12,502 research outputs found
The difficulty of folding self-folding origami
Why is it difficult to refold a previously folded sheet of paper? We show
that even crease patterns with only one designed folding motion inevitably
contain an exponential number of `distractor' folding branches accessible from
a bifurcation at the flat state. Consequently, refolding a sheet requires
finding the ground state in a glassy energy landscape with an exponential
number of other attractors of higher energy, much like in models of protein
folding (Levinthal's paradox) and other NP-hard satisfiability (SAT) problems.
As in these problems, we find that refolding a sheet requires actuation at
multiple carefully chosen creases. We show that seeding successful folding in
this way can be understood in terms of sub-patterns that fold when cut out
(`folding islands'). Besides providing guidelines for the placement of active
hinges in origami applications, our results point to fundamental limits on the
programmability of energy landscapes in sheets.Comment: 8 pages, 5 figure
Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime
The Sweet-Parker layer in a system that exceeds a critical value of the
Lundquist number () is unstable to the plasmoid instability. In this paper,
a numerical scaling study has been done with an island coalescing system driven
by a low level of random noise. In the early stage, a primary Sweet-Parker
layer forms between the two coalescing islands. The primary Sweet-Parker layer
breaks into multiple plasmoids and even thinner current sheets through multiple
levels of cascading if the Lundquist number is greater than a critical value
. As a result of the plasmoid instability, the system
realizes a fast nonlinear reconnection rate that is nearly independent of ,
and is only weakly dependent on the level of noise. The number of plasmoids in
the linear regime is found to scales as , as predicted by an earlier
asymptotic analysis (Loureiro \emph{et al.}, Phys. Plasmas \textbf{14}, 100703
(2007)). In the nonlinear regime, the number of plasmoids follows a steeper
scaling, and is proportional to . The thickness and length of current sheets
are found to scale as , and the local current densities of current
sheets scale as . Heuristic arguments are given in support of theses
scaling relations.Comment: Submitted to Phys. Plasma
Online, interactive user guidance for high-dimensional, constrained motion planning
We consider the problem of planning a collision-free path for a
high-dimensional robot. Specifically, we suggest a planning framework where a
motion-planning algorithm can obtain guidance from a user. In contrast to
existing approaches that try to speed up planning by incorporating experiences
or demonstrations ahead of planning, we suggest to seek user guidance only when
the planner identifies that it ceases to make significant progress towards the
goal. Guidance is provided in the form of an intermediate configuration
, which is used to bias the planner to go through . We
demonstrate our approach for the case where the planning algorithm is
Multi-Heuristic A* (MHA*) and the robot is a 34-DOF humanoid. We show that our
approach allows to compute highly-constrained paths with little domain
knowledge. Without our approach, solving such problems requires
carefully-crafting domain-dependent heuristics
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