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This research work focusses on examining the attributes of ion-acoustic waves (IA waves) in a plasma environment embodying superthermal-trapped electron distributions, characterised by the parameters (kappa ) and (beta ) representing superthermality and trapping respectively. The study utilises a modified nonlinear Schrödinger equation (m-NLSE) derived using the reductive perturbation method (RPM) to model the dynamics of modulated wave packets in this plasma framework. The study investigates the impact of superthermality ((kappa )) and trapping ((beta )) parameters on the envelopes of IA waves. The research explores the conditions for modulational instability (MI) of IA waves, characterised by the dispersion-nonlinearity product PQ in the m-NLSE. Bright and dark solitons are observed corresponding to different signs of PQ, i.e., (PQ<0) and (PQ>0) indicating the presence of modulationally unstable and stable regimes, respectively. The cutoff wavenumber (k_{c}) at which MI enters increases with decreasing superthermality (increasing (kappa )). Interestingly, (k_{c}) is observed to be independent of the trapping parameter ((beta )), suggesting that electron trapping does not significantly influence the onset of MI. Further, the effects of (kappa ) and (beta ) on the maximum growth rate ((Gamma _{textrm{max}})) and the modulational wavenumber ((K_{textrm{max}})) associated with MI are also investigated.

In our previous work Burtebayev et al, Int J Mod Phys E 28, 1950028 (2019), we presented the angular distribution (AD) for ({}^{10})B ions elastically scattered from the ({}^{12})C target at (E_{text {lab}}({}^{10}text {B})=) 41.3 MeV. The measured data exhibited a pronounced increase in cross-sections at backward angles. This is mostly attributed to the effect of deuteron transfer between the colliding nuclei. In this work, we present the inelastic ADs for the same system leading to the (J^{pi } = 2^{+}, E_{x}=) 4.439 MeV and (J^{pi } = 3^{-}, E_{x} =) 9.641 MeV excited states of the ({}^{12})C nucleus. The measured inelastic ({}^{12})C(({}^{10})B, ({}^{10})B)({}^{12})C(^{*}) ADs, together with the previously measured elastic ({}^{12})C(({}^{10})B,({}^{10})B)({}^{12})C ADs at (E_{text {lab}}({}^{10}text {B})=) 17.5, 18, 41.3 and 100 MeV, are analysed within the methods of distorted wave Born approximation (DWBA) and coupled reaction channels (CRC) using the new B3Y and the standard M3Y effective interaction potentials. Spectroscopic amplitude (SA) values were determined for the ({}^{12}text {C}rightarrow {}^{10}text {B} + d) configuration.

In medical applications, carbon nanotubes (CNTs) are used as adaptable drug carriers for targeted delivery, utilising their ability to exactly encapsulate and release therapeutic compounds, and as contrast agents in cutting-edge imaging modalities like MRI and CT scans. The current investigation deals with the unsteady flow of hybrid nanofluid via an expanding/contracting surface. The flow of hybrid nanofluid for the conjunction of magnetisation, radiating heat and additional heat source energies the flow properties. The role of suction/injection is vital for the flow through the permeable medium. The hybrid nanofluid is a composite of single-wall carbon nanotube (SWCNT) and multi-wall carbon nanotube (MWCNT) nanoparticles in the base liquid water. Appropriate similarity transformation converts the governing PDEs to nonlinear ODEs. Further, these are handled numerically retaining shooting-based Runge–Kutta fourth-order technique. The physical consequence of various constraints affecting the flow are explained using graphs and numerical outcomes relating to rate coefficients are shown via tabular form.

The influence of various thermal properties of nanoparticles in several applications in industries, engineering, biomedical, etc. has gained the interest of researchers drastically. The current investigation aims in presenting the performance of various thermophysical properties, such as viscosity, conductivity, specific heat, etc. under the influence of various shapes of the nanoparticles on the flow of ternary hybrid nanofluid over an infinite vertical plate embedding within a permeable medium. The conducting fluid under an applied magnetic field with thermal radiation enriches the flow properties. Suitable similarity rules combined with similarity variables and stream function are adopted to transform the governing phenomena into a non-dimensional form. Further, analytical approaches, such as Laplace transformation technique is embraced for solving this unsteady system of equations. The graphs and tables present the physical behaviour of the contributing factors with a correlative result. The physical behaviour of these factors is described briefly and important outcomes are also depicted as a conclusive remark. It is observed that the enhanced magnetisation and heavier density of the ternary hybrid nanofluid decelerate the velocity distribution significantly whereas the cooling of the surface due to thermal Grashof number augments the fluid velocity. Further, the higher conductivity of the ternary nanofluid along with increasing thermal radiation increases the fluid temperature.

