scholarly journals Energy Spectra of Ensemble of Nonlinear Capillary Waves on a Fluid

2021 ◽  
Vol 9 (12) ◽  
pp. 1422
Author(s):  
Elena Tobisch ◽  
Alexey Kartashov
Keyword(s):  
Kinetic Equation ◽  
Energy Spectrum ◽  
Wave Spectrum ◽  
Capillary Waves ◽  
Energy Spectra ◽  
Dynamic Equations ◽  
Turbulent Regime ◽  
Nonlinear Interactions ◽  
Wave Interactions ◽  
Energy Cascades

The problem of spectral description of the nonlinear capillary waves on the fluid surface is discussed. Usually, three-wave nonlinear interactions are considered as a major factor determined by the energy spectrum of these waves in the kinetic wave turbulent regime. We demonstrate that four-wave interactions should be taken into account. In this case, there are two possible scenarios for the transfer of energy over the wave spectrum: kinetic and dynamic. The first is described by the averaged stochastic interaction of waves using the kinetic equation, while the second is described by dynamic equations written for discrete modes. In this article, we compare the time scales, spectral shapes, and other properties of both energy cascades, allowing them to be identified in an experiment.

On the Importance of the Exact Nonlinear Interactions in the Spectral Characterization of Rogue Waves

2018 ◽  
Author(s):  
Sonia Ponce de León ◽  
Alfred R. Osborne ◽  
Carlos Guedes Soares
Keyword(s):  
Wave Spectrum ◽  
Wave Model ◽  
Rogue Waves ◽  
Clear Understanding ◽  
Nonlinear Interactions ◽  
Wave Interactions ◽  
Nonlinear Part ◽  
Wave Dynamics ◽  
Spectral Wave Model ◽  
Future Work

This work is focused on the analysis of the wave action equation with full 4-wave interactions (Snl4). For this purpose, we have applied a state-of-the-art spectral wave model (Wave Watch III), using an exact method for the calculation of the full nonlinear Boltzmann interactions in the evolution of the wave spectrum. We emphasize the use of the exact WRT method [Van Vledder, 2006] for the computation of the Snl4 interactions instead of the approximate DIA method. The WRT algorithm includes the full Boltzmann integrations. We discuss how the WRT method is important in any assessment of rogue waves in the ocean and discuss how the enhanced spectral peak assists the formation of rogue waves packets. We demonstrate how the most nonlinear part of the peak of the spectrum is reduced in amplitude when the nonlinear interactions are instead computed using the DIA interactions. These results suggest that a clear understanding of the physics of nonlinear interactions and of rogue wave dynamics requires the use of the full Boltzmann interactions. Future work would include faster WRT computations so that practical forecasting/hindcasting can become possible using the full four-wave interactions.

Diffraction properties of a strongly bent diamond crystal used as a dispersive spectrometer for XFEL pulses

2019 ◽  
Vol 26 (4) ◽  
pp. 1069-1072 ◽  
Author(s):  
Liubov Samoylova ◽  
Ulrike Boesenberg ◽  
Aleksandr Chumakov ◽  
Vladimir Kaganer ◽  
Ilia Petrov ◽  
...  
Keyword(s):  
Experimental Data ◽  
Energy Spectrum ◽  
Strain Gradient ◽  
Free Electron ◽  
Diamond Crystal ◽  
Energy Spectra ◽  
Theoretical Modelling ◽  
Free Electron Lasers ◽  
X Ray ◽  
Stochastic Nature

Self-amplified spontaneous emission (SASE) enables X-ray free-electron lasers (XFELs) to generate hard X-ray pulses of sub-100 fs duration. However, due to the stochastic nature of SASE, the energy spectrum fluctuates from pulse to pulse. Many experiments that employ XFEL radiation require the resolution of the spectrum of each pulse. The work presented here investigates the capacity of a thin strongly bent diamond crystal to resolve the energy spectra of hard X-ray SASE pulses by studying its diffraction properties. Rocking curves of the symmetric C*(440) reflection have been measured for different bending radii. The experimental data match the theoretical modelling based on the Takagi–Taupin equations of dynamical diffraction. A uniform strain gradient has proven to be a valid model of strain deformations in the crystal.

scholarly journals Energy spectra of muonic atoms in quantum electrodynamics

2019 ◽  
Vol 204 ◽  
pp. 05007 ◽  
Author(s):  
A. E. Dorokhov ◽  
A. A. Krutov ◽  
A. P. Martynenko ◽  
F. A. Martynenko ◽  
O. S. Sukhorukova
Keyword(s):  
Experimental Data ◽  
Perturbation Theory ◽  
Energy Spectrum ◽  
Hyperfine Structure ◽  
Nuclear Structure ◽  
Quantum Electrodynamics ◽  
Vacuum Polarization ◽  
Energy Spectra ◽  
Hyperfine Splittings ◽  
S States

