International Journal of Modern Physics B

Analysis of simple analytical wave solutions to nonlinear evolution equations is a fascinating and growing area of knowledge in highly nonlinear sciences. The Riccati equation rational expansion technique is being used in the paper to establish the exact traveling wave solutions of the Phi-4 model. We have investigated certain types of explicit solutions using this technique, such as periodic, hyperbolic, and rational solutions with some free parameters. The solitary wave solutions are derived from the traveling wave solutions when the parameters are set to particular values. In mathematical physics, it is discovered that the implemented technique is more effective for finding the analytical wave solution of nonlinear evolution models. The approach stands out for its simple and quick computation procedure.

Monovalent nontransition metals are robust Fermi liquids. They defy superconductivity even at lowest temperatures (Li is a minor exception: $T_c\approx 0.4$ mK). However, Thapa, Pandey, Ghosh and collaborators have reported, from 2018, signals for transient and unstable granular superconductivity at ambient temperatures in Ag nanoparticles embedded in Au matrix. We develop a theory, where competing superconducing, CDW and SDW orders lose and get confined (go off-shell). They leave behind a robust Fermi liquid on-shell. A single half filled band crossing the Fermi level provides a number of special k-space regions for singlet stabilizing umklapp pair scattering and superconductivity stabilizing repulsive pair scattering. Carefully designed perturbations could deconfine a confined superconductivity. We suggest that electron transfer (doping) from Ag nanoparticles to Au matrix (with a higher electronegativity), quasi 2D structural reconstructions (e.g., 9R structure), electronically decoupled 2D patches and 1D segments expose confined superconductivity. Beneath a calm Fermi sea, strong supercurrents may exist in several metals.

The electromagnetic induction induced by neuron membrane potential plays an important role in regulating its electrical activities, bistability and hidden dynamics. In this paper, a nonsmooth threshold control strategy is proposed, in which the membrane potential is utilized as the threshold to determine the switching function corresponding to the electromagnetic induction intensity and external stimulus current. Consequently, a four-dimensional Filippov-type HR neuron model is established. First, the existence, stability and global bifurcation behaviors of equilibrium points of two subsystems are discussed by using stability theory and numerical simulation. Then, the bistable behavior and evolution modes of subsystems are investigated based on the two-parameter bifurcation analysis. Further, the existence of various equilibrium points and sliding dynamics of the system are analyzed by Filippov convex method and Utkin’s equivalent control method. Finally, the sliding firing modes and multistable features under the control of the threshold are revealed by the method of fast-slow variable dissection. These results will provide useful theoretical support for understanding the hidden dynamic mechanism of neurons and constructing functional neural networks.

In this work, heat transfer enrichment using nanofluid in a lid-driven porous cavity having an isothermal solid block has been investigated numerically through three distinct cases based on the moving direction of horizontal wall(s). The modeled governing partial differential equations are numerically solved by SIMPLE algorithm and the resulting outcomes are validated with previous works both in qualitative and quantitative nature. Numerical results of various emerging parameters such as Richardson number ($0.01\le \mathrm{\text{Ri}}\le 100$), Darcy number (10${}^{-5}\le \mathrm{\text{Da}}\le 10^{-1}$), Block length ($0.25\le \mathrm{\text{BL}}\le 0.75$) and volume fraction of suspended nanoparticles ($0.0\le \varphi \le 0.05$) were discussed. The results clearly show that the direction of moving walls plays a crucial role on the flow and heat transfer, in particular, the opposite direction of moving walls yields the highest heat transfer rate. In addition to that, significant influence of isothermal block is found and determined that the block length of 0.75 causes the maximum rate of heat transfer in the entire system.

The current paper focused on an unsteady bio-convective Maxwell nanofluid flow subject to convective boundary conditions through an exponentially stretching curved surface. The transportation of heat and mass are observed with thermophoresis and Brownian effect along with chemical reaction. The mathematical flow model is converted into a system of nonlinear system of ODEs via suitable transformation. The numerical solution of a nonlinear system of equations is established with the help of bvp4c MATLAB technique. It is deeply studied that in the curved surface, the pressure is never ignored. The graphical representation of several parameters along the temperature, concentration, microorganism density and velocity distribution is presented. It is examined that the greater estimation of curvature parameter boosts the temperature of fluid and concentration of nanoparticles, although a reverse trend is seen for the velocity profile. Further, it is examined from the numerical values that the heat and mass transfer rate reduce consequently with the enlargement of the curvature parameter.

The flow of viscoelastic fluid owing to stretching surfaces (SSs) has become well-known among the demanding study fields of fluid mechanics due to its numerous practical applications. As a result, the major goal of this work is to scrutinize the three-dimensional (3D) unsteady flow of second-grade nanofluid. A magnetic field influences the fluid when an indefinitely long, straight wire delivers an electric current. Thermal radiation is taken into consideration while studying heat transmission characteristics. The effective thermal conductivity of nanofluid flow is scrutinized by adopting Koo–Kleinstreuer–Li (KKL) nanofluid model. Through suitable transformations, relevant flow expressions are converted to ordinary differential equations (ODEs). The numerical approach Runge–Kutta–fourth–fifth Fehlberg’s order method (RKF-45) with shooting technique is used to solve the generated ODEs. Further, it was noted that the CPU time to estimate the solutions of flow fields was less than (2.23 s). The outcome reveals that the rise in values of the time-dependent parameter positively impacts both velocity and thermal profiles. The improved heat transport is seen for augmented values of radiation and ferromagnetic interaction parameters.

