Polarization of plane wave propagating inside elastic hexagonal system solids

Based on the reported physical parameters for hexagonal system solids,we have calculated the effects of anisotropy on polarization of plane P-wave propagation.Herein we report the results of calculations and the newly observed physical phenomena.It is found that,for a given propagation,if the polarization is parallel to the wave vector,so also to the Poynting vector.In such a case,the phase velocity is identical to the energy velocity;the quasi P-wave degenerates to a pure P-wave along the propagation.It is also noted that if the polarization is parallel to the Poynting vector but not to the wave vector,the propagating wave cannot be a pure P-wave.Furthermore,the polarization in a quasi P-wave may deviate from the wave vector for more than 45°,but the deviation from the Poynting vector is always less than 45°.The energy velocity of a quasi SV-wave can be larger than that of the quasi P-wave in some propagation directions,even though the phase velocity of a quasi SV-wave may never be larger than either the phase velocity or energy velocity of the quasi P-wave.Finally,in case of parameters ε=0 and δ*≠0,the polarization of a quasi P-wave has an observed symmetry at a 45°phase angle.The anisotropy of a hexagonal system solid determines if a pure P-wave can be created and what the propagation direction is for a plane wave propagating inside such a hexagonal system solid.     

Ideal Mixture Approximation of Cluster Size Distributions at Low Density

We consider an interacting particle system in continuous configuration space. The pair interaction has an attractive part. We show that, at low density, the system behaves approximately like an ideal mixture of clusters (droplets): we prove rigorous bounds (a) for the constrained free energy associated with a given cluster size distribution, considered as an order parameter, (b) for the free energy, obtained by minimising over the order parameter, and (c) for the minimising cluster size distributions. It is known that, under suitable assumptions, the ideal mixture has a transition from a gas phase to a condensed phase as the density is varied; our bounds hold both in the gas phase and in the coexistence region of the ideal mixture. The present paper improves our earlier results by taking into account the mixing entropy.     

Further Implications of the Bessis–Moussa–Villani Conjecture

We find further implications of the BMV conjecture, which states that for hermitian matrices B≥0 and A, the function is the Laplace transform of a positive measure supported on [0,∞].     

Ergodicity of a Single Particle Confined in a Nanopore

We analyze the dynamics of a gas particle moving through a nanopore of adjustable width with particular emphasis on ergodicity. We give a measure of the portion of phase space that is characterized by quasiperiodic trajectories which break ergodicity. The interactions between particle and wall atoms are mediated by a Lennard-Jones potential, so that an analytical treatment of the dynamics is not feasible, but making the system more physically realistic. In view of recent studies, which proved non-ergodicity for systems with scatterers interacting via smooth potentials, we find that the non-ergodic component of the phase space for energy levels typical of experiments, is surprisingly small, i.e. we conclude that the ergodic hypothesis is a reasonable approximation even for a single particle trapped in a nanopore. Due to the numerical scope of this work, our focus will be the onset of ergodic behavior which is evident on time scales accessible to simulations and experimental observations rather than ergodicity in the infinite time limit.     

A highly accurate method to solve Fisher’s equation

In this study, we present a new and very accurate numerical method to approximate the Fisher’s-type equations. Firstly, the spatial derivative in the proposed equation is approximated by a sixth-order compact finite difference (CFD6) scheme. Secondly, we solve the obtained system of differential equations using a third-order total variation diminishing Runge–Kutta (TVD-RK3) scheme. Numerical examples are given to illustrate the efficiency of the proposed method.     

Latex-mediated synthesis of ZnS nanoparticles: green synthesis approach

A low-cost, green synthesis of ZnS nanoparticles is reported using 0.3 % latex solution prepared from Jatropha curcas L. ZnS nanoparticles were characterized by X-ray diffraction, selected area electron diffraction, transmission electron microscopy, energy dispersive analysis of X-rays, UV–vis optical absorption and photoluminescence techniques. Fourier Transform Infrared Spectroscopy was performed to find the role of cyclic peptides namely curcacycline A (an octapeptide), curcacycline B (a nonapeptide) and curcain (an enzyme) as a possible reducing and stabilizing agents present in the latex of J. curcas L. The average size of ZnS nanoparticles was found to be 10 nm. Latex of J. curcas L. itself acts as a source of sulphide (S⁻²) ions that are donated to Zn ions under present experimental conditions. Source of sulphide (S⁻²) ions is still unclear, but we speculate that cysteine or thiol residues present in enzyme curcain may be donating these sulphide (S⁻²) ions.     

Coupled-channel analysis for 20.4 MeV energy of p-<Superscript>64</Superscript>Zn inelastic scattering

In this study, a coupled-channel (CC) analysis of the elastic and the inelastic scattering of 20.4 MeV polarized protons from a ⁶⁴Zn target leading to the deformed 2⁺, 3−, 2₂⁺2_2^+ states was performed. The CC potential parameters and the deformation parameters of the excited states corresponding to the best fit to the experimental differential cross-sections and the analysing powers data were determined. For 2₂⁺2_2^+ excited state, a mixed type was used and a good fit to the data was provided. The CC calculation results were compared to the pure distorted wave Born approximation (DWBA) calculation results which were calculated using the new parameters. All calculations were conducted using the computer code ECIS06.