Pramana最新文献

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.

This study examines the bioconvective transport of magnetohydrodynamic (MHD) silver (Ag)/titanium dioxide ((hbox {TiO}_2)) hybrid nanofluid including oxytactic micro-organisms over a stretching sheet, using heat radiation in a Darcy–Brinkman–Forchheimer (DBF) porous medium to forecast fluid dynamics. Through the use of a suitable similarity transformation, the governing partial differential equations (PDEs) are transformed into coupled nonlinear ordinary differential equations (ODEs). The resultant ODEs are numerically solved by transforming the boundary value problem into a simplified initial value problem using BVP4C and the shooting method, with specified parameters. The Forchheimer number and porosity parameter adversely affect the velocity field. Skin friction is reduced by 84%. 711% for thermal slip parameter (B_2) and 97.531% for magnetic parameter M addition of 1% Ag( +) (hbox {TiO}_2). The Sherwood number of oxygen concentration is considerably influenced by the nanofluid volume fraction (phi _1 (mathrm Ag/water)) and the hybrid nanofluid volume fraction (phi _2 (mathrm Ag+TiO_2/water)). The bioconvection Peclet number significantly influences the Sherwood number of micro-organisms.

This exploration aims to extract some new exact solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation (BKPE) that plays a significant role in fluid dynamics. Based on the N-soliton solutions extracted by the Hirota bilinear method, the Y-shape and X-shape soliton solutions and the breather wave solutions are derived by assigning resonant conditions and conjugate conditions, respectively. Furthermore, three powerful tools, namely the Bernoulli sub-equation function method, Wang’s direct mapping method-II and Kudryashov method, are employed to explore the diverse travelling wave solutions, which includes the kink solitary wave, anti-kink solitary wave, periodic wave and singular wave solutions. The wave structures of the attained solutions are displayed as diagrams using Maple. As we all know, the outcomes presented in the study are all brand new and have not been reported in other work, which can enable us to better understand the dynamic behaviours of the considered equation.

Choosing a specific direction for the propagation of laser field waves often presents a challenge for researchers studying laser-assisted ultrafast quantum processes. They are faced with the question of why exactly a particular direction and not another. This paper resolves the discussion in this issue regarding decay processes. Therefore, we study theoretically the pion decay process in the presence of a circularly polarized laser field propagating along an arbitrary general direction. Using the first Born approximation and the Dirac-Volkov states for charged particles, we derive an analytic expression for the decay rate. Our results show that, when the pion is at rest, the direction of the laser field has no significant effect on the decay rate, justifying the common practice of choosing a convenient direction in previous studies. However, when the pion is in motion, the decay rate is affected by the laser wave vector’s orientation relative to the pion’s momentum. The effect is more pronounced when the wave vector is collinear with the pion’s motion than when it is perpendicular. This study generalizes previous results found for a field with a wave vector along the z-axis in [Phys. Rev. D 102, 073006 (2020)] and provides a theoretical foundation for future investigations into laser-assisted decay processes involving moving particles. The influence of the laser field on the total decay rate has also been analyzed and discussed.

In the cone–disk system, the apex of the cone is in contact with the disk, making a conical region, in which the fluid flow is analysed. This type of flow problem has a variety of biomedical application including DNA sequencing, biochemical detection, cell analysis, conical diffusers, viscosimeters, etc. The effect of Hall current and radiation on the flow of blood containing gold nanoparticles is theoretically analysed in a cone–disk system for a single-phase nanofluid model. Four configurations of the cone–disk system, including stationary disk and rotating cone, stationary cone and rotating disk, co-rotation of disk and cone and counter-rotation of disk and cone, are studied for the gap angle (frac{pi }{4}). The non-linear partial differential equations describing three-dimensional axisymmetric flow in a cone–disk system are converted into nonlinear ordinary differential equations using the one-parameter Lie group approach. The self-similar model is then solved numerically using the bvp5c package of MATLAB and shown graphically to analyse the influence of various parameters involved in the study for all four configurations of the cone–disk system. It is observed that rotation of the disk/cone gives rise to high centrifugal forces resulting in an outward radial flow. Further, it is noted that Hall current enhances the velocity and radiation parameter reduces the temperature.