Tunable dispersion relations manipulated by strain in skyrmion-based magnonic crystals

We theoretically investigate the propagation characteristics of spin waves in skyrmion-based magnonic crystals. It is found that the dispersion relation can be manipulated by strains through magneto-elastic coupling. Especially, the allowed bands and forbidden bands in dispersion relations shift to higher frequency with strain changing from compressive to tensile,while shifting to lower frequency with strain changing from tensile to compressive. We also confirm that the spin wave with specific frequency can pass the magnonic crystal or be blocked by tuning the strains. The result provides an advanced platform for studying the tunable skyrmion-based spin wave devices.

Dispersion Relations in Diffraction in Time

In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, g(x′)=±Sgn(x′)g(x′), which defines the property of being a truncated functions at the origin. On the other hand, we prove that the wave-function of a generalized diffraction in time problem is just the Fourier-transform of a truncated function. Consequently, the existence of dispersion relations for the diffraction in time wave-function follows. We derive these explicit dispersion relations.

Analysis of Wave Nonlinear Dispersion Relations

The nonlinear dispersion relations and modified relations proposed by Kirby and Hedges have the limitation of intermediate minimum value. To overcome the shortcoming, a new nonlinear dispersion relation is proposed. Based on the summarization and comparison of existing nonlinear dispersion relations, it can be found that the new nonlinear dispersion relation not only keeps the advantages of other nonlinear dispersion relations, but also significantly reduces the relative errors of the nonlinear dispersion relations for a range of the relative water depth of 1<kh<1.5 and has sufficient accuracy for practical purposes.

Dispersion relation of internal waves in thewestern equatorial Pacific Ocean

Based mainly on TOGA-COARE data, that is, the CTD data from R/V Xiangyanghong No. 5 (Pu et al., 1993), the temperature and current data from the Woods Hole mooring and other deep current data, the layered numerical profiles of buoyancy frequency and mean current components are figured out. A numerical method calculating internal wave dispersion relation without background shear current, used by Fliegel and Hunkins (1975), is improved to be fit for the internal wave equation with mean currents and their second derivatives. The dispersion relations and wave functions of the long crested internal wave progressing in any direction can be calculated conveniently by using the improved method. A comparison between the calculated dispersion relation in the paper and the dispersion relation in GM spectral model of ocean internal waves (Garret and Munk, 1972) is performed. It shows that the mean currents are important to the dispersion relation of internal waves in the western equatorial Pacific Ocean and that the currents make the wave progressing co-directional with (against) the currents stretched (shrink). The influence of the mean currents on dispersion relation is much stronger than that of their second derivatives, but that on wave function is less than that of their second derivatives. The influences on wave functions result in the change of vertical wavenumber, that is, making the wave function stretch or shrink. There exists obvious turning depth but no significant critical layer absorption is found.

Nonlinear Dispersion Relation in Wave Transformation

A nonlinear dispersion relation is presented to model the nonlinear dispersion of waves over the whole range of possible water depths. It reduces the phase speed over prediction of both Hedges′ modified relation and Kirby and Dalrymple′s modified relation in the region of 1< kh <1 5 for small wave steepness and maintains the monotonicity in phase speed variation for large wave steepness. And it has a simple form. By use of the new nonlinear dispersion relation along with the mild slope equation taking into account weak nonlinearity, a mathematical model of wave transformation is developed and applied to laboratory data. The results show that the model with the new dispersion relation can predict wave transformation over complicated bathymetry satisfactorily.

Dispersion relation of excitation mode in strongly interacting fermions matter

This paper analyses the dispersion relation of the excitation mode in non-relativistic interacting fermion matter. The polarization tensor is calculated with the random phase approximation in terms of finite temperature field theory. With the polarization tensor, the influences of temperature, particle number density and interaction strength on the dispersion relation are discussed in detail. It finds that the collective effects are qualitatively more important in the unitary fermions than those in the finite contact interaction matter.

The surface plasmon polariton dispersion relations in a nonlinear-metal-nonlinear dielectric structure of arbitrary nonlinearity

The analytic surface plasmon polaritons （SPPs） dispersion relation is studied in a system consisting of a thin metallic film bounded by two sides media of nonlinear dielectric of arbitrary nonlinearity is studied by applying a generalised first integral approach. We consider both asymmetric and symmetric structures. Especially, in the symmetric system, two possible modes can exist： the odd mode and the even mode. The dispersion relations of the two modes are obtained. Due to the nonlinear dielectric, the magnitude of the electric field at the interface appears and alters the dispersion relations. The changes in SPPs dispersion relations depending on film thicknesses and nonlinearity are studied.

