Linear Dispersion Curve Research Articles

Generation of Localized Modes in an Electrical Lattice Using Subharmonic Driving

We show experimentally and numerically that an intrinsic localized mode (ILM) can be stably produced (and experimentally observed) via subharmonic, spatially homogeneous driving in the context of a nonlinear electrical lattice. The precise nonlinear spatial response of the system has been seen to depend on the relative location in frequency between the driver frequency, ω(d), and the bottom of the linear dispersion curve, ω(0). If ω(d)/2 lies just below ω(0), then a single ILM can be generated in a 32-node lattice, whereas, when ω(d)/2 lies within the dispersion band, a spatially extended waveform resembling a train of ILMs results. To our knowledge, and despite its apparently broad relevance, such an experimental observation of subharmonically driven ILMs has not been previously reported.

Electronic Properties of Graphite with Rotational Stacking Arrangement

The electronic structure of graphite is studied using the generalized tight-binding approximation. We investigate how the energy spectra around the Fermi energy of graphite depend on interlayer stacking arrangement. We find that graphite and bilayer graphene with rotational stacking arrangement are metals with a massless Dirac fermion at the Fermi level, as is the case for isolated graphene sheets. Due to the spatially separated K points on each layer, two pairs of linear dispersion curves cross at the Fermi energy and are expected to exhibit characteristics different from those of graphite with AB stacking.

Vlasov simulations of trapping and inhomogeneity in Raman scattering

We study stimulated Raman scattering (SRS) in laser-fusion conditions with the Eulerian Vlasov code ELVIS. Back SRS from homogeneous plasmas occurs in sub-picosecond bursts and far exceeds linear theory. Forward SRS and re-scatter of back SRS are also observed. The plasma wave frequency downshifts from the linear dispersion curve, and the electron distribution shows flattening. This is consistent with trapping and reduces the Landau damping. There is some acoustic ($\omega\propto k$) activity and possibly electron acoustic scatter. Kinetic ions do not affect SRS for early times but suppress it later on. SRS from inhomogeneous plasmas exhibits a kinetic enhancement for long density scale lengths. More scattering results when the pump propagates to higher as opposed to lower density.

Second-harmonic generation of Bogoliubov excitations in a two-component Bose-Einstein condensate

A second-harmonic generation (SHG) is predicted for the Bogoliubov excitations in a two-component Bose-Einstein condensate. It is shown that, because the linear dispersion curve of the excitations displays two branches, the phase-matching condition for the SHG can be fulfilled if the wave vectors and frequencies of fundamental and second-harmonic waves are selected suitably from different branches. The nonlinearly coupled envelope equations for the SHG are derived by using a method of multiple scales. The explicit solutions of these envelope equations are provided and the conversion efficiency of the SHG is also discussed.

Doppler radar measurements of wave groups and breaking waves

A 3‐GHz Doppler radar has been used to study wave dynamics and backscatter from the sea surface at low grazing angles. Vertical polarization results are dominated by Bragg scatter even at low (∼8°) grazing angles. Horizontal polarization results, however, show a strong upwind‐downwind asymmetry with additional, high‐velocity intermittent scatter in the upwind direction associated with steep or breaking waves. These characteristics have been exploited to distinguish spilling breaking events from the background Bragg scatter. While these “spikes” at a single range may appear random in time, the combined range and time information reveals a well‐determined propagation pattern. It is shown that for a developing sea in deep water, group behavior modulates the occurrence of wave breaking. The frequency‐wavenumber spectrum shows a clear separation between the linear dispersion curve and nonlinear effects related to breaking. The most important nonlinear feature is a line near the dominant wave group velocity which is identified with the spectrum of breaking intermittency. The slope of this line suggests that the wave components which are most likely to break lie at frequencies significantly above the dominant wave frequency.

Nonexistence of gap solitons in nonlinearly coupled systems

We consider a model consisting of two subsystems with crossing linear dispersion curves, in the case when the coupling between the subsystems is purely nonlinear, so that the crossing does not give rise to a gap in the linear spectrum. We demonstrate that there is a fairly general mechanism precluding the existence of (bright) solitons in systems of this type.

