International Journal of Modern Physics B

Using the Darboux transformation method, the general Lax equation is solved and a collection of new exact solutions together with one-soliton solutions, singular one-soliton solutions, periodic solutions, singular periodic solution, two-soliton solutions, singular two-soliton solutions, two-periodic solutions and singular two-periodic solutions is obtained. Using traveling wave transformation, the Lax equation is transfigured to a conservative dynamical system (CDS) of dimension four with three equilibrium points involving two parameters $\gamma$ and v. The CDS has various quasi-periodic motions for fixed values of the parameters $\gamma$ and v at different initial conditions. Furthermore, effects of the parameters $\gamma$ and v are shown on the quasiperiodic motions of the CDS by means of phase sections and time series plots. This approach can be applied to a heterogeneity of nonlinear model equations or partial differential equations for describing their inherent nonlinear phenomena.

Graph theory has many applications in chemistry and is used to analyze molecular structures. Topological descriptors are numerical numbers that contain chemical information and provide structural features of a compound associated with a chemical approach. The purpose of the topological index is to study the physicochemical properties of molecular structures. This paper investigates the molecular graph of 2D silicon carbide structures. The scope of this paper is to determine the highest thermal stability property among silicon carbide structures using topological indices.

The stability of the Tracking Wheel Mobile Robot with Teleoperation System and Path Following Method is discussed in this study. The path is to be tracked by the host computer which is the master robot. The response from the robot is captured on camera. As the slave robot approaches the target position, the camera captures the response robot’s position and as well as moving trajectory. The host computer receives all of the images, enabling mobile robot deviation recoveries. The slave robot can use teleoperation to follow the sensor based on the decisions made by the master robot. The Lyapunov function in the Fuzzy Neural Network (FNN) control structure assures the system’s stability and satisfactory performance. It supports a mobile robot’s ability to adhere to a reference trajectory without deviating from it. Finally, the outcome of the simulation demonstrates that our controller is capable of tracking different environmental conditions and maintaining stability.

Today, with real-life problems, modeling is a primary step in organizing, analyzing and optimizing them. Queueing theory is a particular approach used to model this category of issues. Space constraints, feedback, service dependency, etc. are often inseparable from the issues they create. In light of this objective, this research presents a model and analysis of the steady-state behavior of an $M/G/1$ feedback retrial queue with two dependent phases of service under a Bernoulli vacation policy. The service times for the two stages are often independent in normal queueing frameworks. We presume that they are dependent random variables in this case. Indeed, this dependence is one-way (i.e., the service time of the second phase has no effect on the service time of the first phase). Yet, the first phase service time has an impact on the second phase service time. In order to determine the steady-state probabilities and probability-generating functions (PGF) for the different states, the supplementary variable technique (SVT) was utilized. Furthermore, a broad range of performance metrics had been established. The generated metrics are then envisioned and validated with the aid of graphs and tables. Additionally, a nonlinear cost function is constructed, which is subsequently minimized by distinct approaches like particle swarm optimization (PSO), artificial bee colony (ABC) and genetic algorithm (GA). Furthermore, we used certain figures to examine the convergence of these optimization methods. Finally, validation outcomes are compared with neuro-fuzzy results generated with the “adaptive neuro-fuzzy inference system” (ANFIS).

