, which induces superfluidity when repulsive nearest-neighbor interactions are included in the…
The geometry of optical lattices can be engineered allowing the study of atomic transport along paths arranged in patterns that are otherwise difficult to probe in the solid state. A question readily accessible to atomic systems is related…
I present an overview of the research I have conducted for the past ten years in algebraic, bijective, enumerative, and geometric combinatorics. The two main objects I have studied are the permutahedron and the associahedron as well as the…