Related papers: Discrete Folding
As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility.…
We study the transverse cracking of the 90 degree ply in [0/90] cross-ply laminates by means of a discrete element method. To model the 90 degree ply a two-dimensional triangular lattice of springs is constructed where nodes of the lattice…
The coupled evolution of an eroding cylinder immersed in a fluid within the subcritical Reynolds range is explored with scale resolving simulations. Erosion of the cylinder is driven by fluid shear stress. K\'arm\'an vortex shedding…
Anisotropic D-dimensional polymerized phantom membranes are investigated within a nonperturbative renormalization group (NPRG) framework. One focuses on the transition between a high-temperature, crumpled, phase and a low-temperature,…
The mechanical properties of thermally excited two-dimensional crystalline membranes can depend dramatically on their geometry and topology. A particularly relevant example is the effect on the crumpling transition of holes in the membrane.…
A folding of a branched cover of the 3-sphere that is branched over a knot is a continuous map of the cover into the product of the sphere with a disk that has the property that the projection onto the sphere factor induces the covering.…
Aiming at the study of critical phenomena in the presence of boundaries with a non-trivial shape we discuss how lattices with an adaptive lattice spacing can be implemented. Since the parameters of the Hamiltonian transform non-trivially…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
We investigate the crumpling of a sheet as it is repeatedly crushed onto itself by rolling it into a cylinder and twisting it axially while allowing the end-to-end length to evolve freely. As deduced from its plastic deformations, the sheet…
A tethered surface model is investigated by using the canonical Monte Carlo simulation technique on a torus with an intrinsic curvature. We find that the model undergoes a first-order phase transition between the smooth phase and the…
We suggest a 3D phase field model to describe 3D cell spreading on a flat substrate. The model is a simplified version of a minimal model that was developed in [1]. Our model couples the order parameter $u$ with 3D polarization…
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,…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…
The main purpose of the paper is to demonstrate that condition of invariance with respect to the Legendre transformations allows effectively isolate the class of integrable difference equations on the triangular lattice, which can be…
We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differential equations. In particular, we study the correspondence…
In this paper, we present a principled method to model general planar sliding motion with distributed convex contact patch. The effect of contact patch with indeterminate pressure distribution can be equivalently modeled as the contact…
A laterally confined thin elastic sheet lying on a liquid substrate displays regular undulations, called wrinkles, characterized by a spatially extended energy distribution and a well-defined wavelength $\lambda$. As the confinement…
The suppression of antiferromagnetic ordering in geometrically frustrated Hubbard models leads to a variety of exotic quantum phases including quantum spin liquids and chiral states. Here, we focus on the Hubbard model on one of the…
We study the mechanism of loop condensation in the quantum dimer model on the triangular lattice. The triangular lattice quantum dimer model displays a topologically ordered quantum liquid phase in addition to conventionally ordered phases…
The moduli space of triangles is a two-dimensional space that records triangle shapes in the plane, considered up to similarity. We study the subset corresponding to \textit{lattice triangles}, which are triangles whose vertices have…