Volume 80, Issue 1

In this study, the Kundu–Eckhaus represents the propagation of femtosecond light pulse in optical fibers is solved using symmetry technique. As a result, a finite Lie group of four vector fields is yielded. Then a similarity transformation is obtained using a linear combination of the four vector fields, which considers the general transformation for any used transformation before. According to that, the Kundu–Eckhaus is reduced to an auxiliary equation. By solving the auxiliary equation many novel solitary wave solutions were obtained. Finally, the propagation of the amplitude bright soliton is discussed, and it was found that the chirp wave depends on the amplitude function and is affected by the sign of the Raman parameter.

This paper presents numerical solutions of nonlinear evolution equations using a hybrid collocation method. Nonlinear evolution equations, including the regularized long wave (RLW) equation and the modified regularized long wave (MRLW) equation, play a crucial role in modeling various physical phenomena. A hybrid collocation technique is used for estimating and examining the characteristics of the solitary waves, including their shape, structure, and propagation. The Crank–Nicolson method is used for time discretization and the hybrid collocation method for space discretization. The Fourier series analysis has been used to analyze the stability of the proposed method, and it is established that the hybrid collocation method is unconditionally stable. The accuracy of the proposed scheme is checked by computing the error norm  L ∞ and the three invariants. The novelty of the method lies in deriving new approximations for the second derivative and applying it on time-dependent nonlinear partial differential equations. A comparison with existing techniques in the literature is conducted to check the improvements in results. The numerical outcomes show that the proposed scheme effectively depicts the conservation laws of solitary waves. The values of three invariants at different time levels have been shown to coincide with their analytical values. The propagation of one, two, and three solitary waves, development of the Maxwellian initial condition into one, two, and more solitary waves, and wave undulations have been illustrated graphically. The method captures the collisions between solitary waves very accurately. Our findings demonstrate that the new cubic B-spline approach offers an accurate and effective solution for the nonlinear evolution equations.

The key solution to the now-a-days energy crisis is the conversion of waste heat into useful electrical energy. In this work, the structural, electronic, and thermoelectric characteristics of EuMg 2 X 2 (X = P, As, Sb, Bi) zintl materials have been investigated comprehensively through first principles studies. Structural analysis shows that our measured values fit well with the previous available experimental data. Three potential functionals, PBE GGA, TB-mBJ, and hybrid functional (YS-PBE0), have been used to study the electronic behavior of the titled compounds. EuMg 2 X 2 (X = P, As, Sb, Bi) reveal band gaps of 0.83 eV, 0.72 eV, 0.34 eV, and 0.41 eV, respectively, through hybrid functional (YS-PBE0). Density of states (DOS) and partial density of states (PDOS) studies reveals the role offered by different atomic orbitals in the formation of electronic band structures of the samples. Similarly, thermoelectric tone of the said compounds is calculated by virtue of BoltzTraP2 computational code. The ultralow thermal conductivity and optimum level of carriers’ concentration encompass these materials to be good thermoelectrics with better and reasonable thermoelectric efficiency (ZTe).

This study investigated the impact of incorporating a CrFeNiTiZn High Entropy Alloy (HEA) into the A356 aluminum matrix through the friction stir processing (FSP) technique. The CrFeNiTiZn HEA, renowned for its compositional complexity and high-performance potential, was incorporated into the A356 alloy with different weight percent combinations to enhance its mechanical and tribological characteristics. The results revealed a refined microstructure characterized by solid solution phases and potential intermetallic compound formation due to the HEA addition for A356/2 %Cr2 %Fe2 %Ni2 %Ti2 %Zn composition. Strong interfacial bond strength was also observed among the matrix and reinforcement particles for the A356/2 %Cr2 %Fe2 %Ni2 %Ti2 %Zn composition. The number of grains was found to be about 1820.34 (average grain size is 686 µm) for A356/2 %Cr2 %Fe2 %Ni2 %Ti2 %Zn processed composite with FSP per square inch at 500 magnifications. The A356/2 %Cr2 %Fe2 %Ni2 %Ti2 %Zn composite exhibited improved tensile strength (35.70 %) and hardness (63.33 %) after the addition of 2 %Cr2 %Fe2 %Ni2 %Ti2 %Zn into A356 alloy, attributed to the strengthening effect of HEA particles. Furthermore, wear resistance is notably enhanced, likely due to the synergistic effects of the HEA’s inherent hardness and the modified microstructure.

Resonant acoustic band gap materials have steered a new sensing technology era. This study is presented to investigate of the one-dimensional (1D) phononic crystals (PnCs), involving periodic, as well as quasi-periodic 1D layered PnCs represented as a highly sensitive biosensor to detect and monitor the quality of milk. In this regard, the numerical findings show that the examined periodic PnCs structure outperformed the quasi-periodic structure. In particular, it provides a wider phononic band gap and greater sensitivity as well. In addition, the quasi-periodic design (especially Fibonacci sequence S4) introduces multiple resonance peaks via transmission spectra, which may lead to some conflicts during the detection process. The findings reveal that the frequency of the resonant peak can effectively change with varied milk solution concentrations and temperatures. The optimized sensor is capable of differentiating between concentrations ranging between 0 and 50 % with a 10 % step, and it can also differentiate between temperatures, which range between 5 °C and 50 °C. This makes it ideal for precise detection of other liquids and solutions. The sensor performs efficiently for all milk solution concentrations. Here, the findings demonstrated that the examined defective PnC structure exhibited the most favorable sensitivity of the value of 94.34 MHz, so it showed the highest sensitivity when varying milk concentrations. In addition, the configurated sensor provided high QF and FOM values of 3,853.645161 and 157.42, respectively. On the other hand, the sensor performs very well for all temperatures of the milk solution. As such, the S 4 quasi-periodic structure is characterized as the optimal sensor structure when varying temperatures, introducing a sensitivity of 4.78 MHz/°C, QF of 4,278.521, and FOM of 7.48 °C −1 .