In the present paper, the PHONON DISPERSION CURVES ((PDC)) of some equiatomic liquid alkali binary alloys are reported in second order approach through the equation given by Hubbard and Beeby (HB). The pair correlation function g (r) is directly computed from the interatomic pair potential, which is used in the present computation. Two different forms of local field correction functions proposed by Hartree (H) and Ichimaru-Utsumi (IU) are used in the present study the screening dependence of the PHONON frequencies in the equiatomic liquid alkali binary alloys. The pseudo-alloy-atom (PAA) model is applied for the first time for the alloying elements.

Although many phenomena in condensed matter Physics can be understood on the basis of a model, there are also considerable number of physical properties of solid which can not be explained except in the framework of lattice dynamics.We have calculated the PHONON frequencies of NaCl, using an approach which is a combination of frozen PHONON and force constants methods in the framework of density functional pseudo-potential theory. The DISPERSION relation CURVES were calculated along symmetry direction Δ, ∑ and Λ. We also calculated Grunesein parameters for all modes at X and L points in Brillion zone. The calculations are made in the framework of density functional and pseudo-potential theory, using super cell method, with the valence orbitals expanded in plane waves.

Poly (vinylidene chloride) (PVDC) is a barrier polymer which has a wide scope in food packaging industries. A comprehensive study of the normal modes and their DISPERSION in PVDC using Wilson’s GF matrix method as modified by Higgs is reported. It provides a detailed interpretation of IR and Raman spectra. Characteristic feature of DISPERSION CURVES, such as regions of high density-of-states, repulsion, and character mixing of DISPERSION modes, are discussed. Heat capacity has been calculated in the range 50–500 K via density-of-states using Debye relation. It is in fairly good agreement with the experimental data. Heat capacity behavior of PVDC with temperature was observed nearly linear in nature. Heat capacity provides a relationship between microscopic behavior and a macroscopic property. The thermal stability of a polymeric system and its interactive nature with other properties, such as PHONON-PHONON coupling is also related to thermodynamic behavior. The present study provides a theoretical framework to understand experimental measurements.

Rayleigh waves are surface waves which are dispersive in layered media. In order to study Rayleigh wave DISPERSION, there are several methods. Among these methods the application of matrix methods for elastic layered media is preferred to other methods. In the matrix method for a layered medium, boundary conditions for different interfaces are satisfied to obtain a relation for calculating Rayleigh wave DISPERSION which should be resolved by numerical methods. A program for the computing of Rayleigh waves DISPERSION was developed. The resulted DISPERSION CURVES from this program werecompared to similar methods which showed good agreement. According to the resulted graphs, wherever the earth structure is complex the DISPERSION CURVES also will be complex and different models will be moved oscillatory. Phase and group velocity CURVES tend to lower values when there is a surface sedimentary layer in the earth model. Thus, synthesis of these CURVES leads to clarification of different seismic phases, history of waves propagation from source to receiver and consequently imaging of earth structure.

The first-principles calculations of the structural, Elastic, and PHONON DISPERSION properties of cubic structure of tungsten trioxide have been performed with a Generalized Gradient Approximation (GGA) and ultrasoft-pseudopotential method based on the density functional theory. The pressure dependence of the elastic constants, bulk modulus, shear modulus, Young modulus, elastic Debye temperature, elastic anisotropy factor, Poisson ratios, Ductility, elastic velocities and Kleinmann parameter are presented. An analysis for the calculated elastic constants has been made to reveal the mechanical instability of WO3 up to 150 GPa. From the PHONON DISPERSIONs of WO3, it is seen that the PHONON frequencies increase as the volume decreases. The results show that the lattice constant and cell volume are in good agreement with experimental results. The elastic properties of tungsten trioxide, cubic, are examined for the first time.

The speci cation of soil surface layers is one of the most important parameters in civil engineering, geotechnics, and geophysics. The surface layer of the soil with lateral variation was modeled at di erent angles in  nite element software. In each model, the shot was applied on two sides of the geophone array and the seismic wave data were recorded by geophones. Using the windowing methods of di erent lengths and moving along the array, the various geophone data were placed in di erent windows. Next, for each windowing, the frequency-wavenumber spectrum was obtained using the double Fourier transform, and then, the DISPERSION curve was plotted. In this regard, the variations in the resolution of the frequency-wavenumber spectrum and DISPERSION curve were investigated for di erent window lengths. The phase velocity changes due to the changes in the lateral variation angles were also investigated. For the media with lateral variation, the DISPERSION CURVES could be obtained along the array and the location of the start and end of lateral variation in the corresponding phase velocity range could be achieved with acceptable accuracy, and the estimated phase velocity could be used as initial velocities in the inversion and speci cation of soil surface layers.

Shear-wave velocity () is an important parameter used for site characterization in geotechnical engineering. However, DISPERSION curve inversion is challenging for most inversion methods due to its high non-linearity and mix-determined trait. In order to overcome these problems, in this study, a joint inversion strategy is proposed based on the particle swarm optimization (PSO) algorithm. The seismic data considered for designing the objects are the Rayleigh wave DISPERSION curve and seismic refraction travel time. For joint inversion, the objective functions are combined into a single function. The proposed algorithm is tested on two synthetic datasets, and also on an experimental dataset. The synthetic models demonstrate that the joint inversion of Rayleigh wave and travel time return a more accurate estimation of VS in comparison with the single inversion Rayleigh wave DISPERSION CURVES. To prove the applicability of the proposed method, we apply it in a sample site in the city of Tabriz located in the NW of Iran. For a real dataset, we use refraction microtremor (ReMi) as a passive method for getting the Rayleigh wave DISPERSION CURVES. Using the PSO joint inversion, a three-layer subsurface model was delineated.The results obtained for the synthetic datasets and field dataset show that the proposed joint inversion method significantly reduces the uncertainties in the inverted models, and improves the revelation of boundaries.

The Born effective charges, zone center PHONON modes and infrared reflectivity spectra at normal incidence on the [100] and [001] surface of BaWO4 were calculated, using density functional perturbation theory. The calculated born effective charges display large deviations from nominal ionic charges, reflecting the mixed ionic-covalent nature of the chemical bonding. The PHONON modes were identified in terms of symmetry species, using group theory and character table of C4h point group. The calculated PHONON frequencies were in good agreement with the reported experimental values. The obtained results predict the frequency of a Raman active Bg mode that has not been earlier observed experimentally.