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Title: Energy Harvesting Performance of a Flapping Foil with Leading Edge Motion
F or c e d at a f or a fl a p pi n g f oil e n er g y h ar v e st er wit h a cti v e l e a di n g e d g e m oti o n o p er ati n g i n t h e l o w r e d u c e d fr e q u e n c y r a n g e i s c oll e ct e d t o d et er mi n e h o w l e a di n g e d g e m oti o n aff e ct s e n er g y h ar v e sti n g p erf or m a n c e. T h e f oil pi v ot s a b o ut t h e mi dc h or d a n d o p er at e s i n t h e l o w r e d u c e d fr e q u e n c y r a n g e of 𝑓𝑓 𝑓𝑓 / π‘ˆπ‘ˆ ∞ = 0. 0 6 , 0. 0 8, a n d 0. 1 0 wit h 𝑅𝑅 𝑅𝑅 = 2 0 ,0 0 0 βˆ’ 3 0 ,0 0 0 , wit h a pit c hi n g a m plit u d e of πœƒπœƒ 0 = 7 0 ∘ , a n d a h e a vi n g a m plit u d e of β„Ž 0 = 0. 5 𝑓𝑓 . It i s f o u n d t h at l e a di n g e d g e m oti o n s t h at r e d u c e t h e eff e cti v e a n gl e of att a c k e arl y t h e str o k e w or k t o b ot h i n cr e a s e t h e lift f or c e s a s w ell a s s hift t h e p e a k lift f or c e l at er i n t h e fl a p pi n g str o k e. L e a di n g e d g e m oti o n s i n w hi c h t h e eff e cti v e a n gl e of att a c k i s i n cr e a s e d e arl y i n t h e str o k e s h o w d e cr e a s e d p erf or m a n c e. I n a d diti o n a di s cr et e v ort e x m o d el wit h v ort e x s h e d di n g at t h e l e a di n g e d g e i s i m pl e m e nt f or t h e m oti o n s st u di e d; it i s f o u n d t h at t h e m e c h a ni s m f or s h e d di n g at t h e l e a di n g e d g e i s n ot a d e q u at e f or t hi s p ar a m et er r a n g e a n d t h e m o d el c o n si st e ntl y o v er pr e di ct s t h e a er o d y n a mi c f or c e s.  more » « less
Award ID(s):
1804964
NSF-PAR ID:
10113840
Author(s) / Creator(s):
Date Published:
Journal Name:
Dissertation
ISSN:
1455-1802
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  5. Abstract

    We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in$\mathsf {Quasi}\text {-}\mathsf {NP} = \mathsf {NTIME}[n^{(\log n)^{O(1)}}]$Quasi-NP=NTIME[n(logn)O(1)]and other complexity classes do not have small circuits (in the worst case and/or on average) from various circuit classes$\mathcal { C}$C, by showing that$\mathcal { C}$Cadmits non-trivial satisfiability and/or#SAT algorithms which beat exhaustive search by a minor amount. In this paper, we present a new strong lower bound consequence of having a non-trivial#SAT algorithm for a circuit class${\mathcal C}$C. Say that a symmetric Boolean functionf(x1,…,xn) issparseif it outputs 1 onO(1) values of${\sum }_{i} x_{i}$βˆ‘ixi. We show that for every sparsef, and for all β€œtypical”$\mathcal { C}$C, faster#SAT algorithms for$\mathcal { C}$Ccircuits imply lower bounds against the circuit class$f \circ \mathcal { C}$f∘C, which may bestrongerthan$\mathcal { C}$Citself. In particular:

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    #SAT algorithms for$2^{n^{{\varepsilon }}}$2nΞ΅-size$\mathcal { C}$C-circuits running in$2^{n-n^{{\varepsilon }}}$2nβˆ’nΞ΅time (for someΞ΅> 0) implyQuasi-NPdoes not have$(f \circ \mathcal { C})$(f∘C)-circuits of polynomial size.

    Applying#SAT algorithms from the literature, one immediate corollary of our results is thatQuasi-NPdoes not haveEMAJ∘ACC0∘THRcircuits of polynomial size, whereEMAJis the β€œexact majority” function, improving previous lower bounds againstACC0[Williams JACM’14] andACC0∘THR[Williams STOC’14], [Murray-Williams STOC’18]. This is the first nontrivial lower bound against such a circuit class.

     
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