International Journal of Modern Physics B

Various forms of rational solitons, breathers, rogue wave, periodic wave and multiwave for Davydov solitons in $\alpha$-helix proteins are described in this paper. We will figure out periodic wave, rogue wave, multiwave, $M$-shaped solutions, homoclinic breathers, kink cross rational solutions, periodic cross kink, periodic cross rational solitons, generalized breather, Akhmediev breather and Kuznetsov–Ma breather. We will also discuss some interactions between them. At the end, we will provide the graphical representation of our newly discovered solutions.

The thermal enhancement of industrial and engineering processes with interaction of nanofluids is exclusively important and presents applications in extrusion systems, heat transfer devices, electronic chips, chemical reactions, nuclear processes, etc. Owing to such motivated significance of nanofluids, the aim of this investigation is to present the heat and mass transfer phenomenon in the Couple stress nanofluid flow containing the microorganism due to oscillatory stretched surface. Additionally, the Darcy–Forchheimer applications, nonuniform heat source and nonlinear thermal radiation effects are considered. The modification in the concentration equation is done by activation energy. The independent variables in the defined flow system are decreased via suitable variables. The computation is simulated using the homotopy analysis method. It is noticed that the magnitude of velocity periodically decreases for larger values of suction parameter and inertia coefficient. The presence of an external heat source parameter enhanced the temperature profile. Moreover, the increment in the suction parameter improves the heat and mass transfer rate.

Different mathematics forms of entangled state can judge prepared many particles is if entangled. Entangled state is a key role of quantum information technology. The more entangled states are generated, the better performances are presented. In order to make it more convenient to generate entangled state or judge the state prepared is entangled, we investigate three-qubit GHZ state and expand recurrence relation based on an expand recurrence relation of multi-qubit state. Furthermore, new forms of maximally five and seven-qubit entangled states are reconstructed via three-qubit GHZ state. These new forms stand for universal law of n-qubit and $n+2$-qubit can have direct application in quantum entangle state generation and quantum communications.

In this research paper, we observed the Prandtl–Eyring magneto hydrodynamic fluid model (PE-MHDFM) by applying the Bayesian regularization scheme as backpropagated artificial neural networks (BRS-BANNs). Effect of suction/injection at the wall is the source of convective steady flow. The nonlinear partial differential equations (PDEs) of PE-MHDFM are converted into ordinary differential equations (ODE) by applying some suitable similarity transformation. These ODEs are solved by utilizing Lobatto IIIA numerical procedure to acquire the reference dataset for different scenarios of BRS-BANN. The reference dataset is used to design the solver BRS-BANN. Further, the performance of BRS-BANN is clarified by MSE results, error analysis plots, regression and error histogram. Moreover, the solution of PE-MHDFM is observed through the validation, training and testing procedures. It is observed that the best correlation between the targeted values outcomes of the study is matched effectively, which definitely authenticates the validity and reliability of the designed solver. Furthermore, the impacts on the velocity profile and temperature profile are examined by the variation of different physical quantities along with their comparison with state-of-the-art Lobatto IIIA numerical approach.

The investigation of Computational Fluid Dynamics (CFD) focuses on the mechanical properties of a Rabinowitsch fluid model that was constructed with the help of a stenosed elliptic conduit using the well-known Finite Volume Method (FVM). If you are interested in studying physiology or biomedicine, you will find that the Rabinowitsch fluid model in peristalsis is very helpful. This is because it is used to move blood around the heart and lungs, as well as in sanitary fluid transport systems, the transfer of corrosive fluids and innovative pharmaceutical delivery systems. By using the Cartesian coordinates, it is feasible to get the elliptic domain for this duct model. Additionally, the equation of an ellipse is used in the boundary conditions for this duct in order to maintain the elliptic cross-section for this duct in its current state. The Partial Differential Equations (PDEs) for the velocity profile may be determined as soon as the issue is recast in a form that does not need any dimensions to be specified. With the assistance of boundary conditions that are provided, these PDEs are solved over elliptical cross-sections, and after that, numerical solutions are obtained for them. A dilatant fluid represents state $\gamma <0$, a Newtonian fluid represents state $\gamma =0$ and a pseudoplastic fluid represents state $\gamma >0$ in this model, making it significant. The desired model is computed numerically. FVM is used to study the results at a low Reynolds number (around $2.3\times {10}^6)$. The goal is to theoritically analyze the transmission of heat and fluid resistance to the flow. The CFD findings with experimental data are compared to confirm the model predictions. A CFD model based on the FVM and experimental data from a flow cell is used to study how fluid moves through the ducts. This study focuses on the pressure, velocity and temperature fields of a fluid moving through a stenosed duct.

