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This paper explores the (2 + 1)-dimensional complex modified Korteweg–de Vries (cmKdV) system using the Jacobi elliptic function expansion method. The primary goal is to analyse modulation instability and derive innovative soliton solutions. We then solve the resulting equation using the Jacobi elliptic function expansion method, which is capable of producing a wide variety of solutions, including periodic, kink and bright soliton solutions. Figures show graphical representations of the found solutions in multiple-dimension computations using 2D, 3D and contour sketches. The findings indicate that the technique used are effective and reliable tools that can be used to solve a variety of nonlinear differential equations.

This work is mainly devoted to the study of a family of compact stars representing anisotropic fluids in the background of alternate gravity. In this paper, we obtain a solution for a new class of anisotropic configuration satisfying the embedding Class 1 Karmarkar condition. We conducted the investigation with the help of(f(mathcal {R},mathcal {T})) gravity theory, where (mathcal {R}) and (mathcal {T}) denote the Ricci scalar and the energy momentum tensor, respectively. By considering the compact stars to be static and spherically symmetric and with equally distributed anisotropic matter in them, the relation between the metric potentials (textrm{e}^{nu }) and (textrm{e}^{mu }) is obtained satisfying the Karmarkar condition. It has been observed that our model is well-mannered (i.e., the model is well-structured and well-behaved, satisfying all the necessary conditions for a stable structure and ensuring regular, smooth, and physically consistent behaviour) and dealt with every requirement for a stable structure in hydrostatic equilibrium for compact stars, namely PSR B1913(+)16, Cyg X-2 and PSR J1614-2230 for different values of (zeta ), to a great extent.

Scintillator materials are widely used in industrial and medical imaging systems that utilise gamma cameras. This study evaluates image quality by modelling a gamma camera system with a pinhole collimator and a new scintillation detector (lutetium–yttrium oxyorthosilicate (LYSO)). This addition aims to improve the spatial resolution of the imaging system. The system is modelled using the Geant4 application for tomographic emission (GATE 9.1) tools. The pinhole collimator geometry was designed with various diameters and system magnification factors. Spatial resolution is assessed using two parameters: the full-width at half-maximum (FWHM) and the no-reference natural image quality evaluator (NIQE). Results show that both FWHM and NIQE values increase as the diameter of the pinhole collimator increases. Additionally, higher magnification factors improve spatial resolution and NIQE at the same pinhole diameter. The best FWHM value achieved is 0.66 ± 1.4 × 10⁻³ mm with a LYSO scintillation detector. These findings suggest that a gamma camera system equipped with a LYSO scintillation detector and a pinhole collimator has strong potential for high-resolution imaging applications.

This comprehensive study has addressed the various geometrical arrangements of three emitted fragments in ternary fission. The effect of the isobaric property on quantities of ternary fission has also been investigated. In order to measure the isobaric effect in ternary fission, the ternary fission of (^{260}text {Fm}) isotope accompanied by (^{18}text {O}), (^{18}text {F}) light and (^{68}text {Zn}), (^{68}text {Ga}) heavy isobars are studied. For each fixed charged fragment ((text {FCF})), combinations with the lower driving potentials ({(V-Q)}) are selected for further analysis. The Q-value, driving potential (({V-Q)}), barrier penetration probability (P), relative yield and decay constant ((lambda )) of the ternary fission for each combination of every FCF considering a potential consisting Coulomb and proximity potentials based on the Wentzel–Kramers–Brillouin ((text {WKB)}) approximation in the equatorial and collinear geometries are calculated. To investigate the isobaric effects, the results for even–even (^{18}text {O}) are compared with the results of odd–odd (^{18}text {F}) isobars as well as the even–even (^{68}text {Zn}) and odd–odd (^{68}text {Ga}) isobars. It is interesting to get close results for two different isobars. Calculated yields for each FCF were tabulated and plotted versus mass number of the fragments for a detailed analysis. Comparison of the calculated results for each FCF for the same isotope through three fragment geometries, namely the equatorial and collinear, indicating that for light fixed fragment the equatorial geometry is suitable and collinear geometry is an appropriate choice for heavy fixed fragments.

In this work, we study the mixed breather dynamics in the higher-order matrix nonlinear Schrödinger equation. Via the Darboux transformation (DT), we first construct first-order breather solutions and subsequently generalise them to second- and third-order mixed breather solutions incorporating two spectral parameters through a generalised DT. By means of those solutions, we analyse the dynamics of second- and third-order mixed breathers arising from the nonlinear superposition of distinct vector breathers. We demonstrate how double spectral parameters modulate the second-order mixed breathers, highlighting amplitude-dependent behaviours and spectral-parameter-controlled waveform transitions in multi-component nonlinear systems. In addition, we present the third-order mixed breathers, denoting the superposition of a vector breather and a vector degenerate breather.

