Related papers: A coupled surface-Cahn--Hilliard bulk-diffusion sy…
Biological membranes are known to form various structural motifs, from lipid bilayers to tubular filaments and networks facilitating e.g. adhesion and cell-cell communication. To understand the biophysical processes underpinning lipid-lipid…
We study the long-time dynamics of a bulk-surface convective Cahn--Hilliard system describing phase separation processes with bulk-surface interaction. The presence of convection terms leads to a non-autonomous dynamical system and prevents…
Coarse-grained continuous descriptions for lipid bilayers are typically based on minimizing the Helfrich energy. Such models consider the fluid properties of these structures only implicitly and have been shown to nicely reproduce…
Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity…
The study of vesicles in suspension is important to understand the complicated dynamics exhibited by cells in vivo and in vitro. We developed a computer simulation based on the boundary-integral method to model the three dimensional…
Liposomes that achieve a heterogeneous and spatially organized surface through phase separation have been recognized to be a promising platform for delivery purposes. However, their design and optimization through experimentation can be…
Cell proliferation and diffusion can be modeled through reaction-diffusion systems describing the space-time evolution of a density variable. In this work, we present non-linear transformations of heat equation solutions to model cellular…
Biomembranes, which are mainly composed of neutral and charged lipids, exhibit a large variety of functional structures and dynamics. Here, we report a coarse-grained molecular dynamics (MD) simulation of the phase separation and…
The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range…
The lateral diffusion of lipids within membrane is of paramount importance, serving as a central mechanism in numerous physiological processes including cell signaling, membrane trafficking, protein activity regulation, and energy…
Many ternary mixtures composed of saturated and unsaturated lipids with cholesterol (Chol) exhibit a region of coexistence between liquid-disordered $(L_d)$ and liquid-ordered $(L_o)$ domains, bearing some similarities to lipid rafts in…
The behavior of lipid bilayer is important to understand the functionality of cells like the trafficking of ions between cells. Standard procedures to explore the properties of lipid bilayer and hemifused states typically use either…
In this paper we present a derivation and multiscale analysis of a mathematical model for plant cell wall biomechanics that takes into account both the microscopic structure of a cell wall coming from the cellulose microfibrils and the…
In this work, we consider a diffuse interface model for tumour growth in the presence of a nutrient which is consumed by the tumour. The system of equations consists of a Cahn--Hilliard equation with source terms for the tumour cells and a…
A diffused interface model describing the evolution of two conterminous incompressible fluids in a porous medium is discussed. The system consists of the Cahn-Hilliard equation with Flory-Huggins logarithmic potential, coupled via surface…
Pair interactions between active particles need not follow Newton's third law. In this work we propose a continuum model of pattern formation due to non-reciprocal interaction between multiple species of scalar active matter. The classical…
We consider the formation of finite-size domains in lipid bilayers consisting of saturated and hybrid lipids. First, we describe a monolayer model that includes a coupling between a compositional scalar field and a two-dimensional vectorial…
We employ a molecular model to study a ternary mixture of saturated lipid, with tails of sixteen carbons, a mono unsaturated lipid with tails of eighteen carbons, and cholesterol. The model, solved within mean-field theory, produces several…
This article examines the dynamic phase transitions and pattern formations attributed to binary systems modeled by the Cahn-Hilliard equation. In particular, we consider a two-dimensional lattice structure and determine how different…
In this paper we propose a mathematical model of phase separation for a quasi-incompressible binary mixture where the spinodal decomposition is induced by an heat flux governed by the Cattaneo-Maxwell equation. As usual, the phase…