163 research outputs found
Isometric bending requires local constraints on free edges
While the shape equations describing the equilibrium of an unstretchable thin
sheet that is free to bend are known, the boundary conditions that supplement
these equations on free edges have remained elusive. Intuitively,
unstretchability is captured by a constraint on the metric within the bulk.
Naively one would then guess that this constraint is enough to ensure that the
deformations determining the boundary conditions on these edges respect the
isometry constraint. If matters were this simple, unfortunately, it would imply
unbalanced torques (as well as forces) along the edge unless manifestly
unphysical constraints are met by the boundary geometry. In this paper we
identify the source of the problem: not only the local arc-length but also the
geodesic curvature need to be constrained explicitly on all free edges. We
derive the boundary conditions which follow. Contrary to conventional wisdom,
there is no need to introduce boundary layers. This framework is applied to
isolated conical defects, both with deficit as well, but more briefly, as
surplus angles. Using these boundary conditions, we show that the lateral
tension within a circular cone of fixed radius is equal but opposite to the
radial compression, and independent of the deficit angle itself. We proceed to
examine the effect of an oblique outer edge on this cone perturbatively
demonstrating that both the correction to the geometry as well as the stress
distribution in the cone kicks in at second order in the eccentricity of the
edge.Comment: 25 pages, 3 figure
Tension dynamics in semiflexible polymers. Part I: Coarse-grained equations of motion
Based on the wormlike chain model, a coarse-grained description of the
nonlinear dynamics of a weakly bending semiflexible polymer is developed. By
means of a multiple scale perturbation analysis, a length-scale separation
inherent to the weakly-bending limit is exploited to reveal the deterministic
nature of the spatio-temporal relaxation of the backbone tension and to deduce
the corresponding coarse-grained equation of motion. From this partial
integro-differential equation, some detailed analytical predictions for the
non-linear response of a weakly bending polymer are derived in an accompanying
paper (Part II, cond-mat/0609638).Comment: 14 pages, 4 figyres. The second part of this article has the preprint
no.: cond-mat/060963
Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems
This article describes a bridge between POD-based model order reduction
techniques and the classical Newton/Krylov solvers. This bridge is used to
derive an efficient algorithm to correct, "on-the-fly", the reduced order
modelling of highly nonlinear problems undergoing strong topological changes.
Damage initiation problems are addressed and tackle via a corrected
hyperreduction method. It is shown that the relevancy of reduced order model
can be significantly improved with reasonable additional costs when using this
algorithm, even when strong topological changes are involved
Totally Twisted Khovanov Homology
We define a variation of Khovanov homology with an explicit description in
terms of the spanning trees of a link projection. We prove that this new theory
is a link invariant and describe some of its properties. Finally, we provide
some the results of some computer computations of the invariant.Comment: 45 pages, 21 figure
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