3,812 research outputs found
Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis
We consider the frequency domain form of proper orthogonal decomposition
(POD) called spectral proper orthogonal decomposition (SPOD). Spectral POD is
derived from a space-time POD problem for statistically stationary flows and
leads to modes that each oscillate at a single frequency. This form of POD goes
back to the original work of Lumley (Stochastic tools in turbulence, Academic
Press, 1970), but has been overshadowed by a space-only form of POD since the
1990s. We clarify the relationship between these two forms of POD and show that
SPOD modes represent structures that evolve coherently in space and time while
space-only POD modes in general do not. We also establish a relationship
between SPOD and dynamic mode decomposition (DMD); we show that SPOD modes are
in fact optimally averaged DMD modes obtained from an ensemble DMD problem for
stationary flows. Accordingly, SPOD modes represent structures that are dynamic
in the same sense as DMD modes but also optimally account for the statistical
variability of turbulent flows. Finally, we establish a connection between SPOD
and resolvent analysis. The key observation is that the resolvent-mode
expansion coefficients must be regarded as statistical quantities to ensure
convergent approximations of the flow statistics. When the expansion
coefficients are uncorrelated, we show that SPOD and resolvent modes are
identical. Our theoretical results and the overall utility of SPOD are
demonstrated using two example problems: the complex Ginzburg-Landau equation
and a turbulent jet
Farmers\u27 business cooperation in Knox County, Tennessee
The purpose of this study is to analyze the successes and failures of rural cooperative organizations in Knox County, Tennessee.
It is hoped that the information obtained will be helpful in showing the type of organization, method of management, and economic and agricultural conditions which contribute most to the success of farmers’ cooperatives in this county, and in other similar areas
Non-Uniform Stochastic Average Gradient Method for Training Conditional Random Fields
We apply stochastic average gradient (SAG) algorithms for training
conditional random fields (CRFs). We describe a practical implementation that
uses structure in the CRF gradient to reduce the memory requirement of this
linearly-convergent stochastic gradient method, propose a non-uniform sampling
scheme that substantially improves practical performance, and analyze the rate
of convergence of the SAGA variant under non-uniform sampling. Our experimental
results reveal that our method often significantly outperforms existing methods
in terms of the training objective, and performs as well or better than
optimally-tuned stochastic gradient methods in terms of test error.Comment: AI/Stats 2015, 24 page
Jet-edge interaction tones
Motivated by the problem of jet-flap interaction noise, we study the tonal
dynamics that occur when a sharp edge is placed in the hydrodynamic nearfield
of an isothermal turbulent jet. We perform hydrodynamic and acoustic pressure
measurements in order to characterise the tones as a function of Mach number
and streamwise edge position. The distribution of spectral peaks observed, as a
function of Mach number, cannot be explained using the usual edge-tone
scenario, in which resonance is underpinned by coupling between
downstream-travelling Kelvin-Helmholtz wavepackets and upstream-travelling
sound waves. We show, rather, that the strongest tones are due to coupling
between the former and upstream-travelling jet modes recently studied by Towne
et al. (2017) and Schmidt et al. (2017). We also study the band-limited nature
of the resonance, showing a high-frequency cut-off to be due to the frequency
dependence of the upstream-travelling waves. At high Mach number these become
evanescent above a certain frequency, whereas at low Mach number they become
progressively trapped with increasing frequency, a consequence of which is
their not being reflected in the nozzle plane. Additionally, a weaker,
low-frequency, forced-resonance regime is identified that involves the same
upstream travelling jet modes but that couple, in this instance, with
downstream-travelling sound waves. It is suggested that the existence of two
resonance regimes may be due to the non-modal nature of wavepacket dynamics at
low-frequency.Comment: 21 pages, 15 figure
Computing Motion Plans for Assembling Particles with Global Control
We investigate motion planning algorithms for the assembly of shapes in the
\emph{tilt model} in which unit-square tiles move in a grid world under the
influence of uniform external forces and self-assemble according to certain
rules. We provide several heuristics and experimental evaluation of their
success rate, solution length, runtime, and memory consumption.Comment: 20 pages, 12 figure
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