Longitudinal Dispersion Relations Research Articles

Exploring Challenging Properties of Liquid Metallic Systems through Machine Learning: Liquid La and Li4Pb Systems.

In this machine learning (ML) study, we delved into the unique properties of liquid lanthanum and the Li4Pb alloy, revealing some unexpected features and also firmly establishing some of the debated characteristics. Leveraging interatomic potentials derived from ab initio calculations, our investigation achieved a level of precision comparable to first-principles methods while at the same time entering the hydrodynamic regime. We compared the structure factors and pair distribution functions to experimental data and unearthed distinctive collective excitations with intriguing features. Liquid lanthanum unveiled two transverse collective excitation branches, each closely tied to specific peaks in the velocity autocorrelation function spectrum. Furthermore, the analysis of the generalized specific heat ratio in the hydrodynamic regime investigated with the ML molecular dynamics simulations uncovered a peculiar behavior, impossible to discern with only ab initio simulations. Liquid Li4Pb, on the other hand, challenged existing claims by showcasing a rich array of branches in its longitudinal dispersion relation, including a high-frequency LiLi mode with a nonhydrodynamic optical character that maintains a finite value as q → 0. Additionally, we conducted an in-depth analysis of various transport coefficients, expanding our understanding of these liquid metallic systems. In summary, our ML approach yielded precise results, offering new and captivating insights into the structural and dynamic aspects of these materials.

An Orbital Free Ab-initio Molecular Dynamics Study of Liquid Pt for Static and Dynamic Properties

Using the orbital free ab-initio molecular dynamics (OF-AIMD) simulation scheme we have examined the static and dynamic properties of liquid Pt at the thermodynamic state near to its melting point. In this simulation scheme, the Hohenberg and Kohn orbital free density functional theory (OF-DFT) has been employed. In OF-DFT, we have estimated the electron-ion interaction by a local pseudopotential and also controlled the exchange-correlation energy functional by using the local density approximation (LDA). The static properties, for instance, static structure factor, S(q), pair correlation function, g(r), coordination number, Nc, and isothermal compressibility, κT, are examined. Using the familiar single-particle dynamics, the self-diffusion coefficient and self-intermediate scattering function are studied. It is found that the self-intermediate scattering function is controlled by the selfdiffusion coefficient. While for studying the collective dynamics of the system, we have calculated velocity of sound from the longitudinal dispersion relation and shear viscosity from the transverse current correlation function, JT(q, t). The OF-AIMD results are nicely fit with the theoretical and experimental results accessible to us for comparison. Dhaka Univ. J. Sci. 69(3): 179-185, 2022 (June)

Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field

Flexural and longitudinal wave behaviors of nanobeams made of nanoporous-graded materials while surrounded by Winkler-Pasternak foundation, subjected to the longitudinal magnetic field and exposed to the hygrothermal environment are studied analytically. To this end, the governing equation derived by Euler–Bernoulli beam theory in conjunction with the nonlocal strain gradient theory is defined by employing Hamilton’s principle. By adopting an analytic model, the flexural and longitudinal dispersion relations between phase velocity and wave number are derived. The reliability of the present method is confirmed by comparing the obtained results with those stored in the literature. Finally, the effects of the power-law index, porosity volume fraction, nonlocal and material characteristic parameters, uniform temperature and moisture rise, elastic foundation parameters, magnetic field intensity, and wave number are also investigated in detail. It is found that the small-scale parameters are more influential in higher wave numbers where the wavelength is close to the length scale of nanostructures. However, foundation parameters, porosity volume fraction, and longitudinal magnetic field are more influential in lower wave numbers.

