Pramana最新文献

This work investigates the newly proposed integrable (3+1)-dimensional (3D) extended Kairat-X equation. By incorporating Hirota’s bilinear form, various lump and interaction solutions such as periodic-lump interaction, 1-stripe, periodic and lump interaction, 1-stripe-lump interaction, etc. are obtained. Along with these lump interaction solutions, various other types such as wave-type solutions, kink-cross rational solutions and solitary wave solutions are also investigated. Additionally, the innovative soliton-type solutions are provided by the extended transformed rational function technique, which uses the Hirota bilinear representation of the governing model. To highlight the physical features of these solutions, 3D and density plots are generated with the aid of interactive software which gave us a better understanding of the results. These solutions provide a comprehensive study of the dynamical behaviour of novel nonlinear Kairat-X equation.

An experiment was conducted recently at the RIKEN Nishina Center to determine the (beta )-decay half-lives and (beta )-delayed neutron emission probabilities of neutron-rich Pm, Sm, Eu and Gd nuclei. In this study, we calculate the (beta )-decay properties of the aforementioned neutron-rich isotopes and other nuclei. All nuclei considered in this investigation have mass number (A > 155). Compared with the previous calculations, the current results are in better agreement with the measured data. Our model calculations successfully reproduced 100% (71%) of the measured half-lives within a factor of 10 (2). Furthermore, the calculated neutron emission probabilities show good agreement with the measured data. Specifically, our model calculations reproduced 75% of the measured values within a factor of 10. We present the first-ever microscopic calculation of stellar rates for these heavy and neutron-rich exotic nuclei. The stellar rates were found to be significant beyond core densities ((10^{7}) g cm(^{-3})) or at high core temperatures ((sim !! 30) GK) prevailing in the stellar core. The reported weak rates may prove useful for the r-process nucleosynthesis calculations.

In this work, a numerical simulation of the two-stream instability (TSI) in electrostatic plasmas is presented using the particle-in-cell (PIC) method. The TSI is a fundamental phenomenon in plasma physics, where two streams of charged particles with different velocities interact, generating electrostatic waves. These waves can give rise to non-linear structures, such as solitary waves, which are of great interest in applications ranging from nuclear fusion to astrophysics. Different perturbation amplitudes ((A=0.0), 0.1 and 0.5) were explored to analyse how they affect the formation and propagation of electrostatic waves. The results show that in the absence of external perturbations ((A=0.0)) the dynamic interaction between the particle flows generates Langmuir waves, which propagate without significant dissipation. With moderate perturbation ((A=0.1)), the formation of vortices in phase space is observed, which eventually merge to give rise to electrostatic solitary waves (ESW). For larger perturbation amplitudes ((A=0.5)), the system enters a non-linear regime, where interactions between particles and fields give rise to non-dispersive solitary waves, such as Bernstein–Greene–Kruskal (BGK) waves. The PIC method has proven to be an effective tool for capturing both linear and non-linear effects of the TSI. These findings not only contribute to a better understanding of plasma dynamics, but also highlight the importance of the PIC method for studying non-linear phenomena in complex systems.

In this study, we examine a system of coupled particles governed by two distinct types of interacting forces: the harmonic force and the Morse force. The dimer is modelled to move within a double-well potential while being subjected to power-limited (PL) coloured noise. This type of noise has a constant variance property and a constant power spectrum. The escape rate of the dimer demonstrates a non-monotonic dependence with respect to the variations of correlation time, (tau ), of the power-limited noise, suggesting the occurrence of the resonant activation phenomenon. The characteristic time-scale of the power-limited coloured noise together with the coupling constant, (kappa ) of the dimer influence the hopping mechanism of the dimer, which plays an important role in the transport phenomenon. Thus, the overall escape rate of the dimer is attributed to the combined competitive effects of the coupling constant of the dimer, the intensity, D and the correlation time, (tau ) of the power-limited noise.

Divergent solutions are ubiquitous with perturbation methods. We utilise continued functions, such as the continued exponential, to converge divergent series in perturbation approaches for energy eigenvalues of helium, the Stark effect and the Zeeman effect on hydrogen. We observe that convergence properties are obtained similar to those of the Padé approximation, which is extensively used in literature. Free parameters are not used, which influence the convergence, and only the first few terms in the perturbation series are implemented.

Nonlinear stochastic conformable equations are crucial for understanding complex real-world phenomena across various scientific fields, including plasma physics, wave propagation and conceptual modelling. In this study, we introduce and analytically investigate the stochastic space–time conformable phi-four (STCPF) equation for the first time. This equation is particularly significant in particle and plasma physics, where nonlinear wave interactions and stochastic effects are prevalent. To solve the stochastic STCPF equation, we propose a novel conformable sinh-Gordon method (CSGM) and compare its effectiveness with the modified tanh-function method (MTFM). Through these approaches, we derive stochastic soliton solutions and analyse their dynamic behaviour. Additionally, we explore the influence of time-dependent stochastic parameters on soliton structures by illustrating the solutions through 3D and contour plots. The findings reveal that temporal variations in the stochastic parameter significantly impact soliton height and shape, leading to multiple solitons.

This paper explores the complex dynamics of time-dependent, two-dimensional flow of an incompressible fractional Nadeem trigonometric non-Newtonian (NTNN) fluid experiencing cosine oscillations in a rectangular duct caused by an external magnetic field. The primary goal is to find practical analytical solutions for the fluid flow described by a time-fractional derivative-based initial-boundary value problem. A method employing both Laplace and double Fourier sine transforms is used to simplify the governing equations. A detailed parametric analysis is performed to examine how the fractional order α, rheological parameter N, oscillation frequency ω, time t and magnetic field strength M affect the velocity profile and shear stress of the fluid. The results indicate that increasing values of α, N, ω and t lead to higher fluid flow, while stronger magnetic fields produce a damping effect. In certain limiting cases, the model reduces to the conventional NTNN and classical Newtonian fluid flows, thereby confirming the versatility and robustness of the analytical solution.

This paper analyses the analytical approximation solution for linear and nonlinear systems of fractional differential equations (FDEs) using shifted Legendre polynomials. We show how to solve nonlinear fractional problems by applying the operational matrix technique with the Caputo derivative. The Legendre operational matrix, derived using orthogonality properties, is implemented in dynamical fractional problems. By transforming the FDEs into a system of nonlinear algebraic equations, and applying Newton’s iterative scheme with an initial guess, we obtain polynomial coefficients that yield the approximate solution. We provide convergence analysis and an illustrative example to validate the proposed method. Furthermore, we analyse the nonlinear fractional SIS epidemic model and nonlinear coupled systems using the spectral collocation method. Numerical simulations and graphical results demonstrate the efficacy of the spectral collocation and Euler methods for solving real-world problems involving fractional-order differential equations.

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.