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Most physical systems, whether classical or quantum mechanical, exhibit spherical symmetry. Angular momentum, denoted as (ell ), is a conserved quantity that appears in the centrifugal potential when a particle moves under the influence of a central force. This study introduces a formalism in which (ell ) plays a unifying role, consolidating solvable central potentials into a superpotential. This framework illustrates that the Coulomb potential emerges as a direct consequence of a homogeneous (r-independent) isotropic superpotential. Conversely, an (ell )-independent central superpotential results in a 3-dimensional harmonic oscillator (3-DHO) potential. Moreover, a local (ell )-dependent central superpotential generates potentials applicable to finite-range interactions such as molecular or nucleonic systems. Additionally, we discuss generalisations to arbitrary D dimensions and investigate the properties of the superpotential to determine when supersymmetry is broken or unbroken. This scheme also shows that the free-particle wave function in three dimensions is obtained from the spontaneous breakdown of supersymmetry and clarifies how a positive 3-DHO potential, as an upside-down potential, can have a negative energy spectrum. We also present complex isospectral deformations of the central superpotential and superpartners, which can have interesting applications for open systems in dynamic equilibrium. Finally, as a practical application, we apply this formalism to specify a new effective potential for the deuteron.

In this work, we have obtained new phantom fluid-type traversable wormhole (WH) solutions in the context of (f(mathcal {R}, T)) modified gravity. We investigate the potential that some equations of state (EoS), specifically phantom energy, which describes the accelerated expansion of the universe, could support the existence of traversable wormholes. This cosmic fluid thus offers us a plausible explanation for the occurrence of WH geometries. We construct two WH models with matter Lagrangian density (mathcal {L}_{m}=-(-rho +mathcal {P}_{r}+2mathcal {P}_{t})) and inspect numerous characteristics of these models under the WH geometry. The first WH solution (WH-I) is discovered by utilising a linear barotropic equation of state (EoS) connected with phantom energy (omega <-1) indicating the presence of the phantom fluid and pointing to the Universe’s expansion, while in the second WH (WH-II) solution, we take into account an interesting EoS (rho =eta (mathcal {P}_{t}-mathcal {P}_{r})) to generate a WH model. Additionally, it showed that the phantom fluid WH-I solution violates the radial null energy condition (NEC) while tangential NEC is satisfied. On the other hand, for the WH-II solution, NEC is violated. Extensive detailed discussions of the matter components have been done via graphical analysis. The obtained WH geometries satisfy a stable WH’s physically acceptable criteria.

The dynamical probing and linear offset boosting of constants in Josephson junction (JJ) instigated by the Wien bridge oscillator (JJIWBO) are investigated in this paper. Via numerical simulations, the JJIWBO unveiled bistable periodic oscillations, bistable periodic doubling with an evolving path to bistable chaotic characteristics, monostable chaotic behaviours and monostable periodic characteristics. The numerical dynamics are realised by the microcontroller validation (MCV) scheme. Two constant parameters are introduced in the rate equations of JJIWBO to implement the linear offset boosting of constants based on the two voltage variables. It is demonstrated that the polarity of the chaotic voltage and phase difference signals can be flexibly changed by varying one of the two constant parameters which is different from zero and the other constant parameter is zero. When two constant parameters have the same value, the chaotic voltages and phase difference signals can switch between bipolar and unipolar signals flexibly by changing the unique constant parameter.

The purpose of this study is to investigate the transient dynamics of a third-grade fluid, which can undergo exothermic reactions in a saturated porous microchannel. The adverse pressure gradient force constitutes the primary flow driver. In addition to exothermic reactions, the system is also subjected convective cooling at the microchannel boundaries. Newton’s law of cooling and Arrhenius kinetics are employed to model the boundary cooling and exothermic reactions, respectively. The temperature-dependent fluid viscosity is modelled via a Nahme-type law and the porous material between the parallel microchannels is assumed to have constant permeability. To account for this, the unsteady modified Darcy’s law is applied, effectively capturing the impact of porosity. Computational solutions are employed to solve the non-homogeneous partial differential equations (PDEs) for the flow temperature and velocity. These computational solutions are developed from efficient, convergent and unconditionally stable, semi-implicit finite difference (SIFD) methods. Examining the thermodynamic and fluid-dynamical consequences of variations in the numerical exponent (aleph ) and exothermic reaction parameter (delta _2) are the principal motives of the study. A comparative evaluation of the thermal runaway susceptibility of the numerical exponent parameter for two distinct types of fluids is outlined, indicating that the ranking of susceptibility ranges from most to least susceptible in the bimolecular case, the Arrhenius case and the sensitised case. Newtonian fluids are the most prone to non-Newtonian fluids. Additionally, the study systematically explores the sensitivity of field variables to changes in different flow parameters through graphical representations and shows that the fluid variables increase with the increase in Reynolds number, viscosity parameter and Brinkman number, while decrease for the third-order parameter and porous medium parameter. The obtained results are qualitatively discussed and compared with the published data.

