International Journal of Modern Physics C

Carbon nanotubes (CNTs) influenced nanofluid is gaining popularity in the industry for solar energy and scratch heat exchanger applications. Consequently, this research focuses on evaluating the impact of nonlinear thermal radiation from a CNT-based nanofluid on an unsteady three-dimensional nonasymmetric Homann stagnant flux as a function of length and radius. CNTs have remarkable thermal physical properties that appear to be critical for nonlinear thermal transport. As a result, the nonlinear heat transfer properties of H₂O composed of single or multiple wall CNTs are studied. The nanomaterial has a length and radius of approximately $3\mathrm{\text{nm}}\le L\le 70\mathrm{\text{nm}}$ and $10\mathrm{\text{nm}}\le R\le 40\mathrm{\text{nm}}$. Partially differential equations with appropriate similarity transformations serve as a mathematical model for the process. The numerical solution of the simplified system of equations is achieved via the use of the well-known Runge–Kutta (RK) method in conjunction with the shooting approach. An effective way to show how a component affects velocity and temperature, skin frictions in both direction and Nusselt number are utilized in graphical representations. Increasing the unsteadiness parameter causes a reduction in the temperature profile and the velocity profile in both directions. As $\epsilon$ grows larger with $\varphi$, the skin friction in both directions decreases, while the Nusselt number profile grows larger. In addition, the variation in the Nusselt number is included in the tables, along with a comparison of the model without radiation to the model with radiation.

An attempt is made to analyze the effects of micropolar fluid squeezing film implementation between porous elliptical plates under the application of an external magnetic field. The appropriate improved hydromagnetic Reynolds equation governing the pressure distribution is acquired. The Reynolds equation is solved for lubrication features such as pressure distribution, load-carrying capacity and time-height relationships. It is noticed that a micropolar lubricant with a magnetic field may considerably impart a much-appreciated increase in load-carrying capacity, pressure distribution and response time compared to the classical case. Nevertheless, it is found that, as with the magnetic field, the larger values of the fluid gap number and the coupling number increase lubrication characteristics. Also, it is found that such a bearing cannot support a large number of lubrication characteristics because of the pores on the main path of fluid flow.

According to a remarkable result, the polarization diffusion coefficient of drugs, such as those that slow down and ease the body, may be determined based on the rise in magnetism that follows. This research examines how a magnetic field impacts the Casson-type flow of a viscous, incompressible hybrid nanofluid that naturally flows across two parallel plates. Copper (Cu) and aluminum-oxide (Al₂O${}_3)$ are the two nanoparticles and their physical properties are intended to be the foundation fluids, together with water and sodium alginate as based fluids. The revised fractional model is investigated using the Laplace transformation using the most current and updated definition of the fractional-order derivative with memory effect, i.e. Prabhakar fractional derivative. The impacts of various constraints on distinct nanoparticles are investigated and visually depicted. As a result, we have concluded that a drop in volumetric percentage reduces fluid velocity. The water-based hybrid nanofluid (HNF) has a more significant influence on the temperature and momentum profile than the sodium alginate-based HNF due to the physical appearances of the investigated nanoparticles. The Casson fluid parameter augmentation also regulates the velocity profile by decreasing the velocity field.

This work examines the Stefan blowing effect on the magnetized stagnation point flow of Prandtl–Eyring nanoliquid along a nonlinear elongating surface under the influence of numerous slips. In this study, the impressions of internal heat sources, nonlinearly varying radiation, activation energy with binary chemical reactions, viscous dissipation, and Joule dissipation are taken into account. The thermal flux associated with thermal radiation is computed using Rosseland’s approximation for an optically thick environment. The controlling dimensional mathematical equations are transformed into nondimensional representations using appropriate similarity transmissions. Numerical temperature, velocity, and concentration solutions are obtained using a shooting method based on secant iteration and the Runge–Kutta–Fehlberg method. Using tabular and graphical displays of numerical data, the physical effects of a number of relevant parameters on the nanoliquid temperature, velocity, and concentration are examined. By contrasting the current results with information that has already been published for a few limiting circumstances, the validity of the acquired results is demonstrated. The effects of physical features on the local surface drag coefficient, rates of mass and heat transfer are demonstrated using numerical data shown in tabular form. For increasing values of the Stefan blowing parameter, fluid velocity decreased. The fluid temperature tends to rise as a result of thermal radiation.