This paper focuses on the problem of finite-time flocking in the multi-agent nonholonomic system with proximity graph. With the aid of singular communication function and results from graph theory, a novel distributed control protocol is proposed, where each agent merely obtains state information of its neighbors. Based on the theory of finite-time stability, the proposed protocol can achieve flocking within a finite-time and an upper bound on the setting time can be derived. Furthermore, we can deduce several sufficient conditions to the problem under the assumption that the positions and relative distances of agents are unknown. These sufficient conditions show that there are always suitable gains that enable our proposed protocol to perform finite-time flocking control and maintain the connectivity of the graph for any given initial connected graphs. Finally, the theoretical results are validated by numerical simulations.

The ${\text{CoSb}}_{0.82}$–Sn section of the Co–Sb–Sn ternary system was studied by methods of physicochemical analysis. It is shown that the section is quasi-binary, its phase diagram is of a simple eutectic type, with a limited region of solid solutions based on ${\text{CoSb}}_{0.82}$, the boundary of which at room-temperature reaches $\sim 1$ mol% Sn. The temperature dependences of some thermoelectric parameters of (${\text{CoSb}}_{0.82}$)${}_{1-x}$${\text{Sn}}_x$ solid solutions have been studied. The thermodynamic functions of a pure ${\text{CoSb}}_{0.82}$ and a solid solution alloy of composition (CoSb${}_{0.82}$)${}_{0.99}$Sn${}_{0.01}$ are calculated.

This paper deals with the study of an incompressible electro-magneto-hydrodynamic (EMHD) Jeffrey fluid flow over a vertical nonlinear stretching surface of variable thickness. Heat and mass transfer effects are analyzed by considering different source terms like viscous dissipation, Ohmic heating, thermophoresis, Brownian motion, thermal heat source, exponential heat source and activation energy. Governing equations for the flow system are converted into dimensionless forms using appropriate similarity transformations. The solution for the resulting governing equations is obtained by using the shooting technique with RK-4 method. The effects of various physical parameters such as magnetic field parameter $(M)$, Grashof number (Gr), solutal Grashof number $(G_c)$, Brownian diffusion parameter $(N_b)$, thermophoresis diffusion parameter $(N_t)$, thermal heat source parameter $(Q_t)$, exponential heat source parameter $(Q_e)$, Prandtl number (Pr) and Lewis number (Le) are presented with the help of graphs. It is observed that the heat transfer effects increase by increasing thermal and exponential heat sources, and mass transfer effects enhance by increasing the activation energy. Entropy generation for this flow system is also analyzed. Entropy decreases with an increase in the electric field parameter. In contrast, the Bejan number initially increases with an increase in the electric field parameter. After some particular value of electric field parameter, it changes its behavior in the boundary layer and decreases with an increase in the electric field parameter. Entropy and Bejan number increase with an increment in the concentration difference parameter. The accuracy of the results is validated by those of published literature and found in reasonable justification. The present results may be helpful in many engineering and industrial applications like manufacturing lubrication, natural gas networks, cooling nuclear reactors and spray processes.

In this scientific work, we explore the solutions of an important mathematical model appearing in the nonlinear elastic inhomogeneous Murnaghan’s rod (NEIMR) or called doubly dispersive equation (DDE) with a useful and powerful analytical technique; which is the extended Kudryashov method with the Bernoulli–Riccati approach. In our research, we have successfully obtained some important solutions of the above-mentioned model such as topological, nontopological, singular solitons, singular periodic and rational solutions. Using the appropriate values of the parameters, we clearly plotted the solutions of the model, 3D, 2D and contour plots. We think that the method used in the study and the results obtained will be an effective motivation tool for many researchers doing research in this field.

Numerous industrial and technical dynamic applications of non-Newtonian liquid flow research in thermal and process engineering are increasing every day, owing to their multifunctional relevance. The viscometric flow, heat and mass transfer of an incompressible third-grade liquid model across an exponentially inclined plate according to all of these potential implications are studied in this paper. The inclusion of elements such as mixed convection, heat sink/source, activation energy, thermal heat flux and chemical reaction improves the flow model’s novelty. Using the appropriate similarity transformations, the existing governing expressions are transmuted into nonlinear ordinary differential equations (ODEs). The resulting nonlinear ODEs are numerically solved via the Runge–Kutta (RK) technique in conjunction with a shooting strategy. The dimensionless parameters are graphically illustrated and discussed for the involved profiles. The viscosity of the liquid drops for increased fluid variable, which enhances the velocity field. The velocity profile is declined continuously throughout the boundary layer with increasing buoyancy ratio parameter. The thermal profile inclines for growing values of the radiation and heat source/sink parameters.