The heat transfer characterisation of the three-phase local thermal non-equilibrium analysis due to the nanofluid (solid particle phase and the base fluid phase) and the absorbing phase (due to the porous surface) is performed for a third-grade nanofluid impinging over a receding surface. The mathematical formulation of the physical model includes the Rivlin–Ericksen tensor for fluids of grade three with appropriate restriction to viscous flows and also incorporates the Buongiorno nanofluid model for studying the impact of thermophoresis and Brownian motion. The resultant governing time-dependent partial differential equations has been converted to ordinary differential equations by applying similarity transformation. The computational results are obtained using the finite-difference approach in the Matlab software. The non-Newtonian and the time-dependent flow phenomena demands an additional boundary condition to ensure the uniqueness of the solution. With a general third-grade assumption with the wall shrinking and unsteadiness, the resultant equations govern the occurrence of dual solution in the obtained numerical results. The stability investigation reports the existence of multiple (dual) solutions due to the unsteadiness imparted in the flow and the flow behaviour of both the stable and unstable solutions are revealed. The boundary layer characteristics are explored for various vital physical parameters, such as material parameter, porous permeability parameter, Brownian motion parameter, thermophoresis parameter, inter-phase heat transfer coefficient, modified thermal capacity ratio, modified thermal diffusivity ratio and buoyancy ratio parameter. The temperature distribution across different phases is analysed for the stable solutions.

Holmium orthophosphate (HoPO₄) was prepared using the solid-state method. The XRD pattern analyses have proved that HoPO₄ crystallises in the tetragonal structure (I4₁(/)amd). The maximum magnetic entropy change (−(Delta {S}_{text{M}}^{text{max}})) and the relative cooling power (RCP) reach 34.5 J(/)kg·K and 414.84 J kg⁻¹ at 2.4 K under a magnetic field of 50 kOe, respectively. The lowest transition temperature and the large magnetocaloric effect (MCE) showed that HoPO₄ is a potential candidate for superfluid helium magnetic refrigeration applications.

This work evaluates the performance of frequency-modulated noise reduction-differential chaos shift keying (FM-NR–DCSK) when using a compound chaotic sequence (CCS) under a multipath fading channel. To construct a more complex and random CCS, the outputs of chaotic maps like the logistic map, tent map, Chebyshev map and Henon map are incorporated. In this scheme, the CCS is first frequency-modulated (FM) to generate a signal with constant energy per bit. This improves the bit error rate (BER) performance of noise reduction-differential chaos shift keying (NR–DCSK). The functionality of the CCS-based FM-NR–DCSK system is being assessed in the presence of both additive white Gaussian noise (AWGN) and alpha–mu (α–µ) fading to determine its efficacy. In conclusion, we analyse the effectiveness of the CCS compared to other existing chaotic maps.

The rapid development of quantum magnonics can be attributed to its potential applications in quantum computing, information processing and the creation of hybrid quantum systems. Quantum quasiparticles, known as magnons, undergo Bose condensation at high densities, a phenomenon observed during radiofrequency excitation. This phenomenon was initially discovered in the antiferromagnetic superfluid (^3)He. Magnonic superfluidity effects, Josephson effect and magnon tunnelling were also observed in this system. Similar effects have been identified in yttrium iron garnet at room temperature, suggesting the possibility of utilising these effects in a manner akin to superconductivity. In this article, we conduct simulations of magnon tunnelling processes across the energy gap, aiming to compare these simulations with experimental findings.

Hydrothermally grown NiO nanoflakes have been investigated here for their resistive switching (RS) and photoabsorption characteristics. The formation and disruption of the conducting filament (CF) under an applied external electric field leads to bistable resistive switching in the grown NiO nanoflakes. Comprehensive investigations of the I–V behaviour show that the formation and rupturing of the CF depend on the concentration of the metallic Ni. Interestingly, photoabsorption response demonstrates a nearly similar behaviour in UV and visible regions for nanoflakes grown at low reaction time, but an enhanced UV response for the flakes obtained at larger reaction times. These nanoflakes displaying multifunctional properties of photoabsorption and RS behaviour, that can be modulated with reaction time, are attractive for optoelectronic, electrochromic and RS-based memory applications.

This research work aims to explain the model and assessment of a differential mathematical system of the magneto-bioconvection of the Williamson nanofluid model (MBWNFM) by capitalising on the strength of the stochastic technique through computational intelligence of Bayesian regularisation back-propagated neural networks (CIBRB-NNs). This facilitates a more accurate, reliable and proficient computation of the dynamics. A reference dataset is built using the Adams technique in the Mathematica software to depict multiple situations and account for numerous influential parameters of the MBWNFM. The reference data results are split into 70% for training and 30% for validation and testing methods. This approach aims to enhance the accuracy of the approximated results and enable them to be compared with established solutions. The demonstration of the accuracy and efficiency of the created CIBRB-NNs involves a comparison of the results obtained from the dataset using the Adams approach, by adjusting several influential parameters which include magnetic parameter ((M)), bioconvection Lewis Number ((L_{b})), thermal diffusivity ((alpha)) and thermal Biot number ((gamma)). The stability and accuracy of CIBRB-NNs are validated using various methodologies, including the analysis of fitness curves depicting mean square error, regression studies, evaluation of error using histogram plots and measurement of absolute errors. The excellent measures of performance in terms of MSE are achieved at levels 4.50e-12, 6.73e-13, 1.07e-13, 7.08e-13, 4.77e-13 and 1.70e-13 against 82, 150, 98, 83, 170 and 189 epochs. The error analysis of the proposed and reference datasets shows that CIBRB-NNS is authentic and precise, ranging from e-09 to e-04 for all scenarios.