1,701 research outputs found
Forced sloshing of inviscid fluids
Forced sloshing motion of inviscid fluids in rigid cylinder
Qualitative properties of large buckled states of spherical shells
A system of 6th-order quasi-linear Ordinary Differential Equations is analyzed to show the global existence of axisymmetrically buckled states. A surprising nodal property is obtained which shows that everywhere along a branch of solutions that bifurcates from a simple eigenvalue of the linearized equation, the number of simultaneously vanishing points of both shear resultant and circumferential bending moment resultant remains invariant, provided that a certain auxiliary condition is satisfied
Steady-state MreB helices inside bacteria: dynamics without motors
Within individual bacteria, we combine force-dependent polymerization
dynamics of individual MreB protofilaments with an elastic model of
protofilament bundles buckled into helical configurations. We use variational
techniques and stochastic simulations to relate the pitch of the MreB helix,
the total abundance of MreB, and the number of protofilaments. By comparing our
simulations with mean-field calculations, we find that stochastic fluctuations
are significant. We examine the quasi-static evolution of the helical pitch
with cell growth, as well as timescales of helix turnover and denovo
establishment. We find that while the body of a polarized MreB helix treadmills
towards its slow-growing end, the fast-growing tips of laterally associated
protofilaments move towards the opposite fast-growing end of the MreB helix.
This offers a possible mechanism for targeted polar localization without
cytoplasmic motor proteins.Comment: 7 figures, 1 tabl
Spatial chaos of an extensible conducting rod in a uniform magnetic field
The equilibrium equations for the isotropic Kirchhoff rod are known to form
an integrable system. It is also known that the effects of extensibility and
shearability of the rod do not break the integrable structure. Nor, as we have
shown in a previous paper does the effect of a magnetic field on a conducting
rod. Here we show, by means of Mel'nikov analysis, that, remarkably, the
combined effects do destroy integrability; that is, the governing equations for
an extensible current-carrying rod in a uniform magnetic field are
nonintegrable. This result has implications for possible configurations of
electrodynamic space tethers and may be relevant for electromechanical devices
Discrete Formulation for the dynamics of rods deforming in space
We describe the main ingredients needed to create, from the smooth lagrangian
density, a variational principle for discrete motions of a discrete rod, with
corresponding conserved Noether currents. We describe all geometrical objects
in terms of elements on the linear Atiyah bundle, using a reduced forward
difference operator. We show how this introduces a discrete lagrangian density
that models the discrete dynamics of a discrete rod. The presented tools are
general enough to represent a discretization of any variational theory in
principal bundles, and its simplicity allows to perform an iterative
integration algorithm to compute the discrete rod evolution in time, starting
from any predefined configurations of all discrete rod elements at initial
times
Polygonization of carbon nanotubes
We use a multiscale procedure to derive a simple continuum model of
multiwalled carbon nanotubes that takes into account both strong covalent bonds
within graphene layers and weak bonds between atoms in different layers. The
model predicts polygonization of crossections of large multiwalled nanotubes as
a consequence of their curvature-induced turbostratic structure
Toughening and asymmetry in peeling of heterogeneous adhesives
The effective adhesive properties of heterogeneous thin films are
characterized through a combined experimental and theoretical investigation. By
bridging scales, we show how variations of elastic or adhesive properties at
the microscale can significantly affect the effective peeling behavior of the
adhesive at the macroscale. Our study reveals three elementary mechanisms in
heterogeneous systems involving front propagation: (i) patterning the elastic
bending stiffness of the film produces fluctuations of the driving force
resulting in dramatically enhanced resistance to peeling; (ii) optimized
arrangements of pinning sites with large adhesion energy are shown to control
the effective system resistance, allowing the design of highly anisotropic and
asymmetric adhesives; (iii) heterogeneities of both types result in front
motion instabilities producing sudden energy releases that increase the overall
adhesion energy. These findings open potentially new avenues for the design of
thin films with improved adhesion properties, and motivate new investigation of
other phenomena involving front propagation.Comment: Physical Review Letters (2012)
Curvature condensation and bifurcation in an elastic shell
We study the formation and evolution of localized geometrical defects in an
indented cylindrical elastic shell using a combination of experiment and
numerical simulation. We find that as a symmetric localized indentation on a
semi-cylindrical shell increases, there is a transition from a global mode of
deformation to a localized one which leads to the condensation of curvature
along a symmetric parabolic crease. This process introduces a soft mode in the
system, converting a load-bearing structure into a hinged, kinematic mechanism.
Further indentation leads to twinning wherein the parabolic crease bifurcates
into two creases that move apart on either side of the line of symmetry. A
qualitative theory captures the main features of the phenomena and leads to
sharper questions about the nucleation of these defects.Comment: 4 pages, 5 figures, submitted to Physical Review Letter
Elastic cavitation, tube hollowing, and differential growth in plants and biological tissues
Elastic cavitation is a well-known physical process by which elastic materials under stress can open cavities. Usually, cavitation is induced by applied loads on the elastic body. However, growing materials may generate stresses in the absence of applied loads and could induce cavity opening. Here, we demonstrate the possibility of spontaneous growth-induced cavitation in elastic materials and consider the implications of this phenomenon to biological tissues and in particular to the problem of schizogenous aerenchyma formation
Rotating strings
Analytical expressions are provided for the configurations of an
inextensible, flexible, twistable inertial string rotating rigidly about a
fixed axis. Solutions with trivial radial dependence are helices of arbitrary
radius and pitch. Non-helical solutions are governed by a cubic equation whose
roots delimit permissible values of the squared radial coordinate. Only curves
coplanar with the axis of rotation make contact with it.Comment: added to discussion and made small revisions to tex
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