Recent advancements in hybrid nanomaterials have improved thermal significance of the base fluids. The hybrid nanofluids, which comprise two distinct type of nanoparticles, have highly strengthened thermal activities, because of which they have applications in solar energy, power production, thermal devices, cooling phenomenon, etc. This study is to explore the thermal impact of the hybrid nanofluid by entertaining the oblique stagnation point flow. In this study, a hybrid nanofluid comprising silver (Ag) and alumina (Al({}_{2})O({}_{3})) magnetised nanoparticles with water (H({}_{2})O) along with ethylene glycol (C({}_{2})H({}_{6})O({}_{2})) base fluids has been deliberated. A reformed heat flux framework (Cattaneo–Christov) has been followed to modify the energy equation. The flow comprises porous media maintaining suction effects. The heat transfer is observed to break through the nonlinear radiated effects. Runge–Kutta–Fehlberg fifth-order (RKF 5) scheme is implemented for performing the numerical simulations of dimensionless governing equations. Analysis was done to check the contribution of physical flow parameters. The observations conclude that when the free stream stagnation flow coefficient is prominent, the oblique velocity decreases. The interruption of hybrid nanomaterial effectively enhances the impact of heat transfer due to porous medium and suction parameter.

Pollutant discharge is crucial for environmental management and numerous industry sectors. One method to assess how effectively the wastewater treatment techniques reduce pollutant levels is to analysis waste discharge concentrations. Recent research focussed on looking at the relationship between the fluid flow and the concentration of the contaminants released. The current study examines the unstable, incompressible, mixed convection of nanofluids through an infinite plate with the consequence of the porous material, pollutant concentration and thermal radiation. The partial differential equations (PDEs) and boundary conditions are reduced by non-similarity transformation to a collection of non-dimensional PDEs, which are later solved by employing the Crank–Nicolson finite difference technique. The effects of several dimensionless factors on the flow, temperature and concentration profiles are depicted visually. Some engineering coefficients are also examined. Major outcomes are, the velocity, energy and concentration profiles drop as the suction parameter rises. As the porosity constraints escalate, the velocity drops. The concentration declines as the Schmidt number enhances. The concentration increases as the local pollutant external source parameter and external pollutant source variation parameter rises. The temperature escalates as the heat radiation parameter rises. With an increment in the Grashof number, the velocity also rises. Several significant engineering processes, such as the preservation of food, manufacturing facilities, industrial waste, resources for petroleum gas extraction, nuclear power plants, insulating materials and packed-bed storage containers, rely on fluid flow via an infinite plate in the presence of pollutant concentration.

The ((2+1))-dimensional Broer–Kaup equations model the movement of long, dispersive gravity waves travelling in opposite directions within a body of water of constant depth. This system has significant implications across various scientific fields, such as plasma physics and nonlinear optical fibre communications. In this paper, we employed a classical Lie symmetry analysis to investigate the analytical solutions and soliton behaviour of the equations. To highlight the originality of our work, we compared our results with previous studies. The authors emphasise that no one could have obtained such a new class of solutions as those derived in this study without restricting all arbitrary functions involved in infinitesimal test problems. The authors did not apply any restrictions to (f_1 (y)) and (f_2 (t)), and (f_3 (t)) is chosen as (frac{a_0}{2}f'_2(t)) (where (a_0 ne 0) is a constant for further integration), which increases the generality of the answers and provides additional opportunities to describe physical occurrences. To further demonstrate the integrability of the (2+1)-coupled Broer–Kaup equations (CBKEs) (1), conserved vectors were also utilised. We used the Lie symmetry method to change the original set of partial differential equations into a similar set of ordinary differential equations that are limited in a certain way. This procedure made integration easier. Our examination of soliton dynamics provides valuable insights into the physical characteristics of the solutions. Additionally, we utilised conserved vectors to demonstrate the integrability of the system. The outcomes of this research significantly enhance the practical applications of the Broer–Kaup equations.

The experimental angular distribution data for the deuteron(+) ²⁴Mg elastic scattering system at energies between 8.65 and 170 MeV were re-analysed using the nuclear optical model. Three types of real optical potentials are considered: phenomenological Woods–Saxon, microscopic folding based on effective nucleon–nucleon interactions (CDM3Y6 and JLM) and cluster-folded potentials. A combination of volume and surface imaginary potentials is important for accurately describing the experimental data. A surface contribution to the real potential simulates the dynamical polarisation potential caused by deuteron breakup, improving agreement with the measured cross-sections without needing coupled-channel calculations. The energy dependence of potential parameters, along with other calculated quantities, is also examined. Both the phenomenological and the re-normalised cluster-folded potentials show good agreement with the experimental results, with the latter aligning well with the standard re-normalised folding potential in previous studies.

Nanomaterials elegantly amplify the thermal applications in different engineering processes and industrial fluids. In the era of nanotechnology, various sources have been specified to improve the thermal phenomenon and heat transfer performances. Recently, development in machine learning has suggested artificial neural network (ANN) algorithms to optimise the results and achieve peak performance. This work aims to present a novel ANN analysis for the slip flow of a viscoelastic nanofluid problem by assessing heat and mass transfer. The unsteady flow of the viscoelastic nanofluid over an oscillatory stretched surface has been considered. The radiative impact is utilised. The higher-order slip relations are imposed on the flow problem. The whole problem is modelled in partial differential equations. The computational fluid dynamics (CFD) simulations are performed using an implicit finite difference scheme. It is claimed that the current research problem is the first initiative for the ANN framework regarding the periodically oscillatory stretching surface flow. The physical impact of the problem is presented via a graphical approach.