Modern Physics Letters B

The stabilization of grain boundaries (GBs) is beneficial for improving the stability and mechanical properties of nanocrystalline (NC) metals. Molecular dynamics (MD) calculations were performed to investigate the shear response of Ni $\mathrm{\Sigma }$17 [110](223) symmetrical tilt GB. It was found that under the action of shear, the nucleation and evolution of the GB source Shockley partial dislocations ultimately result in the low-energy-state transformation of the GB structure units (SUs). However, the Ag atom contained in the GB increases the shear stress and strain required for the GB relaxation, and the strain range for the GB relaxation is expanded, indicating the inhibitory effect of the Ag atom on the structural relaxation of Ni $\mathrm{\Sigma }$17 [110](223) GB. As the temperature increases from 10 K to 250 K, the structural relaxation of Ni $\mathrm{\Sigma }$17 [110](223) GB becomes easier to proceed. In addition to segregation-induced GB stabilization, strain-induced GB relaxation and the roles of foreign atom and temperature clarified in this work could provide several new entry points for stabilizing high-energy GBs.

This paper focuses on the Davey–Stewartson (DS)-II equation, and the extended modified auxiliary equation mapping (EMAEM) architectonic is used to develop a new set of solutions such as kink, singular kink, rational, combined soliton-like solutions, bell-type solutions, trigonometric and hyperbolic solutions. Furthermore, this study reveals that the used technique is efficient for solving other nonlinear evolution equations (NLEEs). The Painleve test ($P$-test) will also be used to examine the integrability of the DS-II equation. Finally, graphical simulations are designed to show the exact behavior of solutions as well as the efficacy of the suggested strategy.

In this paper, the soliton solutions and dynamical wave structures for the generalized (3+1)-dimensional shallow water wave (SWW) equation, which is an important physical property in ocean engineering and hydrodynamics, are presented. The generalized exponential rational function (GERF) method is used to investigate the closed-form wave solutions of the generalized SWW equation, which is used to describe the evolutionary dynamics of SWW. We successfully archive a variety of soliton solutions such as exponential solutions, kink wave solutions, non-topological solutions, periodic singular solutions, and topological solutions. These newly established results are also important for understanding the wave-propagation and dynamics of exact solutions of the equation, which is of great significance in physical oceanography and chemical oceanography. Eventually, it is shown that the proposed GERF technique is effective, robust, and straightforward and is also used to solve other types of higher-dimensional nonlinear evolution equations. In our work, we have used Mathematica extensively for such complicated algebraic calculations.

This paper studies the Hirota–Maxwell–Bloch (H–MB) system and its nonlocal form. Based on the Darboux Transformations (DTs), for H–MB system, we present general double breathers, what is more, we take appropriate modulation frequency and position parameters to investigate the generative mechanism of rogue wave sequences and different periodic breather sequences. For nonlocal Hirota–Maxwell–Bloch (NH–MB) system, we discuss symmetry preserving and broken soliton solutions under zero background. Besides, we present nine combinations of dark and antidark soliton solutions under continuous waves background when PT-symmetry is broken.

This paper discusses the results of the research carried out to study the structure, optical properties and thermophysical properties of a sample (nanopowder with a true density of 4.96 g/cm³, a particle size of 60 nm and a purity of 98.5%, SkySpring Nanomaterials, USA) with high purity. Based on the results of X-ray diffraction, the crystalline phase of MnFe₂O₄ ferrite nanoparticles was completely obtained and the values of the lattice parameters were determined. The results of the MID-IR analysis showed that the absorption coefficient $(\alpha )$ reaches its maximum value at 748 cm${}^{-1}$ wave number. The optical properties of the as-prepared nanostructures were also investigated by VERTEX 70 V diffuse reflectance spectroscopy (DRS). As can be seen from the results of the DSC analysis, the effects occurring in the temperature range up to $300^{\circ }$C clearly reflect the nature of the phase transitions and the amount of energy generated in the ferrite samples.

We present the complete analysis of traveling wave solutions to a special kind of nonlinear Schrödinger equation with logarithmic nonlinearity, and obtain all traveling wave solutions. As a result, we prove this equation does not have any Gaussian traveling wave solution. However, by modifying this equation into another form, we can actually obtain a Gaussian traveling wave solution, which verifies the conclusion that existing Gaussian traveling solution requires two restrictions: (1) balance between the dispersion terms and logarithmic nonlinearity; and (2) balance of the parameters.

In this article, the space-time fractional perturbed nonlinear Schrödinger equation (NLSE) in nanofibers is studied using the improved $tan(\varphi (\xi )/2)$ expansion method (ITEM) to explore new exact solutions. The perturbed nonlinear Schrodinger equation is a nonlinear model that occurs in nanofibers. The ITEM is an efficient method to obtain the exact solutions for nonlinear differential equations. With the help of the modified Riemann–Liouville derivative, an equivalent ordinary differential equation has been obtained from the nonlinear fractional differential equation. Several new exact solutions to the fractional perturbed NLSE have been devised using the ITEM, which is the latest proficient method for analyzing nonlinear partial differential models. The proposed method may be applied for searching exact travelling wave solutions of other nonlinear fractional partial differential equations that appear in engineering and physics fields. Furthermore, the obtained soliton solutions are depicted in some 3D graphs to observe the behaviour of these solutions.