The Lane–Emden–Fowler-type equations along with boundary conditions form nonlinear singular boundary value problems. Analytical solutions to this type of problem are not easy, which draws the attention of the researchers toward their numerical solutions. Many methods have been used to provide numerical solutions to this type of problem. In this study, we have proposed the quasilinear Bessel polynomial collocation method (QBPCM) for the solution of these problems. The accuracy and efficiency of the QBPCM have been demonstrated by solving several nonlinear singular models that arise in real-life problems. It has been shown that the numerical results obtained by the proposed method have excellent agreement with the exact solutions and better accuracy than other methods.

This research aims to study the different phenomena of generalized Rayleigh waves (RWs) in composite structures with piezoelectric material and corrugated surfaces. A thin piezoelectric layer that is precisely attached to an elastic substrate with initial stresses makes up the structure under consideration. By resolving the related electromechanical field equations, expressions for the displacement potential function are produced for both the elastic substrate and the piezoelectric layer. The frequency equations of the studied wave have been discovered as determinants for electrically open and short conditions. There have been both numerical illustrations and graphical demonstrations. On the stage speed of the combined RW, the impact of the grooved border, initial pressure, piezoelectric constant, dielectric constant, and thickness of the piezoelectric layer have been studied. Additionally, the analytical solution to the issue is compared to and shown to be in good agreement with the stiffness matrix approach result. This study offers a theoretical foundation for creating and developing piezoelectric composite-based devices. It has been found that the generalized RW velocity declines with the increase of the values of $\widetilde{e_{15}}$ and ${\epsilon }_{11}$ and an inverse relationship has been found with the increase of the value of $H$. In addition, it has also been noticed that the velocity profile of the generalized RW is greatly influenced by the size of the corrugation (measured at the upper layer).

In this work, we study a simple mathematical model to analyze the emergence and control of radicalization phenomena, motivated by the recent far-right extremist events in Brazil, occurred in 8 January 2023. For this purpose, we considered a compartmental SIS-like model that takes into account only the right electors, for simplicity. The model considers radical and moderated right electors, and the transitions between the two compartments are ruled by probabilities, taking into account pairwise social interactions and the important influence of social media through the dissemination of fake news. The role of the Brazilian Federal Supreme Court on the control of such violent activities is also considered in a simple way. The analytical and numerical results show that the influence of social media is essential for the spreading and prevalence of radicalism in the population. In the presence of such social media, we show that radicalism can be controlled, but not extincted, by an external influence, that models the acting of the Federal Supreme Court over the violent activities of radicals. If the social media effect is absent, the radicalism can disappear of the population, and this phenomenon is associated with an active-absorbing nonequilibrium phase transition, like the one that occurs in the standard SIS model.

Numerous studies have recently focused on enhancing the efficiency of solar chimney power plants (SCPP) and increasing their output power during periods of limited solar radiation. One such study proposes a novel solution: combining an SCPP with a gas power plant to create a hybrid power plant that generates power consistently, day and night. The system involves burying pipes underground and channeling the hot gas from the gas power plant through them, rather than releasing it into the atmosphere. This process increases the temperature of the soil beneath the canopy, which in turn raises the air temperature and the velocity of the air. The resulting decrease in air density leads to an increase in output power. Our results show that the performance of solar chimney of soil ground with buried pipe is about 30% higher than sand domain.

The structural phase transition in complex network models is known to yield knowledge relevant for several problems of practical application. Examples include resilience of artificial networks, dynamics of epidemic spreading, among others. The model of random graphs is probably the simplest model of complex networks, and the solution of this model falls into the universality class mean field percolation. In this work, we concentrate on a similar problem, namely, the structural phase transition in the ensemble of random acyclic graphs. It should be noted that several approaches to the problem of random graphs, such as generating functions or the Molloy–Reed criterion, rely on the fact that before the critical point, cycles should not be present in random graphs. In this way, up to the critical point our solution should produce results that are equivalent to these other methods. Our approach takes advantage of the fact that acyclic graphs allow for an exact combinatorial enumeration of the whole ensemble, what leads to an exact expression for the entropy of this system. With this definition of entropy we can determine the onset of the critical transition as well as the critical exponents associated with the transition. Our results are illustrated with Monte-Carlo results and are discussed within the context of general random graphs, as well as in comparison with another model of acyclic graphs.