This research paper shows the insight into the study of magnetohydrodynamics (MHD) reactive nanomaterial flow of Newtonian fluid with Silver (Ag), Ferric Oxide (Fe₃O₄) and Copper (Cu) towards a stretchable surface. The flow is generated subject to stretchable surface with porosity effect. Mixed convection, which is a combination of both free and forced convections, is accounted. The heat source/sink, chemical reaction, Joule heating and activation energy effects are considered in the development of energy and concentration equations. The system of considered problem is solved numerically via shooting method (boundary value problem fourth convergence (bvp4c)) and outcomes are sketched graphically. The engineering impact i.e., skin friction coefficient and Nusselt number is discussed via different parameters and results are displayed in tabular form. The important and main points are listed in the final remarks of the paper. The used nanoparticles have numerous applications in medical industry, applications in sustainability of natural resources and applied mathematics and physics. Also, these nanoparticles can be utilized in engineering sciences, biophysics, high-temperature and cooling process, space technology, biosensors, medicines, cosmetics, paints, medical devices and conductive coatings.

This study extracts heat transfer analysis for the axisymmetric flow of CuO-water nanofluid imposing normal to a spiraling disk uniformly rotating and radially stretching. The combined influence of uniformly rotating and linearly radial stretching surface engenders the logarithmic spirals in motion. The governing system is transformed into a system of the ordinary differential equations that represent the flow. The Tiwari–Das [Int. J. Heat Mass Trans. 50, 2002 (2007)] model is utilized to envisage the heat transfer and other physical properties of the nanofluid. A highly precise numerical technique named as Legendre wavelet-based spectral method is practiced to computing the impacts of the pertinent variables on the flow. The results of physical significance including the wall shear, skin frictions and heat transfer rate are attained for the multiple spiraling parameters and the nanoparticle volume fraction. The asymptotic results for the large spiraling parameter are also presented to analyze the flow behavior for the high spiraling parameter. The influence of the nanoparticles is also investigated and the enhancement in thermal conductivity is measured. The temperature and thermal layer thickness reduce for large spiraling parameter. Also addition of the nanoparticles enhances the heat transfer rate of the nanofluid.

This research paper investigates the heat and mass transport characteristics in an unsteady flow of Maxwell nanofluid (NF). While examining heat transfer properties, thermal radiation is taken into account. Further, copper oxide with water-based NF is considered. The mass transfer and effective thermal conductivity of nanofluid flow are scrutinized by Koo and Kleinstreuer–Li (KKL) NF model. Through apt transformations, relevant flow expressions are converted to ordinary differential equations (ODEs). The numerical approach Runge–Kutta–fourth–fifth Fehlberg’s order process (RKF-45) algorithm with shooting technique is utilized to solve the generated ODEs. Results reveal that, the rise in values of unsteadiness parameter has a positive impact on both concentration and thermal profiles. The Deborah number has constructive impact on heat transport and reverse influence on velocity field. The improved heat transport is seen for augmented values of radiation and heat source/sink parameters. The Brownian motion parameter has positive influence on heat transport and reverse effect on mass transport.

The objective of this work is to explore the flow features and thermal radiation properties of the 2-D Magnetohydrodynamic (MHD) Carreau nanofluid model over an impenetrable stretching surface by utilizing the supervised learning strength of Levenberg–Marquardt backpropagation neural networking technique (LMBNNT). The mathematical formulation for MHD Carreau nanofluid flow model (MHDCNFM) in terms of partial differential equations (PDEs) is transformed into equivalent nonlinear ordinary differential equations (ODEs) by utilizing the similarity transformation and dimensional parameters. A reference dataset of proposed LMBNNT is made for Carreau nanofluid flow model exploiting the strength of Lobatto IIIA technique through the variations of different parameters against the velocity, temperature profile and concentration. These reference datasets are placed for validation, training and testing by LMBNNT and obtained outcomes are compared with reference results to check the accuracy of the designed methodology. The validation of the proposed solution methodology is obtained through the mean square error (MSE), error histogram error profile, regression p lot and fitness plot. MSE values’ accuracy is upto ${10}^{-10}$ which establish the reliability of the LMBNNT. Moreover, due to an increase in Weissenberg number, fluid velocity decays in case of shear thinning liquid and higher values of Biot number enhance the temperature profile and improves the rate of heat transfer. Moreover, the increment in Hartman number reduces the surface drag force and large values of Prandtl number reduce the heat transfer process. These results of all these parameters are expressed in well-organized numerical and graphical forms.