Starting from a more generalized discrete $2\times 2$ matrix spectral problem and using the Tu scheme, some integrable lattice hierarchies (ILHs) are presented which include the well-known relativistic Toda lattice hierarchy and some new three-field ILHs. Taking one of the hierarchies as example, the corresponding Hamiltonian structure is constructed and the Liouville integrability is illustrated. For the first nontrivial lattice equation in the hierarchy, the $N$-fold Darboux transformation (DT) of the system is established basing on its Lax pair. By using the obtained DT, we generate the discrete $N$-soliton solutions in determinant form and plot their figures with proper parameters, from which we get some interesting soliton structures such as kink and anti-bell-shaped two-soliton, kink and anti-kink-shaped two-soliton and so on. These soliton solutions are much stable during the propagation, the solitary waves pass through without change of shapes, amplitudes, wave-lengths and directions. Finally, we derive infinitely many conservation laws of the system and give the corresponding conserved density and associated flux formulaically.

This key purpose of this study is to investigate soliton solution of the fifth-order Sawada–Kotera and Caudrey–Dodd–Gibbon equations in the sense of time fractional local $M$-derivatives. This important goal is achieved by employing the unified method. As a result, a number of dark and rational soliton solutions to the nonlinear model are retrieved. Some of the achieved solutions are illustrated graphically in order to fully understand their physical behavior. The results demonstrate that the presented approach is more effective in solving issues in mathematical physics and other fields.

In this study, we successfully apply Hirota’s bilinear method (HBM) to retrieve the different wave structures of the general $r$th dispersionless Dym equation by considering the test function approaches. The studied model is used to describe the dynamics of deep water waves. We formally retrieve some novel lump periodic, some other new interaction, and breather wave solutions. Moreover, the physical behavior of the reported results is sketched through several three-dimensional, two-dimensional and contour profiles with the assistance of suitable parameters. The acquired results are valuable in grasping the elementary scenarios of nonlinear fluid dynamics as well as the dynamics of engineering sciences in the related nonlinear higher-dimensional wave fields. The gained results are checked and found correct by putting them into the governing equation with the aid of Mathematica. Thus, our strategies through the fortress of representative calculations give a functioning and intense mathematical execution for tackling complicated nonlinear wave issues.

This study focuses on the Ablowitz–Kaup–Newell–Segur (AKNS) water waves equation. Painleve test (P-test) will be implemented to check the integrability of AKNS equation and an extended modified auxiliary equation mapping (EMAEM) architectonic is implemented to get a new set of traveling wave solutions like periodic and doubly periodic, bell type, kink, singular kink, anti-kink, trigonometric, singular, rational, combined soliton like solutions and hyperbolic solutions. Furthermore, it is analyzed that the implemented algorithm is efficient and accurate for solving nonlinear evolution equations (NLEEs). Finally, graphical simulations (2D, 3D and contours) are also provided to illustrate the detailed behavior of the solution and effectiveness of the proposed method.

The materials’ consolidation, especially ceramics, is very important in advanced research development and industrial technologies. Science of sintering with all incoming novelties is the base of all these processes. A very important question in all of this is how to get the more precise structure parameters within the morphology of different ceramic materials. In that sense, the advanced procedure in collecting precise data in submicro-processes is also in direction of advanced miniaturization. Our research, based on different electrophysical parameters, like relative capacitance, breakdown voltage, and $\mathrm{\text{tg}}\delta$, has been used in neural networks and graph theory successful applications. We extended furthermore our neural network back propagation (BP) on sintering parameters’ data. Prognosed mapping we can succeed if we use the coefficients, implemented by the training procedure. In this paper, we continue to apply the novelty from the previous research, where the error is calculated as a difference between the designed and actual network output. So, the weight coefficients contribute in error generation. We used the experimental data of sintered materials’ density, measured and calculated in the bulk, and developed possibility to calculate the materials’ density inside of consolidated structures. The BP procedure here is like a tool to come down between the layers, with much more precise materials’ density, in the points on morphology, which are interesting for different microstructure developments and applications. We practically replaced the errors’ network by density values, from ceramic consolidation. Our neural networks’ application novelty is successfully applied within the experimental ceramic material density $\rho =5.4\times 10^3$ [kg/m³], confirming the direction way to implement this procedure in other density cases. There are many different mathematical tools or tools from the field of artificial intelligence that can be used in such or similar applications. We choose to use artificial neural networks because of their simplicity and their self-improvement process, through BP error control. All of this contributes to the great improvement in the whole research and science of sintering technology, which is important for collecting more efficient and faster results.