International Journal of Modern Physics B

In this study, the Gross–Pitaevskii equation perturbed with multiplicative time noise is under consideration numerically and analytically. The NLSE is a universal governing model that helps in evolution of complex fields that are used in dispersive media. For the numerical solution, we used the stochastic forward Euler (SFE) scheme. To find the exact solutions, we chose the techniques namely ${\varphi }^6$-model expansion. For the analysis of the proposed scheme, we checked the stability of the scheme with the help of Von-Neumann criteria and the consistency of the scheme with the mean of Ito’s sense. The exact solutions of the model are constructed successfully in the Jacobi elliptic function in the form of trigonometric and hyperbolic functions. Last, we compared the graphical behavior of the proposed scheme with some exact solutions by using the unique selection of initial and boundary conditions. The plots are constructed in the form of 3D, line, and contour representation by choosing the different values of parameters.

In this work, dynamic viscosities of hydrocarbons and ionic liquids are studied. At high temperatures in these materials, a decrease in the value of dynamic viscosity was observed. Intermolecular interactions in the objects of study have been studied. It has been established that the intermolecular interaction in hydrocarbons is determined by the Born potential ($\phi \sim r^{-n})$. In this case, the temperature dependence of the dynamic viscosity of hydrocarbons is described by the law $\eta \sim T^{-m}$. It has been established that the dynamic viscosity of hydrocarbons in liquid form has a non-activating character. This occurs directly due to momentum transfer by phonons between adjacent layers located at a distance of nanometers.

The Allen–Cahn equation (ACE), which has applications in solid-state physics, imaging, plasma physics, material science and other fields, is one of the most important models of the modern era for describing the dynamics of oil pollution, reaction-diffusion mechanisms, and the mechanics of crystalline solids. By using the $(\frac{1}{G^{\prime }})$-expansion method (GEM) and the Bernoulli sub-ODE schemes, some new traveling wave solutions for the governing model are created in this study (BSODE). The reduced integrable ordinary differential equation is produced using the traveling wave hypothesis. To better understand their behavior, the 3D, contour, and 2D graphs are displayed for a number of fascinating exact solutions. Additionally, we use numerical simulation to confirm the stability of the derived analytical solutions. It results the propagation of temporal soliton for long time of simulation. These results will be used to explain physical phenomenon in crystalline solids and others fields.

This study is motivated by the recent observed realization of Pseudo Chiral Magnetic Effect (PCME) into the continuum limit of the low-energy tight binding description of graphene. We here proposed the quantum description of PCME by investigating the Landau level structure of the system. The different physical quantities like current, chiral currents, number densities and chiral condensate are discussed in this context with this Landau level description of the system. Further, the effect of different physical conditions to the system is studied by analyzing the behavior of Landau levels under these conditions. This provides a microscopic understanding of the phenomenon. It has been shown that largest contribution to the PCME currents and number densities comes from the spin polarized lowest Landau level which corresponds to the system characteristics at low-temperature and high magnetic field. However, the contribution to the PCME current from the higher Landau levels is just opposite to that from the lowest Landau level. We have further established general expressions for all these physical quantities regarding to any higher-order Landau level.

Surface modification by using citric acid (CA) in the graphene is a process to modify the physicochemical properties of graphene oxide. The strategy that has been proposed depends upon the electrochemical exfoliation of reduced graphene oxide (rGO), and simultaneously, the surface modification of rGO with CA carried out in accordance with the green technique. The synthesis of graphene oxide that has been doped with CA was accomplished via an electrochemical process in an aqueous medium containing fresh lime juice and sulphuric acid (electrolyte heating aided method at $60^{\circ }$C) as an electrolyte. The electrolyte has been prepared using CA & H₂SO₄ (sulphuric acid), and both were mixed in a proportion of 1:2. In order to dilute the H₂SO₄ and perform the sonication, the water that has been pasteurized (according to the USP standards for irrigation) was used. The crystallite size, structural disorder, structure and surface morphology of the CA-doped graphene oxide were identified through X-ray diffraction (XRD) analysis, Raman spectroscopy, Field emission scanning electron microscope (FE-SEM). The presence of oxygen-containing functional group and adsorption has been analyzed using Fourier transform infrared (FTIR), and UV–Vis spectroscopy. The thermal stability of the CA-doped, and without CA-doped thermally reduced graphene oxide (TRGO) has been analyzed via thermogravimetric analysis (TGA). A green, simple, and environmentally friendly method has been demonstrated for the synthesis of CA-doped TRGO by electrochemical synthesis method by using natural dopant.

