Related papers: An Analysis on the Shape Equation for Biconcave Ax…
The classification of the possible equilibrium shapes that a self-gravitating fluid can take in a Riemannian manifold is a classical problem in mathematical physics. In this paper it is proved that the equilibrium shapes are isoparametric…
In this paper, the dynamics of spontaneous shape fluctuations of a single, giant quasi-spherical vesicle formed of a single lipid species is revisited theoretically. A coherent physical theory for the dynamics is developed based on a number…
When a colloidal particle adheres to a fluid membrane, it induces elastic deformations in the membrane which oppose its own binding. The structural and energetic aspects of this balance are theoretically studied within the framework of a…
The instability and periodic deformation of bilayer membranes during freezing processes are studied as a function of the difference of the shape energy between the high and the low temperature membrane states. It is shown that there exists…
In flat geometries, two dimensional hexatic order has only a minor effect on capillary waves on a liquid substrate and on undulation modes in lipid bilayers. However, extended bond orientational order alters the long wavelength spectrum of…
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 behavior of an elastic curve bound to a surface will reflect the geometry of its environment. This may occur in an obvious way: the curve may deform freely along directions tangent to the surface, but not along the surface normal.…
In this paper, we first develop a mathematical model for long-range, hydrophobic attraction between amphiphilic particles. The non-pairwise interactions follow from the first variation of a hydrophobic attraction domain functional. The…
We study the effect of changes in the parameters of a two-dimensional potential energy surface on the phase space structures relevant for chemical reaction dynamics. The changes in the potential energy are representative of chemical…
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…
An overview of some analytical approaches to the computation of the structural and thermodynamic properties of single component and multicomponent hard-sphere fluids is provided. For the structural properties, they yield a thermodynamically…
We consider a well known model for lipid-bilayer membrane vesicles exhibiting phase separation, incorporating a phase field with finite curvature elasticity. We prove the existence of a plethora of equilibria, corresponding to…
The dynamics of amphiphilic films deposited on a solid surface is analyzed for the case when shear oscillations of the solid surface are excited. The two cases of surface- and bulk shear waves are studied with film exposed to gas or to a…
In [12], the authors studied a particular class of equilibrium solutions of the Helfrich energy which satisfy a second order condition called the reduced membrane equation. In this paper we develop and apply a second variation formula for…
Soft elastic capsules which are driven through a viscous fluid undergo shape deformation coupled to their motion. We introduce an iterative solution scheme which couples hydrodynamic boundary integral methods and elastic shape equations to…
In this paper, flows of a viscid fluids on curves are considered. Symmetry algebras and the corresponding fields of differential invariants are found. We study their dependence on thermodynamic states of media, and provide classification of…
A thermodynamically consistent phase-field model is introduced for simulating motion and shape transformation of vesicles under flow conditions. In particular, a general slip boundary condition is used to describe the interaction between…
A geometric interpretation is given for certain elliptic-hyperbolic systems in the plane. Among several examples, one which reduces in the elliptic region to the equations for harmonic 1-forms on the projective disc is studied in detail. A…
The mechanical properties of biological membranes play an important role in the structure and the functioning of living organisms. One of the most widely used methods for determination of the bending elasticity modulus of the model lipid…
Existence and regularity of minimizers for a geometric variational problem is shown. The variational integral models an energy contribution of the interface between two immiscible fluids in the presence of surfactants and includes a…