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...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.展开更多
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. ...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.展开更多
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 th...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.展开更多
This note illustrates the multidimensional dispersion relations that connect the real and imaginary parts of the matrixwhere z(p)) is the boundary value of the impedance
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. B...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.展开更多
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...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.展开更多
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 cub...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.展开更多
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 si...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.展开更多
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 Fourie...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.展开更多
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 state...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.展开更多
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-dependen...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.展开更多
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 compactl...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.展开更多
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 theor...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 andρ-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 obtainα_(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.展开更多
Dispersion characteristics of magnonic crystals have attracted considerable attention because of the potential applications for spin-wave devices.In this work,we investigated the strain-manipulated dispersion characte...Dispersion characteristics of magnonic crystals have attracted considerable attention because of the potential applications for spin-wave devices.In this work,we investigated the strain-manipulated dispersion characteristics of magnonic crystals with Dzyaloshinskii–Moriya interaction(DMI)and discussed the potential applications in spin-wave devices.Here,the ground states and stabilities of the magnonic crystals were investigated.Then,the strain-manipulated dispersion characteristics of the magnonic crystals based on domains and skyrmions were studied.The simulation results indicated that,the applied strain could manipulate the band widths and the positions of the allowed frequency bands.Finally,the realization of magnonic crystal heterojunctions and potential applications in spin-wave devices,such as filters,diodes,and transistors based on strain-manipulated magnonic crystals were proposed.Our research provides a theoretical foundation for designing tunable spin-wave devices based on strain-manipulated magnonic crystals with DMI.展开更多
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.Previousl...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.展开更多
Theoretical analysis has demonstrated that the dispersion relation of chorus waves plays an essential role in the resonant interaction and energy transformation between the waves and magnetospheric electrons.Previous ...Theoretical analysis has demonstrated that the dispersion relation of chorus waves plays an essential role in the resonant interaction and energy transformation between the waves and magnetospheric electrons.Previous quantitative analyses often simplified the chorus dispersion relation by using the cold plasma assumption.However,the applicability of the cold plasma assumption is doubtful,especially during geomagnetic disturbances.We here present a systematic statistical analysis on the validity of the cold plasma dispersion relation of chorus waves based on observations from the Van Allen Probes over the period from 2012 to 2018.The statistical results show that the observed magnetic field intensities deviate substantially from those calculated from the cold plasma dispersion relation and that they become more pronounced with an increase in geomagnetic activity or a decrease in background plasma density.The region with large deviations is mainly concentrated in the nightside and expands in both the radial and azimuthal directions as the geomagnetic activity increases or the background plasma density decreases.In addition,the bounce-averaged electron scattering rates are computed by using the observed and cold plasma dispersion relation of chorus waves.Compared with usage of the cold plasma dispersion relation,usage of the observed dispersion relation considerably lowers the minimum resonant energy of electrons and lowers the scattering rates of electrons above tens of kiloelectronvolts but enhances those below.Furthermore,these differences are more pronounced with the enhancement of geomagnetic activity or the decrease in background plasma density.展开更多
Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of e...Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of exact solutions to the equations of motion of atoms in a body-centered cubic(bcc)lattice is analyzed.These solutions take the form of delocalized nonlinear vibrational modes(DNVMs)and can serve as an excellent test of the accuracy of the interatomic potentials used in MD modeling for bcc crystals.The accuracy of the potentials can be checked by comparing the frequency response of DNVMs calculated using this or that interatomic potential with that calculated using the more accurate ab initio approach.DNVMs can also be used to train new,more accurate machine learning potentials for bcc metals.To address the above issues,it is important to analyze the properties of DNVMs,which is the main goal of this work.Considering only the point symmetry groups of the bcc lattice,34 DNVMs are found.Since interatomic potentials are not used in finding DNVMs,they are exact solutions for any type of potential.Here,the simplest interatomic potentials with cubic anharmonicity are used to simplify the analysis and to obtain some analytical results.For example,the dispersion relations for small-amplitude phonon modes are derived,taking into account interactions between up to the fourth nearest neighbor.The frequency response of the DNVMs is calculated numerically,and for some DNVMs examples of analytical analysis are given.The energy stored by the interatomic bonds of different lengths is calculated,which is important for testing interatomic potentials.The pros and cons of using DNVMs to test and improve interatomic potentials for metals are discussed.Since DNVMs are the natural vibrational modes of bcc crystals,any reliable interatomic potential must reproduce their properties with reasonable accuracy.展开更多
To reduce the spatial simulation error generated by the finite difference method,previous researchers compute the optimal finite-difference weights always by minimizing the error of spatial dispersion relation.However...To reduce the spatial simulation error generated by the finite difference method,previous researchers compute the optimal finite-difference weights always by minimizing the error of spatial dispersion relation.However,we prove that the spatial simulation error of the finite difference method is associated with the dot product of the spatial dispersion relation of the finite-difference weights and the spectrum of the seismic wavefield.Based on the dot product relation,we construct a L_(2) norm cost function to minimize spatial simulation error.For solving this optimization problem,the seismic wavefield infor-mation in wavenumber region is necessary.Nevertheless,the seismic wavefield is generally obtained by costly forward modeling techniques.To reduce the computational cost,we substitute the spectrum of the seismic wavelet for the spectrum of the seismic wavefield,as the seismic wavelet plays a key role in determining the seismic wavefield.In solving the optimization problem,we design an exhaustive search method to obtain the solution of the L_(2) norm optimization problem.After solving the optimization problem,we are able to achieve the finite-difference weights that minimize spatial simulation error.In theoretical error analyses,the finite-difference weights from the proposed method can output more accurate simulation results compared to those from previous optimization algorithms.Furthermore,we validate our method through numerical tests with synthetic models,which encompass homogenous/inhomogeneous media as well as isotropic and anisotropic media.展开更多
This paper theoretically investigates the influence of a cylindrical PN junction on the propagation characteristics of shear cylindrical waves(SCWs)in an infinitely long piezoelectric semiconductor(PS)concentric cylin...This paper theoretically investigates the influence of a cylindrical PN junction on the propagation characteristics of shear cylindrical waves(SCWs)in an infinitely long piezoelectric semiconductor(PS)concentric cylinder structure.This PS concentric cylinder structure is composed of three regions:an inner PS cylinder,an outer PS cylindrical shell,and a cylindrical PN junction at the interface between the two aforementioned regions.First,the basic equations of the PS concentric cylinder structure are derived,taking into account the coupling of the mechanical displacement,electric potential,and charge carrier perturbation in the cylindrical coordinate system.Next,a mathematical model for the SCWs in this PS concentric cylinder structure is established,utilizing the spectral method and considering the physical characteristics of the cylindrical PN junction.Finally,the dispersion and attenuation curves of the SCWs are numerically calculated to discuss the influence of the interface effect resulting from the cylindrical PN junction.It is found that the existence of a cylindrical PN junction can either reduce or enhance the mechanical-to-electrical energy conversion,which is closely related to the doping mode,doping concentration,and curvature radius of the cylindrical interface.A reasonable design of the aforementioned parameters can optimize the wave motion in acoustic equipment formed by PS media with different frequencies or wavelengths.The construction and resolution of the mathematical model as well as the analysis of physical mechanisms can offer theoretical guidance for improving the efficiency of energy conversion from mechanical energy to electrical energy and optimizing the acoustic performance of energy harvesting devices.展开更多
