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 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.

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.

The Dispersion Relation of Internal Wave Extended-Korteweg-de Vries Equation in a Two-Layer Fluid

To understand the characteristics of ocean internal waves better, we study the dispersion relation of extended-Korteweg-de Vries (EKdV) equation with quadratic and cubic nonlinear terms in a two-layer fluid by using the Poincaré-Lighthill-Kuo (PLK) method which is one of the perturbation methods. Starting from the partial differential equation, the PLK method can be used to solve the dispersion relation of the equation. In this paper, we use PLK method to solve the equation and derive the dispersion relation of EKdV equation which is related to wave number and amplitude. Based on the dispersion relation obtained in this paper, the expressions of group velocity and phase velocity of the equation are obtained. Under the actual hydrological data, the influence of hydrological parameters on the dispersion relation for descending internal wave is discussed. It is hope that the obtained results will be helpful to the study of energy transfer and other internal wave parameters in the future.

Quasi-linear analysis of dispersion relation preservation for nonlinear schemes

In numerical simulations of complex flows with discontinuities,it is necessary to use nonlinear schemes.The spectrum of the scheme used has a significant impact on the resolution and stability of the computation.Based on the approximate dispersion relation method,we combine the corresponding spectral property with the dispersion relation preservation proposed by De and Eswaran(J Comput Phys 218:398-416,2006)and propose a quasi-linear dispersion relation preservation(QL-GRP)analysis method,through which the group velocity of the nonlinear scheme can be determined.In particular,we derive the group velocity property when a high-order Runge-Kutta scheme is used and compare the performance of different time schemes with QL-GRP.The rationality of the QL-GRP method is verified by a numerical simulation and the discrete Fourier transform method.To further evaluate the performance of a nonlinear scheme in finding the group velocity,new hyperbolic equations are designed.The validity of QL-GRP and the group velocity preservation of several schemes are investigated using two examples of the equation for one-dimensional wave propagation and the new hyperbolic equations.The results show that the QL-GRP method integrated with high-order time schemes can determine the group velocity for nonlinear schemes and evaluate their performance reasonably and efficiently.

Optical theorem,crossing property,and derivative dispersion relations:implications on the asymptotic behavior of σ_(tot)(s) and ρ(s)

In this paper,we present some results on the behavior of the total cross section and p-parameter at asymptotic energies in proton-proton(pp) and antiproton-proton(pp) collisions.Hence,we consider three of the main theoretical results in high energy physics:the crossing property,derivative dispersion relation,and optical theorem.The use of such machinery facilitates the derivation of analytic formulas for a wide set of the measured global scattering parameters and some important relations between them.The suggested parameterizations approximate the energy dependence for the total cross section and ρ-parameter for pp and pp with a statistically acceptable quality in the multi-TeV region.Additionally,the qualitative description is obtained for important interrelations,namely difference,sum,and ratio of the antiparticle-particle and particle-particle total cross sections.Despite the reduced number of experimental data for the total cross section and p-parameter at the TeV-scale,which complicates any prediction for the beginning of the asymptotic domain,the fitting procedures indicates that asymptotia occur in the energy range 25.5-130 TeV.Moreover,in the asymptotic regime,we obtain α_(P)=1.A detailed quantitative study of the energy behavior of the measured scattering parameters and their combinations in the ultra-high energy domain indicates that the scenario with the generalized formulation of the Pomeranchuk theorem is more favorable with respect to the original formulation of this theorem.

Accurate correction of arbitrary spin fermion quantum tunneling from non-stationary Kerr-de Sitter black hole based on corrected Lorentz dispersion relation

According to a corrected dispersion relation proposed in the study on the string theory and quantum gravity theory,the Rarita-Schwinger equation was precisely modified,which resulted in the Rarita-Schwinger-Hamilton-Jacobi equation.Using this equation,the characteristics of arbitrary spin fermion quantum tunneling radiation from non-stationary Kerr-de Sitter black holes were determined.A number of accurately corrected physical quantities,such as surface gravity,chemical potential,tunneling probability,and Hawking temperature,which describe the properties of black holes,were derived.This research has enriched the research methods and enabled increased precision in black hole physics research.