The effect of thickness on the mechanics of nanobeams

Nonlocal strain gradient models are being used more and more extensively in examining the size-dependent effects on the statical and dynamical behaviors of micro/nano-structures. However, for the fake of simplification, the size-dependent effects are often assumed to be neglected in the thickness direction of beams and plates. This simplification is originally aiming at reducing the complexity of the studied beam and plate problems while retaining all the most important mechanical features. Based on the nonlocal strain gradient model without the thickness effect, the size-dependent effect may reveal stiffness-softening or stiffness-hardening effect, which only depends on the values of strain-gradient and stress-gradient parameters but is independent on the geometric feature. In this paper, a nonlocal strain gradient beam model incorporating the thickness effect is developed for the size-dependent buckling analysis of nanobeams, and closed-form solutions are derived for post-buckling configuration and critical buckling force. When incorporating the size-dependent effect of thickness, it is found that the stiffness-softening and stiffness-hardening effects depend not only on the ratio of stress-gradient parameter to strain-gradient parameter, but also on the geometric feature (slenderness ratio). Interestingly, the stiffness-softening effect can be only found for the longitudinal dispersion relation of Silicon, while the stiffness-hardening effect may be observed for the buckling behaviors of nanobeams made of Silicon due to the size-dependent effect of thickness.

Collective modes in simple melts: Transition from soft spheres to the hard sphere limit

We study collective modes in a classical system of particles with repulsive inverse-power-law (IPL) interactions in the fluid phase, near the fluid-solid coexistence (IPL melts). The IPL exponent is varied from n = 10 to n = 100 to mimic the transition from moderately soft to hard-sphere-like interactions. We compare the longitudinal dispersion relations obtained using molecular dynamic (MD) simulations with those calculated using the quasi-crystalline approximation (QCA) and find that this simple theoretical approach becomes grossly inaccurate for n,gtrsim 20. Similarly, conventional expressions for high-frequency (instantaneous) elastic moduli, predicting their divergence as n increases, are meaningless in this regime. Relations of the longitudinal and transverse elastic velocities of the QCA model to the adiabatic sound velocity, measured in MD simulations, are discussed for the regime where QCA is applicable. Two potentially useful freezing indicators for classical particle systems with steep repulsive interactions are discussed.

Ion-acoustic and Buneman instabilities in collisional plasmas with q-nonextensive distribution

The ion-acoustic and Buneman instabilities are studied in a current carrying plasma by taking into account the collisional effects and q-nonextensive distribution function. Using the kinetic theory and Bhatnagar–Gross–Krook collision model, a generalized dielectric permittivity function in the presence of moving electrons and electron and ion–neutral collision frequency is derived. The longitudinal dispersion relation in the Buneman and ion-acoustic instability limit is obtained. The results of the Buneman instability shows that the collision frequency, the q-parameter and electron drift velocity affect the growth rate of the instability. Finally, the profile of the ion-acoustic growth rate indicates that by increasing the ion to electron temperature ratio the instability growth rate decreases.

Study on longitudinal dispersion relation in one-dimensional relativistic plasma: Linear theory and Vlasov simulation

The dispersion relation of one-dimensional longitudinal plasma waves in relativistic homogeneous plasmas is investigated with both linear theory and Vlasov simulation in this paper. From the Vlasov-Poisson equations, the linear dispersion relation is derived for the proper one-dimensional Jüttner distribution. Numerically obtained linear dispersion relation as well as an approximate formula for plasma wave frequency in the long wavelength limit is given. The dispersion of longitudinal wave is also simulated with a relativistic Vlasov code. The real and imaginary parts of dispersion relation are well studied by varying wave number and plasma temperature. Simulation results are in agreement with established linear theory.

Molecular dynamics study of the longitudinal modes in disparate-mass binary liquid mixtures

A series of molecular dynamics simulations of simple liquid binary mixtures of soft spheres with disparate-mass particles were carried out to investigate the origin of the marked differences between the dynamic structure factors of some liquid binary mixtures such as the Li0.7Mg0.3 and Li0.8Pb0.2 alloys. It is shown that the facility for observing peaks associated with fast-propagating modes in the partial Li-Li dynamic structure factor of Li0.8Pb0.2 should be mainly attributed to the structure of this alloy, which is characterized by an incipient ABAB ordering as found in molten salts. The longitudinal dispersion relations at intermediate wave vectors obtained from the longitudinal current spectra are very similar for the two alloys and reflect the existence of both fast-and slow-propagating modes of kinetic character associated with light and heavy particles, respectively. The influence of the hardness of the repulsive potential cores as well as the composition of the mixture on the longitudinal collective modes is also discussed.

