International Journal of Modern Physics B

One of the interesting topics of recent research is the study of the Weibel electromagnetic instability growth rate in the interaction of high-intensity lasers with the dense plasma of fusion fuel pellets. In this paper, the effect of stresses caused by laser ponderomotive force on the growth rate of Weibel instability in the nonlinear phase is investigated. The growth of the nonlinear phase of Weibel instability growth rate, which is the saturation phase of Weibel instability, in the presence of stress leads to viscosity turbulence. The results show that the coefficient of reduction of fuel viscosity in the presence of the stress flow is about 0.0014 due to the anomalous transfer mechanism caused by the nonlinear growth of the Weibel instability.

As a special gas target with large aspect ratio, the planar symmetric gas jet has attracted some interests in High Harmonic Generation (HHG). It can be produced by gas adiabatic expansion through a supersonic slit nozzle into vacuum. In this work, the spatial distributions of atomic density are investigated in detail along the short side, the long side and the gas jet flow of the planar symmetric argon gas jet based on ANSYS Fluent. The results indicate that along the long side, the planar symmetric jet provides the advantages of high atomic density and the large dimension of uniform atomic density distribution. The density distribution profile is similar to the Gaussian one along the short side. The atomic density at the center of the jet outside the nozzle is lower and decreases much faster than that expected by idealized straight streamline model due to the lateral expansion of gas jet at slit nozzle width.

In order to investigate the significance of electron–phonons interaction in the origin of high $T_c$ superconductivity, we synthesized Cd-doped Cu${}_{0.5}$Tl${}_{0.5}$(BaCa)(CaMg)${}_{1.5}$Cu${}_{4-y}$Cd_yO${}_{12-\delta }$ ($y=0$, 1, 2, 3) samples and studied the superconducting properties. Onset temperature of the superconductivity Cu${}_{0.5}$Tl${}_{0.5}$(BaCa)(CaMg)${}_{1.5}$Cu${}_{4-y}$Cd_yO${}_{12-\delta }$ ($y=0$, 1, 2, 3) samples suppress with the increased Cd doping ratio in the final. The phonon modes are associated to the vibrations of apical and planar oxygen whereas the CuO₂ planar oxygen modes are observed to harden with increasing Cd ratio in sample doping. The phase relaxation time is suppressed for the superconducting charge carriers in Cd-doped samples. The energy amount required to break the Cooper pairs apart increases. Dielectric measurements of Cu${}_{0.5}$Tl${}_{0.5}$(BaCa)(CaMg)${}_{1.5}$Cu${}_{4-y}$Cd_yO${}_{12-\delta }$ ($y=0$, 1, 2, 3) samples have been done.

The onset of thermal instability with hybrid nanoparticles Al₂O₃–Cu in nanofluid is investigated with the combined effects of variable gravity, variable heat source and Lorentz force in a porous medium. Its applications are in many areas like chemical engineering, geophysics, astrophysics, etc. Based on literature, many gravity variations are assumed in the present analysis, along with a space-dependent heat source/sink parameter that varies along the width of the channel. The finite difference-based Lobatto IIIa method has been applied to solve the system under no nanoparticle flux and rough boundary conditions, and approximate analytical results are generated for some special cases. The roughness parameters (${\lambda }_1,{\lambda }_2$), Darcy number (Da), gravity variation function ($G(z)$), and Chandrasekhar number (Q) delay the onset of convection and thus stabilize the system. It is also observed that an increase in the Lewis number Le, power index in variable heat source, and the nanoparticle Rayleigh concentration number Rn decreases the critical Rayleigh number $R_{\theta ,c}$ which destabilizes the system, and increases the critical wave number, which enlarges the convection cell size. In the case of exponential variation ($1-e^z$) in the gravity variation parameter, the system becomes stabilized due to a delay in the onset of convection. In addition, we have considered multilayer perceptron-artificial neural network (MLP-ANN) computation to predict the critical Rayleigh number as per function of important controlling parameters. The data set of 625 observations is chosen keeping 70% for testing, 15% for training and 15% for validation using efficient Levenberg−Marquardt back propagation algorithm with optimal accuracy measures i.e., root mean square deviation (RMSE), root mean relative error (RMRE) and $R^2$ (coefficient of determination). Finally, the regression plots are drawn that correlate, target and output data.

Nuclear magnetic resonance (NMR) is a phenomenon whereby magnetization is excited when static and time varying magnetic fields are applied simultaneously on a given medium such as human blood. The effect of the magnetization causes the protons of the medium to spinning. For several decades now, a set of three Bloch equations are used to describe the dynamics of the spinning protons. Exact solution of the Bloch equations has been the endeavors of many workers with partial success. In about a decade now, a milestone was the appearance of a single NMR fluid flow equation derived from the three set of Bloch equations. The single equation has been found insuperable up to now, defying all efforts to yield a closed form solution. Motivated by the exigency to achieve complete magnetization expression as a function of time and distance, for NMR signal calculations or experiments, we have actualized a closed form solution. We used the method of Laplace transforms and ultimately applied complex inversion theorem to obtain the inverse Laplace transforms. Our final expression is a labyrinth of several oscillatory systems that are characteristics of a nonlinear phenomenon. This is cognate with concepts of chaos.