To address the urgent demand for the miniaturization and multifunctional integration of high-frequency Rayleigh surface wave devices in 5G communication technology,the propagation characteristics of Rayleigh surface w...To address the urgent demand for the miniaturization and multifunctional integration of high-frequency Rayleigh surface wave devices in 5G communication technology,the propagation characteristics of Rayleigh surface waves in an elastic half-space attached by a nanoscale piezoelectric semiconductor(PSC)thin layer with flexoelectricity and size-effects are systematically investigated.Based on the Hamiltonian principle,the elastic dynamic equations and Gauss's theorem of electrostatics are obtained.The eigenvalue problem is numerically solved with a genetic algorithm in MATLAB,and the dispersion properties are obtained.The effects of various key factors,including the flexoelectricity,inertia gradients,strain gradients,electric field gradients,PSC layer thickness,steady-state carrier concentration,and bias electric fields,on the propagation and attenuation characteristics of Rayleigh surface waves are analyzed.The results demonstrate that the increases in the flexoelectric coefficient and strain gradient characteristic length lead to an increase in the real part of the complex phase velocity,while the increases in the inertia gradient characteristic length,electric field gradient characteristic length,PSC layer thickness,and steady-state carrier concentration result in a decrease.Additionally,the bias electric fields significantly influence the Rayleigh surface wave attenuation.The present findings are crucial for the accurate property evaluation of miniaturized highfrequency Rayleigh wave devices,and provide valuable theoretical support for their design and optimization.展开更多
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10504025)the National Key Basic Research Program of China (Grant No. 2007CB607501)the Natural Science Foundation for Distinguished Young Scholars of Hubei Province, China
文摘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.
文摘This note illustrates the multidimensional dispersion relations that connect the real and imaginary parts of the matrixwhere z(p)) is the boundary value of the impedance
基金This work was financially supported by the Key Project of National Natural Science Foundation of China (Grant No.50339010) and the Key Project of Chinese Ministry of Education (Grant No.03095)
文摘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.
基金supported by the National Basic Research Program of China (Grant No. 2010CB923202)
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 40731056, 10778613 and 10575018)the National Basic Research Program of China (Grant No 2008CB787103)
文摘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.
基金supported by the National Basic Research Program of China (Grant No.2010CB923202)
文摘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.
基金Supported by National Natural Science Foundation of China under Grant No.10861008the "211 Project" Innovative Talents Training Program of Inner Mongolia University and Grant-in-Aid for Scientific Research from Inner Mongolia University of Technology under Grant No.ZS201032
文摘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.
基金Project supported by the National Key R&D Program of China (Grant No. 2017YFB0406000)the Southeast University “Zhongying Young Scholars”Project
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant No.10573004
文摘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.
基金supported by National Natural Science Foundation of China (No.90405004)
文摘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.
基金UFSCar for the financial supportsupported partly by NRNU MEPhI Program"Priority 2030"。
文摘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 andρ-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 obtainα_(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.
文摘Dispersion characteristics of magnonic crystals have attracted considerable attention because of the potential applications for spin-wave devices.In this work,we investigated the strain-manipulated dispersion characteristics of magnonic crystals with Dzyaloshinskii–Moriya interaction(DMI)and discussed the potential applications in spin-wave devices.Here,the ground states and stabilities of the magnonic crystals were investigated.Then,the strain-manipulated dispersion characteristics of the magnonic crystals based on domains and skyrmions were studied.The simulation results indicated that,the applied strain could manipulate the band widths and the positions of the allowed frequency bands.Finally,the realization of magnonic crystal heterojunctions and potential applications in spin-wave devices,such as filters,diodes,and transistors based on strain-manipulated magnonic crystals were proposed.Our research provides a theoretical foundation for designing tunable spin-wave devices based on strain-manipulated magnonic crystals with DMI.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41822504, 42175099, 42027804, 42075073 and 42075077)the National Center of Meteorology, Abu Dhabi, UAE under the UAE Research Program for Rain Enhancement Science+4 种基金LIU is supported by the U.S. Department of Energy Atmospheric System Research (ASR) Program (DE-SC00112704)Solar Energy Technologies Office (SETO) under Award 33504LUO is supported by Research Fund of Civil Aviation Flight University of China (J2022-037)LI is supported by Research Fund of Civil Aviation Flight University of China (09005001)WU is supported by Research on Key of Manmachine Ring in Plateau Flight (FZ2020ZZ03)
文摘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.
