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In this work, we explore the bright soliton solutions of a non-local variant of the complex modified Korteweg–de Vries (cmKdV) equation, characterised by shifted reverse space–time (mathcal{P}mathcal{T})-symmetry. Employing the bilinear method and (tau )-functions of KP hierarchy, we obtain exact solutions in determinant representation that inherently preserve the symmetry structure of the equation. A detailed analysis of the one-soliton case reveals a distinct inverse relationship between soliton velocity and amplitude, and notably, the amplitude can diverge to infinity through the adjustment of a velocity-independent parameter, unlike in the local cmKdV case. For multi-soliton solutions, we perform a long-time asymptotic analysis, showing that the solutions decompose into superpositions of individual bright solitons. Furthermore, we rigorously examine their interaction dynamics, confirming that the collisions are purely elastic and accompanied by quantifiable phase shifts and positional displacements. The findings shed new light on the rich and previously unexplored interaction behaviur of solitons in this class of non-local integrable models.

Alpha decay characteristics of 134 even–even, 243 odd-A and 68 odd–odd heavy nuclei are investigated using the improved Coulomb and proximity potential model (CPPM). The CPPM is improved by introducing an empirical diffuseness parameter (b) that depends upon the isospin and reduced mass of the parent nucleus in the expression for the proximity potential. The predictions of the CPPM with (b = 1) fm and that with the calculated values of the diffuseness parameter are compared with the experimental values. Improvement in the predictive power of the CPPM is observed when the empirical diffuseness parameter is included in the calculations. The experimental alpha decay half-lives are well reproduced. The barrier penetrability and alpha preformation factor are also estimated through the CPPM calculations. The importance of the use of an accurate value of the surface diffuseness in the alpha and cluster decay half-life calculations became evident from our study. The calculations are also performed by using the Viola–Seaborg formula and the Horoi formula, two most successful empirical formulae. The lowest standard deviation is obtained for the CPPM calculations with the empirical diffuseness parameter.

The wedge surface in ternary hybrid nanofluid research is important because it facilitates the design of more effective systems, including heat and mass transfer, enhances the understanding of the flow and thermal properties in complicated geometries and aids in simulating real-world engineering problems. This work examines the two-dimensional steady incompressible non-Newtonian flow of a ternary hybrid nanofluid comprising Al₂O₃, graphene and CNT nanoparticles with the base fluid engine oil across a wedge surface. This work analyses the flow behaviour under the effect of suction/injection, magnetic field, radiation parameter, natural convection, Hartree pressure gradient parameter and the Falkner–Skan parameter. The Maxwell fluid model is considered under the impact of natural convection and thermal radiation on the flow over the wedge surface. To solve the mathematical model, the authors used the function of bvp4 in MATLAB software. Also, soft computing techniques, fuzzy particle swarm optimisation and artificial neural networks are used to improve the analysis of predicting the Nusselt number. From the results, it is seen that the radiation parameter has a significant influence on the heat transfer rate. Across all studies, for both artificial neural networks (ANN) and fuzzy particle swarm optimization (FPSO), the mean squared error (MSE) values are very close to 0 and the coefficient of correlation (R) values are very close to 1, indicating a low error in the forecasts.

The quark gluon plasma as a unique state of matter is investigated in the extended quasiparticle model by the momentum-dependent interaction. The self-consistent thermodynamics is realised through an effective bag constant. The equation of state and the speed of sound are calculated for different sets of quark mass scales and coupling constants. It is found that the equation of state becomes hard and close to the Stefan–Boltzmann (SB) limit with the combination effect of the momentum-dependent factor and the running coupling interactions. Moreover, the corresponding sound velocity is more close to the lattice simulation result. It is concluded that the momentum-dependent scale and the running coupling interaction are necessary for the quasiparticle model to be consistent with the lattice result.

This paper presented a sixth-order iterative scheme for solving nonlinear equations. The method involves four function evaluations per iteration and possesses an efficiency index of nearly 1.56. For establishing the reliability and robustness of the method, a mathematical convergence analysis is provided. Comparisons with other methods of the same order of convergence available in the literature demonstrate the accuracy and reduced cost of the proposed method. Large-scale numerical experimentation on a variety of test functions also establishes the effectiveness of the method. Plots of residual fall demonstrate the scheme’s behaviour of rapid convergence, whereas large-scale stability analysis of the scheme highlights its insensitivity to different conditions. These findings in aggregate highlight the potential of the method for fast and reliable numerical problem-solving in real-world applications.

