Vol. 67 No. 3 May-Jun (2021): Revista Mexicana de Física

Phase transitions in aluminum nitride (AlN) were investigated by first principles total energy calculations. Three AlN crystal structures were considered: rock salt (NaCl), zinc blende and wurtzite. The cohesion energy was calculated within both GGA and LDA formalisms. According to the cohesion energy results, the ground state corresponds to the hexagonal wurtzite phase, in agreement with experimental evidence. However, the zinc blende and NaCl phases may be formed as metastable structures. To determine the energy gap the modified Becke-Johnson pseudopotential was applied, with results showing good agreement with the experimental data. The ground state structure exhibits direct electronic transitions. However, the zinc blende and NaCl phases show indirect band gap. Provided that external pressures may induce transitions from wurtzite to zinc blende or rock salt, these transitions were also investigated. Estimation of the pressure at the phase transition indicates that small pressures are needed to achieve such transitions.

The purpose of this paper is to present a shallow-water-type model with multiple inhomogeneous layers featuring variable linear velocity vertical shear and startificaion in horizontal space and time. This is achieved by writing the layer velocity and buoyancy fields as linear functions of depth, with coefficients that depend arbitrarily on horizontal position and time. The model is a generalization of Ripa's (1995) single-layer model to an arbitrary number of layers. Unlike models with homogeneous layers the present model is able to represent thermodynamics processes driven by heat and freshwater fluxes through the surface or mixing processes resulting from fluid exchanges across contiguous layers. By contrast with inhomogeneous-layer models with depth-independent velocity and buoyancy, the model derived here can sustain explicitly at low frequency a current in thermal wind balance (between the vertical vertical shear and the horizontal density gradient) within each layer. In the absence of external forcing and dissipation, energy, volume, mass, and buoyancy variance constrain the dynamics; conservation of total zonal momentum requires in addition the usual zonal symmetry of the topography and horizontal domain.  The inviscid, unforced model admits a formulation suggestive of a generalized Hamiltonian structure, which enables the classical connection between symmetries and conservation laws via Noether's theorem.  A steady solution to a system involving one Ripa-like layer and otherwise homogeneous layers can be proved formally (or Arnold) stable using the above invariants. A model configuration with only one layer has been shown previously to provide: a very good representation of the exact vertical normal modes up to the first internal mode; an exact representation of long-perturbation (free boundary) baroclinic instability; and a very reasonable representation of short-perturbation (classical Eady) baroclinic instability. Here it is shown that substantially more accurate overall results with respect to single-layer calculations can be achieved by considering a stack of only a few layers. A similar behavior is found in ageostrophic (classical Stone) baroclinic instability by describing accurately the dependence of the solutions on the Richardson number with only two layers.

We report a theoretical study to determine the temperature profiles due to the continuous and
constant injection of hot water through a line source, into a homogeneous fluid-saturated porous medium which has had initially a constant temperature T∞. In our treatment we have taken in to account the simultaneous injection of constant fluxes of volume fluid, q, and of heat, φ. By using a far-field description, we found similarity solutions for the dimensionless temperature depending on the Peclet number, P e, as the single parameter of the problem.

In this paper, we studies chirped solitary waves in two-Core optical fibers with coupling-coefficient dispersion and intermodal dispersion. To construct chirp soliton, the couple of nonlinear Schrödinger equation which describing the pulses propagation along the two-core fiber have been reduced to one equivalent equation. By adopting the traveling-waves hypothesis, the exact analytical solutions of the GNSE were obtained by using three relevant mathematical methods namely the auxiliary equation method, the modified auxiliary equation method and the Sine-Gordon expansion approach. Lastly, the behavior of the chirped like-soliton solutions were discussed and some contours of the plot evolution of the bright and dark solitons are obtained.

