scholarly journals Asymptotics for metamaterials and photonic crystals

2013 ◽  
Vol 469 (2152) ◽  
pp. 20120533 ◽  
Author(s):  
T. Antonakakis ◽  
R. V. Craster ◽  
S. Guenneau
Keyword(s):  
High Frequency ◽  
Negative Refraction ◽  
Low Frequency ◽  
Neumann Boundary ◽  
Ring Resonators ◽  
Split Ring ◽  
Long Wavelength ◽  
Physical Effects ◽  
Directive Antenna ◽  
High Frequency Waves

Metamaterial and photonic crystal structures are central to modern optics and are typically created from multiple elementary repeating cells. We demonstrate how one replaces such structures asymptotically by a continuum, and therefore by a set of equations, that captures the behaviour of potentially high-frequency waves propagating through a periodic medium. The high-frequency homogenization that we use recovers the classical homogenization coefficients in the low-frequency long-wavelength limit. The theory is specifically developed in electromagnetics for two-dimensional square lattices where every cell contains an arbitrary hole with Neumann boundary conditions at its surface and implemented numerically for cylinders and split-ring resonators. Illustrative numerical examples include lensing via all-angle negative refraction, as well as omni-directive antenna, endoscope and cloaking effects. We also highlight the importance of choosing the correct Brillouin zone and the potential of missing interesting physical effects depending upon the path chosen.

Preferential acceleration of heavy ions from thermal velocities

1968 ◽  
Vol 46 (10) ◽  
pp. S638-S641 ◽  
Author(s):  
D. B. Melrose
Keyword(s):  
Frequency Spectrum ◽  
High Frequency ◽  
Heavy Ions ◽  
Crab Nebula ◽  
Low Frequency ◽  
High Frequency Waves ◽  
Hydromagnetic Waves ◽  
The Crab Nebula ◽  
Low Frequency Waves

The acceleration of ions from thermal velocities is analyzed to determine conditions under which heavy ions can be preferentially accelerated. Two accelerating mechanisms involving high-and low-frequency hydromagnetic waves respectively are considered. Preferential acceleration of heavy ions occurs for high-frequency waves if the frequency spectrum falls off faster than (frequency)−1. For the low-frequency waves heavy ions are less effectively accelerated than lighter ions. However, very heavy ions can be preferentially accelerated, the abundances of the very heavy ions being enhanced by a factor Ai over the thermal abundances. Acceleration of ions in the envelope of the Crab nebula is considered as an example.

Integrity Diagnosis Method of Bolted Joint Based on Time Fluctuation of Reflection Intensity Caused by Nonlinear Wave Modulation

2014 ◽  
Author(s):  
Takashi Tanaka ◽  
Arata Masuda ◽  
Akira Sone
Keyword(s):  
Nonlinear Wave ◽  
High Frequency ◽  
Low Frequency ◽  
Bolted Joint ◽  
Contact Interface ◽  
Wave Modulation ◽  
Diagnosis Method ◽  
Time Fluctuation ◽  
High Frequency Waves ◽  
Reflection Intensity

This study presents the integrity diagnosis method of the bolted joint based on nonlinear wave modulation. When the structure that has the contact interface is vibrating at low-frequency, the contact interface is tapping and clapping due to low-frequency vibration. In this condition, the scatter characteristics, such as wave transmissivity and reflectivity, of high-frequency waves in vicinity of the contact interface are fluctuated in synchronization with low-frequency excitation because of the contact acoustic nonlinearity. The time fluctuation of reflection intensity, which expresses the reflectivity in the specific location, of high-frequency waves at the contact interface is given as the reflection intensity map which plots time-spatial map. In this paper, experiment using the beam specimen which has single bolted joint is conducted to examine the performance of the evaluation index based on the fluctuation amplitude of reflection intensity.

The origin of fluctuations and cross-field transport in idealized magnetic confinement systems

1981 ◽  
Vol 300 (1456) ◽  
pp. 547-557 ◽  
Keyword(s):  
Electric Fields ◽  
High Frequency ◽  
Scaling Laws ◽  
Scaling Law ◽  
Low Frequency ◽  
Magnetic Confinement ◽  
Upper Bounds ◽  
Transport Processes ◽  
General View ◽  
Long Wavelength

The study of plasma fluctuations and confinement in idealized systems such as octupoles and levitrons has contributed to the understanding of cross-field transport processes. The linear theory of plasma instabilities that cause fluctuations is well developed and can predict growth rates γ and wavelengths θ x around lines of force. However, the theoretical prediction of cross-field transport coefficient D ± is restricted to quasilinear estimates of upper bounds (for example, D = 1 2 γ λ x 2 ) because of the complexity of the full nonlinear calculation. Such quasilinear estimates usually far exceed the measured values and are of limited worth. A general view of the results from octupole and levitron experiments shows that under collisional conditions ( λ ei / L < 0 ) the diffusion coefficient, D , scales in the same way as classical collisional diffusion ( D α n / T e 1 2 B 2 ). Agreement is closely approached in many cases, sometimes even in the presence of fluctuations. Under collisionless conditions ( D α n / T e 1 2 B 2 ), Bohm diffusion scaling ( D α T e / B ) is found in the few cases where the scaling law has been determined. This behaviour is consistent with the general scaling laws of Connor & Taylor (1977) but is not understood in detail. In addition there is evidence, both experimental and theoretical, that long-wavelength low-frequency electric fields (convection cells) can be generated nonlinearly from high-frequency fluctuations and can contribute to cross-field transport

scholarly journals Propagation of high frequency waves in the quiet solar atmosphere

