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The coincidence site lattices (CSLs) of prominent 4-dimensional lattices are considered. CSLs in 3 dimensions have been used for decades to describe grain boundaries in crystals. Quasicrystals suggest to also look at CSLs in dimensions…

We study classical hard-core dimer models on three-dimensional lattices using analytical approaches and Monte Carlo simulations. On the bipartite cubic lattice, a local gauge field generalization of the height representation used on the…

We initiate a systematic study of lattices of thick subcategories for arbitrary essentially small triangulated categories. To this end we give several examples illustrating the various properties these lattices may, or may not, have and…

Tracking of plant cells in images obtained by microscope is a challenging problem due to biological phenomena such as large number of cells, non-uniform growth of different layers of the tightly packed plant cells and cell division.…

Multiphase field models have emerged as an important computational tool for understanding biological tissue while resolving single-cell properties. While they have successfully reproduced many experimentally observed behaviors of living…

Stochastic models for the development of cracks in 1 and 2 dimensional objects are presented. In one dimension, we focus on particular scenarios for interacting and non-interacting fragments during the breakup process. For two dimensional…

Here, we investigate the fractal-lattice Hubbard model using various numerical methods: exact diagonalization, the self-consistent diagonalization of a (mean-field) Hartree-Fock Hamiltonian and state-of-the-art Auxiliary-Field Quantum Monte…

Measuring comodules are defined and shown to provide a useful generalization of the set of maps between modules with a broad range of applications. Three applications are described. Connections on bundles are described in terms of measuring…

The dynamics of globally coupled map lattices can be described in terms of a nonlinear Frobenius--Perron equation in the limit of large system size. This approach allows for an analytical computation of stationary states and their…

We calculate the lattice dispersion relation for three dimensional simulations of scalar fields. We argue that the mode frequency of scalar fields on the lattice should not be treated as a function of the magnitude of its wavevector but…

The phase field crystal model allows the study of materials on atomic length and diffusive time scales. It accounts for elastic and plastic deformation in crystal lattices, including several processes such as growth, dislocation dynamics,…

A random matrix model to describe the coupling of m-fold symmetry in constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that…

We investigate the phase diagrams of two-dimensional lattice dipole systems with variable geometry. For bipartite square and triangular lattices with tunable vertical sublattice separation, we find rich phase diagrams featuring a sequence…

The multifractal spectrum of various three-dimensional representations of Packed Swiss Cheese cosmologies in open, closed, and flat spaces are measured, and it is determined that the curvature of the space does not alter the associated…

This is an experimental case study in real algebraic geometry, aimed at computing the image of a semialgebraic subset of 3-space under a polynomial map into the plane. For general instances, the boundary of the image is given by two highly…

We propose a new, efficient multi-scale method to decompose a map (or signal in general) into components maps that contain structures of different sizes. In the widely-used wave transform, artifacts containing negative values arise around…

We investigate the iterative construction of discrete Laplacians on 2D square lattices, revealing emergent fractal-like patterns shaped by modular arithmetic. While classical 2222-style iterations reproduce known structures such as the…

In this paper, we introduce a three-dimensional mathematical model of collagen contraction with microbuckling based on the two-dimensional model previously developed by the authors. The model both qualitatively and quantitatively replicates…

This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We…

Three-dimensional shell-like structures can be obtained spontaneously at the microscale from the self-folding of 2D templates of rigid panels. At least for simple structures, the motion of each panel is consistent with a Brownian process…