基金supported by the National Natural Science Foundation of China (NSFC) through Grant Number 42074193
文摘Theoretical analysis has demonstrated that the dispersion relation of chorus waves plays an essential role in the resonant interaction and energy transformation between the waves and magnetospheric electrons.Previous quantitative analyses often simplified the chorus dispersion relation by using the cold plasma assumption.However,the applicability of the cold plasma assumption is doubtful,especially during geomagnetic disturbances.We here present a systematic statistical analysis on the validity of the cold plasma dispersion relation of chorus waves based on observations from the Van Allen Probes over the period from 2012 to 2018.The statistical results show that the observed magnetic field intensities deviate substantially from those calculated from the cold plasma dispersion relation and that they become more pronounced with an increase in geomagnetic activity or a decrease in background plasma density.The region with large deviations is mainly concentrated in the nightside and expands in both the radial and azimuthal directions as the geomagnetic activity increases or the background plasma density decreases.In addition,the bounce-averaged electron scattering rates are computed by using the observed and cold plasma dispersion relation of chorus waves.Compared with usage of the cold plasma dispersion relation,usage of the observed dispersion relation considerably lowers the minimum resonant energy of electrons and lowers the scattering rates of electrons above tens of kiloelectronvolts but enhances those below.Furthermore,these differences are more pronounced with the enhancement of geomagnetic activity or the decrease in background plasma density.
基金support of the RSF Grant No.24-11-00139(analytics,numerical results,manuscript writing)Daxing Xiong acknowledges the support of the NNSF Grant No.12275116,the NSF Grant No.2021J02051,and the startup fund Grant No.MJY21035For Aleksey A.Kudreyko,this work was supported by the Bashkir StateMedicalUniversity StrategicAcademic Leadership Program(PRIORITY-2030)(analytics).
文摘Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of exact solutions to the equations of motion of atoms in a body-centered cubic(bcc)lattice is analyzed.These solutions take the form of delocalized nonlinear vibrational modes(DNVMs)and can serve as an excellent test of the accuracy of the interatomic potentials used in MD modeling for bcc crystals.The accuracy of the potentials can be checked by comparing the frequency response of DNVMs calculated using this or that interatomic potential with that calculated using the more accurate ab initio approach.DNVMs can also be used to train new,more accurate machine learning potentials for bcc metals.To address the above issues,it is important to analyze the properties of DNVMs,which is the main goal of this work.Considering only the point symmetry groups of the bcc lattice,34 DNVMs are found.Since interatomic potentials are not used in finding DNVMs,they are exact solutions for any type of potential.Here,the simplest interatomic potentials with cubic anharmonicity are used to simplify the analysis and to obtain some analytical results.For example,the dispersion relations for small-amplitude phonon modes are derived,taking into account interactions between up to the fourth nearest neighbor.The frequency response of the DNVMs is calculated numerically,and for some DNVMs examples of analytical analysis are given.The energy stored by the interatomic bonds of different lengths is calculated,which is important for testing interatomic potentials.The pros and cons of using DNVMs to test and improve interatomic potentials for metals are discussed.Since DNVMs are the natural vibrational modes of bcc crystals,any reliable interatomic potential must reproduce their properties with reasonable accuracy.
基金supported by the Marine S&T Fund of Shandong Province for Pilot National Laboratory for Marine Science and Technology(No.2021QNLM020001)the Major Scientific and Technological Projects of Shandong Energy Group(No.SNKJ2022A06-R23)+1 种基金the Funds of Creative Research Groups of China(No.41821002)the Major Scientific and Technological Projects of CNPC(No.ZD2019-183-003).