Deformed dispersion relation constraint with hydrogen atom 1S-2S transition

We use the latest results of the ultra-high accuracy 1S-2S transition experiments in the hydrogen atom to constrain the forms of the deformed dispersion relation in the non-relativistic limit.For the leading correction of the non-relativistic limit,the experiment sets a limit at an order of magnitude for the desired Planck-scale level,thereby providing another example of the Planck-scale sensitivity in the study of the dispersion relation in controlled laboratory experiments.For the next-to-leading term,the bound is two orders of magnitude away from the Planck scale,however it still amounts to the best limit,in contrast to the previously obtained bound in the non-relativistic limit from the cold-atom-recoil experiments.

In-medium pion dispersion relation and medium correction of Nπ■Δ near the threshold energy of pion production

Transport models cannot simultaneously explain very recent data on pion multiplicities and pion charged ratios from central collision of Sn+Sn at 0.27 A GeV.This stimulates further investigations on the pion dispersion relation,in-medium Nπ→Δ cross sections,and Δ→Nπ decay widths near the threshold energy or at subthreshold energy of pion production in isospin asymmetric nuclear matter.In this study,the pion dispersion relation,in-medium Nπ→Δ cross section,and Δ→Nπ decay width near the threshold energy are investigated in isospin asymmetric nuclear matter by using the one-boson-exchange model.With the consideration of the energy conservation effect,the in-medium Nπ→Δ cross sections are enhanced at s1/2 <1.11 GeV in a nuclear medium.The prediction of pion multiplicity and π-/π+ ratios near the threshold energy could be modified if this effect is considered in transport model simulations.

Exact relations for two-photon-exchange effect in elastic ep scattering by dispersion relation and hadronic model

The two-photon-exchange(TPE)effect plays a key role in extracting the form factors(FFs)of the proton.In this work,we discuss several exact properties of the TPE effect in the elastic ep scattering.By taking four low energy interactions as examples,we analyze kinematical singularities,asymptotic behaviors,and branch cuts of TPE amplitudes.The analytical expressions clearly indicate several exact relations between the dispersion relation(DR)and hadronic model(HM)methods.This suggests that the two methods must be modified to general forms,while novel forms yield the same results.After the modification,new DRs include a non-trivial term with two singularities.Furthermore,new DRs automatically include contributions due to the seagull interaction,meson-exchange effect,contact interactions,and off-shell effect.To analyze the elastic e^(±)}p scattering data sets,the new forms must be used.

Relationships between Cloud Droplet Spectral Relative Dispersion and Entrainment Rate and Their Impacting Factors

Cloud microphysical properties are significantly affected by entrainment and mixing processes.However,it is unclear how the entrainment rate affects the relative dispersion of cloud droplet size distribution.Previously,the relationship between relative dispersion and entrainment rate was found to be positive or negative.To reconcile the contrasting relationships,the Explicit Mixing Parcel Model is used to determine the underlying mechanisms.When evaporation is dominated by small droplets,and the entrained environmental air is further saturated during mixing,the relationship is negative.However,when the evaporation of big droplets is dominant,the relationship is positive.Whether or not the cloud condensation nuclei are considered in the entrained environmental air is a key factor as condensation on the entrained condensation nuclei is the main source of small droplets.However,if cloud condensation nuclei are not entrained,the relationship is positive.If cloud condensation nuclei are entrained,the relationship is dependent on many other factors.High values of vertical velocity,relative humidity of environmental air,and liquid water content,and low values of droplet number concentration,are more likely to cause the negative relationship since new saturation is easier to achieve by evaporation of small droplets.Further,the signs of the relationship are not strongly affected by the turbulence dissipation rate,but the higher dissipation rate causes the positive relationship to be more significant for a larger entrainment rate.A conceptual model is proposed to reconcile the contrasting relationships.This work enhances the understanding of relative dispersion and lays a foundation for the quantification of entrainment-mixing mechanisms.

