相关论文: Rigidity and stability of spheres in the Helfrich …
A cell membrane can be simply regarded as composite material consisting of lipid bilayer, membrane cytoskeleton beneath lipid bilayer, and proteins embedded in lipid bilayer and linked with membrane cytoskeleton if one only concerns its…
Amphiphilic polymers in aqueous solutions can self-assemble to form bilayer membranes, and their elastic properties can be captured by the well-known Helfrich model involving several elastic constants. In this paper, we employ the…
In this article we review the present knowledge on the elastic properties of membranes of biological origin. Assuming the fluid mosaic hypothesis, we consider the phospholipid bilayer as the structural base of a biological membrane. We…
We theoretically study the elastic deformation of a fluid membrane induced by an adhering spherical colloidal particle within the framework of a Helfrich energy. Based on a full optimization of the membrane shape we find a continuous…
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…
The Helfrich energy is commonly used to model the elastic bending energy of lipid bilayers in membrane mechanics. The governing differential equations for certain geometric characteristics of the shape of the membrane can be obtained by…
In the context of Rosenfeld's Fundamental Measure Theory, we show that the bending rigidity is not equal to zero for a hard-sphere fluid in contact with a curved hard wall. The implication is that the Hadwiger Theorem does not hold in this…
Recent theoretical advances in elasticity of membranes following Helfrich's famous spontaneous curvature model are summarized in this review. The governing equations describing equilibrium configurations of lipid vesicles, lipid membranes…
The Helfrich model is a fundamental tool for determining the morphology of biological membranes. We relate the geometry of an important class of its equilibria to the geometry of sessile and pendant drops in the hyperbolic space ${\bf…
The buckling instabilities of core-shell systems, comprising an interior elastic sphere, attached to an exterior shell, have been proposed to underlie myriad biological morphologies. To fully discuss such systems, however, it is important…
The energetically most efficient way how a deformed red blood cell regains equilibrium is mathematically described by the gradient flow of the Canham-Helfrich functional, including a spontaneous curvature and the conservation of surface…
Using the density functional formalism we derive expression for the distortion free energy for systems with continuous broken symmetry and use it to derive expression for the elastic constants of smectic phases in which director is tilted…
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…
The so-called ``symplectic method'' is used for studying the linear stability of a self-gravitating collisionless stellar system, in which the particles are also submitted to an external potential. The system is steady and spherically…
The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent field theory, applied to a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents. Examining the…
Using fully minimized fundamental measure functionals, we investigate free energies, vacancy concentrations and density distributions for bcc, fcc and hcp hard-sphere crystals. Results are complemented by an approach due to Stillinger which…
The Helfrich bending energy plays an important role in providing a mechanism for the conformation of a lipid vesicle in theoretical biophysics, which is governed by the principle of energy minimization over configurations of appropriate…
In this paper we consider the evolution of regular closed elastic curves $\gamma$ immersed in $\R^n$. Equipping the ambient Euclidean space with a vector field $\ca:\R^n\rightarrow\R^n$ and a function $f:\R^n\rightarrow\R$, we assume the…
We develop a self-consistent free-energy framework in which membrane shape and osmotic pressure are determined simultaneously in a finite reservoir by minimizing bending elasticity and solute entropy. Solute conservation makes osmotic…
Hydrodynamics can be consistently formulated on surfaces of arbitrary co-dimension in a background space-time, providing the effective theory describing long-wavelength perturbations of black branes. When the co-dimension is non-zero, the…