Vol. 67 No. 6 Nov-Dec (2021): Revista Mexicana de Física

Recently, non-linear fractional partial differential equations are used to model many phenomena in applied sciences and engineering. In this study, the modified simple equation scheme is implemented to obtain some new traveling wave solutions of the non-linear conformable time-fractional approximate long water wave equation and the non-linear conformable coupled time-fractional Boussinesq-Burger equation, which are used in the expression of shallow-water waves. The time- fractional derivatives are described in terms of conformable fractional derivative sense. Consequently, new exact traveling wave solutions of both equations are achieved. The graphics and correctness of the wave solutions are obtained with the Mathematica package program.

One of the most important tools for expressing physical phenomena in the world around us is to express problems using differential equations with partial derivatives. This importance has attracted the attention of many researchers. The result of these considerations has been the invention and application of various analytical and numerical methods in solving this category of equations. In this work, we make use of a newly-developed technique called the generated exponential rational function method to compute the exact solution of the Davey-Stewartson equation. According to all research studies I have done so far, there is no similar research work carried out in the present paper. The results attest to the efficiency of the proposed method. The method used in this paper has the ability to be employed in other cases in solving equations with relative derivatives.

The generalized fractional perturbed (3+1)-dimensional Zakharov–Kuznetsov (PZK) equation which appear in the magnetized two-ion-temperature dusty plasma and quantum physics is considered. The sub-equation method in the conformable sense is proposed to obtained closed-form analytical solutions to this equation. The newly solutions obtained by the proposed method are kink-shape, multi-soliton, solitary wave, bell-shaped solitons, and periodic solutions that are substantial in the field of mathematical physics and can be of relevance in the field of plasma physics, also for future research.

The Hybrid Reverse Monte Carlo (HRMC) simulation has been widely used as a very useful method for displaying the pair partial distribution functions (PDFs) g(r) eliminating as soon as possible the artificial satellite peaks appear by the RMC simulation. The HRMC is an extension of the RMC algorithm, which introduces an energy penalty term (potential) in the acceptance criteria.
The glass retains the structure presented by the liquid at the glass transition temperature Tg, and the thermodynamic properties are influenced by these structural modifications. We are interested in this study to apply the structural parameters g(r), obtained from HRMC simulation, to determine some structural and thermodynamic properties for the BaMn(Fe=V)F7 Fluoride glass.
The calculated structural properties such as the running coordination number n(r) were in good agreement with coordination constraint. We suggest also that the structural parameters g(r) is a good tool to determine the thermodynamic properties as the energy of the system.

Some ferromagnetic alloys which adopt the perovskite or double-perovskite structure exhibit some remarkable properties, such as electromagnetic effects, charge and orbital ordering, i.e., dielectric and magnetoresistance effects in the same time. These phenomena are related to both electrical conductivity and spin orbit orientation. In order to optimize and explore the structural, magnetic and electronic properties of GdxBa1-xRuO3 alloy, we investigated here the first-principles calculations using the generalized gradient approximation (GGA+U+SO) as implemented in the Wien2K package. The concentration classification of GdxBa1-xRuO3 alloy with (x = 0, 0.125, 0.25, 0.5, 0.875, 1) is given. In this work, we have identified features such transition phases, spin ordered and charge conduction that enable a priori of both crystal structure and magnetic behavior prediction.
Our considerable GdxBa1-xRuO3 alloy is a half-metallic in the cubic phase, and, Mott insulator for x=0.875 and semiconductor for x=1 in the orthorhombic phase. The GdxBa1-xRuO3 alloy therefore undergoes a transition between a cubic phase and another orthorhombic at x = 0.5. It is clear that at this point our alloy (Gd0.5Ba0.5RuO3) is at the same time FM and AFM A-type, in another way, we can say that A-AFM and FM configurations coexist in our alloys. In the case of our GdxBa1-xRuO3 alloy, we can see that the total magnetic moment increases linearly with the concentrations "x" since it has passed from 15.99 μB for x = 0 to 39.95 μB for x = 0.5, this is valid in the cubic phase. That is related to a heavily magnetic moment of spin in the Ru atom which increases also linearly with increasing x, while the magnetic moment of Gd decreases slightly. In the orthorhombic phase, its value remains zero regardless of the concentration because we are in an antiferromagnetic (AF) configuration. The collaboration of the 3d-Ru and 2p-O states is suggested to play an important role for the ferromagnetism in the considered alloy. These orbitals were the most regular in the two bands respectively: the conduction band and the valence band in the two phases given here (cubic and orthorhombic). We also note the mixed collaboration of the states 3d-Ba. On the other hand, the contribution of 3d-Gd states was only effective in the band of conduction, at the time when that of the 4f-Gd states was noticed especially in the orthorhombic phase.

