Pramana最新文献

We apply the technique of renormalisation group (RG) to investigate periodic solutions of the modified Rayleigh–Liénard oscillator, both in presence of usual integer order damping and fractional order damping. In the latter case, a parametric driven periodic external force is also taken into account. The existence of limit cycle solutions is evident in both scenarios.

The performance of heat transportation fluids in thermal engineering applications enforces us to investigate the combined impacts of magnetisation and radiating heat considering a hybrid nanofluid flow. The transport phenomena of the proposed hybrid nanofluid through a curved surface in a porous medium are analysed by considering ferrite nanoparticles. The surface is preamble and expanding/contracting exponentially. Additionally, it is not wise to neglect the role of Joule dissipation since properties of magnetisation are involved in the proposed phenomena. To analyse the system, a suitable similarity rule is employed to change the governing equation into an ordinary equation. The resulting set of equations is then numerically solved by implementing the “Runge–Kutta” method associated with the “shooting technique”. The quantitative numerical values coincide with prior published work showing validation of the current result vis-à-vis the convergence criteria. However, the findings of the result reveal that the magnetisation and thermal radiation significantly improve the fluid flow and enhance the rate coefficients. Due to the impressive utility of the heat transport phenomenon in manufacturing various electronic devices, cooling of microchips, drug delivery processes, etc. the role of nanoparticles presents its vital role.

The space–time fractional Kraenkel–Manna–Merle system (FKMMS) is a mathematical physics system that is particularly established to outline the transmission of nonlinear short waves in ferromagnetic materials considering the impact of a zero conductivity external field. Motivated by this application, the current investigation seeks to thoroughly examine the space–time FKMMS with conformable fractional derivatives. Generalised EDAM (gEDAM), an improved variant of the modified extended direct algebraic method (EDAM), is utilised to efficiently find a collection of analytical travelling wave solutions in the form of rational, hyperbolic, exponential and trigonometric functions. Through a careful selection of particular values for the parameters associated with the arbitrary functions contained in the obtained solutions, the inferred solutions yield various new forms for travelling waves and other soliton-type structures. Within the scope of FKMMS, our analytical investigation identified many kink solitons, including kink, anti-kink, bell-shaped dark and brilliant kink. An analysis is conducted on the effects of several factors associated with the obtained solutions, including the space- and time-fractional parameters on the shock and solitary wave profiles. This work may provide critical new understandings for researchers, engineers and physicists working with ferromagnetic materials. Regarding the real-world occurrences seen throughout their experimental research, it can offer helpful insights.

SnTe, the lead-free and environmentally friendly material, has gained recognition as a low band-gap thermoelectric material. However, it encounters challenges due to the presence of a significant concentration of intrinsic tin vacancies and its extremely small band gap of 0.18 eV. These factors contribute to a low Seebeck coefficient (S) and high electronic thermal conductivity. These challenges can be overcome by tuning the band gap of SnTe which enhance its thermoelectric behaviour. In our study, we investigate the thermoelectric properties of the bulk SnTe by systematically increasing the band gap while keeping the carrier concentration fixed. By varying the band gap from 0.14 to 0.8 eV, we observe significant enhancements in the thermoelectric performance of the material. Specifically, the power factor reaches a value of 420 (upmu )W cm(^{-1}) K(^{-2}) and the electronic thermal conductivity decreases to 2.3 W m(^{-1}) K(^{-1}) when the band gap is 0.8 eV and the carrier concentration is (10^{18}) cm(^{-3}). Moreover, the figure of merit (ZT) value of SnTe can be improved up to 15 times. This study can motivate further experimental investigation on interesting compounds.

The spin-dependent hole transport in the CdTe(/)CdMnTe heterostructure with double barriers and double δ-potentials is studied. Since the considered heterostructure is symmetric and no external field is applied, only the Dresselhaus spin–orbit interaction is included in the study. The transfer matrix method is used to analyse the spin-dependent transmission of holes. The double δ-potential height and the distance between them influence the transmission coefficient, polarisation efficiency and tunnelling time of the light holes (LH) and heavy holes (HH). The contrast in the response of LH and HH in terms of energy at which resonance occurs and polarisation efficiency are reported.

Periodically kicked Floquet systems, such as the kicked rotor, are a paradigmatic and illustrative simple model of chaos. For non-integrable quantum dynamics, there are several diagnostic measures, such as Loschmidt echo, autocorrelation function and out of time order correlator (OTOC) to study the presence of (or the transition to) chaotic behaviour. We analytically compute these measures in terms of the eigensystem of the unitary Floquet operator of the driven quantum systems. We use these expressions to determine the time variation of the measures for the quantum-kicked rotor (QKR) on the torus, for the integrable as well as the chaotic case. For a simpler integrable variant of the kicked rotor, we also give a representation theoretic derivation of its dynamics.