文摘To reduce the spatial simulation error generated by the finite difference method,previous researchers compute the optimal finite-difference weights always by minimizing the error of spatial dispersion relation.However,we prove that the spatial simulation error of the finite difference method is associated with the dot product of the spatial dispersion relation of the finite-difference weights and the spectrum of the seismic wavefield.Based on the dot product relation,we construct a L_(2) norm cost function to minimize spatial simulation error.For solving this optimization problem,the seismic wavefield infor-mation in wavenumber region is necessary.Nevertheless,the seismic wavefield is generally obtained by costly forward modeling techniques.To reduce the computational cost,we substitute the spectrum of the seismic wavelet for the spectrum of the seismic wavefield,as the seismic wavelet plays a key role in determining the seismic wavefield.In solving the optimization problem,we design an exhaustive search method to obtain the solution of the L_(2) norm optimization problem.After solving the optimization problem,we are able to achieve the finite-difference weights that minimize spatial simulation error.In theoretical error analyses,the finite-difference weights from the proposed method can output more accurate simulation results compared to those from previous optimization algorithms.Furthermore,we validate our method through numerical tests with synthetic models,which encompass homogenous/inhomogeneous media as well as isotropic and anisotropic media.
基金Project supported by the National Natural Science Foundation of China(Nos.12202039,52204085,and 52474123)。
文摘This paper theoretically investigates the influence of a cylindrical PN junction on the propagation characteristics of shear cylindrical waves(SCWs)in an infinitely long piezoelectric semiconductor(PS)concentric cylinder structure.This PS concentric cylinder structure is composed of three regions:an inner PS cylinder,an outer PS cylindrical shell,and a cylindrical PN junction at the interface between the two aforementioned regions.First,the basic equations of the PS concentric cylinder structure are derived,taking into account the coupling of the mechanical displacement,electric potential,and charge carrier perturbation in the cylindrical coordinate system.Next,a mathematical model for the SCWs in this PS concentric cylinder structure is established,utilizing the spectral method and considering the physical characteristics of the cylindrical PN junction.Finally,the dispersion and attenuation curves of the SCWs are numerically calculated to discuss the influence of the interface effect resulting from the cylindrical PN junction.It is found that the existence of a cylindrical PN junction can either reduce or enhance the mechanical-to-electrical energy conversion,which is closely related to the doping mode,doping concentration,and curvature radius of the cylindrical interface.A reasonable design of the aforementioned parameters can optimize the wave motion in acoustic equipment formed by PS media with different frequencies or wavelengths.The construction and resolution of the mathematical model as well as the analysis of physical mechanisms can offer theoretical guidance for improving the efficiency of energy conversion from mechanical energy to electrical energy and optimizing the acoustic performance of energy harvesting devices.
基金supported by the Singapore Ministry of Education(MOE)Academic Research Fund(AcRF)Tier 1(Nos.RG145/23 and RG78/24)the National Natural Science Foundation of China(No.U24A2005)Ningbo Natural Science Foundation(No.2024J183)。
文摘To address the urgent demand for the miniaturization and multifunctional integration of high-frequency Rayleigh surface wave devices in 5G communication technology,the propagation characteristics of Rayleigh surface waves in an elastic half-space attached by a nanoscale piezoelectric semiconductor(PSC)thin layer with flexoelectricity and size-effects are systematically investigated.Based on the Hamiltonian principle,the elastic dynamic equations and Gauss's theorem of electrostatics are obtained.The eigenvalue problem is numerically solved with a genetic algorithm in MATLAB,and the dispersion properties are obtained.The effects of various key factors,including the flexoelectricity,inertia gradients,strain gradients,electric field gradients,PSC layer thickness,steady-state carrier concentration,and bias electric fields,on the propagation and attenuation characteristics of Rayleigh surface waves are analyzed.The results demonstrate that the increases in the flexoelectric coefficient and strain gradient characteristic length lead to an increase in the real part of the complex phase velocity,while the increases in the inertia gradient characteristic length,electric field gradient characteristic length,PSC layer thickness,and steady-state carrier concentration result in a decrease.Additionally,the bias electric fields significantly influence the Rayleigh surface wave attenuation.The present findings are crucial for the accurate property evaluation of miniaturized highfrequency Rayleigh wave devices,and provide valuable theoretical support for their design and optimization.
