International Journal of Modern Physics B

This work devotes to explore abundant optical and other soliton solutions to fiber Bragg gratings with dispersive reflectivity having Kerr law of nonlinear refractive index. Bragg gratings are no doubt a technological spectacle that sustained balance between dispersion and nonlinear effects that leads to a stable transmission of solitons across intercontinental distances. Three reliable integration norms namely ($\frac{G^{\prime }}{G^2}$)-expansion function method, generalized tanh method and generalized Kudryashov method are engaging to devise optical dark, singular, combo, complex and periodic solutions. The reported solutions contain key applications in engineering and physics. These solutions define the wave performance of the governing models, actually. By the choice of suitable parametric values, the dynamics of the evaluated results are exemplified by sketching their 2D, 3D and contour profiles to understand the real phenomena for such sort of nonlinear models. The novelty of the gained outcomes is manifested by a detailed comparison with the results that already exist. The outcomes disclose that our schemes are very active reliable, concise, outspoken, appropriate, useful and skilled for attaining the exact solutions of such kind of problems which minimize the computational work and give it a wide range of applications.

In this study, the improved $({\wp }^{\prime }/\wp )$ expansion method and Exp${}_a$ function method are used to construct the newly closed-form exact solutions for the deoxyribonucleic acid (DNA) model which includes hyperbolic, trigonometric and exponential solutions. These solutions include a wealth of information regarding the dynamical behavior of homogeneous long elastic rods with circular cross-sections. These rods comprise a pair of polynucleotide rods of the DNA molecule that are connected by an elastic diaphragm, demonstrating the involvement of the hydrogen bond in this communication. The performance of these approaches demonstrates their use and efficacy in solving a variety of nonlinear evolution problems of integer and fractional order. The physical significance of the established and the obtained solutions has been shown via 3D shapes. It is worth noting that the solutions obtained here via the proposed schemes are more generalized and can be helpful to demonstrate the internal interaction of the DNA model arising in mathematical biology. The proposed method has been used to obtain exact traveling wave solutions for fraction nonlinear partial differential equations (NPDEs) arising in nonlinear sciences.

The flow of air containing small particles past a pointed area of an aircraft, bullet and bonnet of vehicles exhibits the flow over paraboloid surface of revolution. Therefore, the study of Al₂O₃-H₂O nanofluid over upper paraboloid horizontal surface of revolution (UPHSR) is organized. The concerned model develops via thermal conductivity dealing with the particles shape factor and similarity transforms. Afterward, numerical analysis is performed and the influences of pertinent parameters on the velocity and temperature $𝜃(\eta )$ in Al₂O₃-H₂O are examined. The deep inspection of the results in the view of physics behind them revealed that Al₂O₃-H₂O drops for the stringer magnetic field. Further, nonlinear thermal radiations and internal heat generation made Al₂O₃-H₂O a better heat conductor which increased its applications in a broad zone.

In this paper, we study rogue wave solutions of the $AB$ system under the background of Jacobian elliptic functions. First, we introduce the Jacobian elliptic functions dn and cn through traveling wave transformation. Next, we derive the expression of spectral parameters $\lambda$ and rogue wave with periodic background by nonlinearization of the Lax pair and the Darboux transformation (DT) method. At last, we present the dynamic evolution process of the $AB$ system in some figures.

Tight-binding models represent one of the basic approaches for studying the topological states of a matter. In the given account, we consider a tight-binding model set by a matrix Hamiltonian over 2D Brillouin zone. The corresponding multiband energy spectrum gives rise to non-Abelian gauge construction formed by the non-Abelian Berry connection $A_{\mu }$. The main gauge invariant quantities in such cases are the eigenvalues of Wilson loops. The purpose followed is the search for any special (on top of general) properties of Wilson loops for 2D tight-binding models which impose certain restrictions on the structure of its eigenvalues. The non-Abelian Berry connection is shown to be pure gauge with point-like singularities. The corresponding curvature tensor $F_{\mu \nu }={\partial }_{\mu }{A}_{\nu }-{\partial }_{\nu }{A}_{\mu }+i[A_{\mu },A_{\nu }]$ vanishes throughout the Brillouin zone except the isolated points where $F_{\mu \nu }$ is singular. Combining such behavior of $F_{\mu \nu }$ with non-Abelian Stokes theorem allows to avoid the path-ordering procedure in calculating the Wilson loops. In this approach, we show that Wilson loops are endowed by the group structure isomorphic to the fundamental group of the Brillouin zone. The latter is the Abelian group $Z\times Z$ forcing the set of eigenvalues of Wilson loops to comprise of two fixed phases associated with the two primitive elements (generators) of $Z\times Z$.

