Excitation of kinetic Alfvén waves by streaming ions in a dusty magnetoplasma with generalized (r,q) distribution function

We investigate the parallel streaming effects on the dispersion characteristics of a kinetic Alfvén wave (KAW) in a low β dusty magnetoplasma. To analyse the influence of streaming ions obeying generalized (r, q) distribution function, hot and magnetized electrons, and mobile charged dust, a theoretical approach has been used for the instability analysis by employing two potential theories. A linear kinetic dispersion relation of Alfvén waves is derived, whose solutions are used to interpret the numerical and analytical results. The solutions of dispersion relation indicate that the characteristics of KAWs are transformed when generalized (r, q) distribution function is employed instead of its Maxwellian counterpart. We also found that the unstable modes have a strong dependence on spectral indices r and q , dust parameters, and plasma β . For the excitation of KAWs, the streaming velocity has been observed to be within the sub-Alfvén range, whereas when it extends to the super-Alfvén range, the growth rates are significantly suppressed. The observations further show that an ambient magnetic field and superthermal particles inhibit the growth of an electromagnetic wave to a significant degree and have a stabilizing effect on the wave mode, whereas an increasing concentration of low-energy particles contributes to enhancing growth rates.     

Effect of viscosity on dust–ion acoustic shock wave in dusty plasma with negative ions

The properties of dust–ion acoustic (DIA) shock wave in a dusty plasma containing positive and negative ions is investigated. The reductive perturbation method has been used to derive the Korteweg–de Vries–Burgers equation for dust acoustic shock waves in a homogeneous, unmagnetized and collisionless plasma whose constituents are Boltzmann distributed electrons, singly charged positive ions, singly charged negative ions and cold static dust particles. The KdV–Burgers equation is derived and its stationary analytical solution is numerically analyzed where the effect of viscosity on the DIA shock wave propagation is taken into account. It is found that the viscosity in the dusty plasma plays as a key role in dissipation for the propagation of DIA shock.     

Spherical Kadomtsev–Petviashvili equation for dust acoustic waves with dust size distribution and two-charges-ions

The nonlinear dust acoustic waves in dusty plasmas with negative as well as positive ions and the combined effects of bounded spherical geometry and the transverse perturbation and the size distribution of dust grains are studied. Using the perturbation method, a spherical Kadomtsev–Petviashvili (SKP) equation that describes the dust acoustic waves is deduced.     

Effect of dust charge variation on dust—acoustic solitary waves in a magnetized two—ion—temperature dusty plasma

The effect of dust charge variation on the dust-acoustic solitary structures is investigated in a warm magnetized two-ion-temperature dusty plasma consisting of a negatively and variably charged extremely massive dust fluid and ions of two different temperatures. It is shown that the dust charge variation as well as the presence of a second component of ions would modify the properties of the dust-acoustic solitary structures and may exite both dust-acoustic solitary holes (soliton waves with a density dip) and positive solitons (soliton waves with a density hump).     

The effects of dust temperature and the dust charge variation in a dusty plasma with vortex—like ion distribution

By considering both the dust temperature and the dust charge variation in dusty plasma with vortex-like ion distribution, we obtained a modified Korteweg－de Vries equation. It indicates that the effect of dust charge variation can cause the one-dimensional soliton amplitude to become larger, and the dust temperature can cause the soliton amplitude to become larger as well. Moreover, as the dust temperature increases, the soliton amplitude will increase.     

Analytical evaluation of the plasma dispersion function for a Fermi—Dirac distribution

An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed.The new method has been developed using the binomial expansion theorem and the Gamma functions.The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function.The resulting series present better convergence rates.Several acceleration techniques are combined to further improve the efficiency.The obtained results for the plasma dispersion function are in good agreement with the known numerical data.     

Modulational instability of ultra-low-frequency shear dust Alfvén waves in a plasma medium of positive and negatively charged dust fluids

The propagation of finite amplitude ultra-low-frequency shear dust Alfvén (SDA) waves, and their modulational instability in a magnetized plasma medium of positive and negatively charged dust fluids have been theoretically investigated by using the reductive perturbation method. The derivative nonlinear Schrödinger equation is derived to examine the stability analysis of such SDA waves. It is found that the SDA waves propagating in such an opposite polarity dust plasma medium are modulationally unstable, and that the instability criterion and the growth rate of these unstable SDA waves in such a novel opposite polarity dust plasma medium are found to be significantly different from those in electron–ion or electron–positron plasma media. The implications of the present investigation in different space environments and laboratory devices are briefly discussed.     