This study is important for the fields of pharmaceutical nano-drug suspension, biomedical engineering, pressure surges and food processing systems. The slip condition is necessary for polishing internal cavities and artificial heart valves in a variety of manufactured objects, micro- or nano-channels, and applications. Low Reynolds number (Re$\to 0)$ and long wavelength ($\delta \ll 1$) considerations are used in the formulation of the mathematical model at low non-Newtonian parameter values, nonlinear boundary conditions and the governing nonlinear equation are analytically solved using the perturbation method. The graphs of frictional force, pressure rise, velocity, pressure gradient, and streamline graphs are done using Wolfram MATHEMATICA software. In this paper, we compared the results of the total slip condition with those of the first-order slip condition and the absence of any slip effects. It has been noticed that increasing the suction and injection parameters leads to a decrease the pressure rate with complete slip effects, partial slip effects and no slip effects. We show that an increase in the third grade fluid parameter $\mathrm{\Gamma }$ increases the magnitude of axial velocity. From a physical perspective, it shows the shear thinning characteristic, which causes a decrease in viscosity and an increase in fluid velocity. Frictional force behaves differently when compared to pressure rate. In other words, the pressure gradient acts as an obstacle to the peristalsis-driven flow. The objective of the study is to find the impact of the peristaltic flow phenomena and the impact of peristaltic on third-grade non-Newtonian fluid where the suction and injection are prevailing which is similar to the thing in biomechanical devices, like blood vessels, etc. there is a change of oxygen and carbon dioxide from the tissue layer to the fluid within the blood vessel.

The terminology “climate change” refers to changes that occur over longer periods of time in the climate and weather patterns of the world. This paper investigates the climate changing patterns by providing a relationship between carbon dioxide emissions and natural parameters such as temperature and precipitation anomaly. The irregularity of the temperature anomaly and precipitation anomaly is analyzed using the fractal dimension via the Hurst exponent. The range of fractal dimensions for the parameters is estimated between 1.01 and 1.60. From the obtained values of fractal dimension, the parameters are classified and their short-term forecast is presented from 2023 to 2032 using the autoregressive integrated moving average model.

This study investigates the effects of complete slip conditions on the peristaltic pumping of a Casson nanofluid with suction and injection in a vertical due to the crucial role that nano liquids play in a variety of technological and medical fields, particularly in peristalsis, a mechanism that transports liquids. The Casson fluid belongs to a class of non-Newtonian fluids that, through a particular stress threshold magnitude, exhibit elastic solid behavior before changing to liquid behavior. These fluids have several uses in engineering, food preparation, drilling and other fields. After establishing the governing conservation equations, the resulting flow model is effectively simulated using the realistic assumptions of a long wavelength and a low Reynolds number. The temperature distributions, velocity, pressure rate per wavelength and nanoparticle concentration of the resulting flow problem have been solved analytically. The effects of all physical factors on temperature, velocity, concentration fields, pressure rate, frictional force and pressure gradient are graphically examined using Wolfram MATHEMATICA software. There are a variety of biofluids that cannot be classified as liquids. For example, blood contains WBC, RBC and plasma. It is essential to model biofluids (blood) as nanofluids given the physical properties of these biofluids. According to reports, one of the finest yield stress models is the Casson model, and blood exhibits a similar behavior. We took these facts into consideration when thinking about Casson nanofluid flow in a vertical layer under peristalsis. Additionally, the suction and injection mechanisms can be used to represent the exchange of carbon dioxide in bold. In order to understand how blood flows through small blood vessels, this model must be examined. The obtained results show that the Newtonian case and those found in the literature have a very good agreement. Since the liquid moves faster and more effectively when the value is increased, it becomes clear that this increases the strength of the velocity.  In other words, nanoperistaltic pumps can maintain a pressure differential that increases or decreases at all operating flow rates with an increasing thermophoresis effect. Furthermore, it is obvious that the pressure reduction in a Casson fluid is greater than in a Newtonian fluid.

Nonlinear partial differential equations (NLPDEs) have emerged as a major focus of study in a variety of nonlinear science disciplines. This is because in general, mathematical, physics and engineering problems may be stated by NLPDEs. It may be noted that a specific kind of exact/analytical solution called traveling wave solutions for NLPDEs has great significance. In this regard, this paper addresses the traveling wave solution to the new coupled Konno–Oono equation (NCKOE), a set of NLPDE. A traveling wave transformation and the Riccati–Bernoulli sub-ode method (RBSOM) are used here to retrieve the exact/analytical traveling wave solution of the NCKOE. By using the above-mentioned approach, NLPDEs can be updated toward a collection of algebraic equations. Further, different types of solitary wave solitons, Trigonometric function solutions, Hyperbolic soliton solutions and dark bright solitons to the NCKOE have been successfully retrieved. Importantly, the newly derived solutions adhere to the main equation when they are inserted into the governing equations. Furthermore, through an appropriate selection of parameters, three-dimensional and two-dimensional figures are presented for physical illustration of the obtained solutions. These visual representations serve to showcase the effectiveness, conciseness and efficiency of the applied techniques.