Vacuum polarization, nuclear structure and recoil, radiative corrections to the hyperfine structure of S-states in muonic ions of lithium, beryllium and boron are calculated on the basis of quasipotential method in quantum electrodynamics. We consider contributions in first and second orders of perturbation theory which have the order α5 and α6 in the energy spectrum. Total values of hyperfine splittings are obtained which can be used for a comparison with future experimental data.

scholarly journals Measurement of ambient neutrons in an underground laboratory at the Kamioka Observatory

2018 ◽  
Vol 2018 (12) ◽  
Author(s):  
Keita Mizukoshi ◽  
Ryosuke Taishaku ◽  
Keishi Hosokawa ◽  
Kazuyoshi Kobayashi ◽  
Kentaro Miuchi ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Energy Spectrum ◽  
Neutron Flux ◽  
Thermal Neutron Flux ◽  
Spectral Shape ◽  
Underground Laboratory ◽  
Energy Spectra ◽  
Detector Response ◽  
Total Neutron ◽  
Important Input

Abstract Ambient neutrons are one of the most serious backgrounds for underground experiments searching for rare events. The ambient neutron flux in an underground laboratory at the Kamioka Observatory was measured using a $\mathrm{^3He}$ proportional counter with various moderator setups. Since the detector response largely depends on the spectral shape, the energy spectra of the neutrons transported from the rock to the laboratory were estimated by Monte Carlo simulations. The ratio of the thermal neutron flux to the total neutron flux was found to depend on the thermalizing efficiency of the rock. Therefore, the ratio of the count rate without a moderator to that with a moderator was used to determine this parameter. Consequently, the most likely neutron spectrum predicted by the simulations for the parameters determined by the experimental results was obtained. The result suggests an interesting spectral shape, which has not been indicated in previous studies. The total ambient neutron flux is $(23.5 \pm 0.7 \ \mathrm{_{stat.}} ^{+1.9}_{-2.1} \ \mathrm{_{sys.}}) \times 10^{-6}$ cm$^{-2}$ s$^{-1}$. This result, especially the energy spectrum information, could be a new and important input for estimating the background in current and future experiments in the underground laboratory at the Kamioka Observatory.

scholarly journals Accelerated procedure to solve kinetic equation for neutral atoms in a hot plasma

2018 ◽  
Vol 09 (05) ◽  
pp. 1850048 ◽  
Author(s):  
Mikhail Z. Tokar
Keyword(s):  
Monte Carlo ◽  
Kinetic Equation ◽  
Energy Spectrum ◽  
Erosion Rate ◽  
Fusion Reactor ◽  
Two Dimensional ◽  
First Wall ◽  
One Dimensional ◽  
Hot Plasma ◽  
Electrons And Ions

By reaching the first wall of a fusion reactor, charged plasma particles, electrons and ions are recombined into neutral molecules and atoms of hydrogen isotopes. These species recycle back into the plasma volume and participate, in particular, in charge–exchange (cx) collisions with ions. As a result, hot atoms with chaotically directed velocities are generated and some of them hit the wall. Statistical Monte Carlo methods often used to model the behavior of cx atoms are too time-consuming for comprehensive parameter studies. Recently1 an alternative iteration approach to solve one-dimensional kinetic equation2 has been significantly accelerated, by a factor of 30–50, by applying a pass method to evaluate the arising integrals from functions, involving the ion velocity distribution. Here, this approach is used by solving a two-dimensional kinetic equation, describing the transport of cx atoms in the vicinity of an opening in the wall, e.g., the entrance of a duct guiding to a diagnostic installation. To assess the erosion rate and lifetime of the installation, one need to know the energy spectrum of hot cx atoms escaping from the plasma into the duct. Calculations are done for a first mirror of molybdenum under plasma conditions expected in a fusion reactor like DEMO.3,4 The results of kinetic modeling are compared with those found by using a diffusion approximation5 relevant for cx atoms if the time between cx collisions with ions is much smaller than the time till the ionization of atoms by electrons. The present more exact kinetic consideration predicts a mirror erosion rate by a factor of 2 larger than the approximate diffusion approach.