In this paper, the fundamental semiconductor properties of Hg_1-xCd_xTe and Hg_1-xZn_xTe are investigated by ab initio calculations based on the FP-LAPW method.   Structural properties have been calculated using LDA and GGA approximations. The electronic properties are studied using the LDA and GGA approximations, and the potential TB-mBJLDA coupled with the lattice parameters a_LDA and a_GGA. The optical properties are determined from the optimal gap energies based on the TB-mBJLDA potential. Lattice parameters a_LDA obtained by the LDA calculations predict values that are in good agreement with the experimental results and are better than those results obtained by the GGA calculations.  The use of TB-mBJLDA potential coupled with the lattice parameter a_GGA gives gap energy values in good agreement with the experimental results for all alloys except  Hg_1-xZn_xTe (x=0.5, 0.75) where the (TB-mBJ LDA+a_LDA) is more suitable. Optical constants are calculated from the dielectric function in the energy range (0-30 eV).  The spectrum of real and imaginary parts of the dielectric function, the energy loss function, the refractive index, the extinction coefficient, the absorption coefficient, and the reflectivity show that optical properties of Hg_1-xCd_xTe are comparable to those of  Hg_1-xZn_xTe. Our results are found to be in reasonable agreement with existing data reported in the literature.

The ab initio calculations based on the density functional theory (DFT) using the self-consistent Full potential linearized augmented plane wave (FPLAPW) method were performed to explore the electronic structures, thermodynamic and thermoelectric properties of new rattling Full Heusler alloys Ba2AgZ (Z = As, Sb, Bi). Results showed that the AlCu2Mn-type structure state is energetically the most stable structure. The results show that the electronic property of these cubic Rattling Heusler alloys have a semiconducting behavior with indirect band gaps Eg (L-D). The predicted band gaps were found to be 0.566, 0.548 and 0.433 eV for Z = As, Sb and Bi, respectively. The thermodynamic properties comprising the thermal expansion coefficient, heat capacity, entropy and Debye temperature parameter were evaluated at various pressures from 0 to 15 GPa. Thermoelectric properties of the Ba2AgZ (Z= As, Sb, Bi) materials are additionally computed over an extensive variety of temperature and it is discovered that all compounds exhibit ultralow thermal conductivity, good Seebeck coefficients and large high power factors, thus resulting they are suitable for use in thermoelectric device applications.

Small-scale fluid transport methods have grown significantly in recent years, mainly in applications in microfluidic systems. Therefore, the present study analyzes the movement of two-layers of immiscible fluids within a parallel flat plates microchannel. The fluid layers are composed of a Newtonian fluid and a power-law fluid. The pumping is produced by magnetohydrodynamics effects that act on the non-Newtonian conducting fluid dragging the non-conducting Newtonian fluid by viscous forces. Under the consideration of a laminar, incompressible, and unidirectional flow, the dimensionless mathematical model is established by the momentum equations for each fluid, together with the corresponding boundary conditions at solid-liquid and liquid-liquid interfaces. The problem formulation is semi-analytically solved using the Newton-Raphson method. The results are presented as a function of the velocity profiles and flow rate, showing interesting behaviors that depend on the physical and electrical properties of each fluid and flow conditions via the dimensionless parameters such as the flow behavior index, a magnetic parameter related to Lorenz forces, the fluids viscosity ratios and the dimensionless liquid-liquid interface position. This work contributes to the understanding of the various immiscible non-conducting fluids pumping techniques that can be used in microdevices.

Using the reductive perturbation method, we have derived the Zakharov-Kuznetsov (ZK) equation for a multi-component plasma model consisting of electrons, positrons and the uid ions with positive and negative charges. The extended homogenous balance method has been applied to obtain the soliton solution in addition to many traveling wave solutions. various physical parameters have different effects on the profile of the solitary wave pulses which can show the propagation of the ion acoustic waves in laboratory plasmas and many astrophysical plasma systems as in Earth's ionosphere.

In this work, the behaviour of magneto-hydrodynamic waves in optically thin plasmas considering dissipative processes, thermal and magnetic diffusion, a given ionization, and the heating and cooling functions are investigated for several particular cases. A numerical eigenvalues analysis of the dimensionless secular equations according to various cases is performed for the entire set of MHD equations.

Recently, within a generalized Hubbard model which includes correlated nearest (∆t) and next-nearest hopping interactions (∆t_3 ), a comparative study between d- and s^*- wave superconducting ground states on a square lattice was performed. It was found that the critical temperature of transition T_c (n), as a function of the electron concentration n, reaches a maximum (T_(c-max) at a given optimal doping (n_op) for each value of the ratio (t’)⁄t, where t and t’ are the tight-binding nearest and next-nearest hopping parameter of a square lattice, respectively. From all values obtained for T_(c-max) ((t’)⁄(t,n_op) a global minimum one was encountered for both symmetries. Likewise, in the same space, a minimal ground state energy E_g was also obtained. For d-wave channel both minima are localized around the same optimal doping, however, for s^* symmetry, the two minima are located at different electron concentrations. In this work, we additionally study how the p-wave ground-state energy and the critical temperature depend on the hoppings parameters and the electron concentration. The results show that for p-wave, minimum global values of  and  in the space do exist too, they are found around half filling but, as occurs for s^*- wave, the minimum of T_(c-max) does not occur at the same point as . Moreover, we present a ground-state phase diagram in the space (t’)⁄(t,n_op) where it is possible to find zones of coexistence and competition between the s^*-, p- and d-wave symmetries. Also, an analysis of the shape of the Fermi surface and the single-particle energy, as functions of the wave vector of an electron in the Cooper pair, has been done for different regions of the mentioned space.

