Related papers: On the Equilibrium Shape of Erythrocytes
The parametric equations of the plane curves determining the equilibrium shapes that a uniform inextensible elastic ring or tube could take subject to a uniform hydrostatic pressure are presented in an explicit analytic form. The…
Most of the intra-cellular events involved in the initiation and propagation phases of this process has now been identified astrocytes. The control of the spread of intracellular calcium signaling has been demonstrated to occur at several…
A set in the Euclidean plane is said to be biconvex if, for some angle $\theta\in[0,\pi/2)$, all its sections along straight lines with inclination angles $\theta$ and $\theta+\pi/2$ are convex sets (i.e, empty sets or segments).…
In this paper we consider the isoperimetric profile of convex cylinders $K\times\mathbb{R}^q$, where $K$ is an $m$-dimensional convex body, and of cylindrically bounded convex sets, i.e, those with a relatively compact orthogonal projection…
The phenotypic equilibrium, i.e. heterogeneous population of cancer cells tending to a fixed equilibrium of phenotypic proportions, has received much attention in cancer biology very recently. In previous literature, some theoretical models…
In this paper we deal with problems concerning the volume of the convex hull of two "connecting" bodies. After a historical background we collect some results, methods and open problems, respectively.
A phase field model for dealing with shape instabilities in fluid membrane vesicles is presented. This model takes into account the Canham-Helfrich bending energy with spontaneous curvature. A dynamic equation for the phase-field is also…
In this article, the formation of biconcave vesicle according to the minimization bending energy (Helfrich's model) is studied. We present that in order to have biconcave shape vesicle, there are necessary conditions on the parameters of…
We comment on the article by Fujimoto (1997 J. Phys. A: Math. Gen., Vol. 30, 3779), where the exact equilibrium crystal shape (ECS) in the critical Q-state Potts model on the square lattice was calculated, and its equivalence with ECS in…
Motivated by recent experimental work on multicomponent lipid membranes supported by colloidal scaffolds, we report an exhaustive theoretical investigation of the equilibrium configurations of binary mixtures on curved substrates. Starting…
Several characterizations of complex ellipsoids among convex bodies in Cn, in terms of their sections and projections are proved. Characterizing complex symmetry in similar terms is an important tool.
Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [Pizer et al., 2003]) yield rich geometrical features that can be useful for analyzing the shape of sheet-like biological…
Let us consider the set of all joint probabilities generated by local binary measurements on two separated quantum systems of a given local dimension d. We address the question of whether the shape of this quantum body is convex or not. We…
In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies. The original inequalities provide an optimal relation between the volume of a convex body and the volume of…
A trichotomy theorem for countable, stable, unsuperstable theories is offered. We develop the notion of a `regular ideal' of formulas and study types that are minimal with respect to such an ideal.
This article is a survey of recent results on slicing inequalities for convex bodies. The focus is on the setting of arbitrary measures in place of volume.
Topics in the description of the properties of charmonium states are reviewed with an emphasis on specific theoretical ideas and methods of relating those properties to the underlying theory of Quantum Chromodynamics.
We obtain a formula for the number of horizontal equilibria of a planar convex body $K$ with respect to a center of mass $O$ in terms of the winding number of the evolute of $\partial K$ with respect to $O$. The formula extends to the case…
In this note we study the expected value of certain symplectic capacities of randomly rotated centrally symmetric convex bodies in the classical phase space.
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…