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Edge mode based graphene nanomechanical resonators for high-sensitivity mass sensor
We perform both molecular dynamics simulations and theoretical analysis to
study the sensitivity of the graphene nanomechanical resonator based mass
sensors, which are actuated following the global extended mode or the localized
edge mode. We find that the mass detection sensitivity corresponding to the
edge mode is about three times higher than that corresponding to the extended
mode. Our analytic derivations reveal that the enhancement of the sensitivity
originates in the reduction of the effective mass for the edge mode due to its
localizing feature
Black Hole Mass Formula Is a Vanishing Noether Charge
The Noether current and its variation relation with respect to diffeomorphism
invariance of gravitational theories have been derived from the horizontal
variation and vertical-horizontal bi-variation of the Lagrangian, respectively.
For Einstein's GR in the stationary, axisymmetric black holes, the mass formula
in vacuum can be derived from this Noether current although it definitely
vanishes. This indicates that the mass formula of black holes is a vanishing
Noether charge in this case. The first law of black hole thermodynamics can
also be derived from the variation relation of this vanishing Noether current.Comment: 7 page
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