2008 ◽  
pp. 87-99 ◽  
Author(s):  
A. Andic
Keyword(s):  
Solar Atmosphere ◽  
High Frequency ◽  
Low Frequency ◽  
Magnetic Structures ◽  
Partial Heating ◽  
Fabry Perot ◽  
High Frequency Waves ◽  
Propagation Of Waves ◽  
The Waves ◽  
Low Frequency Waves

High-frequency waves (5 mHz to 20 mHz) have previously been suggested as a source of energy accounting for partial heating of the quiet solar atmosphere. The dynamics of previously detected high-frequency waves is analyzed here. Image sequences were taken by using the German Vacuum Tower Telescope (VTT), Observatorio del Teide, Izana, Tenerife, with a Fabry-Perot spectrometer. The data were speckle reduced and analyzed with wavelets. Wavelet phase-difference analysis was performed to determine whether the waves propagate. We observed the propagation of waves in the frequency range 10 mHz to 13 mHz. We also observed propagation of low-frequency waves in the ranges where they are thought to be evanescent in the regions where magnetic structures are present.

scholarly journals Energy Transfer from High-Shear, Low-Frequency Internal Waves to High-Frequency Waves near Kaena Ridge, Hawaii

2012 ◽  
Vol 42 (9) ◽  
pp. 1524-1547 ◽  
Author(s):  
Oliver M. Sun ◽  
Robert Pinkel
Keyword(s):  
Internal Waves ◽  
High Frequency ◽  
Low Frequency ◽  
Buoyancy Frequency ◽  
Reynolds Stresses ◽  
Turbulent Dissipation ◽  
Transfer Rates ◽  
Energy Transfers ◽  
High Frequency Waves ◽  
Parametric Subharmonic Instability

Abstract Evidence is presented for the transfer of energy from low-frequency inertial–diurnal internal waves to high-frequency waves in the band between 6 cpd and the buoyancy frequency. This transfer links the most energetic waves in the spectrum, those receiving energy directly from the winds, barotropic tides, and parametric subharmonic instability, with those most directly involved in the breaking process. Transfer estimates are based on month-long records of ocean velocity and temperature obtained continuously over 80–800 m from the research platform (R/P) Floating Instrument Platform (FLIP) in the Hawaii Ocean Mixing Experiment (HOME) Nearfield (2002) and Farfield (2001) experiments, in Hawaiian waters. Triple correlations between low-frequency vertical shears and high-frequency Reynolds stresses, 〈uiw∂Ui/∂z〉, are used to estimate energy transfers. These are supported by bispectral analysis, which show significant energy transfers to pairs of waves with nearly identical frequency. Wavenumber bispectra indicate that the vertical scales of the high-frequency waves are unequal, with one wave of comparable scale to that of the low-frequency parent and the other of much longer scale. The scales of the high-frequency waves contrast with the classical pictures of induced diffusion and elastic scattering interactions and violates the scale-separation assumption of eikonal models of interaction. The possibility that the observed waves are Doppler shifted from intrinsic frequencies near f or N is explored. Peak transfer rates in the Nearfield, an energetic tidal conversion site, are on the order of 2 × 10−7 W kg−1 and are of similar magnitude to estimates of turbulent dissipation that were made near the ridge during HOME. Transfer rates in the Farfield are found to be about half the Nearfield values.

Dynamic Variational-Asymptotic Procedure for Laminated Composite Shells—Part II: High-Frequency Vibration Analysis

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
Chang-Yong Lee ◽  
Dewey H. Hodges
Keyword(s):  
High Frequency ◽  
Vibration Analysis ◽  
Shell Theory ◽  
Low Frequency ◽  
Normal Displacement ◽  
Difficult Situation ◽  
Long Wavelength ◽  
First Approximation ◽  
Low Frequency Vibration ◽  
Characteristic Wavelength

Shell theories intended for low-frequency vibration analysis are frequently constructed from a generalization of the classical shell theory in which the normal displacement (to a first approximation) is constant through the thickness. Such theories are not suitable for the analysis of complicated high-frequency effects in which displacements may change rapidly along the thickness coordinate. Clearly, to derive by asymptotic methods, a shell theory suitable for high-frequency behavior requires a different set of assumptions regarding the small parameters associated with the characteristic wavelength and timescale. In Part I such assumptions were used to perform a rigorous dimensional reduction in the long-wavelength low-frequency vibration regime so as to construct an asymptotically correct energy functional to a first approximation. In Part II the derivation is extended to the long-wavelength high-frequency regime. However, for short-wavelength behavior, it becomes very difficult to represent the three-dimensional stress state exactly by any two-dimensional theory; and, at best, only a qualitative agreement can be expected. To rectify this difficult situation, a hyperbolic short-wave extrapolation is used. Unlike published shell theories for this regime, which are limited to homogeneous and isotropic shells, all the formulas derived herein are applicable to shells in which each layer is made of a monoclinic material.

Low Frequency Ultra-Thin Compact Metamaterial Absorber Comprising Split-Ring Resonators

2014 ◽  
Vol 31 (6) ◽  
pp. 067801 ◽  
Author(s):  
Bao-Qin Lin ◽  
Xin-Yu Da ◽  
Shang-Hong Zhao ◽  
Wen Meng ◽  
Fan Li ◽  
...  
Keyword(s):  
Low Frequency ◽  
Metamaterial Absorber ◽  
Ring Resonators ◽  
Split Ring ◽  
Split Ring Resonators
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