Volume 74, Issue 4

By employing the Madelung transformation, the time-dependent harmonic oscillator with friction described by the Schrödinger equation is reduced to a hydrodynamic system. An exponential elliptic vortex ansatz is introduced, and thereby a finite-dimensional nonlinear dynamical system is obtained. Time-modulated physical variables corresponding to the divergence, spin, shear, and normal deformation rates of the Madelung velocity field are introduced, and the dynamical system is reducible to a form amenable to general solutions. In particular, three typical elliptical vortex solutions termed pulsrodons are derived, and their behaviours are simulated. These solutions have recently found applications in oceanic and atmospheric dynamics. Moreover, it is shown that the harmonic oscillator with friction has an underlying integrable structure of Ermakov–Hamiltonian type.

The potential dependence of the contact angle between a gold electrode and lithium, sodium, potassium, rubidium, and caesium chloride melts was studied using the meniscus weight method to establish the patterns of wettability of solid surfaces by ionic melts when changing the composition of the salt phase and the jump of the electric potential. It is found that the forms of the contact angle versus the potential curve of Au change from a convex to a camel-like shape with two maxima upon replacing the lithium chloride with the caesium chloride melt. This phenomenon is explained by the assumption that the adsorption of the halide anions at the positively charged electrode surface has a chemical rather than electrostatic character. The adsorption process is accompanied by a charge transfer through the interface and the formation of covalent bonds between the adsorbent and adsorbate.

The complex scaling method is applied to probe the resonances of a Dirac particle in the Eckart potential, along with the corresponding energies and widths obtained. Then, the dependence of the resonant energies and widths on the parameters of the potential is checked. The results indicate that the energy and width of the pseudospin doublets preserve a good pseudospin symmetry. Furthermore, the quality of pseudospin symmetry is correlated with the parameters of the Eckart potential.

The notions of artificial Hamiltonian (partial Hamiltonian) and partial Hamiltonian operators are used to derive the first integrals for the first order systems of ordinary differential equations (ODEs) in epidemiology, which need not be derived from standard Hamiltonian approaches. We show that every system of first order ODEs can be cast into artificial Hamiltonian system q˙=∂H∂p$\dot{q}=\frac{{\partial H}}{{\partial p}}$, p˙=−∂H∂q+Γ(t,q,p)$\dot{p}=-\frac{{\partial H}}{{\partial q}}+\Gamma(t,\;q,\;p)$ (see [1]). Moreover, the second order equations and the system of second order ODEs can be written in the form of artificial Hamiltonian system. Then, the partial Hamiltonian approach is employed to derive the first integrals for systems under consideration. These first integrals are then utilized to find the exact solutions of models from the epidemiology for a distinct class of population. For physical insights, the solution curves of the closed-form expressions obtained are interpreted in order for readers understand the disease dynamics in a much deeper way. The effects of various pertinent parameters on the prognosis of the disease are observed and discussed briefly.

The standard interpretations of special relativity (Einstein–Minkowski) and general relativity (GR) lead to a drastically changed notion of time: the eternalism or block universe theory. This has strong consequences for our thinking about time and for the development of new fundamental theories. It is therefore important to check this thoroughly. The Lorentz–Poincaré interpretation, which sees the relativistic effects as following from a “true” Lorentz contraction of all objects in their motion through the ether, uses a conservative concept of time and is in the absence of gravitation indistinguishable from the standard interpretation; but there exists currently no accepted gravitation theory for it. The scalar ether theory of gravitation is a candidate for such a theory; it is presented and discussed. The equations of motion for a test particle are derived; the case of a uniformly moving massive body is discussed and then specialized to the case of spherical symmetry. Formulas for the acceleration of test particles are given in the preferred frame of the ether and in the rest frame of the massive body that moves with velocity V with respect to the ether. When the body rests in the ether ( V = 0 ), the acceleration is up to order c −2 identical to GR. The acceleration of a test particle for V ≠ 0 is given; this makes it possible to fit observations in celestial mechanics to ephemerides with V as a free parameter. The current status of such fits (although to ephemerides and not to observations) is presented and discussed.