Nonlinear Dispersion Effect on Wave Transformation

—A new nonlinear dispersion relation is given in this paper.which can overcome the limitationof the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple(1986).and which has a better approximation to Hedges'empirical relation than the modified relations by Hedges(1987).Kirby and Dalrymple(1987)for shallow waters.The new dispersion relation is simple in form.thusit can be used easily in practice.Meanwhile,a general explicit approximation to the new dispersion rela-tion and other nonlinear dispersion relations is given.By use of the explicit approximation to the newdispersion relation along with the mild slope equation taking into account weakly nonlinear effect.amathematical model is obtained,and it is applied to laboratory data.The results show that the model de-veloped with the new dispersion relation predicts wave transformation over complicated topography quitewell.

Adjoint Method-Based Algorithm for Calculating the Relative Dispersion Ratio in a Hydrodynamic System

Relative dispersion ratio(RDR)can be used to quantify the deviation behavior of a water parcel’s trajectory caused by a disturbance in a hydrodynamic system.It can be calculated by using a standard method for determining relative dispersion(RD),which accounts for the growth of the deviation of a cluster of particles from a specific initial time.However,the standard method for computing RD is time consuming.It involves numerous computations on tracing many water parcels.In this study,a new method based on the adjoint method is proposed to acquire a series of RDR fields in one round of tracing.Through this method,the continuous variation in the RDR corresponding to a time series of the disturbance time t can be obtained.The consistency and efficiency of the new method are compared with those of the standard method by applying it to a double-gyre flow and an unsteady Arnold-Beltrami-Childress flow field.Results show that the two methods have good consistency in a finite time span.The new method has a notable speedup for evaluating the RDR at multiple t.

Propagation of surface magnetoplasmon polaritons in a symmetric waveguide with two-dimensional electron gas

The properties of surface magnetoplasmon polaritons(SMPPs)in a symmetric structure,composed of two semi-infinite regions of high-density two-dimensional electron gas(2DEG)separated by a thin film in Voigt configuration,are investigated.The normal and absorption dispersion relations for the transverse magnetic polarization are derived by correlating Maxwell’s equation and the boundary conditions.It is demonstrated that the features of SMPPs are greatly influenced by the external magnetic field,collision frequency of 2DEG,the dielectric constant,and the thickness of the thin film,suggesting that the locations and propagation lengths of SMPPs can be governed accordingly.It is shown that the symmetry of the physical geometry preserves the symmetry of the dispersion relations of SMPPs.Furthermore,it is discovered that as the external magnetic field increases,the penetration depth of SMPPs decreases,while their energy loss reduces,implying that plasmons can propagate for longer distances.Additionally,it is observed that SMPPs in the symmetric configuration have a longer lifetime than those in the asymmetric configuration.

New Numerical Scheme for Simulation of Hyperbolic Mild-Slope Equation

The original hyperbolic mild-slope equation can effectively take into account the combined effects of wave shoaling,refraction, diffraction and reflection, but does not consider the nonlinear effect of waves, and the existing numericalschemes for it show some deficiencies. Based on the original hyperbolic mild-slope equation, a nonlinear dispersion rela-tion is introduced in present paper to effectively take the nonlinear effect of waves into account and a new numericalscheme is proposed. The weakly nonlinear dispersion relation and the improved numerical scheme are applied to thesimulation of wave transformation over an elliptic shoal. Numerical tests show that the improvement of the numericalscheme makes efficient the solution to the hyperbolic mild-slope equation. A comparison of numerical results with experi-mental data indicates that the results obtained by use of the new scheme are satisfactory.

