International Journal of Modern Physics B最新文献

We study actions of Möbius group on two sub-populations in the solvable chimera model proposed by Abrams et al. Dynamics of global variables are given by two coupled Watanabe–Strogatz systems, one for each sub-population. At the first glance, asymptotic dynamics in the model seem to be very simple. For instance, in the stable chimera state distributions of oscillators perform a simple rotation after a certain (sufficiently large) moment. However, a closer look unveils that dynamics are subtler that what can be observed from evolution of densities of oscillators’ phases. In order to gain the full picture, one needs to investigate dynamics on the transformation group that acts on these densities. Such an approach emphasizes impact of the “hidden” variable that is not visible on macroscopic level. More precisely, we demonstrate that the chimera model is an intriguing example of the classical system that exhibits the holonomy in fiber bundles of the group of Möbius transformations.

In this paper, Kudryashov and modified Kudryashov methods are implemented for the first time to compute new exact traveling wave solutions of the space-time fractional $(3+1)$-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation and Calogero–Bogoyavlenskii–Schiff and Bogoyavlensky Konopelchenko (CBS-BK) equation. With the help of wave transformation, the aforementioned fractional differential equations are converted into nonlinear ordinary differential equations. The purpose of this paper is to devise novel exact solutions for the space-time-fractional $(3+1)$-dimensional CBS and the space-time-fractional CBS-BK equations by utilizing the Kudryashov and modified Kudryashov techniques. The solutions, thus, acquired are demonstrated in figures by choosing appropriate values for the parameters. The solutions derived take the form of various wave patterns, including the kink type, the anti-kink type and the singular kink wave solutions. The obtained solutions are indeed beneficial to analyze the dynamic behavior of fractional CBS and CBS-BK equations in describing the interesting physical phenomena and mechanisms. The obtained solutions are entirely new and can be considered as a generalization of the existing results in the ordinary derivative case. The techniques presented here are very simple, efficacious and plausible and hence can be employed to attain new exact solutions for fractional PDEs.

The sperm propelling mechanism has been proposed as a possible resource for soft micro-robots in confined spaces, with potential applications in biomedical engineering. Human sperm cells essentially swim through the non-Newtonian liquid (cervical mucus) to reach their target. Thus, sperm cells swimming through non-Newtonian fluids is not vital only for physiology, but also for the fabrication of swimming micro-robots. Inspired by these remarkable applications, we examine the basic mechanics of spermatozoa motility using an undulating sheet model. This undulating sheet is bounded between two rigid walls which is self-propeling in the negative axial direction. The liquid around the spermatozoa is taken as Carreau fluid with electro-osmotic properties. The application of the lubrication approximation results in the reduction of momentum equations. The resulting ODE is solved numerically via the finite difference method and MATLAB’s built-in routine bvp5c. The unknowns that are present in the boundary conditions are refined by the root-finding algorithm. Power losses, cell speed, flow rate, velocity of the fluid, and streamline pattern are visualized by graphs. The findings of this study have important implications for the designing and optimization of electrically controlled microswimmers.

This paper presents a model of nonisothermal blood flow through a diseased arterial segment due to the presence of stenosis and thrombosis. The rheological properties of the blood in the annulus are captured by utilizing micropolar fluid model. The equation describing the blood flow and heat transfer is developed under the assumption that stenosis growth into the lumen of the artery is small as compared to the average radius of the artery. Biological processes like intimal proliferation of cells or changes in artery caliber may be activated by small growths that cause moderate stenotic blockages. Closed-form solutions for temperature, velocity, resistance impedance and wall shear stress are obtained and then utilized to estimate the impact of various physical parameters on micropolar blood flow. Graphs are plotted to illustrate variations in temperature, velocity, shear stress at the wall and resistance impedance against different controlling parameters. The results are also validated via the bvp4c approach.