Due to the lack of theoretical basis for the determination of process parameters, there are problems such as incomplete melting and excessive melting in the molten pool for laser processing, which ultimately cause the increase of defects such as air hole and crack. The melting behavior of Ti–Al binary alloy during laser processing is studied on the atomic scale by molecular dynamics simulation. The embedded atom method potential is adopted to establish the melting model of Ti–Al binary alloy. According to the changes of temperature, atomic structure and mean square displacement, the influence of different process parameters on the melting behavior of Ti–Al binary alloy is discussed. The results show that a short temperature drops from initial melting to complete melting. Mean square displacement increases rapidly with the increase of laser time after completely melting. The atoms start to move violently and the atomic structure is completely transformed into other structure. The heating and cooling rate increases with the increase of power. The laser power has little effect on the overall distribution of atoms after completely melting and only affects the variation rate of various physical quantities in melting process. The research results provide a deeper practical and theoretical evidence for the determination and optimization of the 3D printing and laser heat treatment.

Aluminum alloys are used to make wheels that are suitable for aeroplanes and automobiles, as well as all types of ground vehicles and watercraft. Aluminum alloys are made through melting, sintering (assembly of formed parts utilizing metal particles that melt together at intense temperatures), or mechanical braiding. Aluminum alloys have had a major impact on aeroplane manufacturing. Aluminum alloys like AA7075 and AA7072 are especially useful in transportation applications including maritime, aviation, and automotive, and are also utilized in the construction of bicycles, glider rock climbing equipment, and planes. This attempt sheds light on the magnetically influenced methanol-based micropolar nanofluid containing aluminum alloy nanoparticles (AA7075) over a variable thickened stretching sheet. A variable magnetic field is applied normal to the flow direction. The flow is considered at a stagnation point. Also, the Joule heating impact is considered in this analysis. The similarity transformations are used for the transformation of partial differential equations into ordinary differential equation. The authors have chosen to solve the proposed model with the help of NDSolve technique which can handle a wide range of ordinary and partial differential equations (ODEs and PDEs). The results showed that, as the volume fraction of AA7075 nanoparticles grows the velocity profile of the AA7075–methanol nanofluid decreases, while the microrotation and temperature profiles of the AA7075–methanol nanofluid increases. The velocity profile of the AA7075–methanol nanofluid reduces, while the microrotation and temperature profiles of the AA7075–methanol nanofluid increase with the increasing magnetic parameter. The growing micropolar parameter augments the velocity and temperature profiles of the AA7075–methanol nanofluid, whereas a dual impact of the micropolar parameter is found against the microrotation profile of the AA7075–methanol nanofluid. The growing variable wall thickness factor augments the velocity, microrotation and temperature profiles of the AA7075–methanol nanofluid. It is found that the embedded factors highly affected the AA7075–methanol nanofluid as compared to methanol fluid.

In this paper, we have employed two different forms of mathematical methods, namely the extended simple equation method, and modified $F$-expansion method to establish several types of solutions of the generalized Kadomtsev–Petviashvili modified equal width-Burgers (G-KP-MEW-B) equation that is used to designate the propagation of long-wave with dissipation and dispersion in nonlinear media. A suitable transform is applied to convert into an ordinary differential equation. As a result, after implementation of the proposed schemes, distinct types of solutions are obtained in the form of exponential hyperbolic, trigonometric and rational functions. To analyze the physical phenomena of the model, some constructed solutions are plotted in 2-dimensional and 3-dimensional by inserting the specific values to attached parameters. Hence, the recommended schemes are highly admirably mathematical tools to evaluate the wave solutions of various models in nonlinear science.

For the existing quantum threshold signature protocols based on entangled state, it is difficult to prepare quantum resources. Meanwhile, for the quantum threshold signature protocols based on single-particle sequence, it has disadvantages of high computation and communication consumptions. To remedy these shortcomings, in this paper, we proposed a quantum threshold signature protocol based on mutual unbiased basis (MUB). In initialization stage, the message owner Alice prepares a quantum sequence $Q$ with length of $p$, each single particle in $Q$ is chosen from MUBs. The signature key is generated by Alice using threshold secret-sharing distribution algorithm, the verification key is generated by $t$ signers via threshold secret-sharing recovery algorithm. In signature generation phase, the signers execute the signature algorithm sequentially until the last signer and then obtain the final signature, next send it to verifier. In signature verification phase, the verifier Ver verifies the original message and the final signature using the verification key. Security analysis shows that the proposed protocol can resist interception-forgery attack, collusion attack and denial attack. Performance analysis shows that the proposed protocol is easier to prepare quantum resources than similar protocols, and has lower communication consumption, especially when the number of signers $n\ge 3$ and increase gradually. Finally, the correctness of the proposed protocol is verified by simulation experiment on quantum cloud platform.

This study investigates the nonlinear Klein–Gordon equation (KGE). We successfully construct some new topological kink-type, non-topological, singular solitons, periodic waves and singular periodic wave solutions to this nonlinear model by using the extended ShGEEM, rational sine-cosine extended (ERSC), and sinh-cosh (ERSCh) methods. In addition, a numerical method for solving the KGE is described in this paper. We use a combination of two numerical techniques called fictitious time integration method and the group preserving scheme (GPS). Fictitious time integration method converts the main equation into a new problem then the GPS is used to gain the numerical solutions. Few experiments are provided to successfully demonstrate the correctness of the approach.