In this article, we first offer the approach of quasi magnetic Lorentz flux of quasi velocity magnetic flows of particles by the quasi frame in 3D space. Eventually, we obtain new optical conditions of quasi magnetic Lorentz flux by using directional quasi fields. Moreover, we determine quasi magnetic Lorentz flux for quasi vector fields. Also, we give new constructions for quasi curvatures of quasi velocity magnetic flows by considering Heisenberg ferromagnetic spin. Finally, magnetic flux surface is demonstrated in a static and uniform magnetic surface by using the analytical and numerical results.

This paper addresses the Heisenberg ferromagnetic spin chain equation with beta time derivative. Integration schemes are used to study this equation. They are generalized Kudryashov method and modified exp -expansion function method. Dark, bright and dark-bright soliton solutions of this equation are procured.

In this article we  discussed the analytical analysis of perturbed nonlinear fractional Schr$\ddot{o}$dinger equation with the help of our new introduced technique extended modified auxiliary equation mapping method(EMAEMM). By using this newly proposed technique we have found some new  and more general variety of exact traveling wave solutions which are collecting some kind of semi half bright, semi half dark, doubly periodic,  dark, combined, periodic, bright, half dark and half bright via three parametric values which is the primary key point of difference of our technique. These results are highly applicable to develop new theories of plasma physics, quantum mechanics, biomedical problems, soliton dynamics, nuclear physics, optical physics, fluid dynamics, electromagnetism, industrial studies, mathematical physics, and in many other natural and physical sciences. For detailed physical dynamical representation of our results we have shown them with graphs in different dimensions via Mathematica 10.4 to get more understanding to observe the behavior of different new dynamical shapes of solutions.

To confine vector bosons in the four dimensional sector of a domain wall spacetime, we propose a mechanism in which the interaction among vectors is propagated via the self-interaction of the scalar wall.  In the process, the vector acquires an asymptotic mass, defined by the bulk cosmological constant, and it ends up coupled to the wall by the tension of the brane. The mechanism is applied on the Randall Sundrum scenario and regular versions of it, and on singular domain walls. In any case, the  electrostatic potential between two charged particles is defined by both the vector state attached to the wall and a continuous tower of massive vector states that propagate freely along the scenario's extra dimension.

Generalized Kudryashov method has been used to private type of nonlinear fractional differential equations. Firstly, we proposed a fractional complex transform to convert fractional differential equations into ordinary differential equations. Three applications were given to demonstrate the effectiveness of the present technique. As a result, abundant types of exact analytical solutions are obtained.

We developed a somewhat novel fractional-order calculus workbench as a certain generalization of the Khalil’s conformable derivative. Although every integer-order derivate can naturally be consistent with fully physical-sense problem’s quotation, this is not the standard scenario of the non-integer-order derivatives, even aiming physics systems’s modelling, solely.We revisited a particular case of the generalized conformable fractional derivative and derived a differential operator, whose properties overcome those of the integer-order derivatives, though preserving its clue advantages.Worthwhile noting, that two-fractional indexes differential operator we are dealing, departs from the single-fractional index framework, which typifies the generalized conformable fractional derivative. This distinction leads to proper mathematical tools, useful in generalizing widely accepted results, with potential applications to fundamental Physics within fractional order calculus. The later seems to be especially appropriate for exercising the Sturm-Liouville eigenvalue problem, as well as the Euler-Lagrange equation and to clarify several operator algebra matters.

The factorization of inhomogeneous Li\'enard equations is performed showing that through the factorization conditions involved in the method one can obtain forcing terms for which closed-form solutions exist. Because of the reduction of order feature of factorization, the solutions are simultaneously solutions of first-order differential equations with polynomial nonlinearities. Several illustrative examples of such solutions are presented, generically having rational parts and consequently singularities.

We show that the conditions for the separability of the Hamilton-Jacobi equation given by the Stäckel theorem imply that, making use of the elementary Lagrangian formalism, one can find $n$ functionally independent constants of motion, where $n$ is the number of degrees of freedom. We also show that this result can be linked to the fact that the Lagrangian for a system of this class is related to the sum of $n$ one-dimensional Lagrangians, if one makes use of multiple local times.

