29,047 research outputs found
Locally addressable tunnel barriers within a carbon nanotube
We report the realization and characterization of independently controllable
tunnel barriers within a carbon nanotube. The nanotubes are mechanically bent
or kinked using an atomic force microscope, and top gates are subsequently
placed near each kink. Transport measurements indicate that the kinks form
gate-controlled tunnel barriers, and that gates placed away from the kinks have
little or no effect on conductance. The overall conductance of the nanotube can
be controlled by tuning the transmissions of either the kinks or the
metal-nanotube contacts.Comment: related papers at http://marcuslab.harvard.ed
Spinor Fields and Symmetries of the Spacetime
In the background of a stationary black hole, the "conserved current" of a
particular spinor field always approaches the null Killing vector on the
horizon. What's more, when the black hole is asymptotically flat and when the
coordinate system is asymptotically static, then the same current also
approaches the time Killing vector at the spatial infinity. We test these
results against various black hole solutions and no exception is found. The
spinor field only needs to satisfy a very general and simple constraint.Comment: 19 page
Trading Safety Versus Performance: Rapid Deployment of Robotic Swarms with Robust Performance Constraints
In this paper we consider a stochastic deployment problem, where a robotic
swarm is tasked with the objective of positioning at least one robot at each of
a set of pre-assigned targets while meeting a temporal deadline. Travel times
and failure rates are stochastic but related, inasmuch as failure rates
increase with speed. To maximize chances of success while meeting the deadline,
a control strategy has therefore to balance safety and performance. Our
approach is to cast the problem within the theory of constrained Markov
Decision Processes, whereby we seek to compute policies that maximize the
probability of successful deployment while ensuring that the expected duration
of the task is bounded by a given deadline. To account for uncertainties in the
problem parameters, we consider a robust formulation and we propose efficient
solution algorithms, which are of independent interest. Numerical experiments
confirming our theoretical results are presented and discussed
Averaging approximation to singularly perturbed nonlinear stochastic wave equations
An averaging method is applied to derive effective approximation to the
following singularly perturbed nonlinear stochastic damped wave equation \nu
u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on an open bounded domain
\,, \,. Here is a small parameter
characterising the singular perturbation, and \,, \,, parametrises the strength of the noise. Some scaling transformations
and the martingale representation theorem yield the following effective
approximation for small , u_t=\D u+f(u)+\nu^\alpha\dot{W} to an error of
\ord{\nu^\alpha}\,.Comment: 16 pages. Submitte
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