Relativistic kinetic theory of waves in isotropic plasmas

The properties of longitudinal and transverse oscillations in isotropic unmagnetized plasmas of arbitrary composition are investigated on the basis of the Maxwell equations and the relativistic Vlasov equation. We show that in such plasmas (i) superluminal longitudinal and transverse waves undergo no collisionless Landau damping; and (ii) all isotropic particle distributions functions are stable against the excitation of longitudinal and transverse waves. Specializing to the textbook example of longitudinal fluctuations in a pure-electron equilibrium plasma, we derive various analytical expressions for the longitudinal dispersion relation valid for any value of the electron plasma temperature characterized by the dimensionless parameter μ = m e c 2 /k B T e , which allow simpler approximations for non-relativistic (μ >> 1) and ultrarelativistic (μ > 1 can be expressed in terms of the Fried and Conte plasma dispersion function, but does not agree with the earlier results of Landau, Jackson and others, which were calculated starting from the non-relativistic form of the Vlasov-Maxwell equations. We establish a significant difference in the argument of the plasma dispersion function. This difference only shows up because we have started from a relativistically correct formulation of the kinetic theory, and it profoundly influences the results for the real and imaginary part of the frequency also for non-relativistic plasma temperatures. We show that the non-relativistic limit of the longitudinal dispersion relation reduces to the Landau-Jackson form only if the (unphysical) limit of an infinitely large value of the speed of light c → ∞ is taken.

Modification of plasma edge fluctuations using electrostatic probes in Keda Tokamak-5C

The experiments to characterize the modification of edge fluctuations using electrostatic probes have been performed on Keda Tokamak-5C (KT-5C) [World Survey of Activities in Controlled Fusion Research, Nuclear Fusion Special Supplement (International Atomic Energy Agency, Vienna, 1991), p. 190]. The results show that the externally excited perturbation propagates in the direction of electron directional movement. The observed phenomena are mainly related to the electrons, and can be well explained by the proposed dynamic theory of the ballistic mode. The experimental correlation coefficient and the longitudinal dispersion relation are in good agreement with the proposed ballistic model.

Longitudinal oscillations in hot isotropic Maxwellian plasmas

Using the relativistic Vlasov equation and the appropriate Maxwell–Boltzmann–Jüttner distribution for the unperturbed plasma thermal equilibrium state, it is demonstrated that the longitudinal dispersion relation in warm isotropic Maxwellian plasmas has two real roots with superluminal phase speed below a characteristic wave number kc that is determined by the plasma frequency and the plasma temperature. The superluminal oscillations undergo no Landau damping. The relativistically correct analysis leads to markedly different results than previous nonrelativistic work which incorrectly yielded a nonzero imaginary part of the roots for all phase speeds.

Many-body optics I. Dielectric constants and optical dispersion relations

This paper is the first of three papers constituting a preliminary mathematical discussion preparatory to the presentation of a series of papers on the observable macroscopic optical properties of a many-body molecular fluid. These properties are viewed wholly as consequences of microscopic many-body interactions, and the theory to be presented is largely concerned with a microscopic theory of the complex refractive index and associated optical response functions: it is nowhere phenomenological. In this paper the classical integral equation, which can be derived from the quantal theory and is fundamental to the optical theory, is presented in limited form (restricted to two-particle interactions) and rigorously solved. Both longitudinal and transverse dispersion relations are obtained and these are generalized to include correlations between sets of particles of any number and to two- (and by implication to multi-) component molecular-fluid systems. All the longitudinal dispersion relations are new results. The theory is strictly a refractive index theory and not a dielectric constant theory: in consequence, the longitudinal dispersion relations admit frequencies close to, but not precisely at, the zeros of the corresponding transverse wave number, and this departure from the conventional picture is associated with the theory of optical scattering. The `local' optical field is due to two- and many-particle complex interaction terms: it mixes `transverse photons' and `longitudinal photons', and both kinds of photon contribute to each dispersion relation. The theory of how this complex local field describes external scattering, Cerenkov radiation and the contribution of virtual photon exchange to the ground-state energy will be developed later. For a theory of external scattering it is necessary to break translational invariance: as a consequence, the optical `extinction theorem', due in the first instance to P. P. Ewald, plays a very significant role in the theory.