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Skyrmions, which are topologically stable magnetic structures, have manifested promising features to be used as an information carrier in new-age, non-volatile data storage devices. In this article, Co(/)Pt square nanostructure with Co-free layer thickness in the range of 1–5 nm and first- and second-order anisotropy constants are taken to study the controlled formation of skyrmions. The magnetisation dynamics controlled by the current-induced spin transfer torque help to nucleate skyrmions by transforming the perpendicularly magnetised ground state. This process leads to a stable state of the isolated skyrmions via a complex transformation of the Neel wall following its image inversion. Skyrmion numbers vary with increasing thickness as the current density gradually increases. The impact of higher-order anisotropy constants (up to the second order) on the relaxed state of a system, compared to the first-order anisotropy alone, has been examined. Additionally, the effect of temperature on the formation of skyrmions has been analysed for all thicknesses.

This article studies the (3 + 1)-dimensional extended Zakharov–Kuznetsov (EZK) model describing the propagation of solitary waves across a magnetised dusty plasma. An analysis of the nonlinear three-dimensional dust-ion-acoustic solitary wave propagation in a magnetised two-ion-temperature dusty plasma is conducted. The sine–Gordon expansion method (SGEM) and ((1/{G}^{prime})) technique are implemented to discover new complex analytical solutions of the (3 + 1)-dimensional EZK model. These solutions comprise rational, exponential and hyperbolic functions. We plotted 3D, 2D and contour plots for some of the solutions for suitable parametric values. The graphs describe the change in the behaviour of solutions as values of free parameters are varied. All obtained solutions are checked using Maple software.

Nuclei in the rare-earth region are known to be strongly deformed and show rotational bands up to high spins. Ground state and high spin states of Yb and Er isotopes ((Nge 100)) have been studied using the Hartree–Fock–Bogoliubov approach as well as the projected shell model. A large number of quasiparticle bands are observed in these nuclei and the present study explores the possible origins of some of them. Projected shell model with variable pairing can provide a good description of the ground-state bands up to very high spins.

Influential node identification has long been a focal point for researchers. Existing methods primarily focus on the individual topological characteristics of the nodes, making it difficult to accurately identify key nodes within a network. This paper introduces an improved local gravity model (ILGM) that incorporates node position, paths, quantity and injection to evaluate the influence of each node. The ILGM further explores the topological characteristics of neighbouring nodes, incorporating path and quantity data from adjacent nodes. This enhancement significantly improves the accuracy of the algorithm’s results. Empirical evaluations conducted on five real-world networks and one artificial network demonstrate that the proposed model effectively identifies influential nodes in complex networks.

We consider a modified Rosenzweig–MacArthur model that incorporates the negative impact of resource on the consumer. This negative effect of the resource has been empirically examined within various ecological systems. It plays a crucial role in driving transitions towards consumer extinction through multistability. Specifically, we show that the negative effect results in the bistability between two steady-state solutions for smaller values of the positive impact of resource on the consumer, whereas higher positive impact facilitates the coexistence of oscillatory behaviour and steady-state solution. We show that the presence of the predator’s negative efficiency facilitates abrupt transitions to distinct dynamical states in both forward and backward traces. We also show that the preferred state of the finite steady state for the persistence of both consumer and resource populations can be achieved for intermediate ranges of consumer’s positive and negative efficiency rates, carrying capacity and mortality rate of the consumer. We find that a large consumer’s negative efficiency rate always drives the system to the extinction of the consumer. We have derived analytical stability conditions for transcritical, Hopf and saddle-node bifurcations by a linear stability analysis, which agrees with the simulation results depicted in the two-parameter phase diagrams.

A predator–prey model with Holling type-I and type-III functional responses, where the disease spreads between the prey, is considered in this paper. In consideration of the ecological balance, a harvest term is added to the predator. The positivity and boundedness of the solutions are discussed. Then, the conditions of the equilibrium points are analysed. According to the Routh–Hurwitz criterion, the local stability of equilibrium points can be analysed. For the disease-free equilibrium point, harvest rate h is selected as the bifurcation parameter. For the positive equilibrium point of the system, we choose infection rate b as the bifurcation parameter. By calculating and analysing the corresponding characteristic equations, the existence of Hopf bifurcation at equilibrium points is investigated. On the basis of high-dimensional bifurcation theory, we can obtain formulas which can decide the direction, period and stability of Hopf bifurcation of the system. To substantiate the theory, time history, bifurcation diagram and phase diagrams at different equilibrium points are drawn. In a disease-free environment, it may occur that the predator will prey on the prey in large numbers and eventually leads to the death of the prey. According to the numerical results, it can be seen that proper harvesting of predators is conducive to the stable development of the population. In a diseased ecology, when the infection rate experiences (b^{*}), the stability of the system changes and the prey population can adapt to such changes better. It helps to eliminate some old and weak species to reduce the consumption of resources.