Molecular dynamics simulations are employed to investigate the deformation response of borophene sheet for tension along the armchair direction under two different loading conditions. The stress–strain behaviour of borophene is found to be almost similar for the two loading conditions. The value of Young’s modulus (388 N/m) at 1 K is greater than the Young’s modulus (309 N/m) of graphene showing greater stiffness of borophene in this configuration. The peak stress decreases with an increase in temperature for both the loading conditions and the decrease in peak stress with temperature can be well described by an exponentially decaying function. The stress–strain behaviour is almost insensitive to the applied strain rate for both loading conditions. The pre-existing defects significantly affect the peak tensile stress. A void formed by vacancies in the system has a greater effect on peak tensile stress than a random distribution of the same number of vacancies in the system.

Recent research has indicated that the standard model (SM), while historically highly effective, is found to be insufficient due to its prediction of zero mass for neutrinos. With the exception of a few, the majority of the parameters related to neutrinos have been determined by neutrino oscillation experiments with excellent precision. Experiments on neutrino oscillation and neutrino mixing have shown that neutrinos are massive. To fill in gaps, discrete symmetries are becoming more common alongside continuous symmetries while describing the observed pattern of neutrino mixing. Here, we present a (T_7) flavour symmetry to explain the masses of charged leptons and neutrinos. The light neutrino mass matrix is derived using seesaw mechanism of type I, which involves the Dirac neutrino mass matrix as well as the right-handed neutrino mass matrix. For normal and inverted mass hierarchies, we estimate the Pontecorvo–Maki–Nakagawa–Sakata matrix ((U_{textrm{PMNS}})), three mixing angles, (theta _{12}), (theta _{23}) and (theta _{13}), the masses of three neutrinos, effective Majorana neutrino mass parameter (langle m_{ee} rangle ) and the other model parameters by using a powerful meta-heuristic and population-based optimisation algorithm, i.e. particle swarm optimisation (PSO).

This research extensively investigates the solitary wave solutions of the time-fractional Murray equation (TFME), a prevalent framework in diverse scientific and engineering disciplines. Three mathematical methods, the extended simple equation method, the modified extended auxiliary equation mapping method and the modified F-expansion method, are employed to derive analytical solutions in the form of trigonometric, hyperbolic, exponential and rational functions. To analyse the physical behaviour of the concerned model, some solutions are plotted in two and three dimensions by imparting particular values to the parameters under the constraint condition of each selective solution. Mathematica 13.0, the computational software, is used to handle all calculations as well as all plotted graphs of the concerned solutions. The derived results have numerous applications to understand the fluid dynamics and wave propagation, particularly in biological systems and potentially in modelling tsunami waves. Hence, this study has applications in nonlinear science. It is vital to perceive that our proposed methods are genuine, suitable and well-ordered for nonlinear fractional partial differential equations (NLFPDEs).

In this work, we study the E1 decay processes, (^3P_1) (rightarrow ) (^3S_1gamma ) and (^3S_1) (rightarrow ) (^3P_1gamma ), in the framework of Bethe–Salpeter equation and calculate their decay widths. We have used algebraic forms of the Salpeter wave functions obtained through the analytic solutions of the mass spectral equations for the ground and excited states of (^3S_1) and (^3P_1) equal mass charmonia in approximate harmonic oscillator basis to do analytic calculations of their decay widths. These decay widths have been compared with data and other models.

The nanofluids of the ternary hybrid provide one special benefit that reduces usage of energy, enhances machine production and increases cooling. In this study, the cooling structure of the cylindrical battery packs are explained and their flow models are set up. For this purpose, this article describes a laminar hybrid convectional inactive ternary hybrid’s point flow nanofluid in the presence of thermal emission. Used bvp4c method is used to solve transformed resulting partial differential equation (PDEs). Three types of nanofluids, (hbox {Fe}_{3}hbox {O}_{4})–(hbox {H}_{2})O, Zn–(hbox {H}_{2})O and (hbox {TiO}_{2})–(hbox {H}_{2})O, that have heat transfer properties, are analysed in depth. We identified that for the cylindrical battery pack, (hbox {Fe}_{3}hbox {O}_{4})–(hbox {H}_{2})O nanofluid is one of the excellent coolants. Further, there is a 73.2652% increase in rate of heat transfer in (hbox {Fe}_{3}hbox {O}_{4})–(hbox {H}_{2})O NFs, 68.441% increase in (hbox {Fe}_{3}hbox {O}_{4}+hbox {Zn}!!-!!hbox {H}_{2})O hybrid nanofluids (HNFs) and 64.9944% increase in (hbox {Fe}_{3}hbox {O}_{4}+hbox {Zn}+hbox {TiO}_{2}!!-!!hbox {H}_{2})O ternary hybrid nanofluids (THNFs).