Monogamy and polygamy for the generalized W-class states using unified-(q,s) entropy

We describe the entanglement distribution and restricted shareability of the multipartite generalized W-class states and their reduced density matrix under arbitrary partitions by using monogamy and polygamy relation based on the unified-(q, s) entropy.Firstly, we provide an analytical formula of unified-(q, s) entanglement(UE) and an analytical lower bound of unified-(q, s) entanglement of assistance(UEo A) for a reduced density matrix of a generalized W-class state. Then, we use these two anal...     

Impacts of fast meteoroids and a plasma–dust cloud over the lunar surface

The possibility of the formation of a plasma–dust cloud in the exosphere of the Moon owing to impacts of meteoroids on the lunar surface is discussed. Attention is focused on dust particles at large altitudes of ~10–100 km at which measurements were performed within the NASA LADEE mission. It has been shown that a melted material ejected from the lunar surface owing to the impacts of meteoroids plays an important role in the formation of the plasma–dust cloud. Drops of the melted material acquire velocities in the range between the first and second cosmic velocities for the Moon and can undergo finite motion around it. Rising over the lunar surface, liquid drops are solidified and acquire electric charges, in particular, owing to their interaction with electrons and ions of the solar wind, as well as with solar radiation. It has been shown that the number density of dust particles in the plasma–dust cloud present in the exosphere of the Moon is ?10^?8 cm^?3, which is in agreement with the LADEE measurements.     

Nonlinear ion-acoustic structures in a nonextensive electron–positron–ion–dust plasma: Modulational instability and rogue waves

The nonlinear propagation of planar and nonplanar (cylindrical and spherical) ion-acoustic waves in an unmagnetized electron–positron–ion–dust plasma with two-electron temperature distributions is investigated in the context of the nonextensive statistics. Using the reductive perturbation method, a modified nonlinear Schrödinger equation is derived for the potential wave amplitude. The effects of plasma parameters on the modulational instability of ion-acoustic waves are discussed in detail for planar as well as for cylindrical and spherical geometries. In addition, for the planar case, we analyze how the plasma parameters influence the nonlinear structures of the first- and second-order ion-acoustic rogue waves within the modulational instability region. The present results may be helpful in providing a good fit between the theoretical analysis and real applications in future spatial observations and laboratory plasma experiments.     

Dispersion and nonlinear frequancy shift of natural waves in the Bose–Einstein condensate

Quantum mechanics equations for a system of the Bose particles are represented in the form of material field equations. A nonlinear equation for the macroscopic one-particle wave function is derived. Using the Krylov–Bogolyubov–Mitropol’skii method for equations in partial derivatives, nonlinear waves in the Bose–Einstein condensate are investigated. In the cubic approximation, dispersion relations for waves are derived and nonlinear frequency shift is calculated in the first- and third-order approximations for the interaction radius.     

Fusion,fission, and annihilation of complex waves for the(2+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff system

With the help of the symbolic computation system, Maple and Riccati equation( ξ= a0+ a1ξ+ a22ξ), expansion method, and a linear variable separation approach, a new family of exact solutions with q = lx + my + nt + Γ(x, y,t) for the(2+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff system(GCBS) are derived. Based on the derived solitary wave solution, some novel localized excitations such as fusion, fission, and annihilation of complex waves are investigated.     

Functional derivative for the distribution function of a Λ-nucleon pair in nuclear matter

An exact expression for the functional derivative of the distribution function of a -nucleon pair in nuclear matter is derived. An approximate expression is also derived by means of the Kirkwood superposition approximation. The latter expression is subsequently used to obtain the Euler equation for the correlation functionf(r1) of a -nucleon pair in nuclear matter.     

An approximate expression for the Wigner-Kirkwood ℏ4 quantum correction to the pair distribution function in a one-component plasma

We propose an accurate approximate expression for the exact ℏ⁴ quantum correction to the pair distribution function g₂^q(r₁₂) that we have derived recently in an OCP using Wigner-Kirkwood ℏ² expansion. Our expression, depending only the classical pair distribution function g₂^c(r₁₂), reproduces the behavior of Wigner-Kirkwood g₂^q(r₁₂) at order ℏ⁴, at small, intermediate and large r₁₂.     

