Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Elastic Surfaces and Shape Equations

In an earlier section, we discussed molecular chains with continuous curvature. These models enable one to st udy polymer conformational structure by means of notions of elasticity theory. As seen, geometrical properties (e.g., curvature, torsion, twist, writhe) and topological properties (e.g., linking) can be used to characterize the molecular shapes of ID models. This approach can be generalized to the study of 2D elastic surfaces. [Pg.228]

Under this assumption, the bending energy Eg can be represented in terms of the membrane s curvature. For this reason. Eg is also referred to as the curvature elastic energy. The curvature of smooth surfaces is characterized by two functions that depend on the local canonical curvatures, h t) and h lr), in a surface element dS centered at r. These functions are the mean curvature, H = ( 1 + hi) , and the Gaussian curvature, K = hih2- In general, H and K change with the point r. [Pg.229]

In the simplest model for analyzing the shape of elastic vesicles with thin fluid membranes, the bending energy is made proportional to the integrated curvatures over the closed membrane surface [Pg.229]

The foregoing expression (Eq. [27]) is known as the Helfrich Hamiltonian.At equilibrium, the vesicle will adopt the shape of the surface 5 that minimizes Eg, subject to two restrictions a constant enclosed volume V and a [Pg.229]

The integral over the Gaussian curvature in Eq. [27] is a topological invariant.i i85 For a closed orientable 2D surface (i.e., one without boundary), the Gauss—Bonnet theorem ties the value of this invariant to the genus g or the Euler—Poincare characteristic x of the surface  [Pg.230]


See other pages where Elastic Surfaces and Shape Equations is mentioned: [Pg.228]   


SEARCH



Elasticity, surface

Shape equations

Surfaces shape

© 2024 chempedia.info