430 research outputs found
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
Unified Description of Aging and Rate Effects in Yield of Glassy Solids
The competing effects of slow structural relaxations (aging) and deformation
at constant strain rate on the shear yield stress of simple model
glasses are examined using molecular simulations. At long times, aging leads to
a logarithmic increase in density and . The yield stress also rises
logarithmically with rate, but shows a sharp transition in slope at a rate that
decreases with increasing age. We present a simple phenomenological model that
includes both intrinsic rate dependence and the change in properties with the
total age of the system at yield. As predicted by the model, all data for each
temperature collapse onto a universal curve.Comment: 4 pages, 3 figure
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
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
Memory in aged granular media
Stimulated by recent experimental results, we simulate
``temperature''-cycling experiments in a model for the compaction of granular
media. We report on the existence of two types of memory effects: short-term
dependence on the history of the sample, and long-term memory for highly
compact (aged) systems. A natural interpretation of these results is provided
by the analysis of the density heterogeneities.Comment: 5 eps figures, uses euromacr.tex and europhys.sty (included
Aging classification in glassy dynamics
We study the out of equilibrium dynamics of several models exhibiting aging.
We attempt at identifying various types of aging systems using a phase space
point of view: we introduce a trial classification, based on the overlap
between two replicas of a system, which evolve together until a certain waiting
time, and are then totally decoupled. We investigate in this way two types of
systems, domain growth problems and spin glasses, and we show that they behave
differently.Comment: 18 pages,9 Postscript figures,uses rotate.sty,epsf.st
Domain growth by isothermal aging in 3d Ising and Heisenberg spin glasses
Non-equilibrium dynamics of three dimensional model spin glasses - the Ising
system FeMnTiO and the Heisenberg like system Ag(11 at%
Mn) - has been investigated by measurements of the isothermal time decay of the
low frequency ac-susceptibility after a quench from the paramagnetic to the
spin glass phase. It is found that the relaxation data measured at different
temperatures can be scaled according to predictions from the droplet scaling
model, provided that critical fluctuations are accounted for in the analyzes.Comment: 5 pages, 3 figure
Phase space geometry and slow dynamics
We describe a non-Arrhenius mechanism for slowing down of dynamics that is
inherent to the high dimensionality of the phase space. We show that such a
mechanism is at work both in a family of mean-field spin-glass models without
any domain structure and in the case of ferromagnetic domain growth. The
marginality of spin-glass dynamics, as well as the existence of a `quasi
equilibrium regime' can be understood within this scenario. We discuss the
question of ergodicity in an out-of equilibrium situation.Comment: 23 pages, ReVTeX3.0, 6 uuencoded postscript figures appende
Localized induction equation and pseudospherical surfaces
We describe a close connection between the localized induction equation
hierarchy of integrable evolution equations on space curves, and surfaces of
constant negative Gauss curvature.Comment: 21 pages, AMSTeX file. To appear in Journal of Physics A:
Mathematical and Genera
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