412 research outputs found
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
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
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
Numerical verification of random phase-and-amplitude formalism of weak turbulence
The Random Phase and Amplitude Formalism (RPA) has significantly extended the
scope of weak turbulence studies. Because RPA does not assume any proximity to
the Gaussianity in the wavenumber space, it can predict, for example, how the
fluctuation of the complex amplitude of each wave mode grows through nonlinear
interactions with other modes, and how it approaches the Gaussianity. Thus, RPA
has a great potential capability, but its validity has been assessed neither
numerically nor experimentally. We compare the theoretical predictions given by
RPA with the results of direct numerical simulation (DNS) for a three-wave
Hamiltonian system, thereby assess the validity of RPA. The predictions of RPA
agree quite well with the results of DNS in all the aspects of statistical
characteristics of mode amplitudes studied here
Dynamics of magnetization on the topological surface
We investigate theoretically the dynamics of magnetization coupled to the
surface Dirac fermions of a three dimensional topological insulator, by
deriving the Landau-Lifshitz-Gilbert (LLG) equation in the presence of charge
current. Both the inverse spin-Galvanic effect and the Gilbert damping
coefficient are related to the two-dimensional diagonal conductivity
of the Dirac fermion, while the Berry phase of the ferromagnetic
moment to the Hall conductivity . The spin transfer torque and the
so-called -terms are shown to be negligibly small. Anomalous behaviors
in various phenomena including the ferromagnetic resonance are predicted in
terms of this LLG equation.Comment: 4+ pages, 1 figur
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