79 research outputs found
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
- …