Motivated by recent researches in magnetic curves and their flows in different types of geometric manifolds and physical spacetime structures, we compute Lorentz force equations associated with the magnetic b-lines in the binormal direction. Evolution equations of magnetic b-lines due to inextensible Heisenberg antiferromagnetic flow are computed to construct the soliton surface associated with the inextensible Heisenberg antiferromagnetic flow. Then, their explicit solutions are investigated in terms of magnetic and geometric quantities via the conformable fractional derivative method. By considering arc-length and time-dependent orthogonal curvilinear coordinates, we finally determine the necessary and sufficient conditions that have to be satisfied by these quantities to define the Lorentz magnetic flux surfaces based on the inextensible Heisenberg antiferromagnetic flow model.

The quantum field theory in de Sitter ambient space provide us with a comprehensive
description of massless gravitational field.
Using the gauge-covariant derivative in the de Sitter ambient space, the gauge invariant Lagrangian density has been found.
In this paper, the equation of the conjugate spinor for massless spin-$\frac{3}{2}$ field is obtained by Euler-Lagrange equation. Then the field equation is written in terms of the Casimir operator of the de Sitter group. Finally, the gauge invariant field equation is presented.

Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

Hulthén plus Hellmann potentials are adopted as the quark-antiquark interaction potential for studying the mass spectra of heavy mesons. We solved the radial Schrödinger equation analytically using the Nikiforov-Uvarov method. The energy eigenvalues and corresponding wave function in terms of Laguerre polynomials were obtained. The present results are applied for calculating the mass of heavy mesons such as charmonium and bottomonium. Four special cases were considered when some of the potential parameters were set to zero, resulting into Hellmann potential, Yukawa potential, Coulomb potential, and Hulthén potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.

Using  proton–proton elastic scattering data  at  TeV and squared four-momentum transfer 0.36 < -t <  0.76 (GeV/c)² for 13 σ_Beam distance  and  0.07 < -t <  0.46 (GeV/c)² for 4.3 σ_Beam distance, form factor of proton is predicted. Simplest version of Chou–Yang model is employed to extract the form factor by fitting experimental data of differential cross section from TOTEM experiment (for 13σ_Beamand 4.3 σ_Beam distance) to a single Gaussian. Root mean square (rms) charge radius of proton is calculated using this form factor.  It is found to be equal to 0.91 fm and 0.90 fm respectively. Which is in good agreement with experimental data and theoretically predicted values.

Copper oxide thin films deposited by sputtering are frequently formed by using metal copper targets in reactive atmospheres. In this report, paramelaconite (Cu4O3) thin films were deposited by non-reactive rf magnetron sputtering. The target used for sputtering was a copper oxide disk fabricated by oxidation of metal copper at 1000 °C for 24 h in air
atmosphere. X-ray diffraction (XRD) results showed that the copper oxide target was mainly composed of cupric oxide (CuO) and cuprous oxide (Cu2O) crystals. Raman analyses suggested that the surface of the copper oxide disk is composed by a (CuO) layer. XRD measurements performed to the copper oxide thin films deposited by non-reactive rf magnetron sputtering showed that the film is composed of (Cu4O3) crystals. However,
Raman measurements indicated that the Cu4O3 thin films are also composed by amorphous CuO and Cu2O.

Using ab-initio calculations, we studied the structural, elastic, and electronic properties of Sc₂SiX compounds with, (X=C, N). The negative formation energy and the positive cohesive energy indicate that these compounds are energetically stable and can be synthesized in normal conditions. Sc₂SiC and Sc₂SiN compounds are mechanically stable, estimated by the individual elastic constants. Elastic constants and modulus increase when C is substituted by N. The elastic anisotropy in Sc₂SiC is high compared to Sc₂SiN. Both nanolaminates are fragile in nature. Sc₂SiC is more conductive than Sc₂SiN. The calculated electron band structures and the density of states imply that the chemical bond in two compounds is a combination of covalent, ionic, and metallic nature. The main factors governing the electronic properties are the hybrid states Sc- 3d, Si-3p, and C -2p and the bond (p-d) stabilizes the structure. Fermi's surface characteristics have been studied for the first time, which are changed when replacing N by C. Based on the estimate of the total energy, we conclude that the replacement of C by N will lead to a stabilization of the hexagonal structure and a decrease of the metallic support.