Implementing New Nonlinear Term in Third Generation Wave Models

2014 ◽  
Author(s):  
Odin Gramstad ◽  
Alexander Babanin
Keyword(s):  
Kinetic Equation ◽  
Spread Spectrum ◽  
Time Scale ◽  
Source Term ◽  
Wave Spectrum ◽  
Wave Model ◽  
Third Generation ◽  
Spectral Evolution ◽  
Linear Interaction ◽  
Wavewatch Iii

The non-linear interaction term is one of the three key source functions in every third-generation spectral wave model. An update of physics of this term is discussed. The standard statistical/phase-averaged description of the nonlinear transfer of energy in the wave spectrum (wave-turbulence) is based on Hasselmann’s kinetic equation [1]. In the derivation of the kinetic equation (KE) it is assumed that the evolution takes place on the slow O(ε−4) time scale, where ε is the wave steepness. This excludes the effects of near-resonant quartet interactions that may lead to spectral evolution on the ‘fast’ O(ε−2) time scale. Generalizations of the KE (GKE) that enable description of spectral evolution on the O(ε−2) time scale [2–4] are discussed. The GKE, first solved numerically in [4], is implemented as a source term in the third generation wave model WAVEWATCH-III. The new source term (GKE) is tested and compared to the other nonlinear-interaction source terms in WAVEWATCH-III; the full KE (WRT method) and the approximate DIA method. It is shown that the GKE gives similar results to the KE in the case of a relatively broad banded and directional spread spectrum, while it shows somewhat larger difference in the case of a more narrow banded spectrum with narrower directional distribution. We suggest that the GKE may be a suitable replacement to the KE in situations where ‘fast’ spectral evolution takes place.

Higher order auto‐spectra by maximum entropy method

Geophysics ◽  
1983 ◽  
Vol 48 (10) ◽  
pp. 1409-1410 ◽  
Author(s):  
Robert Owen Plaisted ◽  
Hugo Gustavo Peña
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Power Spectra ◽  
Higher Order ◽  
Linear Process ◽  
Entropy Method ◽  
Resolving Power ◽  
Energy Spectra ◽  
Nonlinear Interactions

Higher order auto‐spectra, in particular bispectra and perhaps trispectra, are being used increasingly for analyzing various nonlinear interactions in the ocean, e.g., Herring (1980) and McComas and Briscoe (1980). The resolution of these spectra, as with conventional energy spectra, is frequently limited because short data records must be used. The purpose of this note is to present a maximum entropy (MEM) representation for higher order auto‐spectra which has the advantage of the superior resolving power of the MEM technique under these circumstances. The derivation is a generalizaton of the power spectra derived for a linear process (Box and Jenkins, 1970). We derive an MEM representation for bispectra and show that this result can be generalized to auto‐spectra of any order.

The effects of the nature of matter traversed by cosmic rays on their composition and energy spectrum

1968 ◽  
Vol 46 (10) ◽  
pp. S512-S514
Author(s):  
M. V. K. Apparao ◽  
S. Ramadurai
Keyword(s):  
Energy Spectrum ◽  
Cosmic Rays ◽  
Neutral Hydrogen ◽  
Cosmic Ray ◽  
The State ◽  
Energy Spectra ◽  
Ionization Loss ◽  
Usual Assumption ◽  
Considerable Portion ◽  
Nature Of Matter

The effects of the state of ionization of the matter traversed by cosmic rays, and those due to the presence of helium in it, have been studied. The amount of matter traversed by cosmic rays expressed in g/cm2 deduced by the usual assumption that the matter traversed is all neutral hydrogen can be erroneous. The presence of helium increases this value, and a considerable portion of the matter is helium. The ionized (partial) nature of the matter increases the ionization loss of cosmic-ray nuclei. The effect of this on energy spectra has been demonstrated.

A review of the central role of nonlinear interactions in wind—wave evolution

1993 ◽  
Vol 342 (1666) ◽  
pp. 505-524 ◽  
Keyword(s):  
Surface Waves ◽  
Nonlinear Wave ◽  
High Frequency ◽  
Numerical Experiments ◽  
Wind Wave ◽  
Nonlinear Interactions ◽  
Wave Interactions ◽  
Detailed Review ◽  
Local Perturbations

Nonlinear wave-wave interactions play a central role in the development of wind-generated surface waves. A detailed review of com putational techniques which have been proposed for their evaluation is provided. Numerical experiments are used to determine the manner in which the nonlinear terms control spectral development with fetch, the directional spread of the spectrum and the high-frequency spectral tail. In addition, the nonlinear terms have a shape-stabilizing role, continually smoothing local perturbations in the spectrum and forcing it back to a ‘preferred’ shape.

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