Modern Physics Letters B

In actual transportation systems, the response time of drivers to the stimulus from the preceding vehicle varies at different speeds. The traditional car-following model cannot capture the heterogeneity of drivers for the response time is regarded as a constant. This paper designed a sigmoid function to describe the relation between the response time of drivers and the current speed. Then, a new hydrodynamic lattice model is developed by introducing the proposed nonlinear function. The model is analyzed by using Fourier series, and the linear stability criterion is derived. Numerical experiments are conducted in a ring road. Simulation results show that the evolution of density waves occurring in actual traffic is reproduced well. Finally, the model is calibrated and verified with the real data, and the simulation results are quantitatively consistent with the detector data.

In a vapor cell, $\upsilon$ is the average velocity of the moving atoms. When $\upsilon \ll c$, the in-homogeneous broadening of the atomic spectral lines is important when taking into account thermal Doppler broadening. We also discover that the narrowing mechanism for inter-atomic with different components has more influence on the Doppler line-shape. Thus, the spectral line broadening of two-level and three-level multi-mer ${}^{85}Rb$ atom is not only influenced by the in-homogeneous Doppler broadening, but also affected by the Dicke narrowing effect. The fluorescence spectrum affords a good possibility for a detailed study of Dicke narrowing effect and thermal Doppler broadening effect. We analyze the influence of multi-mer ${}^{85}Rb$ atomic system component on resonance fluorescence spectrum (RFS). Based on the quantum regression theorem, we develop a method and derive a general analytical expression for the two-dimensional (2D) fluorescence correlation spectrum of three-level ${}^{85}Rb$ atomic system.

The investigation of heat and mass transfer between two porous disks containing porous media is the focus of this paper. In this research, (Ag–Al₂O₃/water)-based hybrid nanofluid is used. Governing partial differential equations are converted to nonlinear ordinary differential equations by similarity transformations. Numerical solutions to nonlinear systems of equations are achieved using the shooting technique. It is examined how the particle’s diameter and nanolayer thickness affect the thermal conductivity of a hybrid nanofluid. Due to the increment of nanolayer thickness, the Nusselt number increases and vice versa for the radius of the particle. Tables and graphs show how the governing parameters influence velocity, temperature, and mass concentration profiles, as well as physical quantities such as skin friction coefficient and Nusselt number. As the values of the porous medium parameters ($P_m=7$–13) and nanolayer thickness ($h=4$–12) elevate, the flow of skin friction coefficient and Nusselt number escalate in both porous disks. Moreover, as the values of the particle radius ($r=9$% to 12%) and Reynolds number ($\mathrm{\text{Re}}=-$1 to 2) amplify, the flow of heat transfer rate is diminished in the lower disk. Porous materials have a high surface area, which increases the contact area between the nanofluids and the porous medium. Porous materials can enhance the permeability of the fluid, reducing the pressure drop in the system. This can be advantageous in applications where high flow rates and low-pressure drops are desired, such as in heat exchangers or cooling systems. Porous materials can provide trapping sites or adhesion points for the nanoparticles, enhancing their dispersion and stability within the hybrid nanofluids. The porosity of the flow medium can therefore influence the purification and filtration efficiency of the hybrid nanofluids, ensuring their cleanliness and functionality. Understanding and controlling the porosity can help optimize the flow characteristics of the nanofluids in various applications. Overall this field will focus on refining hybrid nanofluid compositions, improving modeling techniques, validating experimental findings, optimizing system designs, and exploring new applications.

The present flow phenomena characterize the behavior of the Brownian motion and thermophoresis considering the Buongiorno model nanofluid through a non-linearly expanding Riga plate. The conjunction of thermal radiation with zero nanoparticle mass flux and convective boundary conditions enriches the thermal properties of the nanofluid. With the recent need in various industrial applications, the biomedical sector, for the design and development of the production process of various equipment, the role of nanofluid is vital. Further, the suitable variables leading to transformation rules are useful to get rid of the dimensional form of the governing equations. Traditional numerical technique with the help of shooting-based Runge–Kutta fourth-order technique is adopted for the solution of a transformed set of equations. The physical behavior of the characterizing components is presented and described briefly. Further, the important outcomes are the use of Hartmann number that overshoots the velocity profile, whereas the heat transfer retards significantly and enhanced thermophoresis attenuates the heat transfer rate.