Plasmon-assisted energy conversion in dye-sensitised solar cells (DSSCs) has been achieved by applying gold (Au) nanoparticles (NPs) inside Titania (TiO₂) photoanodes. Gold nanoparticles (GNPs) were introduced into DSSCs to further enhance their power conversion efficiency (PCE). In this research work, an effort has been made to enhance the optical absorption and improve the performance of DSSCs. By utilising finite-difference time-domain (FDTD) software, GNPs with radii of 15, 25, 35, 45, 55, 65, 75 and 85 nm were produced and introduced into the TiO₂ photoanode. The optimum radius for the optical absorption enhancement was found to be 85 nm because the effect of plasmon coupling is more significant for metal nanoparticle sizes > 60 nm. The effect of various sizes of GNPs on light scattering has also been presented in this study. Moreover, the investigation has focused on the role of incident angle of light source on the absorption in TiO₂ films. It was found that the optimum incident angle for the enhancement of broadband optical absorption in the wavelength range of 450–800 nm is 70°.

Zn22Al2Cu cellular alloy was prepared with six different densities, two microstructures and two cell shapes to determine the effect of these factors on its compressive behavior. NaCl granules with sharp edges, as purchased and with smooth edges obtained by roughly polishing the purchased granules were used as spacers. The elaboration process of the alloy foam consisted of melting the alloy, immersing the granules in the liquid alloy, air-cooling and then dissolving the salt in boiling water. The matrix obtained with the materials had an as-cast microstructure, and a fine microstructure, which was achieved with a heat treatment applied prior to dissolving the NaCl granules. Samples were tested in compression at a 10-3 s-1 strain rate. The smooth shape of the cells caused that the as-cast microstructure in the matrix produces an elastic behavior, which is described by the equation derived by Ashby for the relative elastic modulus and the relative density of sponges. The same type of cell shape embedded in the fine microstructure produces an elastic behavior in compression that depends on the density, which is typical of very low-density foams, although much lower than those achieved in this study. Compressive behavior is chaotic when cells have sharp shape, regardless microstructure type. The alloy studied with 4 mm mean size cells has a compression behavior like a sponge or low-density foam, when its cell walls have smooth contours, and as-cast or fine microstructure, respectively.

A low-temperature synthesis of novel nanostructured Co_xNi_1-xMn_0.5Fe_1.5O₄(x=0,0.25,0.5,0.75,1) ferrites was carried out by sol-gel auto-combustion technique. The obtained nanostructured ferrites were investigated by employing the techniques of powder X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), energy dispersive X-ray spectroscopy (EDX) and vibrating sample magnetometry (VSM). The XRD diffractograms of the prepared ferrites revealed the formation of a spinel phase with face centered cubic (fcc) structure belonging to Fd- m space group.  The average lattice parameter ‘a’ of ferrites exhibited a rise versus a rise in Co²⁺ concentration in accordance with the Vegard’s law. The SEM investigation of NiMn_0.5Fe_1.5O₄ powder revealed an existence of octahedral-shaped morphology of ferrite grains. The TEM investigation of NiMn_0.5Fe_1.5O₄ powder showed nanostructures of ferrite particles with sizes consistent with the crystallite sizes as estimated by Debye-Scherer’s formula. An EDX spectrum of NiMn_0.5Fe_1.5O₄ powder confirmed its elemental composition. The M-H hysteresis loops recorded by VSM at room temperature revealed a dependence of coercivity (H_c), maximum magnetization (M_max) and retentivity (M_r) on Co²⁺concentration. Due to the shape dependence of M-H loops on Co²⁺ concentration in compounds enabled their candidature for applications in memory devices and magnetic sensors.