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Cylindrical interfaces occur in sheared or deformed emulsions and as biological or technological lipid monolayer or bilayer tubules. Like the corresponding spherical droplets and vesicles, these cylinder-like surfaces may host orientaional…
Biomembranes, primarily composed of lipid bilayers, are not merely passive barriers but dynamic and complex materials whose shapes are governed by the principles of soft matter physics. This review explores the shape problem in biomembranes…
Rigidity transitions in simple models of confluent cells have been a powerful organizing principle in understanding the dynamics and mechanics of dense biological tissue. In this work we explore the interplay between geometry and rigidity…
Biomembranes and vesicles consisting of multiple phases can attain a multitude of shapes, undergoing complex shape transitions. We study a Cahn--Hilliard model on an evolving hypersurface coupled to Navier--Stokes equations on the surface…
This review reports some key results in theoretical investigations on configurations of lipid membranes and presents several challenges in this field which involve (i) exact solutions to the shape equation of lipid vesicles; (ii) exact…
Understanding interactions between membranes requires measurements on well-controlled systems close to natural conditions, in which fluctuations play an important role. We have determined, by grazing incidence X-ray scattering, the…
We consider the mass preserving $L^2$-gradient flow of the strong scaling of the functionalized Cahn Hilliard gradient flow and establish the nonlinear stability of a manifold comprised of quasi-equilibrium bilayer \muckmucks up to the…
The structure of membrane-active peptides and their interaction with lipid bilayers can be studied in oriented lipid membranes deposited on solid substrates. Such systems are desirable for a number of surface-sensitive techniques. Here we…
We propose a unifying phase-space approach to the construction of mutually unbiased bases for a two-qubit system. It is based on an explicit classification of the geometrical structures compatible with the notion of unbiasedness. These…
Scattering structure factors provide essential insight into material properties and are routinely obtained in experiments, computer simulations, and theoretical analyses. Different approaches favor different geometries of the material. In…
We present a simple, and physically motivated, coarse-grained model of a lipid bilayer, suited for micron scale computer simulations. Each ~25 nm^2 patch of bilayer is represented by a spherical particle. Mimicking forces of hydrophobic…
Here we study the shapes of droplets captured between chemically distinct parallel plates. This work is a preliminary step toward characterizing the influence of second-phase bridging between biomolecular surfaces on their solution…
Changes in the geometry and topology of self-assembled membranes underlie diverse processes across cellular biology and engineering. Similar to lipid bilayers, monolayer colloidal membranes have in-plane fluid-like dynamics and out-of-plane…
In this work, we study a phase-field model for curvature-driven pattern formation in biomembranes. The model is derived as a gradient flow of an energy functional that approximates the two-phase Canham--Helfrich energy. This leads to a…
Many cell functions require a concerted effort from multiple membrane proteins, for example, for signaling, cell division, and endocytosis. One contribution to their successful self-organization stems from the membrane deformations that…
Soft interfaces formed by lipid membranes are fundamental to living cells, synthetic cells, and membrane-based soft materials. However, a quantitative framework linking molecular organization with nonlinear interfacial mechanics remains…
We consider a discrete-continuum model of a biomembrane with embedded particles. While the membrane is represented by a continuous surface, embedded particles are described by rigid discrete objects which are free to move and rotate in…
Lipid membranes regulate the flow of materials and information between cells and their organelles. Further, lipid composition and morphology can play a key role in regulating a variety of biological processes. For example, viral uptake,…
This article summarizes a variety of physical mechanisms proposed in the literature, which can generate micro- and nanodomains in multicomponent lipid bilayers and biomembranes. It mainly focusses on lipid-driven mechanisms that do not…
Shapes of planar lipid monolayer domains at the air-water interface are theoretically and numerically investigated by minimizing the formation energy of the domains which consist of the surface energy, line tension energy, and dipole…