International Journal of Modern Physics B

In this communication, we report a typical structural, optical and electrical analysis of thin films of hole transport material (HTM) based on aromatic phenyl benzidine derivative (N,N${}^{\prime }$-Di-1-naphthyl-N,N${}^{\prime }$-diphenylbenzidine) deposited by thermal evaporation technique onto the glass substrate. The effect of substrate temperature on the physical and electronic properties of these organic thin films for perovskite solar cells (PSCs) applications has been investigated. The films have been characterized by FTIR, XRD, SEM, UV–Vis spectroscopy and photoluminescence spectroscopy. Electrical conductivity and activation energies of films have also been calculated. From FTIR data of fabricated films and powder, it was found that the compound does not decompose during the thermal evaporation process as observed vibrational frequencies of films and the powder are the same. From the results, it has been determined that the substrate temperature has a huge impact on the physical structure and has also influenced the optical, electrical properties of the films. As observed from the studies it appears that these amorphous films with bandgap near to 3eV and suitable conductivity have potential for photovoltaics layer devices. From this study, it can be concluded that N,N${}^{\prime }$-Di-1-naphthyl-N,N${}^{\prime }$-diphenylbenzidine can be used as an active hole transport layer in PSCs.

The main goal of this research work is to explore novel soliton solutions and dynamics of solitonic structures to asymmetric Nizhnik–Novikov–Veselov (ANNV) equations by two methods, namely, the generalized exponential rational function (GERF) method and the modified extended tanh expansion (METE) method. These techniques are the most effective and reliable tools for solving nonlinear equations with partial derivatives. The used methods provide a wide range of soliton solutions that can motivate applied scientists and researchers for these specific structures. These acquired solutions are in the form of exponential, trigonometric and hyperbolic functions including, $tan,sin,sec,cot,\text{csc},sinh,tanh,\mathrm{\text{sech}},cosh,$ $coth,\mathrm{\text{csch}}$ and of their combinations. It has also been observed that the obtained soliton solutions of the ANNV equations are bell-shape, anti-bell-shape, periodic solution, multisoliton and different types of soliton solutions. To illustrate the physical features and dynamics characteristics of some obtained solutions, three-dimensional (3D) and two-dimensional (2D) figures are exhibited through the Mathematica software. The methods applied in this paper are suitable to study the soliton solutions for the ANNV equation without producing the complexities in some other known analytical method. Finally, the employed methods can be earmarked easily for solving various classes of nonlinear evolution equations appearing in mathematical physics, fluid dynamics, plasma physics, nonlinear waves and nonlinear sciences.

In this paper, we study the third-order nonlinear Schrödinger equation (NLSE) and optical metamaterial (OM) with quadratic-cubic nonlinearity (OM-QCNL) to describe the properties and presence of propagating solitary waves (SW) in a fibre optic medium. We present an effective field amplitude ansatz that allows us to obtain SW using the governing model. More specifically, in the presence of all orders of dispersion and various nonlinear variables, we find SW solutions of dipole, bright, dark and other forms. The graphical representation of these waves will also be presented.

Many of the real-life problems including dynamical structures can be modeled in the shape of differential equations. A number of analytic and numerical methods are being proposed for the solution of these differential equations but for some instances, we may come across a few limitations attached to them. However, theoretically strong and computationally favorable tools such as artificial neural networks can be utilized to approximate the solutions of these differential equations. In this work, we developed mathematical models for some biophysics systems on the basis of their dynamical behavior and opted a neural network having single hidden layer of 50 neurons and Broyden–Fletcher–Goldfarb–Shanno algorithm as an optimizer to simulate the results for population of micro-organisms. The graphical representations of the results obtained both from the neural network and analytic methods are compared for different parameters and we got almost the same results.

For decades, the difficulty of tackling a strong coupling model with a perturbative approach remained despite numerous inquiries. In this work, a typical mean field theory procedure transforms a strong coupling Hamiltonian into a weak one, which can be solved with a perturbative approach. The Hamiltonian of two-dimensional free electron gas with Hubbard on-site interaction is calculated as a test of the new procedure. Consequently, the spectral characteristics of the cuprates “peak-dip-hump” are reproduced. The result is compared with the past theoretical investigations, e.g., quantum Monte Carlo method, density matrix renormalization group, tensor network methods, etc. which agree well with the spectral curve.

In this work, we are concerned with generating solutions of a class of Convection–Diffusion–Reaction (CDR) equation from the solutions of another CDR equation through the Darboux transformations. The method is elucidated by cases with certain types of the reaction coefficients. We have also discussed briefly supersymmetric pairs of CDR equations connected through similarity solutions.