Structural factors in clays influence their physical properties. Therefore, it is particularly important to understand the effects of heat treatment on the structure of the material during the ceramic process. In this work, we have analyzed clays from quarries in the Cerro de Pasco region, Peru, to evaluate their characteristics and the structural changes produced by heating, particularly in the interlaminar region. The samples were thermally treated between 150 ^oC and 800 ^oC with intervals of 50 ^oC. To evaluate the structural changes produced by temperature, X-ray diffraction were carried out before and after each heat treatment. The qualitative analysis of the measurements allowed to identify the mineralogical composition of the samples, finding phases of calcium montmorillonite, kaolinite, illite and quartz. The quantitative analysis by the Rietveld method found structural changes, particularly in the Ca-montmorillonite expansive clay. It was also possible to determine the decrease in the weight percentage of the kaolinite until the collapse of its structure between 450 °C and 500 °C. The illite presented greater thermal stability, with slight variations in its weight percentage during heat treatment, without compromising its structure. Although the quartz phase did not show relevant structure changes, it slightly increased its weight percentage with increasing temperature.

Volumetric modulated arc radiotherapy treatments (VMAT) can achieve highly conformed dose distributions, however, due to the complexity of the technique, there may have differences between the planned and administered dose distributions, generated by the precision in the dose calculation of the treatment planning system (TPS) or by the errors associated with it. One way to quantify the difference between both dose distributions is by using the gamma index; however, there is no accord regarding the parameters that should be used in its analysis. On the other hand, this gamma index may depend on the pathology and the area to be treated. For this reason, the present work aims to evaluate different parameters of the analysis of the gamma index for breast cancer treatments, these are local and global normalization, the analysis criteria (1%/1 mm, 2%/2 mm, 3%/2 mm, 2%/3 mm, 3%/3 mm and 5%/3 mm) and the low dose threshold (LDT) of 5% and 10%. For this, 30 treatment plans performed with VMAT technique in a 6 MV Infinity linear accelerator (Elekta, Stockholm, Sweden) were analyzed, calculated with the TPS Monaco V.5.11.03 (Elekta, Stockholm, Sweden) and measured with the Octavius 4D system (PTW, Freiburg, Germany). The results of the analysis of the global gamma index were of a gamma passing rate (%GP) greater than 95% for analysis criteria of 3%/3 mm and 5%/3 mm, however, for these same parameters in the local gamma index analysis the results are 85.8% and 91.1% respectively. In addition, from the LDT evaluation, it is observed that there is a mean increase of %GP for the local gamma index analysis and a mean decrease of %GP for the global gamma index analysis, for the LDT from 5% to 10%. On the other hand, the standard deviation is lower in the global gamma index analysis than in the local one, and it decreases when the analysis criteria are less strict. It is concluded that there is not a great difference in choosing the LDT of 5% or 10%. When the gamma analysis criteria are less strict, the %GP increases both for the analysis of the local and global gamma index, taking this into account, each parameter should be used carefully according to the treatment plan to be analyzed, taking into account the advantages and disadvantages of each parameter.

Intracavity energy rate in a soliton mode-locked fibre laser is derived by solving the Haus master equation. The influence of net gain, absorber response, saturation energy, nonlinearity and absorption are investigated on stable/unstable states. Intracavity modes include the zeroth, first and higher order solitons. Accordingly, chaotic regime as well as breather modes is recognized as a conventional intracavity state. However, tuning the control parameters also results in a reverse bifurcation and thus returning to a stable state. Accordingly, a chaos-based encryption/decryption system is proposed taking the advantage of using a single-side control process; both the encryption and decryption procedures can be achieved by one of the actions of increasing/decreasing the control parameters.

The dynamics of an integer-order and fractional-order Lorenz like system called Shimizu-Morioka system is investigated in this paper. It is shown thatinteger-order Shimizu-Morioka system displays bistable chaotic attractors, monostable chaotic attractors and coexistence between bistable and monostable chaotic attractors. For suitable choose of parameters, the fractional-order Shimizu-Morioka system exhibits bistable chaotic attractors, monostable chaotic attractors, metastable chaos (i.e. transient chaos) and spiking oscillations. The bifurcation structures reveal that the fractional-order derivative affects considerably the dynamics of Shimizu-Morioka system. The chain fractance circuit is used to designand implement the integer- and fractional-order Shimizu-Morioka system in Pspice. A close agreement is observed between PSpice based circuit simulations and numerical simulations analysis. The results obtained in this work were not reported previously in the interger as well as in fractional-order Shimizu-Morioka system and thus represent an important contribution which may help us in better understanding of the dynamical behavior of this class of systems.

In this paper we analyze the Effcient Market Hypothesis for automated high-frequency stock markets. Using the Hurst exponent as a measure of eciency, we show that the time series of highfrequency stock prices do not follow random walks, rejecting then (as we discuss in the text) the EMH for these markets.