In this work, we investigate a theoretical study of the stationary entanglement of an optomechanical system by adding a Kerr medium in the cavity where the mechanical resonator is perturbatively connected to an auxiliary qubit. The degree of entanglement between the cavity field and the mechanical system is measured by using the logarithmic negativity. We show that optomechanical entanglement is decreased by Kerr interaction due to photon blockage enhanced by mirror–qubit coupling, we also show that this enhancement is influenced by the temperature. In addition, we find that, in the presence of the mirror–qubit coupling, entanglement can arise with far weaker optomechanical coupling. The proposed scheme shows that the presence of the mirror–qubit coupling and Kerr medium is an effective control for an optomechanical system.

In this work, new traveling wave solutions are generated for the system that models nematicons in liquid crystals using the $(1∕G^{\prime })$-expansion method. In the equation system, nonlinearity is taken into account for Kerr law and Power law. Also, the existence of exact solutions under restriction conditions is guaranteed. We suggest that the solutions produced are of a different type than the solutions in the literature. Figures representing the intensity of the produced traveling wave solutions are presented. In addition, the simulation of the solitary wave is made for different values of the parameter that affects the inclination angle of the molecules in the nematicons mechanism in liquid crystals. How classical solitary wave behavior translates into triangular wave behavior is discussed. We believe this paper will provide an important perspective on the problems encountered in various application areas such as fluid dynamics, chemical engineering, chaos and complex networks in terms of investigating different mechanisms by taking into account nonlinearity factors.

In this research, the nonlinear mathematical model for enzyme-catalyzed reaction–diffusion phenomena has been analyzed for the exact solutions investigated analytically. As a result, it is critical to investigate this concept from a mathematical standpoint. The ${\varphi }^6$-model expansion method is used to extract the analytical solutions which give the chemical concentration. These variables behave differently depending on the diffusion and dimensionless input flux rate parameter. Furthermore, the existence of these solutions is also discussed under different constraint conditions and variables of chemical concentrations are represented in hyperbolic, trigonometric and rational forms. For various values, the 3D behavior of these concentrations is also depicted.

In this research, we used the Riccati equation approach to establish new exact solution sets for a new $(3+1)$-dimensional Korteweg–de Vries (KdV) equation, which is an enlarged version of the time-fractional Kadomtsev–Petviashvili equation. Additionally, using the Mathematica symbolic computation program, approximate solutions to the equation, applying the residual power series method (RPSM), have been obtained. A comparison table and various graphical representations have been presented to demonstrate the validity of the solutions. The numerical findings indicate the effectiveness of both approaches in finding exact and approximate solutions to nonlinear fractional differential equations.

The thermal prospective of hybrid nanofluid is more impressive and presents many dynamical applications in solar collectors, thermal systems, machining, extrusion processes, nuclear cooling, heating and cooling devices, desalination. Owing to such motivations in mind, this research communicates thermal impact of carbon nanotubes due to inclined plate under the effect of a magnetic field. Both single-walled carbon nanotubes (SWCNTs) and multiple-walled carbon nanotubes (MWCNTs) are considered as nanoparticles to enhance the thermal mechanism of human blood and water base liquids. The mixed convection phenomenon for natural convective flow is considered. The most recent definition of fractional scheme namely Prabhakar derivatives is used to perform the theoretical outcomes. The integral of problem is supported with Laplace transform. The impact of dimensionless parameters on velocity and temperature profiles is studied and graphs are plotted by the mathematical software. The obtained results are compared numerically and graphically by using different inverse techniques known as Stehfest method and Tzou’s methods. It is observed that nanoparticles’ volume fraction boosted the thermal phenomenon more effectively for SWCNTs. The improved velocity profile due to interaction of buoyancy forces is observed.

This paper proposes a fundamentally new approach to the study of stationary states in atoms, which is based on the analysis of the energy of electric and magnetic fields. The circulation of the electromagnetic field in the stationary states of the atom was discovered and the mechanism of optical transitions due to the continuous change of the circulating energy was clarified. The difference between circulating energy flows in the initial and final states is emitted (or absorbed) in the form of a quantum of light. A universal relation for determining the lifetime of excited states is proposed.