The importance of bioconvection into the application of nanoparticles has had a significant impact on fundamental technological and industrial functions in recent years. These discussions are being carried forward by the bioconvection appearance on that flow by attracting nanoparticles into additional features on thermal radiation and activation energy. The investigation had been proposed on the appealing features of the mass and thermal convective boundary constraints. The high desirable subclass on rate-type fluid, especially Williamson fluid, was used to anticipate the absolute rheological parameters. The designated partial differential system was modified along with nonlinear ordinary differential equations applying enhance being related conversion, the designated partial differential system was modified along nonlinear ordinary differential equations. The governing equations are interpreted into ordinary differential equations, and in the following, shooting process was obeyed to build up the mathematical classification on the convert dimensionless flow problem. This value of physical restraint was displayed on the table and plots tests. This noted theoretical imitation could be highly successful in improving the solar energy systems and thermal extrusion processes. The outcomes reported that the rise in Weissenberg number and Hartmann number decreased the nanoparticles velocity distribution. The progressing temperature distribution was observed to develop radiation parameter and thermal conductivity parameter. That was further noted to modify bioconvection Lewis number and Peclet number that were reduced into motile microorganism distribution effectively.

Here, unsteady boundary layer flow under the action of magnetic effect over a moving stagnation surface has been investigated numerically. This study examines non-Newtonian fluid flow with respect to combined effect of magnetic field, movement of surface and time. Governing equations are dimensionless by applying nondimensional quantities. Then system of coupled ordinary differential equations are obtained by appropriate similarly transformations, in terms of the governing parameter including unsteady parameter ($k)$, magnetic number ($M)$, power-law index ($n)$ and three-dimensional parameter ($\alpha )$. Thus, the obtained modelled equations are solved numerically by the shooting technique. The problem’s parameters are thoroughly discussed and verified physically and graphically. The obtained results validate to literature result. The two relevant flows’ velocity profile’s numerical results have been examined.

Non-Newtonian fluids have industrial and technical applications. Several liquids in nature do not have Newtonian viscosities. These fluids include applesauce, polymer mixtures, colloidal and fermented mixtures, clay glazes, paints, lubricants, cement, slush, shampoos, mud, foodstuffs, paper paste, aqueous froths, etc. This study considers stratified flow and variable heat transmission across a stretched surface. The magnetic hydrodynamics and slips’ impacts are illustrated. On the basis of flow assumptions, the mathematical model was created using the Navier–Stokes equation. The boundary layer approximation approach is provided PDEs by working on the Navier–Stokes equation under flow assumptions. This system is converted into ODEs through similarity transformations. Dimensionless system is elucidated by means of RKF-45 technique. The concerning physical parameter effects are elaborated numerically as well as graphically. Based on the findings of the comparison, it was determined that Williamson fluid had superior performance in terms of fluid velocity compared to Maxwell fluid. Furthermore, the temperature of the fluid is greater for booming values of both $e_1$ and $\epsilon$ parameters.

In this paper, the vortices number and the critical atoms number are calculated. Calculations are performed for ultracold trapped Bose gas in two-dimensional deep optical lattice. Hellmann–Feynman theorem is used here to calculate the expectation values of the angular momentum and thermal average of square radius (in situ size). The above-mentioned parameters are calculated from the thermodynamic grand potential $q(\alpha ,s)$. The latter is calculated using a conventional semi-classical approximation. This thermodynamic grand potential allows us to investigate the impacts of the finite size and inter-atomic interaction effects. The obtained result for the vortices number has a peak with increase in the rate of rotation. While the critical atoms number has increase in nature with increase in the critical temperature. These parameters show a major dependence on the inter-atomic interaction, depth of optical lattice and number of particles.

This work explores the feasibility of nonlinear behavior of doubly clamped single-walled boron nitride nanotube (SW-BNNT)-based nanoresonator. A nonlinear mathematical model of wavy SW-BNNT has been developed for analyzing the geometrical nonlinearity. Dynamic responses of nonlinear model have been analyzed for different waviness factors varying from 0.01 to 0.06 using various tools like time series, phase space, Poincaré map and Fast Fourier Transforms (FFTs). For the analysis, 20nm length of SW-BNNT has been considered. It has been observed from nonlinear analysis, that for responses with a lower value of waviness (e.g., 0.01) for 20nm long BNNT, the system’s nature loses its periodicity and shows onset of chaos with dense spectrum in Poincaré maps and irregular pattern in time response. Thus, it is concluded that chaotic response with a less strange attractor has been observed when waviness is 0.01. It is also concluded that, with increase in waviness factor from 0.02 to 0.06, the system showed the multi-periodic response with 2-T, 3-T and 4-T periods. The dynamic responses with varying waviness showed that the system behavior is changing from chaotic to periodic. This change in periodicity is one of the characteristics of chaotic solution.