Positron emission tomography (PET) scans are vital in diagnosing cancer and neurological disorders but raise concerns due to exposure to ionising radiation. This research is focussed on the development of an intelligent regression model to investigate the effective radiation dose received by a patient during the whole-body PET scan. Our newly developed intelligent model refers to the application of artificial intelligence (AI) and machine learning (ML) techniques. Since underfitting and overfitting are basic issues of any ML model, data fitting methodology for developing intelligent regression is taken care of by implementing the least absolute shrinkage and selection operator (Lasso) and ridge regression. In order to have the comparative performance of our model, we have also applied support vector and decision tree-based ML techniques as regressors to predict radiation doses in whole-body PET scans, keeping patient safety in mind. By incorporating patient-specific data and imaging parameters, these models aim to accurately estimate radiation doses, thereby optimising imaging protocols and reducing unnecessary exposure risks. The study uses PET({/})CT data from 2009 to 2012. The linearly-independent covariates applied in this model are age, weight, height, residence time and injected activity and the dependence variable is taken as the effective dose. Model performance is evaluated using root mean square error (RMSE). A systematic exploratory data analysis has been carried out to investigate data cleaning, missing information, scaling and normalisation. The top five organs such as the brain, stomach, kidney, adrenal and spleen are focussed to produce the traditional descriptive statistics of data summary. Least absolute shrinkage and selection operator (lasso) regression exhibit stable RMSE values for organ equivalent doses across genders, while substantial RMSE variations exist among different models and organs, suggesting sensitivity to specific organs and patient gender. Accurate dose estimation is pivotal for risk assessment and protocol optimisation. This study evidenced the need to improve radiation dosimetry for specific organs aiming at patient care and radiology practices by considering individualised factors in dose estimation methodologies to refine PET scan dose estimation methods.

This article uses a finite-element approximation approach for solving a three-dimensional flow problem of a nanofluid influenced by heat transfer due to nanoparticles over a non-linearly stretching sheet within an unbounded domain. Utilising similarity transformations, a well-posed coupled system of nonlinear ordinary differential equations is derived from the governing partial differential equations describing the flow and heat transfer processes. The resulting system is then solved by using quadratic Lagrange polynomials as basic functions over a mesh of different finite elements through the Galerkin finite element (GFE) technique. This implementation is based on a regular grid utilising Lagrange polynomials for solving the converted equations. The effects of various parameters of interest are efficiently discussed with the help of graphs and numeric tables. Both numerical and exact solutions are compared favourably, demonstrating a high level of accuracy. It is noteworthy that the GFE method emerges as a much more stable numerical technique than the other existing analytic and semi-analytical methods. Furthermore, the adopted finite-element method reduces the dimensionality of Sobolev's space's finite-dimensional subspace and also improves the solution's convergence rate. Moreover, the velocity is negative, and its magnitude increases as the stretching rates ratio increases due to the downward flow in the vertical direction. The temperature and heat transmission from the sheet are barely impacted by Brownian motion due to the dominance of other forces and length scales involved in the heat transfer process.

A new generalised non-local nonlinear Schrödinger (NLS) equation is introduced which possesses a Lax pair and is parity–time (PT)-symmetric. Thus, it is confirmed that the generalised non-local NLS equation is integrable. The inverse scattering transform for the generalised non-local NLS equation is developed using a Riemann–Hilbert problem for rapidly decaying initial data and an approach for finding pure soliton solutions is described. The analytical characteristics of the eigenfunctions, scattering data and their symmetries are discussed. Finally, using Mathematica some important two-dimensional plots of the wave solutions are shown to illustrate the dynamics of the model.

In this study, we employ molecular dynamics simulations to develop a large model (19,998 atoms) of liquid SiO₂ at 3500 K. We construct models at different pressures in the 0–100 GPa range using the Beest–Kramer–Santen (BKS) potential and periodic boundary conditions. The goal is to detail the structural transition from the polyamorphic liquid state of SiO₂ to the crystalline stishovite form, which occurs between 45 and 60 GPa. We analyse the polyamorphic state of liquid SiO₂ by examining the formation of SiO_x clusters from 2 to 60 GPa. Beyond 60 GPa, the pair radial distribution functions (PRDFs) for Si–O, O–O and Si–Si display multiple peaks, indicating the crystalline phase. This observation is further supported by examining the bond angle distribution, the fraction of SiO_x units and OSi_x linkages, Si–O bond lengths within SiO_x units, structural visualisations and the analysis of ring statistics in the liquid SiO₂ system, all of which underscore the comprehensive changes in the structure of the system.