525 research outputs found
Weak and strong wave turbulence spectra for elastic thin plate
Variety of statistically steady energy spectra in elastic wave turbulence
have been reported in numerical simulations, experiments, and theoretical
studies. Focusing on the energy levels of the system, we have performed direct
numerical simulations according to the F\"{o}ppl--von K\'{a}rm\'{a}n equation,
and successfully reproduced the variability of the energy spectra by changing
the magnitude of external force systematically. When the total energies in wave
fields are small, the energy spectra are close to a statistically steady
solution of the kinetic equation in the weak turbulence theory. On the other
hand, in large-energy wave fields, another self-similar spectrum is found.
Coexistence of the weakly nonlinear spectrum in large wavenumbers and the
strongly nonlinear spectrum in small wavenumbers are also found in moderate
energy wave fields.Comment: 5 pages, 3 figure
Single-wavenumber Representation of Nonlinear Energy Spectrum in Elastic-Wave Turbulence of {F}\"oppl-von {K}\'arm\'an Equation: Energy Decomposition Analysis and Energy Budget
A single-wavenumber representation of nonlinear energy spectrum, i.e.,
stretching energy spectrum is found in elastic-wave turbulence governed by the
F\"oppl-von K\'arm\'an (FvK) equation. The representation enables energy
decomposition analysis in the wavenumber space, and analytical expressions of
detailed energy budget in the nonlinear interactions are obtained for the first
time in wave turbulence systems. We numerically solved the FvK equation and
observed the following facts. Kinetic and bending energies are comparable with
each other at large wavenumbers as the weak turbulence theory suggests. On the
other hand, the stretching energy is larger than the bending energy at small
wavenumbers, i.e., the nonlinearity is relatively strong. The strong
correlation between a mode and its companion mode is
observed at the small wavenumbers. Energy transfer shows that the energy is
input into the wave field through stretching-energy transfer at the small
wavenumbers, and dissipated through the quartic part of kinetic-energy transfer
at the large wavenumbers. A total-energy flux consistent with the energy
conservation is calculated directly by using the analytical expression of the
total-energy transfer, and the forward energy cascade is observed clearly.Comment: 11 pages, 4 figure
Identification of Separation Wavenumber between Weak and Strong Turbulence Spectra for Vibrating Plate
A weakly nonlinear spectrum and a strongly nonlinear spectrum coexist in a
statistically steady state of elastic wave turbulence. The analytical
representation of the nonlinear frequency is obtained by evaluating the
extended self-nonlinear interactions. The {\em critical\/} wavenumbers at which
the nonlinear frequencies are comparable with the linear frequencies agree with
the {\em separation\/} wavenumbers between the weak and strong turbulence
spectra. We also confirm the validity of our analytical representation of the
separation wavenumbers through comparison with the results of direct numerical
simulations by changing the material parameters of a vibrating plate
1000 frame/sec Stereo Matching VLSI Processor with Adaptive Window-Size Control
科研費報告書収録論文(課題番号:17300009/研究代表者:亀山充隆/システムインテグレーション理論に基づく高安全知能自動車用VLSIの最適設計
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