The objective of this paper is to investigate the heat transfer mechanism while considering the attributes of viscous dissipation, Joule heating, and nonlinear thermal radiations in the three-dimensional steady incompressible flow of Carreau liquid on an extendable rotating disk. By using the similarity transformation, the governed equations were converted into the nonlinear coupled ordinary differential equations. The essential characteristics of various variables like Prandtl number, Lewis number, Carreau liquid parameter, Brownian motion, thermophoresis parameter, radiation parameter, Eckert number and Hartmann number on velocity, thermal, and concentration are discussed through graphs and tables. The presented investigation divulges that the thermal and mass transfer rates enhance when Brownian motion and thermophoresis processes extended and manifest as opposing features on the concentration field.

The two-level quantum heat engines have been studied extensively. Before that, the optimization of most heat engines was mainly concentrated in non-degenerate cases. We consider the level degeneracy, then calculate the maximum operation time and the irreversible dissipation coefficient of the two-level system under the scheme of linear tuned levels. In the high-temperature limit, we find that the level degeneracy affects the maximum power of the two-level heat engine. Especially in the case of the same degeneracy of the ground state and the excited state, the influence is the greatest. In addition, we also show that the degeneracy does not affect the efficiency at maximum power and the consistent relation of the two-level Carnot-like heat engine.

The measurement of patients’ dosages of radiation caused by medical diagnostics continues to be challenging. A Cantor sequence photonic crystal structure using porous silicon doped with a polymer of polyvinyl alcohol, carbol fuchsin and crystal violet (DPV) is proposed. The influence rules of geometrical and optical parameters such as the radiation doses, number of periods, porosity of porous layers, incident angle and thickness of layers are investigated using MATLAB based on the transfer matrix method. The transmittance of the Cantor sequence of a defective photonic crystal sensor under different conditions is investigated to select the optimum conditions. The proposed system recorded the accepted sensitivity of 0.265nm/Gy, FoM of 6.5Gy${}^{-1}$, Q of 12,701, RS of $6\times 10^{-3}$ and LoD of $8\times 10^{-3}$ for gamma radiation. The suggested detector has simple design, accurate monitoring efficiency and immense potential for gamma radiation sensing.

The study of biological fluids in the presence of a magnetic field is known as biomagnetic fluid dynamics (BFD). The research work in BFD has been rapidly growing due to its applications in developing magnetic devices used for cell separation, targeted drug delivery and cancer tumor treatment. This study aims to examine the biomagnetic fluid flow with pulsatile conditions through a channel when subjected to a magnetic field that varies in space. The nondimensional continuity and momentum equations are solved with the effect of the magnetic field added as a body force. A two-dimensional computational model is developed using the finite volume method and is implemented on a staggered grid system with the help of the semi-implicit fractional step method. The code is written using MATLAB. Numerical simulations are performed by varying the Magnetic, Reynolds and Womersley numbers. Pulsatile flow results indicate the periodic growth and decay of vortices near the source of the magnetic field. With an increase in the magnetic number from 100 to 150, 250 and 500, the maximum vorticity increases by 48.04%, 149.84% and 402.68%. A similar relation is found when varying the Reynolds number, while almost no change is found when varying the Womersley number.

