987 research outputs found
Period fissioning and other instabilities of stressed elastic membranes
We study the shapes of elastic membranes under the simultaneous exertion of
tensile and compressive forces when the translational symmetry along the
tension direction is broken. We predict a multitude of novel morphological
phases in various regimes of a 2-dimensional parameter space
that defines the relevant mechanical and geometrical conditions. Theses
parameters are, respectively, the ratio between compression and tension, and
the wavelength contrast along the tension direction. In particular, our theory
associates the repetitive increase of pattern periodicity, recently observed on
wrinkled membranes floating on liquid and subject to capillary forces, to the
morphology in the regime () where tension is dominant
and the wavelength contrast is large.Comment: 4 pages, 4 figures. submitted to Phys. Rev. Let
Regimes of wrinkling in an indented floating elastic sheet
A thin, elastic sheet floating on the surface of a liquid bath wrinkles when
poked at its centre. We study the onset of wrinkling as well as the evolution
of the pattern as indentation progresses far beyond the wrinkling threshold. We
use tension field theory to describe the macroscopic properties of the deformed
film and show that the system passes through a host of different regimes, even
while the deflections and strains remain small. We show that the effect of the
finite size of the sheet ultimately plays a key role in determining the
location of the wrinkle pattern, and obtain scaling relations that characterize
the number of wrinkles at threshold and its variation as the indentation
progresses. Some of our predictions are confirmed by recent experiments of Ripp
\emph{et al.} [arxiv: 1804.02421].Comment: 22 pages, 11 figures, revised versio
Apologies in the Healthcare System: From Clinical Medicine to Public Health
Alberstein and Davidovitch explore the role of apologies in healthcare systems from a broader perspective. The significance of apology in terms of social solidarity is addressed and the ways in which each apology situation entails a clash between cultural identities are demonstrated. The debate on apology is explored by presenting a public health perspective of apologies following collective traumatic events such as the application of sterilization laws or flawed human experimentations in various settings
Stress field around arbitrarily shaped cracks in two-dimensional elastic materials
The calculation of the stress field around an arbitrarily shaped crack in an
infinite two-dimensional elastic medium is a mathematically daunting problem.
With the exception of few exactly soluble crack shapes the available results
are based on either perturbative approaches or on combinations of analytic and
numerical techniques. We present here a general solution of this problem for
any arbitrary crack. Along the way we develop a method to compute the conformal
map from the exterior of a circle to the exterior of a line of arbitrary shape,
offering it as a superior alternative to the classical Schwartz-Cristoffel
transformation. Our calculation results in an accurate estimate of the full
stress field and in particular of the stress intensity factors K_I and K_{II}
and the T-stress which are essential in the theory of fracture.Comment: 7 pages, 4 figures, submitted for PR
Indentation metrology of clamped, ultra-thin elastic sheets
We study the indentation of ultrathin elastic sheets clamped to the edge of a
circular hole. This classical setup has received considerable attention lately,
being used by various experimental groups as a probe to measure the surface
properties and stretching modulus of thin solid films. Despite the apparent
simplicity of this method, the geometric nonlinearity inherent in the
mechanical response of thin solid objects renders the analysis of the resulting
data a nontrivial task. Importantly, the essence of this difficulty is in the
geometric coupling between in-plane stress and out-of-plane deformations, and
hence is present in the behaviour of Hookean solids even when the slope of the
deformed membrane remains small. Here we take a systematic approach to address
this problem, using the membrane limit of the F\"{o}ppl-von-K\'{a}rm\'{a}n
equations. This approach highlights some of the dangers in the use of
approximate formulae in the metrology of solid films, which can introduce large
errors; we suggest how such errors may be avoided in performing experiments and
analyzing the resulting data
Convergent Calculation of the Asymptotic Dimension of Diffusion Limited Aggregates: Scaling and Renormalization of Small Clusters
Diffusion Limited Aggregation (DLA) is a model of fractal growth that had
attained a paradigmatic status due to its simplicity and its underlying role
for a variety of pattern forming processes. We present a convergent calculation
of the fractal dimension D of DLA based on a renormalization scheme for the
first Laurent coefficient of the conformal map from the unit circle to the
expanding boundary of the fractal cluster. The theory is applicable from very
small (2-3 particles) to asymptotically large (n \to \infty) clusters. The
computed dimension is D=1.713\pm 0.003
New Algorithm for Parallel Laplacian Growth by Iterated Conformal Maps
We report a new algorithm to generate Laplacian Growth Patterns using
iterated conformal maps. The difficulty of growing a complete layer with local
width proportional to the gradient of the Laplacian field is overcome. The
resulting growth patterns are compared to those obtained by the best algorithms
of direct numerical solutions. The fractal dimension of the patterns is
discussed.Comment: Sumitted to Phys. Rev. Lett. Further details at
http://www.pik-potsdam.de/~ander
Roadmap to the morphological instabilities of a stretched twisted ribbon
We address the mechanics of an elastic ribbon subjected to twist and tensile
load. Motivated by the classical work of Green and a recent experiment that
discovered a plethora of morphological instabilities, we introduce a
comprehensive theoretical framework through which we construct a 4D phase
diagram of this basic system, spanned by the exerted twist and tension, as well
as the thickness and length of the ribbon. Different types of instabilities
appear in various "corners" of this 4D parameter space, and are addressed
through distinct types of asymptotic methods. Our theory employs three
instruments, whose concerted implementation is necessary to provide an
exhaustive study of the various parameter regimes: (i) a covariant form of the
F\"oppl-von K\'arm\'an (cFvK) equations to the helicoidal state - necessary to
account for the large deflection of the highly-symmetric helicoidal shape from
planarity, and the buckling instability of the ribbon in the transverse
direction; (ii) a far from threshold (FT) analysis - which describes a state in
which a longitudinally-wrinkled zone expands throughout the ribbon and allows
it to retain a helicoidal shape with negligible compression; (iii) finally, we
introduce an asymptotic isometry equation that characterizes the energetic
competition between various types of states through which a twisted ribbon
becomes strainless in the singular limit of zero thickness and no tension.Comment: Submitted to Journal of Elasticity, themed issue on ribbons and
M\"obius band
Mechanics of large folds in thin interfacial films
A thin film at a liquid interface responds to uniaxial confinement by
wrinkling and then by folding; its shape and energy have been computed exactly
before self contact. Here, we address the mechanics of large folds, i.e. folds
that absorb a length much larger than the wrinkle wavelength. With scaling
arguments and numerical simulations, we show that the antisymmetric fold is
energetically favorable and can absorb any excess length at zero pressure.
Then, motivated by puzzles arising in the comparison of this simple model to
experiments on lipid monolayers and capillary rafts, we discuss how to
incorporate film weight, self-adhesion and energy dissipation.Comment: 5 pages, 3 figure
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