Spectroscopic estimation of plasma parameters,in the 100–400 ns stage,of a laser-induced plasma in vacuum

This work is focused on the interpretation of the emission spectra in laser-induced plasma observed in the phase at 100–400?ns from after the laser pulse, when the discrete emission lines prevail on the continuum emission, can be important to retrieve the initial stage of expansion. A Q-switched neodymium-doped yttrium aluminum garnet laser has been used for the ablation of a lead sample in vacuum. The observed line profiles, corresponding to different species of lead, were analyzed in terms of delay time. Measurements of parameters of the produced plasmas are performed. The results obtained corroborate the importance of considering nonequilibrium effects in the initial stage of plasma expansion. Also, Stark width for two spectral lines of triply ionized lead is given.     

Trajectory equation of a lump before and after collision with other waves for generalized Hirota–Satsuma–Ito equation

Based on the Hirota bilinear and long wave limit methods, the hybrid solutions of m-lump with n-soliton and nbreather wave for generalized Hirota–Satsuma–Ito(GHSI) equation are constructed. Then, by approximating solutions of the GHSI equation along some parallel orbits at infinity, the trajectory equation of a lump wave before and after collisions with n-soliton and n-breather wave are studied, and the expressions of phase shift for lump wave before and after collisions are given. Furthermore, ...     

An analysis of phonon emission as controlled by the combined interaction with the acoustic and piezoelectric phonons in a degenerate III–V compound semiconductor using an approximated Fermi–Dirac distribution at low lattice temperatures

Compound semiconductors being piezoelectric in nature, the intrinsic thermal vibration of the lattice atoms at any temperature gives rise to an additional potential field that perturbs the periodic potential field of the atoms. This is over and above the intrinsic deformation acoustic potential field which is always produced in every material. The scattering of the electrons through the piezoelectric perturbing potential is important in all compound semiconductors, particularly at the low lattice temperatures. Thus, the electrical transport in such materials is principally controlled by the combined interaction of the electrons with the deformation potential acoustic and piezoelectric phonons at low lattice temperatures. The study here, deals with the problem of phonon growth characteristics, considering the combined scattering of the non-equilibrium electrons in compound semiconductors, at low lattice temperatures. Beside degeneracy, other low temperature features, like the inelasticity of the electron–phonon collisions, and the full form of the phonon distribution have been duly considered. The distribution function of the degenerate ensemble of carriers, as given by the heated Fermi–Dirac function, has been approximated by a simplified, well-tested model. The model which has been proposed earlier, makes it much easier to carry out analytically the integrations without usual oversimplified approximations.     

Dynamical analysis of bounded and unbounded orbits in a generalized Hénon–Heiles system

The Hénon–Heiles potential was first proposed as a simplified version of the gravitational potential experimented by a star in the presence of a galactic center. Currently, this system is considered a paradigm in dynamical systems because despite its simplicity exhibits a very complex dynamical behavior. In the present paper, we perform a series expansion up to the fifth-order of a potential with axial and reflection symmetries, which after some transformations, leads to a generalized Hénon–Heiles potential. Such new system is analyzed qualitatively in both regimes of bounded and unbounded motion via the Poincaré sections method and plotting the exit basins. On the other hand, the quantitative analysis is performed through the Lyapunov exponents and the basin entropy, respectively. We find that in both regimes the chaoticity of the system decreases as long as the test particle energy gets far from the critical energy. Additionally, we may conclude that despite the inclusion of higher order terms in the series expansion, the new system shows wider zones of regularity (islands) than the ones present in the Hénon–Heiles system.     

A new method for the analysis of transmission property in carbon nanotubes using Green’s function

A new method for the analysis of electron transmission property in single-walled carbon nanotubes (SWCNTs) using Green’s function is presented in this paper for the first time. Using the proposed method, a new relation for the transmission function through a deformed SWCNT is obtained, which depends on the energy variations and the coupling matrices related to the mechanical deformations applied to the structure of CNT. The obtained new relation is explained by the presented results in the literature.