Stainless steel (SS) is widely used in many fields including aeronautics, automobiles, marine and mechanical industries due to its outstanding feature such as good corrosion resistance and hardness. However, changes in material properties under stress, particularly changes in Young’s modulus, result in the formation of cracks, a reduction in load-bearing capacity, and fatigue damage. So, the structural integrity needs to be evaluated based on a precise measurement of mechanical properties. In this study, Stainless Steel 304 (SS-304) is used as the base material and various tensile stresses are applied ranging from 0MPa to 100MPa with increment of 10MPa in each step. Nondestructive Laser Ultrasound Technique (LUT) has been used to characterize the elastic modulus under various tensile stresses. An inverse program was developed based on the Particle Swarm Optimization (PSO) algorithms to determine material properties. Nonlinear Gauss fitting method was proposed and established the fitting equation and nonlinear curve for Young’s modulus and residual stress. The outcome of this research shows that when tensile stress is applied, the mechanical properties decrease by shifting the dispersion curve and also it is evident that the dispersion curves move toward the high-frequency-thickness while increasing the tensile stress. When the tensile stress was increased from 0MPa to 100MPa, the value of Young’s modulus decreased from 201.7GPa to 193.5GPa. Especially, the predominant changes were observed during 30–100MPa. This observation displays the bonding strength and binding energy between the atomics. Further, the proposed nonlinear Gauss fitting substantiated the experimental values and confirmed that the thickness accuracy is close to the inversion values, with an average difference of 4.32%. This research suggests a potential nondestructive method to determine the residual stress of a material by calculating the changes in the elastic modulus.

In the frame of a time-dependent oscillator model, the field induced by the coupling between the atomic electric dipole and an external X-ray laser field is investigated. The aim of the paper is to asses if in the resonant case (the frequency of the incoming field matches the frequency of the atom’s collective dipole oscillation) the damped collective oscillation induced by the external time-varying electric field can produce a significant amplification of the total electric field at the nucleus position.

Molecular dynamics method was employed to establish the model of three-dimensional cross-linked polystyrene (PS) formed by divinylbenzene (DVB) and PS chains. Density, radial distribution function, free volume fraction, mean square displacement of systems with different cross-linking degrees (DVB contents of 0%, 3.8%, 7.1% and 11.1%) were studied, as well as macroscopic properties such as glass transition temperature, elastic mechanical properties, uniaxial tensile deformation. The results showed that cross-linking algorithm proposed was feasible for constructing cross-linked PS. With the increase of cross-linking degree, cross-linked PS became denser, and glass transition temperature increased, indicating an increase of heat resistance. Compared with uncross-linked PS, elastic modulus of three cross-linked systems increased by 19.26%, 29.56% and 40.19%; bulk modulus increased by 2.9%, 20.98% and 44.03%; and shear modulus increased by 21.05%, 29.82% and 42.98%. Tensile stress-strain curves showed that network structure formed by adding DVB improved yield stress and tensile resistance of PS.

Increasing concentration of carbon dioxide $({\mathrm{\text{CO}}}_2)$ in Earth’s atmosphere due to burning of fossil fuels is a major cause of global warming. To avoid catastrophic consequences of increasing global temperature, the conversion of ${\mathrm{\text{CO}}}_2$ is vital. Incidentally, synergistic effect of ${\mathrm{\text{Ba}}}_{0.7}{\mathrm{\text{Sr}}}_{0.3}{\mathrm{\text{TiO}}}_3$ photocatalyst on ${\mathrm{\text{CO}}}_2$ dissociation in atmospheric pressure planer dielectric barrier discharge is investigated. Maximum dissociation fraction of 37% is achieved in undiluted ${\mathrm{\text{CO}}}_2$, 49% in ${\mathrm{\text{CO}}}_2+\mathrm{\text{Ar}}$ and 44% in ${\mathrm{\text{CO}}}_2+\mathrm{\text{He}}$ at 10kV applied voltage with 10kHz fixed frequency and 200SCCM total flow rate. Transitions from the Angstrom band of CO at 483.5nm and the 2nd positive system of ${\mathrm{\text{N}}}_2$ at 380.4nm are used for molecular actinometry measurements. Rotational temperature is calculated, by employing the Boltzmann plot technique, using rotational spectra of Q-branch of CO (0-1) Angstrom band. To avoid inconsistency in rotational temperature measurement, rotational spectra of 1st negative system of ${\mathrm{\text{N}}}_2$ (0-0) band are also used. For this, synthetic spectra have been fitted over experimentally recorded spectra of 1st negative system of ${\mathrm{\text{N}}}_2$ (0-0) band using LIFEBASE software. Electrical characterization of the discharge suggests that power added to the plasma increased from 1.92 to 6.13W in undiluted ${\mathrm{\text{CO}}}_2$, from 1.81 to 6.4W in ${\mathrm{\text{CO}}}_2+\mathrm{\text{He}}$ and from 1.71 to 7W in case of ${\mathrm{\text{CO}}}_2+\mathrm{\text{Ar}}$ mixture plasma. A higher dissociation fraction is found in the case of ${\mathrm{\text{CO}}}_2-{\mathrm{\text{N}}}_2∕\mathrm{\text{Ar}}$ mixture.