The present study is related to indicating the several effects of the relaxation time, dynamic behaviour of wall properties and slip conditions at the boundaries on the peristaltic locomotion of viscous non-Newtonian Maxwell fluid flow through a two-dimensional (2D) horizontal flexible sinusoidal wave-shaped channel. An approximated theoretical model is constructed. The solution of the governing equations is developed using the perturbation method. Small amplitude ratio “ratio between amplitude of the wave and half channel width” for the wavy transport is considered for describing the velocity and pressure distributions. Different factors of wall features such as damping force coefficient, wall tension parameter, wall bending coefficient and spring stiffness factor in addition to various flow parameters such as the compressibility factor, Reynolds number, slip coefficient and also the main parameter of interest relaxation time are involved in the mathematical calculations and discussed through graphical representation. Graphs for mean axial velocity, perturbation function and velocity at the wall distributions using the previous coefficients are plotted and then discussed in detail. Results indicate that wall properties, compressibility factor and relaxation time in the presence of peristaltic transport have a significant effect on velocity distributions. The damping factor, wall tension, slip parameter and relaxation time are reducing the mean axial velocity and raising the reversal flow but, the wall elasticity factor enhances the mean axial velocity. Also, the liquid compressibility has a strong effect on the dynamics of the flow.

The time-dependent charging phenomenon of dust particles is timely studied in quantum plasmas with low frequency dust dynamical temporal scales referred to as dust acoustic waves. The quantum effects are incorporated through Fermi pressure, exchange-correlation potential as well as the Bohm potential. The quantum fluid model is employed in getting the dispersion relation pointing to the damping instability. The damping instability is analysed across the whole spectrum k , on varying ion-thermal temperature, electron number density and the dust radii. The applications of this work are pointed out in the laboratory and the astrophysical dense plasma systems.

Samarium chloride-thiourea-l-tartaric acid (SCTuT): a semi-organic material was prepared in the form of a single crystal with an orthorhombic crystal structure and a space group P nma . The crystallinity and purity of the single crystals were tested by powder X-ray diffraction. The scanning electron microscopy (SEM) analysis shows the rod-like microstructure. Energy dispersive X-ray analysis has confirmed the elemental composition. Fourier transform infrared and Raman spectroscopy analysis established the mode of coordination and functional groups. The thermal effects such as dehydration, melting and decomposition, etc. were observed by the thermogravimetric and differential thermoanalytical (TGA/DTA) analysis. Linear and non-linear characteristics of the compound were studied in detail. The optical band transitions due to C=O and C=S chromophores remain active in grown crystals and thus are recorded in the UV-Vis optical spectrum. The crystals possess finite values of non-linear absorption, non-linear refraction and third order nonlinearity as confirmed by Z-scan experiments.

The structural parameters, electronic structures, and mechanical and thermodynamic properties of TaSi 2 under different pressures have been completely explored by a combination of density functional theory and quasi-harmonic Debye model. Results show that our computed structural parameters and elastic constants are in consistency with available experimental findings and previous theoretical calculations. The electronic structures of TaSi 2 under different pressures including band structures and density of states are reported. It turns out that TaSi 2 should be metallic. The elastic constants C ij , bulk modulus B , shear modulus G , Young’s modulus E , Poisson’s ratio ν, B / G , Debye temperature θ, and wave velocities under pressures are also evaluated successfully. The calculated C ij obeys the Born–Huang stability criterion, which demonstrates that TaSi 2 is mechanically stable under different pressures. More interestingly, the three-dimensional surface constructions and projections of E and B under different pressures are also systematically evaluated. With the increase of applied pressure, TaSi 2 exhibits subtle anisotropy under zero pressure, and the anisotropy strengthened. Finally, the dependence of the thermodynamic properties on pressure/temperature is obtained and analyzed for the first time.