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Efficient harmonic oscillator chain energy harvester driven by colored noise
We study the performance of an electromechanical harmonic oscillator chain as
an energy harvester to extract power from finite-bandwidth ambient random
vibrations, which are modelled by colored noise. The proposed device is
numerically simulated and its performance assessed by means of the net
electrical power generated and its efficiency in converting the external
noise-supplied power into electrical power. Our main result is a much enhanced
performance, both in the net electrical power delivered and in efficiency, of
the harmonic chain with respect to the popular single oscillator resonator. Our
numerical findings are explained by means of an analytical approximation, in
excellent agreement with numerics
Dendrites and conformal symmetry
Progress toward characterization of structural and biophysical properties of
neural dendrites together with recent findings emphasizing their role in neural
computation, has propelled growing interest in refining existing theoretical
models of electrical propagation in dendrites while advocating novel analytic
tools. In this paper we focus on the cable equation describing electric
propagation in dendrites with different geometry. When the geometry is
cylindrical we show that the cable equation is invariant under the
Schr\"odinger group and by using the dendrite parameters, a representation of
the Schr\"odinger algebra is provided. Furthermore, when the geometry profile
is parabolic we show that the cable equation is equivalent to the Schr\"odinger
equation for the 1-dimensional free particle, which is invariant under the
Schr\"odinger group. Moreover, we show that there is a family of dendrite
geometries for which the cable equation is equivalent to the Schr\"odinger
equation for the 1-dimensional conformal quantum mechanics.Comment: 19 page
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