Solitary waves with damped oscillatory tails: an analysis of the fifth-order Korteweg-de Vries equation

We construct oscillatory solitary wave solutions of a fifth-order Korteweg-de Vries equation, where the oscillations decay at infinity. These waves arise as a bifurcation from the linear dispersion curve at that wavenumber where the linear phase speed and group velocity coincide. Our approach is a wave-packet analysis about this wavenumber which leads in the first instance to a higher-order nonlinear Schrödinger equation, from which we then obtain the steady solitary wave solution. We then describe a complementary normal-form analysis which leads to the same result. In addition we derive the nonlinear Schrödinger equation for all wavenumbers, and list all the various anomalous cases.

Moving and Stationary Self-Localized Magnons as Spin-Wave Solitons in Heisenberg Ferromagnets

A theory of elementary excitations in Heisenberg ferromagnets with anisotropic exchange interactions is formulated without assuming the smallness of spin deviations from the ground state. This is done by using a path integral formalism in the SU(2) coherent state representation combined with the use of the stationary-phase approximation. Equations for spin-deviation field variables are solved in an approximate analytical form to show the existence by the intrinsic nonlinearity of mobile and immobile self-localized magnons in one- and d -dimensional cases, respectively. Discussions are given on their characteristic properties such as the energy eigenvalues lying below the linear spin-wave energy band, dispersion curves and localized-mode profiles. These intrinsic nonlinear modes can be considered as a natural extension of conventional (linear) spin waves to the nonlinear, soliton regime.

Nonlinear Excitations in an Order‐Parameter‐Preserving Antiferromagnet

AbstractIntroducing the Dyson‐Maleev transformation and the coherent state ansatz, soliton‐type nonlinear excitations in an order‐parameter‐preserving antiferromagnet (OPP‐AFM) are investigated with help of the method of multiple scales combined with the long‐wavelength approximation. The soliton frequencies enter into the frequency gap of the linear dispersion curve and denote the nonlinear localized modes of this system. These modes which produce the nonlinearity can be viewed as a two‐magnon bound state.

Magnetoelastic YIG Delay Lines with Linear Dispersion

The internal magnetic field in YIG cones and pyramids has been calculated. With a ratio of the height to the base diameter between 0.7 and 1, constant slopes of the axial fields and hence linear dispersion curves for the magnetoelastic echoes are obtained. The useful frequency range is estimated in terms of the focusing condition for spin waves which requires H(off axis) > H(on axis). Experimentally a nearly linear dispersion curve was obtained with a cone of 4.5-mm height and equal base diameter over a frequency range from 1 to 2 GHz; the dispersion rate was 1.7 nsec/MHz. When the turning surface approaches the region in the crystal where the focusing condition is violated, the echoes are cut off. Measured cutoff lengths and demagnetizing fields agree well with calculations. Similar results have been obtained for pyramids and truncated cones.

The Fine Structures ofHαandDαUnder Varying Discharge Conditions

The fine structures of $\mathrm{H}\ensuremath{\alpha}$ and $\mathrm{D}\ensuremath{\alpha}$ have been observed under varying conditions of excitation in the discharge tube with pure hydrogen and pure deuterium maintained in each case at near liquid-air temperature, and with the aid of a Zeiss triple-prism spectrograph and a pair of Hilger quartz interferometer plates. The interference patterns obtained upon the photographic plates were analyzed with a Moll microphotometer. The microphotometer curves were reduced to intensity curves and to linear dispersion curves in the usual manner. From the final reduced curves analyses were made of the intensities and positions of the fine structure components. Within the limits of error of the observations the positions of the fine structure components were found to be invariant with changing discharge conditions. The average interval between the two main components of the complex was found to be 0.319 ${\mathrm{cm}}^{\ensuremath{-}1}$ for $\mathrm{H}\ensuremath{\alpha}$ and 0.321 ${\mathrm{cm}}^{\ensuremath{-}1}$ for $\mathrm{D}\ensuremath{\alpha}$. The second and third most intense components were optically resolved from each other in $\mathrm{D}\ensuremath{\alpha}$ but not in $\mathrm{H}\ensuremath{\alpha}$. The average interval between these components was found to be 0.130 ${\mathrm{cm}}^{\ensuremath{-}1}$. According to theory these intervals are respectively 0.328 ${\mathrm{cm}}^{\ensuremath{-}1}$ and 0.108 ${\mathrm{cm}}^{\ensuremath{-}1}$.