Metal Organic framework (MOFs) a diverse class of complex organic metal assemblages has been attracting a great interest due to its easy tunability and modified characteristics during the past few years. These nanoscale-to-microscale-sized structures have been employed in different applicative fields due to their striking functional chemistry. Barium MOF synthesis is based on barium metal ions tri-linked organically to form a cubic structure and features photolumincity. Ba-MOF was synthesized by hydrothermal method and structural and optical analysis was performed using X-ray Diffraction (XRD), Scanning Electron Microscopy (SEM), Energy Dispersive Spectroscopy (EDS), Raman Spectroscopy and Zeta Potential. The presence of cubic structure and organic carbon and oxygen linkages was indicated by XRD peaks. EDS directs the presence of barium as well as carbon and oxygen (organic linkers). Raman analysis paid for witnessing the evidence of the synthesis of MOF structure by validating the peak location. The photoluminescence spectrum was applied to measure the bandwidth to study the photoluminescence characteristics. The PL spectrum presented a wide bandwidth of 107.4 nm indicating Ba-MOF to be an efficient photoluminescent nanocomposite for photoluminescence-based applications. Zeta potential value of $-16.8$ mV characterized anionic behavior and high stability of fabricated Ba-MOF.

This work investigates the adsorption behavior of lithium (Li) atoms on zigzag stanene nanoribbon (ZSnNR). This work analyzes the adsorption, open circuit voltage and capacity of Li on ZSnNR. When Li atoms are adsorbed on ZSnNR, it shifts the Fermi level towards the conduction band as compared to the ZSnNR. It indicates a strong interaction between Li and Sn. Our calculations show that the maximum storage capacity of Li on ZSnNR is nearly 200 mAhg${}^{-1}$ and has a low open-circuit voltage of 2.28 V. The reported findings suggest that ZSnNR can be utilized as anode material for Li ion batteries and it establishes the theoretical foundation for future study on ZSnNR and other Li storage architectures.

With the help of commercial software, we have discussed the novel numerical simulations for a two-dimensional rectangular cavity with two square rotating obstacles, Fig. 1, that has fixed dimensions from the reference point (0, 0) placed in it, and we have interpreted a detailed convection analysis for fluid flow that highlights the physical, mathematical and numerical aspects of this system. The square obstacles having an anti-clockwise rotation are heated to a certain temperature, respectively, where the behavior of the fluid distribution depends upon the values of Reynolds number. We have conducted this research by fixing Reynolds number at four different positions like Reynolds 10, 30, 50 and 80. The prime effects of Reynolds number and Prandtl number are highlighted for convection analysis. Finally, we have analyzed the results of velocity, pressure, vorticity and temperature from the viewpoint of numerical simulations. Heat transfer has a huge dependence on the Reynolds number and Prandtl number.

In this paper, the numerical solutions are proposed for the 1D Benjamin–Bona–Mahony (BBM) equation and 2D coupled BBM system by using Galerkin finite element technique. In this regard, the cubic B-splines and linear triangular elements are used, respectively. In 1D space, a proposed numerical scheme is implemented to a test problem including the motion of a single solitary solution. To verify practicality and robustness of our new procedure, the error norms $L_2$, $L_{\infty }$ and three constants $I_1,I_2$ and $I_3$ are evaluated. Stability analysis of the linearized technique indicates that it is unconditionally stable. Moreover, a tsunami wave in 2D space is used to investigate the efficiency of the considered method. Also, the improved $tanh(\mathrm{\Gamma }(\varpi ))$-$coth(\mathrm{\Gamma }(\varpi ))$ function technique (IThChT) and the combined $tan(\mathrm{\Gamma }(\varpi ))$-$cot(\mathrm{\Gamma }(\varpi ))$ function technique (ITCT) are obtained in the mentioned BBM equation. The presented methods are seen to be robust, impressive and economical to employment as compared to the existing finite difference techniques and other earlier papers for discovering the numerical solutions for numerous types of linear and nonlinear PDEs.

Magnetic properties of 3$d$ transition metal ion-doped methaylamonium lead bromide (MAPbBr${}_3)$ have been theoretically studied under the framework of density functional theory. All 3$d$ transition metal ions are doped at the Pb site of MAPbBr₃. Some of the 3$d$ transition metal ions induced a significant amount of magnetic moment with stable ferromagnetic ordering. 3$d$ orbital electrons of the dopants are the main source of magnetism in all cases. Total density of state calculations has been performed to understand the magnetic behavior. Local magnetization density for stable ferromagnetic ordered state has been calculated to understand the local origin of the magnetic moment. Also, band structure and Bader charge analysis have been done for stable ferromagnetic ordered materials. Ferromagnetism along with semiconducting behavior makes it a viable material for spintronics applications.