Related papers: Three-dimensional Folding of the Triangular Lattic…
A model is presented consisting of triangular trimers on the triangular lattice. In analogy to the dimer problem, these particles cover the lattice completely without overlap. The model has a honeycomb structure of hexagonal cells separated…
We develop a model and numerical method to study the large-amplitude flutter of rectangular membranes (of zero bending rigidity) that shed a trailing vortex-sheet wake in a three-dimensional (3D) inviscid fluid flow. We apply small initial…
Triangle-hinge models [arXiv:1503.08812] are introduced to describe worldvolume dynamics of membranes. The Feynman diagrams consist of triangles glued together along hinges and can be restricted to tetrahedral decompositions in a large N…
A recently introduced model describing the folding of the triangular lattice is generalized allowing for defects in the lattice and written as an Ising model with nearest-neighbor and plaquette interactions on the honeycomb lattice. Its…
Triangulations are important objects of study in combinatorics, finite element simulations and quantum gravity, where its entropy is crucial for many physical properties. Due to their inherent complex topological structure even the number…
We report on a result on quantum electrodynamics on a three dimensional Euclidean spacetime. The model is formulated on a toroidal lattice with unit volume and variable lattice spacing. The result is that the renormalized partition function…
We present the results of a large-scale simulation of a Dynamically Triangulated Random Surface with extrinsic curvature embedded in three-dimensional flat space. We measure a variety of local observables and use a finite size scaling…
In a recent paper S. Friedland and the author presented a formal expression for lambda_d(p) of the monomer-dimer problem on a d-dimensional rectangular lattice, which involved a power series in p. Herein, we find simlar expressions for…
We study numerically the curvature tensor in a three-dimensional discrete space. Starting from the continuous metric of a three-sphere, we transformed it into a discrete space using three integers $n_1, n_2$, and $n_3$. The numerical…
We propose an approach to find constant curvature metrics on triangulated closed 3-manifolds using a finite dimensional variational method whose energy function is the volume. The concept of an angle structure on a tetrahedron and on a…
We show that the two-dimensional density-matrix renormalization analysis is useful to detect the symmetry breaking in the fermionic model on a triangular lattice. Under the cylindrical boundary conditions with chemical potentials on edge…
Three-dimensional (3D) printing is a powerful development tool both in industry, as well as in biomedical research. Additive-lathe 3D printing is an emerging sub-class of 3D printing whereby material is layered outward from the surface of a…
The tilings of lozenges in 2 dimensions and of rhomboedra in 3 dimensions are studied when they are constrained by fixed boundary conditions. We establish a link between those conditions and free or periodic boundary ones: the entropy is…
We introduce and study the behavior of a tethered membrane of non-zero thickness embedded in three dimensions subject to an effective self-attraction induced by hydrophobicity arising from the tendency to minimize the area exposed to a…
The dynamics of compaction of hard cross-shaped pentamers on the 2D square lattice is investigated. The addition of new particles is controlled by diffusive relaxation. It is shown that the filling process terminates at a glassy phase with…
The kinetic behavior of a three-dimensional off-lattice heteropolymer model is studied in terms of the time dependence of the average mean-square displacement between configurations. It is found that at short time-scales similar behavior is…
This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…
The biological membrane, which compartmentalizes the cell and its organelles, exhibit wide variety of macroscopic shapes of varying morphology and topology. A systematic understanding of the relation of membrane shapes to composition,…
We present a detailed study of the combinatorial interpretation of matrix integrals, including the examples of tessellations of arbitrary genera, and loop models on random surfaces. After reviewing their methods of solution, we apply these…
In this paper we present a three-dimensional discrete model governing the deformation of a viral capsid, modelled as a regular icosahedron and subjected not to cross a given flat rigid surface on which it initially lies in correspondence of…