Following a thorough analysis of the existing research on periodic electro-osmotic flow in rectangular microchannels, this paper offers a comprehensive investigation of the distinctive characteristics of electromagnetic electro-osmotic flow in Jeffery fluids, emphasising particularly on the combined impact of the intricate interplay between the electric field and electromagnetic forces. A precise analytical expression for the velocity has been successfully derived by employing the technique of variable separation. Moreover, a comprehensive analysis has been conducted utilising intricate calculations and image evaluation to delve into the implications of Hartmann number (Ha), Reynolds number (Re), relaxation time, electrokinetic width and retardation time on the distribution of flow velocity. The findings indicate that as Ha rises, the flow velocity initially gains momentum, but subsequently exhibits a gradual decline. When Re is 0.5, the speed increases by about 29% and then decreases by about 61%. When Re is 4.5, the speed increases by about 20% and then decreases by about 42%. The increase in electrokinetic width and relaxation time results in an increase in speed. When Ha is 0.5, the velocity rises about 29% by the effect of the electrokinetic width and about 730% by the effect of the relaxation time. When Ha is 6, the velocity rises by about 71% by the effect of the electrokinetic width and the velocity rises by about 100% by the effect of the relaxation time. However, an increase in the retardation time and Re will result in a decrease in the flow rate. When Ha is 0.5, the velocity decreases by 83% under the effect of retardation time and 80% under the effect of Re. When Ha is 6, the velocity decreases by 40% under the effect of retardation time and 25% under the effect of Re. It should be emphasised that the velocity distribution of Jeffrey fluid is mainly concentrated near the channel wall, especially when Ha increases, resulting in the fluid velocity tending to be relatively slow. It is particularly interesting that when Ha reaches a high level, the fluid velocity is almost no longer affected by changes in Re. In order to validate the accuracy of this study, the resulting findings were cross-checked with previous findings and these comparisons support that the conclusions of this paper are plausible.

The possibility of a quantum system to exhibit properties that are akin to both the classically held notions of being a particle and a wave, is one of the most intriguing aspects of the quantum description of nature. These aspects have been instrumental in understanding paradigmatic natural phenomena as well as to provide non-classical applications. A conceptual foundation for the wave nature of a quantum state has recently been presented, through the notion of quantum coherence. We introduce here a parallel notion for the particle nature of a quantum state of an arbitrary physical system. We provide elements of a resource theory of particleness, and give a quantification of the same. Finally, we provide evidence for a complementarity between the particleness thus introduced, and the coherence of an arbitrary quantum state.

The present study deals with the dynamics of microelectromechanical system (MEMS) resonators, especially the exploration of strange non-chaotic attractor (SNA) in MEMS resonators. SNAs often arise in systems driven by quasiperiodic forces, where the system is subjected to multiple frequencies that are incommensurate. When we apply the quasiperiodic forces, we identify the presence of SNA regions in the MEMS oscillators through bifurcation and Lyapunov analysis. Subsequently, we analyse the route of SNA in the considered system. In our analysis, the first identified route to SNA is the fractilisation route which is validated through various analyses, such as Poincaré map, distribution of finite-time Lyapunov exponents, Lyapunov variance, singular continuous spectrum and recurrence analysis. Moreover, two additional routes to SNA, namely Haegy–Heamel route and intermittency route, are identified and thoroughly investigated, and the presence of SNA is confirmed using singular continuous spectrum analysis. This work helps to understand SNA that can be important in fields like signal processing, where distinguishing between chaotic and non-chaotic signals is crucial. In particular, the emergence and characterisation of SNAs in MEMS resonators open avenues for further research and applications in nonlinear dynamics and chaotic systems.

The current article unveils the repercussions obtained from analysing the Casson–Williamson nanofluid flow across a curved stretched surface using the Darcy–Forchheimer model. The modelling is contemplated with homogeneous–heterogeneous chemical reactions. The impact of nonlinear thermal radiation, exponential heat source and magnetic field is considered. Further, response surface methodology is a statistical technique used to understand the association of parametric factors under consideration on the response which is the Nusselt number in the present context. The prime aim of this modelling is to give optimal conditions for producing the highest heat transfer rate to build an efficient model with the aid of sensitivity analysis. In addition, entropy propagated in the media is provided to enhance the importance of this investigation. Runge–Kutta–Fehlberg 4–5th order technique has been used to obtain the numerical output. The analysis reveals that the first-order slip component has a negative effect on velocity distribution, whereas the second-order slip factor has the opposite effect. The Nusselt number decreases as the unsteadiness parameter reaches its maximum value and when the sheet is susceptible to intense radiation. Graphical representations of streamlines and isotherms are provided to illustrate the flow and heat distribution. The sensitivity analysis emphasises that the Brownian motion parameter has positive sensitivity, whereas thermophoresis and an exponential heat source have negative sensitivity on the Nusselt number.