Investigating the time–frequency-based phase synchronization between nonstationary time series of the cryptocurrencies’ prices can be a suitable tool to reveal their complicated interactions at different frequencies. In this work, the phase synchronization between 25 cryptocurrencies with the highest capitalization from December 1, 2021 to June 1, 2022 is calculated using the phase-locking value method based on wavelet transform. Then, utilizing the graph theory, the cryptocurrency networks are constructed, and their topological features like path length (PL), clustering coefficient (CC) and node strength are evaluated in various frequencies. This research indicates a strong phase synchronization between the investigated cryptocurrencies, especially in low frequencies. Also, the networks’ high average CC and short PL compared to their equivalent regular and random networks display the small-worldness of the networks. We observe from the obtained results that Bitcoin, Ethereum and Binance currencies, among the most popular cryptocurrencies, have the highest average node strengths at different frequencies. Also, TRON shows the lowest CC and node strength among all currencies, representing its limited phase interaction with other currencies.

This paper conducts a numerical analysis of the behavior of the average value of the Maximum Local Time, $L_n^{\ast }$, in the Simple Random Walk on the square lattice. It has been established in the literature that the sequence ${\zeta }_n:=\frac{{(logn)}^2}{L_n^{\ast }}$ converges to $\pi$. The author found numerical evidence that the average value of ${\zeta }_n$ ($\overline{{\zeta }_n}$) increases until a certain value of $n$, denoted as $n_c$, after which it decreases and approaches $\pi$. Furthermore, estimates are presented for $n_c$ and $\overline{{\zeta }_{n_c}}$.

To explore the rumor propagation dynamics in online social networks (OSNs) and propose the corresponding control strategies, a novel Ignorants-Spreaders-1-Spreaders-2-Removers (I2SR) rumor-spreading model with general incidence is first formulated in heterogeneous networks. This model covers the bilinear incidence and nonlinear incidence, and considers the time delay in the rumor-spreading process, which is universal and practical. We analytically derive the basic reproduction numbers, which determine the existence of rumor-spreading equilibria but also the global dynamics of the model. Moreover, the Lyapunov–LaSalle principle and the graph-theoretic approach prove the global asymptotic stability of the rumor-free/rumor-spreading equilibria in detail. Significantly, the effects of various strategies, including uniform control, targeted control, and acquaintance control, are implemented and compared. Finally, the developed theoretical results are tested via numerical simulations and a real case data of rumors, showing that the model can more accurately simulate rumor-spreading in OSNs.

The intention of this analysis is to declare and demonstrate the complete foundational theorem of existence and uniqueness for fractional conformable initial value time-delayed models incorporating time delays. The utilized proof is based on Picard’s iterative method and the fixed point theorem. Thereafter, to showcase the outcomes of our theoretical research and as an application for numerical solutions, we propose an effective numerical method based on the reproducing kernel Hilbert approximation to solve some fractional time-delayed problems. Afterward, the construction of appropriate Hilbert spaces, derivation of the kernel functions, representation of the unique delayed solution and algorithm solution steps are also discussed and utilized. Indeed, the series solution, the convergence, and the error analysis outcomes are debated and discussed. For comparative analysis, we describe our gained results in the constructed tables and figures which help us to compare the numerical solution with the exact one. Concluding notes, keynotes and future are listed in the closing portion.

The development of microfluidic devices, which handle small volumes of fluids for mechanical, chemical and medical purposes, is accelerating. Drop microfluidics is a booming field. This study aimed to attain a better understanding of drop generation in a cross-junction device. Hence, the generation of drops in the cross-junction microchannel was numerically and two-dimensionally simulated. For this purpose, the open-source code of Gerris was implemented. Also, the effect of Ca and We number on the drop generation process was evaluated. The AMR technique is utilized to simulate drop motion. Six distinct regimes are identified, namely, long alternating (LA), short alternating (SA), alternating with different sizes (ADS), small drops (SD), jetting (J) and parallel (P). In combination with (LA and SA) regimes, the size of one drop is larger than the hydraulic diameter and the other is smaller. In the large alternating regime, the length of the drops decreases when Weber numbers increase and the drop generation frequency increases as the We number increases. In each transition from one regime to another, the pinch-off location suddenly increases, and then in each regime, with the increment of the We number, the location of drop breakage decreases.