A fractional notion of length and an associated nonlocal curvature

Here a new notion of fractional length of a smooth curve, which depends on a parameter $\sigma$, is introduced that is analogous to the fractional perimeter functional of sets that has been studied in recent years. It is shown that in an appropriate limit the fractional length converges to the traditional notion of length up to a multiplicative constant. Since a curve that connects two points of minimal length must have zero curvature, the Euler--Lagrange equation associated with the fractional length is used to motivate a nonlocal notion of curvature for a curve. This is analogous to how the fractional perimeter has been used to define a nonlocal mean curvature.Comment: 20 pages, 3 figure

A PROVINCIAL PERSPECTIVE

International Relations/Trade,

Estimates of regional ET from HCMM data: Summary of 1977 experiment and final arrangement for 1978 in southeastern France test site

There are no author-identified significant results in this report

Homogenization of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics

In this paper we present a derivation and multiscale analysis of a mathematical model for plant cell wall biomechanics that takes into account both the microscopic structure of a cell wall coming from the cellulose microfibrils and the chemical reactions between the cell wall's constituents. Particular attention is paid to the role of pectin and the impact of calcium-pectin cross-linking chemistry on the mechanical properties of the cell wall. We prove the existence and uniqueness of the strongly coupled microscopic problem consisting of the equations of linear elasticity and a system of reaction-diffusion and ordinary differential equations. Using homogenization techniques (two-scale convergence and periodic unfolding methods) we derive a macroscopic model for plant cell wall biomechanics