Motivated by observations about twining plants we study the static equilibrium solutions of untwisted, elastic rods in a helical shape. This work is an extension and specialization of [2]. We extend it by considering rods with intrinsic curvature and we specialize it by only considering helical solutions. Biology motivates these considerations.

This paper proves the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents and elastic labor supply. The method of proof relies on some recent results concerning the existence of Lagrange multipliers in infinite dimensional spaces and their representation as a summable sequence and a direct application of the Brouwer fixed point theorem.

In this paper, we compute the equilibrium configurations of a vesicle membrane under elastic bending energy, with prescribed volume and surface area. A variational phase field method is developed for such a problem. Discrete finite difference approximations and numerical simulations are carried out in the axial symmetrical cases. Different energetic bifurcation phenomena are discussed. 2004 Els...

Wardrop [1] introduced the famous user equilibrium principle for traffic network, which is a scalar equilibrium principle. Smith [2] investigated that a Wardrop's user equilibrium flow is equivalent to the solution of a class of variational inequalities when the travel cost function is a scalar function. Recently, many researchers have proposed equilibrium models based on multicriteria consider...

This paper presents an efficient sharp interface model to study the morphological transformations of misfit particles in phase separated alloys. Both the elastic anisotropy and interfacial energy are considered. The geometry of the material interface is implicitly described by the level set method so that the complex morphological transformation of microstructures can be accurately captured. A ...

The measurement of cell elastic parameters using optical forces has great potential as a reagent-free method for cell classification, identification of phenotype, and detection of disease; however, the low throughput associated with the sequential isolation and probing of individual cells has significantly limited its utility and application. We demonstrate a single-beam, high-throughput method...

The generalized plane quasistatic deformations of linear piezoelectric laminated plates are analyzed by the Eshelby–Stroh formalism. The laminate consists of homogeneous elastic or piezoelectric laminae of arbitrary thickness and width. The three-dimensional differential equations of equilibrium for a piezoelectric body are exactly satisŽ ed at every point in the body. The analytical solution i...

This paper proposes a new fundamental model of deformable objects for real-time and interactive applications. It is based on the mass-and-spring model, but in which the unit of elastic force definition for computation of dynamics is expanded from a spring to a volume element divided by the boundaries formed by mass-and-spring lattice. Displacements of the vertices of the volume element are defi...

A rigid base body, supported by a fixed pivot point, is free to rotate in three dimensions. Multiple elastic subsystems are rigidly mounted on the rigid body; the elastic degrees of freedom are constrained relative to the rigid base body. A mathematical model is developed for this multibody attitude system that exposes the dynamic coupling between the rotational degrees of freedom of the base b...

We develop a diffuse interface model to investigate the three dimensional coarsening in thin films. In this model, both strong surface anisotropy with linear Willmore regularization, elastic stresses and deposition are included. The governing equation for the phase field parameter is a sixth order Cahn-Hilliard Equation due to the presence of surface anisotropy and the linear Willmore regulariz...