Motivated by the non-Fermi liquid (NFL) phase in solvable Hatsugai–Kohmoto (HK) model and ubiquitous quantum oscillation (QO) phenomena observed in strongly correlated electron systems, we have studied the QO in HK model in terms of a combination of analytical and numerical calculation. In the continuum limit, the analytical results indicate the existence of QO in NFL state and its properties can be described by Lifshitz–Kosevich-like formula. Furthermore, numerical calculations with Luttinger’s approximation on magnetic-field-dependent density of state, magnetization and particle’s density agree with the findings of analytical treatment. Although numerical simulation from exact diagonalization exhibits certain oscillation behavior, it is difficult to extract its oscillation period and amplitude. Therefore, more work (especially the large-scale numerical simulation) on this interesting issue is highly desirable and we expect the current HK model study to be helpful in understanding generic QO in correlated electron materials.

In this paper, fully developed forced convective flow properties of hybrid nanofluid through annular sector duct are discussed. The studies of hybrid nanofluid, i.e. the combination of a nanofluid (nanoparticles plus water) with another nanoparticles’ volume fraction, are considered. Hybrid nanofluids become most important due to enhancement in the heat transfer rate. Copper oxide (CuO)–water is taken as the nanofluid. The volume fraction of CuO nanoparticles in water is kept fixed at 4%, whereas the volume fractions of Cu nanoparticles are taken in the range of 0–4% in this study. Under the assumption of hydrodynamically and thermally fully developed flow, the deviation in the velocity components along the axial direction vanishes in the case of momentum equations; however, the deviation in the temperature becomes constant in the case of energy equation. After dimensionless analysis, the finite volume method is applied to find the numerical solutions for velocity, temperature, heat transfer rate and fanning friction factor. During physical analysis, it has been concluded that the percentage enhancement in heat transfer rate is comparably more than fanning friction factor when we increase the volume fraction of Cu nanoparticles in the CuO–water nanofluid. Furthermore, the same observation has been noticed in the case of heat transfer rate when the platelet shape factor of the nanoparticles has been used instead of brick and cylinder shape factors. Increase in fRe is 8.01% when we increase the Cu nanoparticles’ volume fraction from 1% to 4%, whereas the increments in Nu are 15.09%, 18.56% and 20.81% for the brick-, cylinder- and platelet-shaped nanoparticles, respectively, for all values of the ratio of radii, $\widehat{R}$, and apex angle, $2\alpha$, in both thermal cases.

Electron acceleration is investigated in a plasma wake generated via the interaction of a high-intensity laser pulse with the plasma in the presence of a perpendicular magnetic field. For this purpose, using the Maxwell equation, the wakefield profile in the perpendicularly magnetized plasma is obtained and then using the magnetized wakefied the electron energy and momentum equations are numerically solved. It turns out that the electron acceleration in a magnetized wake having a different profile than unmagnetized one increases with the perpendicular magnetic field strength so that in presence of a magnetic field with a strong enough amplitude the acceleration goes beyond the resonance regime. The numerical results demonstrate that the electron could be significantly accelerated in a low-amplitude laser-driven wake in presence of an external perpendicular magnetic field which can be superseded the high-amplitude laser-driven wake acceleration regime. Furthermore, we concluded in such systems that the electron acceleration is drastically sensitive to amplitude and initial phase of the wakefield as well as the initial energy of the electron.

