Area-Constrained Planar Elastica

We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area constraint gives rise to equilibria with remarkable geometrical properties: not only can the Euler-Lagrange equation be integrated to provide a quadrature for the curvature but, in addition, the embedding itself can be expressed as a local function of the curvature. The configuration space is shown to be essentially one-dimensional, with surprisingly rich structure. Distinct branches of integer-indexed equilibria exhibit self-intersections and bifurcations -- a gallery of plots is provided to highlight these findings. Perturbations connecting equilibria are shown to satisfy a first order ODE which is readily solved. We also obtain analytical expressions for the energy as a function of the area in some limiting regimes.Comment: 23 pages, several figures. Version 2: New title. Changes in the introduction, addition of a new section with conclusions. Figure 14 corrected and one reference added. Version to appear in PR

Contour models of cellular adhesion

The development of traction-force microscopy, in the past two decades, has created the unprecedented opportunity of performing direct mechanical measurements on living cells as they adhere or crawl on uniform or micro-patterned substrates. Simultaneously, this has created the demand for a theoretical framework able to decipher the experimental observations, shed light on the complex biomechanical processes that govern the interaction between the cell and the extracellular matrix and offer testable predictions. Contour models of cellular adhesion, represent one of the simplest and yet most insightful approach in this problem. Rooted in the paradigm of active matter, these models allow to explicitly determine the shape of the cell edge and calculate the traction forces experienced by the substrate, starting from the internal and peripheral contractile stresses as well as the passive restoring forces and bending moments arising within the actin cortex and the plasma membrane. In this chapter I provide a general overview of contour models of cellular adhesion and review the specific cases of cells equipped with isotropic and anisotropic actin cytoskeleton as well as the role of bending elasticity.Comment: 24 pages, 9 figures. arXiv admin note: text overlap with arXiv:1304.107

The dynamic stability and nonlinear resonance of a flexible connecting rod: Continuous parameter model

The transverse vibrations of a flexible connecting rod in an otherwise rigid slider-crank mechanism are considered. An analytical approach using the method of multiple scales is adopted and particular emphasis is placed on nonlinear effects which arise from finite deformations. Several nonlinear resonances and instabilities are investigated, and the influences of important system parameters on these resonances are examined in detail.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43330/1/11071_2004_Article_BF00162233.pd

Dividend Stickiness in Japan

markdownabstract__Abstract__ The paper describes the introduction of an emphasis on ‘personal security’ in human security thinking and practice, as part of the ultimately unsuccessful attempt to compartmentalize the pursuit of security. It reviews the past twenty years of attention to ‘personal security’: both in compartments that consider organized physical violence or threats to personal safety and property (‘citizen security’), and as parts of more wide-ranging examination of threats to fulfilment of basic needs and rights, for example in comprehensive mapping exercises undertaken in various UNDP Regional and National Human Development Reports or in studies of women’s security. The paper reflects on the complex process of opening-up conventional security thinking and practice, seeking value-added and depth without shrinking into preconceived compartments