The continuous internal bremsstrahlung spectrum accompanying a beta and neutrino from the (^{14}hbox {C}) isotope was measured by magnetic deflection method in the region of 10–150 keV using a (7.62 ,hbox {cm}times 7.62 ,hbox {cm}) NaI(Tl) scintillation spectrometer. The NaI(Tl) detector was calibrated by the standard radioactive sources. The detector response functions are generated for single-energy gamma photons with the help of experimental detector parameters and the Monte Carlo method. The experimental set-up and the geometry were adjusted carefully to minimise the external bremsstrahlung effect and the undesirable gamma counts from the surroundings in the detector. The raw experimental data were unfolded from the detector response effects by applying the singular value decomposition method. The experimental spectrum was compared with both theoretical and Monte Carlo calculation spectra.

The rotational bands of (^{55})Cr are studied with deformed Hartree–Fock (HF) and angular momentum projection techniques. Energy spectra are calculated up to high spin values (J={37/2}^+). Configuration mixing is performed between different rotational aligned (RAL) bands and the band-mixed result is compared with the experimental bands. One-, three- and five-quasiparticle bands are studied here. Except these, we also predict some structural properties like magnetic dipole moment ((mu )), static quadrupole moment ((Q_0)) and spectroscopic quadrupole moment ((Q_s)) along with deformation parameter for future verification. We used our microscopic model to predict band structures in the high K region too. Reduced transition probabilities, i.e. B(E2) and B(M1) values are calculated for all bands. Signature effect has been observed in low K spectra as well as in reduced transition probabilities.

In our modern world, rumours have triggered chaos and conflicts. Study of the dynamics of rumor propagation helps yield effective countermeasures to resist rumour propagation. It is a major task to study an ordinary differential equation (ODE) model on high-order incidence and treatment function for its dynamical behaviours. First and foremost, we build an ODE model depending on the actual transmission mechanism. Secondly, we study the basic properties of solutions including non-negativity, boundedness and situation of inexistence of the limit cycle. Thirdly, we study the necessary conditions of the equilibrium points for the existence, stability and instability. Furthermore, this study analyses bifurcations induced by parameters around the equilibrium point of rumour-spreading. Finally, several numerical simulations are given to show diverse dynamics behaviours of the model on different parameters and the factors affecting rumour propagation are theoretically analysed, which proves the validity of the theoretical analysis.

We investigate the dynamics of ultrashort pulses in a real-world system featuring periodically distributed dispersion and nonlinearity. We present a precise solution resembling a chirped soliton for the higher-order nonlinear Schrödinger equation (HNLS). This solution incorporates group velocity dispersion (GVD), stimulated Raman scattering (SRS), a third-order dispersion (TOD) term, cubic nonlinear effects and self-steepening (SS) effects with spatially varying coefficients. The derivation is based on specific parametric conditions, accounting for both linear and nonlinear absorption and amplification. The investigation reveals the stability of solitary-like solutions as they propagate over long distances in the medium. Additionally, we furnish parametric conditions that dictate the existence of chirped solitons. The numerical results closely corroborate the outcomes obtained through analytical approaches.

In this paper, we examine the role of the Jacobi last multiplier in the context of two-dimensional oscillators. We first consider two-dimensional unit-mass oscillators admitting a separable Hamiltonian description, i.e., (H = H_1 + H_2), where (H_1) and (H_2) are the Hamiltonians of two one-dimensional unit-mass oscillators. It is shown that there exists a third functionally-independent first integral (Theta ), ensuring superintegrability. Various examples are explicitly worked out. We then consider position-dependent-mass oscillators and the Bateman pair, where the latter consists of a pair of dissipative linear oscillators. Quite remarkably, the Bateman pair is found to be superintegrable, despite admitting a Hamiltonian which cannot be separated into two isolated (non-interacting) one-dimensional oscillators.

Heat absorption and thermal radiation have significant roles in engineering and research. These two principles have applications in thermal transportation, gas turbines, nuclear power plants, electrical fuel, aerospace engineering, projectiles and renewable energy. The present work analyses the stagnation point ternary nanofluid motion over a circulating sphere in the presence of a magnetic field and radiation absorption. The nonlinear controlling equations are replaced by ordinary differential equations by applying a suitable comparison factor. The bvp4c process was used to establish numerical outcomes of the partial differential equations. This mathematical numerical findings are presented graphically. The results of ternary nanoparticles (Cu–Ag–CuO/water), hybrid nanoparticles (Cu–Ag/water) and copper (Cu) nanoparticles have also been compared, and this comparison suggests that ternary nanoparticles (Cu–Ag–CuO/water) are more effective at attenuating hemodynamic factors (such as wall shear stress and heat transfer) than hybrid and copper (Cu) nanoparticles. Comparison with previous literature results is also done and the results are found to be in very good agreement with those published earlier.