Volume 73, Issue 12

For the measurement of attenuation parameters of any material for gamma ( γ )-rays, the narrow-beam transmission geometry is one of the essential requirements. Linear attenuation coefficient ( μ , cm −1 ), half value layer thickness and mean free path are some fundamental parameters used for the analysis of γ -ray attenuation behaviour of any material. The complete experimental setup used to measure these parameters is termed as γ -ray transmission geometry. The geometrical parameters such as the size of collimator aperture, thickness of sample (absorber), source to absorber (SA) distance, absorber to detector distance and source to detector distance (STD) are deciding factors for the nature of γ -ray transmission geometry. A novel geometrical parameter, scattered-to-transmission ratio (STR), has been proposed in this investigation. STR provides qualitative information of various geometrical parameters. It provides influence on the nature of transmission geometry for experimental measurements by various geometrical parameters and buildup factor. To investigate its influence, STR values have been analysed by varying sizes of collimator aperture between 3 and 12 mm and absorber thicknesses between 20 and 280 mm for fixed SA and STD. Six standard building materials (cement black, cement white, clay, red mud, lime stone and plaster of paris) have been used for the investigation. The point isotropic γ -ray sources Cs-137 (3700 M Bq) and Co-60 (370 M Bq) have been used in this study. It has been found that STR provides better information of scattered γ -rays by the material than its buildup factor ( B ). Additionally, CSTR (the critical value of STR) serves as an extensive parameter to distinguish between narrow-beam (good) and broad-beam (poor) γ -ray transmission geometries.

Density functional theory (DFT) investigations on neutral and anionic VF n (n = 1–7) clusters are performed, and the geometric structures, relative stability as well as electronic and spectral [IR, Raman and ultraviolet-visible (UV-Vis)] properties of these clusters are systematically calculated with DFT calculations. The clusters for n ≥ 4 exhibit superhalogen properties with very high electron affinities. Analysis of the interactions between VF 6 and Li indicates high stability of LiVF 6 , where VF 6 acts like fluorine. The IR and Raman spectra reveal that the peaks can be largely assigned to the stretching vibration of F atoms. The highest and next highest UV-Vis absorption peaks within 200–350 nm for neutral and anionic clusters are mainly ascribed to the electronic transitions between F 2p and V 3d orbitals.

Parametric instability of a rotating functionally graded (FG) cylindrical thin shell with axial compression under various boundary conditions is studied in this article. In particular, the shell is subjected to both axial periodic displacement disturbances and a thermal environment. The initial hoop tension and Coriolis effects due to rotation are also considered. The coupled dynamic equations of the shell under multiple conditions are formulated based on Love’s thin-shell theory. The instability boundaries of the shell with different boundary conditions considering thermal factors, axial disturbances, and other system parameters are obtained analytically under the case of primary and combination resonance; numerical illustrations are also given. It is found that high temperature weakens the stability of the system, while axial disturbances show stronger influence on the instability regions of the shell compared to other parameters such as thermal factors and the angular rotation velocity.

We derive the new infinite Sasa–Satsuma hierarchy of evolution equations using an invariant densities approach. Being significantly simpler than the Lax-pair technique, this approach does not involve ponderous 3 × 3 matrices. Moreover, it allows us to explicitly obtain operators of many orders involved in the time evolution of the Sasa–Satsuma hierarchy functionals. All these operators are parts of a generalised Sasa–Satsuma equation of infinitely high order. They enter this equation with independent arbitrary real coefficients that govern the evolution pattern of this multiparameter dynamical system.

It is known that there is no room for anti-particles within the Schrödinger regime in quantum mechanics. In this article, we derive a (non-relativistic) Schrödinger-like wave equation for a spin-1/2$1/2$ free particle in 3 + 1 space-time dimensions, which includes both positive- and negative-energy eigenstates. We show that, under minimal interactions, this equation is invariant under 𝒫𝒯$\mathcal{P}\mathcal{T}$ and 𝒞 discrete symmetries. An immediate consequence of this is that the particle exhibits Zitterbewegung (‘trembling motion’), which arises from the interference of positive- and negative-energy wave function components.

The dispersion relation of electrostatic waves due to multi-drifts is studied in an ambient magnetic field across three-species quantum dusty plasmas. The quantum hydrodynamic model is applied to analyze the effects of the Lorentz and the gravitational forces. It is found that the instability is excited mainly due to the E0×B0\({\mathbf{E}_{0}}\times{\mathbf{B}_{0}}\) drift of the plasma species. However, an additional g0×B0\({\mathbf{g}_{0}}\times{\mathbf{B}_{0}}\) drift associated with dust particles enhances the instability over a wide spectrum of wavevector. The role of a varying magnetic field and the number density of electrons in the wave instability are analyzed graphically. It is noticed that these factors have a significant contribution over the drift instability.

This model characterises the flow behaviour of suspended particles when swallowing through oesophagus. Transport of particle-fluid mixture induced by dilating peristaltic waves on a circular cylindrical tube was considered for investigation. Unsteady closed-form solutions for pressure gradient, velocity and stream function are obtained by applying regular perturbation technique up to the first order of wavenumber (the ratio of the tube radius to the wavelength). It is observed that the axial velocity of the fluid is greater than that of the solid particles almost everywhere. However, at the wall the axial velocity of the fluid is zero due to the no-slip condition imposed on it; but the suspended particulate material has non-zero positive axial velocity. Thus, the axial velocity of the suspended particles near the tube wall is more than that of the fluid velocity. It is further observed that the axial velocity is negative in the regions close to maximum occlusions giving way to instantaneous backward flow. It is also inferred that the maximum axial velocity of the particle-fluid suspension with non-zero wavenumber is more than that of the particle-free fluid with zero wavenumber. We examined the effect of volume fraction of suspended particulate matter on pressure gradient and velocity. An increase in the volume fraction diminished the pumping performance and also the axial and radial velocities. The results are also compared with those which were obtained for zero wavenumber. The outcome of the investigation endorses the doctors’ advice to patients suffering from achalasia, oesophageal stricture and oesophageal tumors to take liquid or food items with lesser solid contents. Streamline patterns are changed by increasing the flow rate while trapping occurs at high flow rates.

First-principles calculations were carried out to explore the structural stability, elastic moduli, ductile or brittle behaviour, anisotropy, dynamical stability, and thermodynamic properties of pure Al and CeT 2 Al 20 (T = Ti, V, Cr, Nb, and Ta) intermetallics. The calculated formation enthalpy and phonon frequencies confirm that these intermetallics satisfy the conditions for structural stability. The elastic constants C ij , elastic moduli B , G , and E , and the hardness H v indicate these intermetallics have higher hardness and the better resistance against deformation than pure Al. The values of Poisson’s ratio ( v ) and B / G indicate that CeT 2 Al 20 intermetallics are all brittle materials. The anisotropic constants and acoustic velocities confirm that CeT 2 Al 20 intermetallics are all anisotropic, but CeV 2 Al 20 , CeNb 2 Al 20 , and CeTa 2 Al 20 are nearly isotropic. Importantly, the calculated thermodynamic parameters show that CeT 2 Al 20 intermetallics exhibit better thermodynamic properties than pure Al at high temperature.