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This paper constructs the travelling wave solutions of the stochastic resonant nonlinear Schrödinger equation that contains the stochastic term with multiplicative white noise based on the complete discriminant system for the polynomial method. By systematically investigating the polynomial law, we derive more abundant forms of travelling wave solutions. Notably, our new insight reveals that the non-averaged state of the solutions enables the characteristics of solitons and periodic modes to be maintained. In contrast, stochastic averaging will lead to changes in the periodic and soliton characteristics. In addition, we present the model diagrams for several specific parameters, which endows physical interpretations to the spatiotemporal structure in the white noise environment.

In this manuscript, a modified (R_I)-type recurrence relation is considered whose recurrence coefficients are perturbed by the addition or multiplication of a constant. Using the perturbed system of recurrence coefficients, perturbed extended relativistic Toda equations are derived. These equations are then represented in a matrix form. This matrix representation helps recover a Lax pair that has already been studied in the literature. Inferences about the stability of the resulting perturbed system of the Toda equations are drawn based on numerical experiments.

We explore the (beta )-decay features of the doubly magic nucleus (^{100})Sn and proton-rich Sn isotopes within the mass range 100(le ) A (le ) 110. Our calculations yield a Gamow–Teller (GT) strength of 4.157 for the transition from the ground state to the lowest excited state of (^{100})Sn, which closely aligns with the recently measured value of 4.381 at RIKEN. The GT strength distributions computed for (^{102-104, 106, 108})Sn exhibit good agreement with experimental observations. Additionally, we compare our GT data with previous theoretical calculations. The predicted half-lives are reproduced within a factor of 2 relative to the experimental values for (^{100-110})Sn. For the first time, we present microscopic calculations of electron capture, (beta ^{+}) decay, and proton emission rates for proton-rich Sn isotopes under stellar conditions. As the core density of a star reaches (10^{11}) g/cm(^3), electron capture rates calculated by up to seven orders of magnitude. In contrast, (beta ^{+}) decay rates remain largely unchanged with variations in core density but exhibit changes of up to three orders of magnitude with increasing core temperatures. A decreasing trend in stellar rates is observed with increasing neutron number N, specifically for even-even and odd-A Sn isotopes. The reported stellar rates provide valuable insights for the rp-process and simulation of post-silicon evolution of massive stars.

This study examines spherically symmetric static empty space solutions within the framework of the (f(R, Sigma , T))-gravity, where (f(R, Sigma , T)) is a general function of the scalar curvature R, the torsion scalar (Sigma ) and the trace of the energy–momentum tensor T. We reduce the modified Einstein equations to a single equation and demonstrate how to construct exact solutions across various (f(R, Sigma , T))-gravity models. Notably, we establish that for a broad class of models, including the (f(R, Sigma , T)=R+Sigma +2 eta T) model, the Schwarzschild metric serves as an exact solution to the field equations, alongside other classes of solutions. We discuss the significance of these findings in the context of solar system constraints on (f(R, Sigma , T)) theories of gravity. Additionally, the effects of space–time torsion and particle spin on the solar system are also explored.

The present work aims to investigate the antimicrobial efficacy of non-metallic sulphur, silica and S@SiO₂ core–shell nanoparticles. The X-ray diffraction (XRD) pattern confirmed that the silica nanoparticles have an amorphous structure. In contrast, the sulphur nanoparticles have a crystalline nature with an orthorhombic α-phase structure and S@SiO₂ nanoparticles suggest the superposition of silica XRD pattern on that of sulphur. UV–Visible spectra of silica, sulphur and S@SiO₂ show the highest absorption peak at 293, 326 and 305 nm, respectively. Fourier-transform infrared spectroscopy (FTIR) spectra of core–shell NPs show the presence of sulphur and silica in the core–shell nanoparticles without any chemical interaction between them. The field-emission scanning electron microscopy (FE-SEM) images revealed that the silica nanoparticles are of uniform spherical shape and the average particle size is approximately 250 nm. The shape of the sulphur nanoparticles was found to be irregular and the average particle size was found to be around 130 nm. The FE-SEM images of the core–shell nanoparticles confirmed the regular spherical shape of S@SiO₂ core–shell nanoparticles with an average particle size of approximately 350 nm. The antimicrobial properties of all the synthesised nanoparticles were examined against animal pathogenic gram-negative bacteria, Escherichia coli, Salmonella and plant pathogenic gram-negative bacteria such as Erwinia amylovora, Xanthomonas oryzae by using agar disk diffusion method. The result shows that uncoated and coated nanoparticles substantially inhibit all the gram-negative bacteria. The results demonstrate that the silica and sulphur nanoparticles show effective antimicrobial efficacy against all the specified bacteria, with concentrations of 1500 and 2000 µg(/)ml being the most effective.

This study explores the effects of MHD and slip velocity on micropolar fluid flow, heat transfer and mass transport over a stretching sheet with heat generation. The impacts of heat generation, thermal conductivity, heat flux, micro-rotation, Prandtl number and Schmidt number were investigated analytically. Similarity transformation is applied to convert the governing partial differential equations into a system of nonlinear ordinary differential equations, which are then solved numerically using the bvp4c method. Graphics are used to illustrate the impact of the relevant parameter on the distribution of velocity, micro-rotation, temperature and concentration. Validation of the solutions is done for some specific cases. Additionally, the consequences of several parameters on the skin friction caused by the primary velocity, Nusselt number and Sherwood number are shown in tabular form. A thorough description and summary of the numerical results for key flow parameters, including the local skin-friction coefficient, wall couple stress and local Nusselt number, are presented in tables. Microparticles have a significant effect on the flow phenomenon. The results are interpreted in detail. This research relates to enhancing electromagnetic fluid management, heat exchangers and industrial processes.

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.