Under investigation in this paper is a generalized Heisenberg ferromagnet (HF) equation which is named the Zhanbota-IIA equation. It is one of the integrable generalizations of the HF equation that plays an important role in nonlinear magnetization dynamics. Through the establishment of the N-fold Darboux transformation, a series of solutions will be obtained, including multi-solitons, one- and two-breathers, first- and higher-order rogue waves. Dynamic behaviors of those solutions will be analyzed, including several structures of rogue waves such as fundamental structure, triangular structure, ring structure and ring-fundamental structure, the coexistence of rogue waves and breathers, i.e. semi-rational solution and the interaction of two breathers.

The aim of this investigation is to arrange partial differential equations (PDEs) into simplified form for gradients (mass and thermal) in the inclined magneto hydrodynamic flow of hybrid (CuO–TiO₂/Water) nanoliquid in a permeable media. The modeled term is extremely nonlinear with the boundary conditions. So, this research focuses on numerical solution by using bvp4c solver in MATLAB software and by applying similarity transformation. Simulations have been done to discover the dynamics of stream and the transport of heat and mass under parametric deviation. To examine the impact of a temperature gradient on the transport of mass and the role of a concentration gradient on the transport of heat energy, outcomes have been documented in tabular form and shown through graphs. Remarkable changes in motion, temperature and concentration are noted when Dufour and Soret numbers vary.

The dominance of Boltzmann–Gibbs distribution (BG) in statistical physics appears to endow an impression that this would be the only statistical approach available. In fact, a large class of statistical approaches already exists. This is generalizing BG statistics referring to various types of nonextensivity, nonadditivity, nonequilibrium, nonlinearity, etc. For instance, $log$ and $exp$ functions play crucial roles in both extensive and nonextensive domains of statistical mechanics. Emerging in a physical system, BG statistics defines extensive entropy which relates the number of microstates to thermodynamic quantities or macroscopic states. In this regard, the Boltzmann distribution, extensive statistics, refers to a well-defined probability distribution, while the various types of nonextensive statistics categorically violate the fourth Shannon–Khinchen additivity axiom. The $log$ and $exp$ distribution functions in BG, Tsallis, and generic statistics are systematically compared. We focus on the mathematical properties of both distribution functions and conclude that their compatibility exclusively depends on the nonextensive parameters, i.e. the mathematical properties of both distribution functions depend on the nonextensive parameters either that of Tsallis- or that of the generic-type of nonextensivity. We also conclude that the statistical nature of the underlying ensemble should be taken into consideration when applying the statistical approach.

The main objective of this research is to analytically study an innovative, viscous, time-independent, and incompressible (HFN) hybrid nanofluid flow on a slanderous stretched surface. This study examines thermal conductivity, heat absorption/omission, thermal radiation, and the magnetic effect of in the existence of HFN. Incorporating an external heat source into the heat transfer process increases the effect of the dissipative heat and thermal radiation. The flow characteristics are governed by the mathematical form which is further transferred to ordinary differential equations (ODEs) via appropriate assumptions regarding similarity variables and stream functions. The strong nonlinearity was successfully solved using the analytical technique homotopy analysis method (HAM) for these nonlinear equations. The results and discussion section provides a thorough explanation of the main outcomes of the study. This research focuses on the enhancement of heat transfer and the effects.

This investigation on micropolar nanofluid flow has garnered significant attention due to its potential applications in various engineering fields. Therefore, exploration on the diversified impact of carbon nanotubes (CNTs) on the flow properties of a micropolar nanofluid through a permeable expanding/contracting surface embedding in a permeable medium with thermal radiation is studied. Moreover, the inclusion of magnetic field enriches the flow properties significantly. The governing equations, which include the conservation of mass, momentum, angular momentum, and energy, are distorted into a set of nonlinear partial differential equations using proper similarity rules. The subsequent equations are then handled numerically by employing shooting based Runge–Kutta fourth-order technique. The effects of various influential parameters, such as the permeability parameter, expansion/contraction ratio, radiation parameter, CNT volume fraction, and the Prandtl number, are investigated. The results reveal that the presence of CNTs significantly alters the flow and heat transfer characteristics of the micropolar nanofluid. The temperature and velocity profiles exhibit nonlinear behavior due to the combined influences of thermal radiation, permeability, and CNT volume fraction.