The priority of research efforts over the past two decades has been focused on the effective detection of harmful gases and the development of small, efficient, and reliable nanodimensional sensors. The adsorption of carbon monoxide (CO) gas molecules on zigzag gallium phosphide nanoribbons (zGaPNRs) has been studied using first-principle calculations within the context of Density Functional Theory (DFT). Here, we have evaluated the potential of single-atom thick zGaPNRs in different configurations of nanoribbons for the detection of CO. Many possible configurations of studying the CO molecule adsorption on zGaPNRs have been explored. It is established that the interaction of CO molecules has an impact on the electrical and transport properties of zGaPNRs. The H-GaP-H is the most stable structure with the binding energy ($E_b$) of −5.70eV. The stability is compromised with CO adsorption with CO-GaP-CO being the least stable structure. Pristine structure is semiconducting with the energy band gap ($E_G$) of −3.95eV. The computed sensitivity (S) values are found to be highest for Co-GaPNRs with the S value of $1.77\times 10^{18}$ and the least sensitive structure is H-GaP-CO with the computed S as $3.84\times 10^{17}$. Additionally, it is noted that CO molecules always establish a stable chemical bond with the nanoribbon edges through the C-side. The unique behavior is revealed by the transport characteristics, which demonstrates that when CO adsorption occurs near the Ga edge, the current magnitude is noticeably greater. Our research demonstrates the potential of specific CO adsorption and detection for the development of nanosensors.

An analytical and numerical formalism is developed to study the influence of the various positions of substitution atoms B on the scattering and transmission vibration modes in quasi-1D monatomic structures A. The matching technique is employed to calculate the dynamical properties and transmittance spectra of two substituted atomic sites. The theoretical formalism gives a complete description of the lattice dynamics and the vibration-waves propagation in the presence of the impurity sites. Numerical calculations are performed for three different positions of the two substituted atoms B in the low-dimensional structure consisting of double monatomic parallel chains. First, we examine the position where the two B atoms are adjacent in the y-direction, afterwards, we place the two sites side by side in the x-direction. Lastly, the two sites are placed in oblique configuration. The obtained results show that phonons associated to the inhomogeneous structures are strongly dependent on the scattering frequency, elastic force parameters and the position of the atomic substituted sites. In the three considered positions, the presence of the B atoms gives rise to localized vibration effects. The fluctuations observed in the vibration spectra are related to resonances due to the coherent coupling between travelling phonons and the localized vibration modes in the neighborhood of the impurity sites.

The metal-doped aluminum nitrides have attracted special attention as new technology-related materials owing to their combination of fullerene-like and metallic properties. The structure, electronic and magnetic properties of the TM@Al${}_{12}$N${}_{12}$ clusters have been investigated by using first principles. The results indicate that the V@Al${}_{12}$N${}_{12}$, Ni@Al${}_{12}$N${}_{12}$, Zr@Al${}_{12}$N${}_{12}$, Rh@Al${}_{12}$N${}_{12}$, Ta@Al${}_{12}$N${}_{12}$ and Pt@Al${}_{12}$N${}_{12}$ clusters display more structural stability than their neighbors. The Sc@Al${}_{12}$N${}_{12}$, V@Al${}_{12}$N${}_{12}$, Mn@Al${}_{12}$N${}_{12}$, Zn@Al${}_{12}$N${}_{12}$, Y@Al${}_{12}$N${}_{12}$, Nb@Al${}_{12}$N${}_{12}$, Tc@Al${}_{12}$N${}_{12}$, Ag@Al${}_{12}$N${}_{12}$, Lu@Al${}_{12}$N${}_{12}$, W@Al${}_{12}$N${}_{12}$ and Hg@Al${}_{12}$N${}_{12}$ clusters are more dynamically stable than their neighbors. The amount of charge transfer between the TM (TM=Ti, Y and Os) atoms and Al${}_{12}$N${}_{12}$ clusters is the most. The maximum spin densities (3.025 $|\mathrm{\text{e}}|$, 2.779 $|\mathrm{\text{e}}|$ and 3.231 $|\mathrm{\text{e}}|$) of the TM@Al${}_{12}$N${}_{12}$ clusters occur at the subgroup VIIB TM@Al${}_{12}$N${}_{12}$ clusters.