The Biswas–Arshed equation (BAE) with space–time dispersion was currently considered in the literature. Optical phenomena embedded in this equation are self-steepening, self-phase modulation and Raman scattering. Here, we consider BAE with gain or loss. It is worth mentioning that the gain or loss has an impact on blowup or decaying solitons propagation in optical fibers, which is novel. Our objective is to find optical soliton solutions of BAE and the aforementioned physical phenomena are investigated in some details. The conditions for the dominance of a phenomenon are predicted. This is physically important to inspect the behavior of solitons prpagation. To this issue, exact solutions of the model equation are derived by using the unified method. The solutions obtained are displayed graphically. Dark soliton, bright soliton, M-shaped soliton, rhombus soliton (which is novel) and chirped soliton with tunneling are observed. The modulation instability is studied and it is found that it triggers when the coefficients of the space–time dispersions are positive.

In this paper, using an improved linear combination operator method and variational technique, the expression of the bound polaron effective mass ratio in a parabolic quantum well is derived. Due to the spin–orbit interaction, the effective mass ratio of bound polaron splits into two branches. The relations among effective mass ratio with temperature, electron–phonon coupling strength and Coulomb bound potential strength are discussed by numerical calculation. The effective mass ratio of polaron is an increasing function of temperature, electron–phonon coupling strength and Coulomb bound potential strength. The absolute value of spin splitting effective mass ratio increases with the increase of temperature, spin–orbit coupling parameter, electron–phonon coupling strength and Coulomb bound potential strength, respectively, and decreases with the increase of velocity. Due to the heavy hole characteristic, the spin splitting effective mass ratio is negative.

The study of nanoliquid characteristics and their heat performance have attracted the interest of engineers. These engineered fluids have high thermal conductivity due to which such liquids are reliable for different engineering applications including heating/cooling of buildings, thermal and mechanical engineering, etc. Therefore, the current research design provides a new ternary nanoliquid model for the heat transport process under induced magnetic field effects, mixed convection, heating source and thermal radiations. The modeling has been done by implementing the ternary fluid characteristics and supportive transformations and then for results simulation; bvp4c is coded successfully. It is scrutinized that a higher inductive magnetic field (0.1–0.4) and nanoparticles amount (0.01–0.07) are better to resist the movement while the wedge parameter (${\lambda }_1)$ promotes it. By promoting the heating source, Eckert and $R_d$, the heat transfer process is observed rapidly while the mixed convective number $\alpha$ controls it. Further, the particular used ternary nanoliquid is examined and found to be good for cooling purposes.

The aim of this research is to investigate the combined effects of thermal and mass stratification on unsteady magnetohydrodynamic nanofluid moving through an exponentially accelerated vertical plate in a porous medium. The governing equations of the problem are solved numerically by using the implicit Crank–Nicolson method. The results of the nanofluid with two different stratification are compared to those obtained without any stratification. The velocity of the nanofluid decreases with both types of stratification, whereas temperature and concentration decrease with thermal stratification and mass stratification, respectively. A variety of parameters, including the volume fraction of nanoparticles, thermal radiation, heat source/sink, and chemical reaction, can be studied using graphs. The important results demonstrate that nanofluids are more thermally conductive than normal fluids. This research holds significant implications in various fields, including power generation, electronic component cooling, and vehicle construction.

In this paper, we discuss the reflection and refraction of an incident P wave or $SV$ wave at the interface of a plane. The plane, which is divided into two halves, is an elastic medium $M_1$ having an incident wave and a thermoelastic diffusion medium $M_2$ with TPLT (i.e., three-phase-lag thermal) and TPLD (i.e., three-phase-lag diffusion) models. It has been noticed that two waves are reflected and four are refracted in an isotropic thermoelastic diffusion medium. Out of the four refracted waves, three are longitudinal waves: a quasi-longitudinal wave $qP,$ a quasi-mass diffusion wave $qV$, a quasi-thermal wave $qT$ and one is a transverse wave $SV$. If we consider the above waves first, the amplitude and energy ratio are calculated by using the surface boundary conditions and then graphically represented to compare the change in energy and amplitude ratio with the change in incident angle for three particular cases. The conservation of energy is depicted by verifying that all the energy sums up to unity. The considered problem has its application in earthquake engineering, astronautics, rocket engineering, seismology and many more engineering areas.