Uncategorized – Page 5 – Mahadevan Natural Philosophy

Elements of Draping

We consider the gravity-induced draping of a 3D object with a
naturally flat, isotropic elastic sheet. As the size of the sheet
increases, we observe the appearance of new folded structures of
increasing complexity that arise because of the competition between elasticity and gravity. We analyze some of the simpler 3D
structures by determining their shape and analyzing their response
and stability and show that these structures can easily switch
between a number of metastable configurations. For more complex draperies, we derive scaling laws for the appearance and
disappearance of new length scales. Our results are consistent with
commonplace observations of drapes and complement large-scale
computations of draping by providing benchmarks. They also yield
a qualitative guide to fashion design and virtual reality animation.

Elastic behavior of cross-linked and bundled actin networks

Networks of cross-linked and bundled actin filaments are ubiquitous in the cellular
cytoskeleton, but their elasticity remains poorly understood. We show that these
networks exhibit exceptional elastic behavior that reflects the mechanical properties of individual filaments. There are two distinct regimes of elasticity, one
reflectingbendingof single filaments and a second reflectingstretchingof entropic
fluctuations of filament length. The mechanical stiffness can vary by several decades with small changes in cross-link concentration, and can increase markedly
upon application of external stress. We parameterize the full range of behavior in
a state diagram and elucidate its origin with a robust model.

Biomimetic ratcheting motion of lubricated hydrogel filaments

Inspired by the locomotion of terrestrial limbless animals, we study
the motion of a lubricated rod of a hydrogel on a soft substrate. We
show that it is possible to mimic observed biological gaits by
vibrating the substrate and by using a variety of mechanisms to
break longitudinal and lateral symmetry. Our simple theory and
experiments provide a unified view of the creeping, undulating,
and inchworming gaits observed in limbless locomotion on land, all
of which originate as symmetry-breaking bifurcations of a simple
base state associated with periodic longitudinal oscillations of a
slender gel. These ideas are therefore also applicable to technological situations that involve moving small, soft solids on
substrates.

Peeling from a patterned thin elastic film

Inspired by the observation that many naturally occurring adhesives arise as textured thin films, we consider the displacement-controlled peeling of a flexible plate
from an incision-patterned thin adhesive elastic layer. We find that crack initiation
from an incision on the film occurs at a load much higher than that required to
propagate it on a smooth adhesive surface; multiple incisions thus cause the crack
to propagate intermittently. Microscopically, this mode of crack initiation and propagation in geometrically confined thin adhesive films is related to the nucleation of
cavitation bubbles behind the incision which must grow and coalesce before a viable
crack propagates. Our theoretical analysis allows us to rationalize these experimental
observations qualitatively and quantitatively and suggests a simple design criterion
for increasing the interfacial fracture toughness of adhesive films

Dynamics of poroelastic filaments

Dynamics of poroelastic filaments,Skotheim, J. and L. Mahadevan, Proceedings of the Royal Society of London (A) , 460, 1995-2020 (2004).

Geometry and physics of wrinkling

The wrinkling of thin elastic sheets occurs over a range of length scales, from the fine scale patterns
in substrates on which cells crawl to the coarse wrinkles seen in clothes. Motivated by the wrinkling of
a stretched elastic sheet, we deduce a general theory of wrinkling, valid far from the onset of the
instability, using elementary geometry and the physics of bending and stretching. Our main result is a
set of simple scaling laws; the wavelength of the wrinkles K1=4, where K is the stiffness due to an
‘‘elastic substrate’’ effect with a multitude of origins, and the amplitude of the wrinkle A . These
could form the basis of a highly sensitive quantitative wrinkling assay for the mechanical characterization of thin solid membranes.

Popliteal instability of bent multi-walled elastic tubes,

Soft slender structures are ubiquitous in natural and artificial systems, in active and passive settings and across scales, from polymers and flagella, to snakes and space tethers. In this paper, we demonstrate the use of a simple and practical numerical implementation based on the Cosserat rod model to simulate the dynamics of filaments that can bend, twist, stretch and shear while interacting with complex environments via muscular activity, surface contact, friction and hydrodynamics. We validate our simulations by solving a number of forward problems involving the mechanics of passive filaments and comparing them with known analytical results, and extend them to study instabilities in stretched and twisted filaments that form solenoidal and plectonemic structures. We then study active filaments such as snakes and other slender organisms by solving inverse problems to identify optimal gaits for limbless locomotion on solid surfaces and in bulk liquids.

Peeling, healing and bursting in lubricated elastic sheets

We consider the dynamics of an elastic sheet lubricated by the flow of a thin layer of fluid that
separates it from a rigid wall. By considering long wavelength deformations of the sheet, we derive an
evolution equation for its motion, accounting for the effects of elastic bending, viscous lubrication, and
body forces. We then analyze various steady and unsteady problems for the sheet, such as peeling,
healing, levitating, and bursting, using a combination of numerical simulation and dimensional analysis.
On the macroscale, we corroborate our theory with a simple experiment, and, on the microscale, we
analyze an oscillatory valve that can transform a continuous stream of fluid into a series of discrete
pulses.

Multiscale methods for modeling protein-DNA complexes

We present a multiresolution approach to modeling complexes between protein and
DNA that contain looped or coiled DNA. The approach combines a coarse-grained model of the DNA
loop, based on the classical theory of elasticity, with an atom level model of proteins and proteinDNA interfaces based on molecular dynamics. The coarse-grained DNA description is controlled
through the atom level protein description and vice versa. The feasibility of the resulting multiscale
modeling approach is demonstrated for a protein-DNA complex in which a protein called the E. coli
lac repressor forces DNA into a 76 base pair loop. The required simulation involves 230,000 atoms,
a number that would triple if both protein and DNA loops were described at the atomic level.

The ‘Cheerios Effect’

Objects that float at the interface between a liquid and a gas interact because of interfacial
deformation and the effect of gravity. We highlight the crucial role of buoyancy in this interaction,
which, for small particles, prevails over the capillary suction that often is assumed to be the
dominant effect. We emphasize this point using a simple classroom demonstration, and then derive
the physical conditions leading to mutual attraction or repulsion. We also quantify the force of
interaction in particular instances and present a simple dynamical model of this interaction. The
results obtained from this model are validated by comparison to experimental results for the mutual
attraction of two identical spherical particles. We consider some of the applications of the effect that
can be found in nature and the laboratory