Nonlinear dynamical magnetosonic wave interactions and collisions in magnetized plasma

The one-dimensional nonlinear dynamical wave interactions in a system of quasineutral two-fluid plasma in a constant magnetic field are investigated.The existence of the travelling wave solutions is discussed.The modulation stability of linear waves and the modulation instability of weakly nonlinear waves are presented.Both suggest that the Korteweg-de Vries(KdV)system is modulationally stable.Besides,the wave interactions including the periodic wave interaction and the solitary wave interaction are captured and presented.It is shown that these interacting waves alternately exchange their energy during propagation.The Fourier spectrum analysis is used to depict the energy transformation between the primary and harmonic waves.It is known that the wave interactions in magnetized plasma play an important role in various processes of heating and energy transportation in space and astrophysical plasma.However,few researchers have considered such magnetohydrodynamic(MHD)wave interactions in plasma.It is expected that this work can provide additional insight into understanding of behaviors of MHD wave interactions.

Resonant surface plasmons of a metal nanosphere treated as propagating surface plasmons

On the assumption that the resonant surface plasmons on a spherical nanoparticle are formed by standing waves of two counter-propagating surface plasmon waves along the surface, by using Mie theory simulation, we find that the dispersions of surface plasmon resonant modes supported by silver nanospheres match with those of the surface plasmons on a semiinfinite medium-silver interface very well. This suggests that the resonant surface plasmons of a metal nanosphere can be treated as a propagating surface plasmon wave.

Modified Wave Particle Duality and Black Hole Physics

de Broglie relation is revisited,in consideration of a generalization of canonical commuting relation.Thepossible effects on particle's localization and black hole physics are also discussed,in a heuristic manner.

Propagation behavior of SH waves in a piezomagnetic substrate with an orthorhombic piezoelectric layer

The dispersion behavior of the shear horizontal(SH) waves in the coupled structure consisting of a piezomagnetic substrate and an orthorhombic piezoelectric layer is investigated with different cut orientations. The surface of the piezoelectric layer is mechanically free, electrically shorted, or open, while the surface of the piezomagnetic substrate is mechanically free, magnetically open, or shorted. The dispersion relations are derived for four electromagnetic boundary conditions. The dispersion characteristics are graphically illustrated for the layered structure with the PMN-PT layer perfectly bonded on the CoFe_2O_4 substrate. The effects of the PMN-PT cut orientations, the electromagnetic boundary conditions, and the thickness ratio of the layer to the substrate on the dispersion behavior are analyzed and discussed in detail. The results show that,(i)the effect of the cut orientation on the dispersion curves is very obvious,(ii) the electrical boundary conditions of the PMN-PT layer dominate the propagation feature of the SH waves, and(iii) the thickness ratio has a significant effect on the phase velocity when the wave number is small. The results of the present paper can provide valuable theoretical references to the applications of piezoelectric/piezomagnectic structure in acoustic wave devices.

Rayleigh-Type Wave in A Rotated Piezoelectric Crystal Imperfectly Bonded on a Dielectric Substrate

Propagation characteristics of Rayleigh-type wave in a piezoelectric layered system are theoretically investigated.The piezoelectric layer is considered as a cubic crystal with finite thickness rotated about Y-axis and is imperfectly bonded onto a semi-infinite dielectric substrate.The imperfect interface between the two constituents is assumed to be mechanically compliant and dielectrically weakly conducting.The exact dispersion relations for electrically open or shorted boundary conditions are obtained.The numerical results show that the phase velocity of Rayleigh-type wave is symmetric with respect to the cut orientation of 45°and can achieve the maximum propagation speed in this orientation.The mechanical imperfection plays an important role in the dispersion relations,further the normal imperfection can produce a significant reduction of phase velocity comparing with the tangential imperfection.Comparing with the mechanical imperfection the electrical imperfection makes a relatively small reduction of phase velocity of Rayleigh-type wave.The obtained results can provide some fundamentals for understanding of piezoelectric semiconductor and for design and application of piezoelectric surface acoustic wave devices.