4,553 research outputs found
Topological Twistons in Crystalline Polyethylene
We introduce an alternate model to describe twistons in crystalline
polyethylene. The model couples torsional and longitudinal degrees of freedom
and appears as an extension of a model that describes only the torsional
motion. We find exact solutions that describe stable topological twistons, in
good agreement with the torsional and longitudinal interactions in
polyethylene.Comment: Latex, 10 pages; some stylistic corrections, to appear in Chemical
Physics Letter
Crescent Singularities in Crumpled Sheets
We examine the crescent singularity of a developable cone in a setting
similar to that studied by Cerda et al [Nature 401, 46 (1999)]. Stretching is
localized in a core region near the pushing tip and bending dominates the outer
region. Two types of stresses in the outer region are identified and shown to
scale differently with the distance to the tip. Energies of the d-cone are
estimated and the conditions for the scaling of core region size R_c are
discussed. Tests of the pushing force equation and direct geometrical
measurements provide numerical evidence that core size scales as R_c ~ h^{1/3}
R^{2/3}, where h is the thickness of sheet and R is the supporting container
radius, in agreement with the proposition of Cerda et al. We give arguments
that this observed scaling law should not represent the asymptotic behavior.
Other properties are also studied and tested numerically, consistent with our
analysis.Comment: 13 pages with 8 figures, revtex. To appear in PR
Spontaneous curvature cancellation in forced thin sheets
In this paper we report numerically observed spontaneous vanishing of mean
curvature on a developable cone made by pushing a thin elastic sheet into a
circular container. We show that this feature is independent of thickness of
the sheet, the supporting radius and the amount of deflection. Several variants
of developable cone are studied to examine the necessary conditions that lead
to the vanishing of mean curvature. It is found that the presence of
appropriate amount of radial stress is necessary. The developable cone geometry
somehow produces the right amount of radial stress to induce just enough radial
curvature to cancel the conical azimuthal curvature. In addition, the circular
symmetry of supporting container edge plays an important role. With an
elliptical supporting edge, the radial curvature overcompensates the azimuthal
curvature near the minor axis and undercompensates near the major axis. Our
numerical finding is verified by a crude experiment using a reflective plastic
sheet. We expect this finding to have broad importance in describing the
general geometrical properties of forced crumpling of thin sheets.Comment: 13 pages, 12 figures, revtex
Measurement of focusing properties for high numerical aperture optics using an automated submicron beamprofiler
The focusing properties of three aspheric lenses with numerical aperture (NA)
between 0.53 and 0.68 were directly measured using an interferometrically
referenced scanning knife-edge beam profiler with sub-micron resolution. The
results obtained for two of the three lenses tested were in agreement with
paraxial gaussian beam theory. It was also found that the highest NA aspheric
lens which was designed for 830nm was not diffraction limited at 633nm. This
process was automated using motorized translation stages and provides a direct
method for testing the design specifications of high numerical aperture optics.Comment: 6 pages 4 figure
Rim curvature anomaly in thin conical sheets revisited
This paper revisits one of the puzzling behaviors in a developable cone
(d-cone), the shape obtained by pushing a thin sheet into a circular container
of radius by a distance [E. Cerda, S. Chaieb, F. Melo, and L.
Mahadevan, {\sl Nature} {\bf 401}, 46 (1999)]. The mean curvature was reported
to vanish at the rim where the d-cone is supported [T. Liang and T. A. Witten,
{\sl Phys. Rev. E} {\bf 73}, 046604 (2006)]. We investigate the ratio of the
two principal curvatures versus sheet thickness over a wider dynamic range
than was used previously, holding and fixed. Instead of tending
towards 1 as suggested by previous work, the ratio scales as .
Thus the mean curvature does not vanish for very thin sheets as previously
claimed. Moreover, we find that the normalized rim profile of radial curvature
in a d-cone is identical to that in a "c-cone" which is made by pushing a
regular cone into a circular container. In both c-cones and d-cones, the ratio
of the principal curvatures at the rim scales as ,
where is the pushing force and is the Young's modulus. Scaling
arguments and analytical solutions confirm the numerical results.Comment: 25 pages, 12 figures. Added references. Corrected typos. Results
unchange
Firm and industry characteristics influencing publications of scientists in large American companies
Symmetry Reduction by Lifting for Maps
We study diffeomorphisms that have one-parameter families of continuous
symmetries. For general maps, in contrast to the symplectic case, existence of
a symmetry no longer implies existence of an invariant. Conversely, a map with
an invariant need not have a symmetry. We show that when a symmetry flow has a
global Poincar\'{e} section there are coordinates in which the map takes a
reduced, skew-product form, and hence allows for reduction of dimensionality.
We show that the reduction of a volume-preserving map again is volume
preserving. Finally we sharpen the Noether theorem for symplectic maps. A
number of illustrative examples are discussed and the method is compared with
traditional reduction techniques.Comment: laTeX, 31 pages, 5 figure
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
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Synthesis, characterisation, and diffusive properties of functionalised nanomaterials
The aim of this thesis was to assess the diffusive properties of functionalised and unfunctionalised nanomaterials in a variety of different media. The main goal was to gain an insight into the fundamental mechanisms underpinning nanoparticle diffusion and how
the surface properties of nanoparticles alter their net movement through different environments. Initially a library of polymer-functionalised silica nanoparticles were synthesised and characterised. The polymers chosen were; poly(ethylene glycol) (PEG), poly(2-oxazolines) (POZ) and poly(n-isopropyl acrylamide) (PNIPAM). Firstly, the diffusion of different sized gold nanoparticles was assessed in concentrations of Pluronic F-127, in order to determine how the solution properties affected diffusion. It was found that as the solution undergoes a transition in response to environmental stimuli, there is an increase in diffusion coefficient; however the area they move in becomes more confined (assessed using a bespoke python script written for use with NTA). PNIPAM- and PNPOZ-silica nanoparticles were assessed for their aggregation and diffusion using DLS, NTA, and SANS. It was found that the position of a nitrogen atom in the amide group, present in both polymers, plays a key role in governing how the particles aggregate in solution, which in turn affects how they diffuse through solvents of varying polarities. POZ-silica nanoparticles were assessed for mucus penetration against a positive control
of PEGylated nanoparticles. It was found that POZ-silica was effective at enhancing nanoparticle mucus penetration, and the hydrophilicity of these polymers plays a key role in determining the degree of permeation (with methylated POZ significantly more diffusive than propylated POZ). These finding provide valuable insight into some of the molecular mechanisms governing
nanoparticle diffusion and how surface chemistry governs these effects
Properties of Ridges in Elastic Membranes
When a thin elastic sheet is confined to a region much smaller than its size
the morphology of the resulting crumpled membrane is a network of straight
ridges or folds that meet at sharp vertices. A virial theorem predicts the
ratio of the total bending and stretching energies of a ridge. Small strains
and curvatures persist far away from the ridge. We discuss several kinds of
perturbations that distinguish a ridge in a crumpled sheet from an isolated
ridge studied earlier (A. E. Lobkovsky, Phys. Rev. E. 53 3750 (1996)). Linear
response as well as buckling properties are investigated. We find that quite
generally, the energy of a ridge can change by no more than a finite fraction
before it buckles.Comment: 13 pages, RevTeX, acknowledgement adde
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