Related papers: On the Equilibrium Shape of Erythrocytes
Measures of erythrocytes volume and surface are helpful in several physiological studies, both for zoologists and veterinarians. Whilst diameter and volume are assessed with ease from observations of blood smears and complete blood count,…
The Helfrich's shape equation of axisymmetric vesicles is studied. A sufficient condition on the physical parameters and some geometric properties are discovered for the biconcave shape.
We present simple parametric equations in terms of Jacobi elliptic functions that provide a realistic model of the shape of human normal erythrocytes as well as of variations in size (anisocytosis) and shape (poikilocytosis) thereof. We…
We study the deformation and motion of an erythrocyte in fluid flows via a lattice Boltzmann method. To this purpose, the bending rigidity and the elastic modulus of isotropic dilation are introduced and incorporated with the lattice…
A mean field theory is developed for the calculation of the surface free energy of the staggered BCSOS, (or six vertex) model as function of the surface orientation and of temperature. The model approximately describes surfaces of crystals…
We introduce a new model of the human corneal stroma, regarded as a fluid-saturated continuum, able to describe surface flattening and thickness thinning observed in several pathological conditions. In contrast with more common approaches…
We study the shapes of human red blood cells using continuum mechanics. In particular, we model the crenated, echinocytic shapes and show how they may arise from a competition between the bending energy of the plasma membrane and the…
We study the conditions on the physical parameters in the Helfrich bending energy of lipid bilayer vesicles. Among embedded surfaces with a biconcave axisymmetric shape, the variation equation is analyzed in detail. This leads to simple…
This chapter discusses the equilibrium crystal shape (ECS) from a physical perspective, beginning with a historical introduction to the Wulff theorem. It takes advantage of excellent prior reviews, particularly in the late 1980's, recapping…
The equichordal point problem is a classical question in geometry, asking whether there exist multiple equichordal points within a single convex body. An equichordal point is defined as a point through which all chords of the convex body…
We study a crystal growth Markov model proposed by Gates and Westcott (\cite{Kinetics1}, \cite{Kinetics2}). This is an aggregation process where particles are packed in a square lattice accordingly to prescribed deposition rates. This model…
We propose a notion of concavity in two-sided many-to-one matching, which is an analogue to the balancedness condition in cooperative games. A stable matching exists when the market is concave. We provide a class of concave markets. In the…
Sickle cell disease causes erythrocytes to become sickle-shaped, affecting their movement in the bloodstream and reducing oxygen delivery. It has a high global prevalence and places a significant burden on healthcare systems, especially in…
It is shown that for any real gas in chemical equilibrium, the convexity proposed by Lax isequivalent to the concavity of the entropy considered as thermodynamic potential and thepositivity of temperature.
In this paper, authors study the convexity and concavity properties of real-valued function with respect to the classical means, and prove a conjecture posed by Bruce Ebanks in \cite{e}.
We introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.
In his paper "Shapes of Polyhedra and Triangulations of the Sphere", Thurston found that the set of shapes of convex polyhedra with prescribed cone-deficits has a complex hyperbolic structure. Inspired by his work, this paper studies the…
Within the framework of the well-known curvature models, a fluid lipid bilayer membrane is regarded as a surface embedded in the three-dimensional Euclidean space whose equilibrium shapes are described in terms of its mean and Gaussian…
Although tissues are usually studied in isolation, this situation rarely occurs in biology, as cells, tissues, and organs, coexist and interact across scales to determine both shape and function. Here, we take a quantitative approach…
Bulk tissue RNA sequencing of heterogeneous samples provides averaged gene expression profiles, obscuring cell type-specific dynamics. To address this, we present a probabilistic hierarchical Bayesian model that deconvolves bulk RNA-seq…