Numerical calculation of dispersion relation for linear internal waves

With the horizontal Coriolis terms included in motion equations and the influence of compressibility of seawater on Brunt-Vaeisiaelae frequency considered, a numerical method of calculating the dispersion relation for linear internal waves, which is an improvement of Cai and Gan （1995）, and hence Fliegel and Hunkins （1975）, had been set up. For different models （Pacific model, Atlantic model and Arctic model）, simulations using the three different methods were compared and the following conclusions were reached： （1） the influence of horizontal Coriolis terms on dispersion relation cannot be neglected and is connected with the direction of the wave celerity, the latitude, and the modes of the wave （2） the effect of compressibility of seawater in stratification is not an important factor for the dispersion relation of linear internal wave, at least for those three models, With the improved method, the wavefunction curves for the Pacific model had also been built.

Dispersion relations of lattice waves in three-dimensional strongly coupled complex plasma crystals

Dispersion relation matrices, with the screened Coulomb interaction between a charged dust particle and all other particles taken into account, are derived for waves in body centred cubic （bcc） and face centred cubic （fcc） lattices in three-dimensional strongly coupled complex plasma crystals separately. The matrices are then calculated in characteristic directions to obtain the longitudinal and transverse eigenmodes. The longitudinal and transverse waves for these cases are discussed separately.

PDRK:A General Kinetic Dispersion Relation Solver for Magnetized Plasma

A general,fast,and effective approach is developed for numerical calculation of kinetic plasma linear dispersion relations.The plasma dispersion function is approximated by J-pole expansion.Subsequently,the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system.Numerical solutions for the least damped or fastest growing modes using an 8-pole expansion are generally accurate;more strongly damped modes are less accurate,but are less likely to be of physical interest.In contrast to conventional approaches,such as Newton＇s iterative method,this approach can give either all the solutions in the system or a few solutions around the initial guess.It is also free from convergence problems.The approach is demonstrated for electrostatic dispersion equations with one-dimensional and twodimensional wavevectors,and for electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with relative parallel velocity flows between species.

The dispersion relations for surface plasmon in a nonlinear-metal-nonlinear dielectric structure

In the asymmetric and symmetric nonlinear-metal-nonlinear dielectric structures, this paper studies the analytic dispersion relation for surface plasmon in a system consisting of a thin metallic film covered on two sides media of intensity-dependent refractive indexes by applying a generalised first integral approach. Especially in the symmetric waveguide structure, two possible modes can exist： the odd mode and the even mode. The dispersion relations of the two modes are obtained. Due to the nonlinear dielectric, the squared magnitude of the electric field at the interface appears and alters the dispersion relations. Numerical results are compared to those from a certain approximate treatment.

Dispersion Relations in Binary Gas Mixtures From a Kinetic Theory

Sound propagation and the initial value problems in gas mixtures of two components are investigated. By using the eigen theory of linearized Boltzmann equations, a model equations is formed, with the use of the Fourier-Laplace transform for model equations derived, the dispersion relations for both components are obtained.

Phonon dispersion relations of crystalline solids based on LAMMPS package

The phonon dispersion relations of crystalline solids play an important role in determining the mechanical and thermal properties of materials.The phonon dispersion relation,as well as the vibrational density of states,is also often used as an indicator of variation of lattice thermal conductivity with the external stress,defects,etc.In this study,a simple and fast tool is proposed to acquire the phonon dispersion relation of crystalline solids based on the LAMMPS package.The theoretical details for the calculation of the phonon dispersion relation are derived mathematically and the computational flow chart is present.The tool is first used to calculate the phonon dispersion relation of graphene with two atoms in the unit cell.Then,the phonon dispersions corresponding to several potentials or force fields,which are commonly used in the LAMMPS package to modeling the graphene,are obtained to compare with that from the DFT calculation.They are further extended to evaluate the accuracy of the used potentials before the molecular dynamics simulation.The tool is also used to calculate the phonon dispersion relation of superlattice structures that contains more than one hundred of atoms in the unit cell,which predicts the phonon band gaps along the cross-plane direction.Since the phonon dispersion relation plays an important role in the physical properties of condensed matter,the proposed tool for the calculation of the phonon dispersion relation is of great significance for predicting and explaining the mechanical and thermal properties of crystalline solids.