In this paper, we formed two graphene/C₂P₄ van der Waals (vdW) heterostructures (HSs) by stacking the graphene and the C₂P₄ monolayer which have been predicted by us. First, we investigated the stability of C₂P₄ monolayer, and calculated the binding energies and flat average differential charge density of two vdW-HSs. Second, we found that two graphene/C₂P₄ vdW-HSs are all direct semiconductors with bandgap as 0.051/0.064eV and 0.536/0.697eV under GGA-PBE/HSE06 functional, respectively, which provides a way to unfold the zero bandgap of graphene or let an indirect monolayer to be a relevant direct semiconductor. Additionally, two graphene/C₂P₄ vdW-HSs possess high absorption coefficients (16%∼18%) for the visible light and higher absorption coefficients (22%) for the near ultraviolet light, respectively. These admirable properties make two vdW-HSs as novel and potential two-dimensional materials applied on optoelectronic, electronic and photovoltaics devices.

In this paper, we use new extended generalized Kudryashov and improved $tan(\frac{\vartheta }{2})$ expansion approaches to investigate Kerr law nonlinearity in the extended Gerdjikov–Ivanov equation in a dense wavelength division multiplexed system. These methods rely on a traveling wave transformation and an auxiliary equation. These approaches successfully extract trigonometric, rational and hyperbolic solutions, along with some appropriate conditions imposed on parameters. To explain the dynamics of soliton profiles, a graphical description of newly discovered solutions is also presented, which exhibits distinct physical significance. The considered methods are recognized as useful and influential tools for creating solitary wave solutions to nonlinear problems in the mathematical sciences.

This paper studies the mixed convective flow of a magnetohydrodynamic micropolar fluid over an extending sheet. The first-order velocity slip condition is taken to observe the slip flow of the fluid. The applications of solar radiation toward the micropolar fluid flow are analyzed in this paper. Furthermore, the Brownian motion, thermophoresis and Joule heating impacts are also studied. Also, the Cattaneo-Christov heat flux model, chemical reaction and activation energy are observed. The leading PDEs have been transformed to ODEs and then solved with the help of homotopy analysis technique. The impacts of different physical parameters have been evaluated theoretically. The outcomes exhibited that the material factors have augmented the microrotation and velocity profiles. Moreover, the velocity slip parameter has a reverse relation with velocity and microrotation profiles, while there is a direct relation of a velocity slip with the energy curve. The velocity profile has increased with higher thermal and mass Grashof numbers. With increasing Brownian motion parameter, the thermal profile is amplified while the concentration profile is declined. On the other hand, the thermal and mass profiles have been boosted with greater thermophoresis parameter. The velocity profile has decreased with higher magnetic parameter, whereas the temperature profile has augmented with higher magnetic parameter. The couple stress and skin friction have been augmented with material parameter, whereas the skin friction has been reduced with thermal and mass Grashof numbers.

The proposed flow problem is to analyze the behavior of dissipative heat on the time-dependent stagnation motion of nanofluids through a permeable surface. A novel approach to thermal buoyancy through the permeable medium enriches the flow properties. In the recent industrial applications for the cooling processes of the device, like the physiological application of the blood flow inside the capillary tube-like artery, drug delivery system, etc., the role of nanofluid is crucial. The proposed model equipped with various physical properties is used to design and subsequent transformation into a non-dimensional form is obtained for a set of similarity variables. Proposed models with different physical properties are designed and subsequent dimensionless transformations are obtained for a similar set of variables. In addition, shooting based Runge-Kutta fourth-order numerical technique is used to solve boundary value problems for nonlinear ordinary systems. The characteristics of the diversified quantities are presented graphically as well as numerically on the flow profile and other profiles. Furthermore, statistical approaches such as t-tests for simulated results of rate coefficients are also presented and validated with the obtained results. However, the important outcomes are presented as; the fluid velocity is controlled by the inclusion of the particle concentration as well as the magnetic parameter further the particle concentration and the dissipative heat encountered by the inclusion of Eckert number enhances the fluid temperature.