Related papers: The flat phase of fixed-connectivity membranes
The description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach from the literature is shown to fail to produce the correct…
In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the…
We analyze a restricted SOS model on a square lattice with nearest and next-nearest neighbor interactions, using Monte Carlo techniques. In particular, the critical exponents at the preroughening transition between the flat and disordered…
We report a numerical simulation for the phase diagram of a simple two dimensional model, similar to one proposed by Noro and Frenkel [J. Chem. Phys. \textbf{114}, 2477 (2001)] for membrane proteins, but one that includes the role of the…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
We discuss the results of a study of restricted solid-on-solid models for fcc (110) surfaces. These models are simple modifications of the exactly solvable BCSOS model, and are able to describe a $(2\times 1)$ missing-row reconstructed…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
We study the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable layer (e.g., bedrock).…
We set up the statistical mechanics for a nearly flat, thermally equilibrated fluid membrane, attached to an elastic network through one of its sides. We predict that the resulting structural (inversion) asymmetry of the membrane, notably…
We address the problem of "phantom" folding of the tethered membrane modelled by the two-dimensional square lattice, with bonds on the edges and diagonals of each face. Introducing bending rigidities $K_1$ and $K_2$ for respectively long…
We report a numerical simulation of the phase diagram of a simple model for membrane proteins constrained to move in a plane. In analogy with the corresponding three dimensional models, the liquid-gas transition becomes metastable as the…
How can dense biological tissue maintain sharp boundaries between coexisting cell populations? We explore this question within a simple vertex model for cells, focusing on the role of topology and tissue surface tension. We show that the…
In this work, we present a computational formulation based on continuum mechanics to study the interaction of fluid membranes embedded with semiflexible filaments. This is motivated by systems in membrane biology, such as cytoskeletal…
One of the major problems in the theory of the porous medium equation is the regularity of the solutions and the free boundaries. Here we assume flatness of the solution in space time cylinder and derive smoothness of the interface after a…
We describe a phase transition that gives rise to structurally non-trivial states in a two-dimensional ordered network of particles connected by harmonic bonds. Monte Carlo simulations reveal that the network supports, apart from the…
We discuss the flatness property of some fiber type contractions of complex smooth projective varieties of arbitrary dimensions. We relate the flatness of some morphisms having one-dimensional fibers with their conic bundles structures,…
In multicomponent membranes, internal scalar fields may couple to membrane curvature, thus renormalizing the membrane elastic constants and destabilizing the flat membranes. Here, a general elasticity theory of membranes is considered that…
We consider a mixture of one neutral and two oppositely charged types of molecules confined to a surface. Using analytical techniques and molecular dynamics simulations, we construct the phase diagram of the system and exhibit the…
Interactions mediated by the cell membrane between inclusions, such as membrane proteins or antimicrobial peptides, play important roles in their biological activity. They also constitute a fascinating challenge for physicists, since they…
The unbinding properties of an interface near structured wedges are investigated by discrete models with short range interactions. The calculations demonstrate that interface unbinding take place in two stages: $i$) a continuous…