Uncategorized – Page 6 – Mahadevan Natural Philosophy

Aging in complex interdependency networks

Although species longevity is subject to a diverse range of evolutionary forces, the mortality curves of a wide
variety of organisms are rather similar. Here we argue that qualitative and quantitative features of aging can be
reproduced by a simple model based on the interdependence of fault-prone agents on one other. In addition to
fitting our theory to the empiric mortality curves of six very different organisms, we establish the dependence
of lifetime and aging rate on initial conditions, damage and repair rate, and system size. We compare the size
distributions of disease and death and see that they have qualitatively different properties. We show that aging
patterns are independent of the details of interdependence network structure, which suggests that aging is a
many-body effect, and that the qualitative and quantitative features of aging are not sensitively dependent on the
details of dependency structure or its formation.

A pendulum in a flowing soap film

We consider the dynamics of a pendulum made of a rigid ring attached to an elastic
filament immersed in a flowing soap film. The system shows an oscillatory instability
whose onset is a function of the flow speed, length of the supporting string, the
ring mass, and ring radius. We characterize this system and show that there are
different regimes where the frequency is dependent or independent of the pendulum
length depending on the relative magnitude of the added-mass. Although the system
is an infinite-dimensional, we can explain many of our results in terms of a one
degree-of-freedom system corresponding to a forced pendulum. Indeed, using the
vorticity measured via particle imaging velocimetry allows us to make the model
quantitative, and a comparison with our experimental results shows we can capture
the basic phenomenology of this system.

Geometric mechanics of periodic pleated origami

Origami structures are mechanical metamaterials with properties that arise almost exclusively from the
geometry of the constituent folds and the constraint of piecewise isometric deformations. Here we
characterize the geometry and planar and nonplanar effective elastic response of a simple periodically
folded Miura-ori structure, which is composed of identical unit cells of mountain and valley folds with
four-coordinated ridges, defined completely by two angles and two lengths. We show that the in-plane and
out-of-plane Poisson’s ratios are equal in magnitude, but opposite in sign, independent of material
properties. Furthermore, we show that effective bending stiffness of the unit cell is singular, allowing us to
characterize the two-dimensional deformation of a plate in terms of a one-dimensional theory. Finally, we
solve the inverse design problem of determining the geometric parameters for the optimal geometric and
mechanical response of these extreme structures

Swarming, swirling and stasis in sequestered bristle-bots

The collective ability of organisms to move coherently
in space and time is ubiquitous in any group of
autonomous agents that can move and sense each
other and the environment. Here, we investigate
the origin of collective motion and its loss using
macroscopic self-propelled bristle-bots, simple
automata made from a toothbrush and powered
by an onboard cell phone vibrator-motor, that can
sense each other through shape-dependent local
interactions, and can also sense the environment nonlocally via the effects of confinement and substrate
topography. We show that when bristle-bots are
confined to a limited arena with a soft boundary,
increasing the density drives a transition from a
disordered and uncoordinated motion to organized
collective motion either as a swirling cluster or a
collective dynamical stasis. This transition is regulated
by a single parameter, the relative magnitude of
spinning and walking in a single automaton. We
explain this using quantitative experiments and
simulations that emphasize the role of the agent
shape, environment and confinement via boundaries.
Our study shows how the behavioural repertoire of
these physically interacting automatons controlled
by one parameter translates into the mechanical
intelligence of swarms.

A cutting edge issue resolved

Planning to have roast turkey at Christmas? You’ll be glad to hear that physicists have revealed exactly how to carve it – using jelly and a fishing line.

Geometric mechanics of curved crease origami

Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian
packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is
folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical
frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold, and
the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically
deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and
oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with
oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is
corroborated by numerical simulations that allow us to generalize our analysis to study structures with
multiple curved creases.

The branch with the furthest reach

How should a given amount of material be moulded into a cantilevered beam clamped
at one end, so that it will have the furthest horizontal reach? Here, we formulate and solve this
variational problem for the optimal variation of the cross-section area of a heavy cantilevered beam
with a given volume V , Young’s modulus E, and density ρ, subject to gravity g. We find that
the cross-sectional area should vary according a universal profile that is independent of material
parameters, with both the length and maximum reach-out distance of the branch that scale as
(EV /ρg)
1/4
, with a universal self-similar shape at the tip with the area of cross-section a ∼ s
3
, s
being the distance from the tip, consistent with earlier observations of tree branches, but with a
different local interpretation than given before. A simple experimental realization of our optimal
beam shows that our result compares favorably with that of our observations. Our results for the
optimal design of slender structures with the longest reach are valid for cross-sections of arbitrary
shape that can be solid or hollow and thus relevant for a range of natural and engineered systems.

Biological Springs and Ratchets

Biological movements are brought about in various ways, and not all of these involve the action of motor proteins. Apart from motor proteins, biological movements can be brought about by components that act like springs and ratchets. Biological springs store potential energy in various protein filament conformations, while biological ratchets act by biasing random Brownian motion and […]

On the growth and form of the gut

The developing vertebrate gut tube forms a reproducible looped pattern as it grows into the body cavity. Here we use
developmental experiments to eliminate alternative models and show that gut looping morphogenesis is driven by the
homogeneous and isotropic forces that arise from the relative growth between the gut tube and the anchoring dorsal
mesenteric sheet, tissues that grow at different rates. A simple physical mimic, using a differentially strained composite
of a pliable rubber tube and a soft latex sheet is consistent with this mechanism and produces similar patterns. We devise
a mathematical theory and a computational model for the number, size and shape of intestinal loops based solely on the
measurable geometry, elasticity and relative growth of the tissues. The predictions of our theory are quantitatively
consistent with observations of intestinal loops at different stages of development in the chick embryo. Our model also
accounts for the qualitative and quantitative variation in the distinct gut looping patterns seen in a variety of species
including quail, finch and mouse, illuminating how the simple macroscopic mechanics of differential growth drives the
morphology of the developing gut.

Unfolding the sulcus

Sulci are localized furrows on the surface of soft materials that form by a compression-induced
instability. We unfold this instability by breaking its natural scale and translation invariance, and compute
a limiting bifurcation diagram for sulcfication showing that it is a scale-free, subcritical nonlinear
instability. In contrast with classical nucleation, sulcification is continuous, occurs in purely elastic
continua and is structurally stable in the limit of vanishing surface energy. During loading, a sulcus
nucleates at a point with an upper critical strain and an essential singularity in the linearized spectrum. On
unloading, it quasistatically shrinks to a point with a lower critical strain, explained by breaking of scale
symmetry. At intermediate strains the system is linearly stable but nonlinearly unstable with no energy
barrier. Simple experiments confirm the existence of these two critical strains.