Dispersion Relation of Linear Waves in Quantum Magnetoplasmas

The quantum magnetohydrodynamic （QMHD） model is applied in investigating the propagation of linear waves in quantum magnetoplasmas. Using the QMHD model, the dispersion equation for quantum magnetoplasmas and the dispersion relations of linear waves are deduced. Results show that quantum effects affect the propagation of electron plasma waves and extraordinary waves （X waves）. When we select the plasma parameters of the laser-based plasma compression （LBPC） schemes for calculation, the quantum correction cannot be neglected. Meanwhile, the corrections produced by the Fermi degeneracy pressure and Bohm potential are compared under different plasma parameter conditions.

Black Hole Entropy with Modified Dispersion Relations

There is much interest in resolving the quantum corrections to Bekenstein-Hawking entropy with a large length scale limit. The leading correction term ＆ given by the logarithm of black hole area with a model-dependent coefficient. Recently the research for quantum gravity implies the emergence of a modification of the energy-momentum dispersion relation （MDR）, which plays an important role in the modified black hole thermodynamics. In this paper, we investigate the quantum corrections to Bekenstein-Hawking entropy in four-dimensional Sehwarzschild black hole and Reissner-Nordstrom black hole respectively based on MDR.

Dispersion Relation of δ Meson and Pion at Finite Nuclear Density in Chiral δ Model

The propagators of pion and sigma meson at a finite nuclear density and zero temperature are studied in chiral σ model. Their dispersion relations are calculated numerically in one-loop approximation. In order to avoid the so-called tachyon pole appearing in the one-loop propagators of pion and sigma meson, we regard the mass of sigma meson mσ as a free parameter and adjust it to fit the nuclear saturation properties. For mσ equal to 3075 MeV, the tachyonpole does not appear at the normal nuclear density. Thus the dispersion relation can be calculated in chiral σ model in one-loop level for the first time.

Dispersion relation of excitation mode in spin-polarized Fermi gas

We study the dispersion relation of the excitation mode in a spin-polarized Fermi gas. In the frame of the imaginarytime finite temperature field theory, the polarization tensor is calculated by taking the random phase approximation. The population imbalance effects on the dispersion relation of the excitation mode and the spin-spin correlation susceptibility are investigated. The numerical results in terms of the imbalance ratio indicate the polarization effects on the dispersion relation and susceptibility X.

Phonon dispersion relations and soft modes of 4 carbon nanotubes

The phonon dispersion relations of three kinds of 4 A carbon nanotubes are calculated by using the density functional perturbation theory. It is found that the frequencies of some phonon modes are very sensitive to the smearing width used in the calculations, and eventually become negative at low electronic temperature. Moreover, two kinds of soft modes are identified for the （5,0） tube which are quite different from those reported previously. Our results suggest that the （5,0） tube remains metallic at very low temperature, instead of the metallie-semiconducting transition claimed before.

Dispersion Relations of Longitudinal Plasmons in One,Two and Three Dimensional Electron Gas of Metals

The longitudinal plasmons are the electrostatic collective excitations of the solid electron gas. In this paper, the dispersion relations of these plasmons for one-, two- and threedimensional electron gas are compactly derived in two approaches with uniform disturbed Coulomb potentials. The first approach is adopted usually in solid state theory that is the so-called random phase approximation （RPA） with the Lindhard dielectric function in the long-wavelength and high-frequency limits. The second method is a typical plasma fluid description that includes the electron fluid equations with the adiabatic process in the jellium model. The disturbed electrostatic （Coulomb） potential produced by the oscillation of electron density is dimensionally dependent and derived from the Poisson equation in Appendix B.

Study on dynamics of shear waves-Ⅰ. Scale analysis and dispersion relation

- Starting from satellite remote sensing data, the dynamical processes of shear waves occurring at the boundary between the western boundary current and the shelf slope water are studied and dynamically analyzed in this study. The average wavelength is 75 km, and the average amplitude (from crest to trough )17 km. the average phase speed 100 cms-1 for the shear waves along the north wall of the Gulf Stream to the east of Cape Hatteras measured from NOAA satellite IR (infrared ) images. The average wavelength of shear waves along the north wall of the Kuroshio Current is 57 km, and the average amplitude 17 km. For the shear waves occurring along the west wall of the Gulf Stream to the south of Cape Hatteras, the average wavelength is 131 km, and the average amplitude 33 km measured from Seasat SAR (synthetic aperture radar )images. The time for one cycle of shear wave event is about one week.In order to explore the dynamical mechanisms of shear waves, we solved the vorticity equation for a stratified fluid, and obtained an analytical expression of dispersion relation of shear waves. The results indicated that there was a parabolic relation between the phase speed and the wavelength of shear waves, and the mean flow field was an important factor in the dispersion relation. The latter point means that the horizontal tangent variation of velocity is a basic condition for shear wave occurrence. Theoretical analyses are confirmed by satellite remote sensing data.