Stability and bifurcation analysis of a delayed innovation diffusion model

In this article, a nonlinear mathematical model for innovation diffusion with stage structure which incorporates the evaluation stage(time delay) is proposed. The model is analyzed by considering the effects of external as well as internal influences and other demographic processes such as emigration, intrinsic growth rate, death rate, etc. The asymptotical stability of the various equilibria is investigated. By analyzing the exponential characteristic equation with delay-dependent coefficients obtained through the variational matrix, it is found that Hopf bifurcation occurs when the evaluation period(time delay, τ) passes through a critical value. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included.     

Optimal treatment of stratified Carreau and Casson nanofluids flows in Darcy-Forchheimer porous space over porous matrix

A comparative three-dimensional (3D) analysis for Casson-nanofluid and Carreau-nanofluid flows due to a flat body in a magnetohydrodynamic (MHD) stratified environment is presented. Flow is estimated to be suspended in a Darcy-Forchheimer medium. Soret and Dufour responses are also accommodated in the flow field. A moving (rotating) coordinate system is exercised to examine the bidirectionally stretched flow fields (flow, heat transfer, and mass transfer). Nanofluid is compounded by taking ethylene glycol/sodium alginate as base fluid and ferric-oxide (Fe₃O₄) as nanoparticles. Governing equations are handled by the application of optimal homotopy asymptotic method (OHAM), where convergence parameters are optimized through the classical least square procedure. The novel mechanism (hidden physics) due to appearing parameters is explored with the assistance of tabular and graphical expositions. Outcomes reveal the double behavior state for temperature field with thermal stratification/Dufour number, and for concentration field with Soret number due to the presence of turning points.     

Multipliers on Vector-valued L~1-spaces for Hypergroups

In this article, we extend the well known Wendel's theorem to the context of vector-valued L~1-spaces on hypergroups. In this regard, various cases have been studied.     

Impact of density-dependent symmetry energy and Coulomb interactions on the evolution of intermediate mass fragments

Within the framework of isospin-dependent quantum molecular dynamics (IQMD) model, we demonstrate the evolution of intermediate mass fragments in heavy-ion collisions. In this paper, we study the time evolution, impact parameter, and excitation energy dependence of IMF production for the different forms of density-dependent symmetry energy. The IMF production and charge distribution show a minor but considerable sensitivity towards various forms of density-dependent symmetry energy. The Coulomb interactions affect the IMF production significantly at peripheral collisions. The IMF production increases with the stiffness of symmetry energy.     

Energy of vanishing flow in heavy-ion collisions: Role of mass asymmetry of a reaction

We aim to understand the role of Coulomb interactions as well as different equations of state on the disappearance of transverse flow for various asymmetric reactions leading to the same total mass. For the present study, the total mass of the system is kept constant (A _TOT = 152) and mass asymmetry of the reaction is varied between 0.2 and 0.7. The Coulomb interactions as well as different equations of state are found to affect the balance energy significantly for larger asymmetric reactions.     

A new approach to model CW CO<Subscript>2</Subscript> laser using rate equations

Two popular methods to analyse the operation of CW CO ₂ lasers use the temperature model and the rate equation model. Among the two, the latter model directly calculates the population densities in the various vibrational levels connected with the lasing action, and provides a clearer illustration of the processes involved. Rate equation models used earlier grouped a number of vibration levels together, on the basis of normal modes of vibrations of CO ₂. However, such grouping has an inherent disadvantage as it requires that these levels be in thermal equilibrium. Here we report a new approach for modelling CW CO ₂ lasers wherein the relevant vibration levels are identified and independently treated. They are connected with each other through the processes of excitation, relaxation and radiative transitions. We use the universally accepted rate coefficients to describe these processes. The other distinguishing feature of our model is the methodology adopted for carrying out the calculations. For instance, the CW case being a steady state, all the rate equations are thus equated to zero. In the prior works, researchers derived analytical expressions for the vibration level population densities, that becomes quite a tedious task with increasing number of levels. Grouping of the vibration levels helped in restricting the number of equations and this facilitated the derivation of these analytical expressions. We show that in steady state, these rate equations form a set of linear algebric equations. Instead of deriving analytical expressions, these can be elegantly solved using the matrix method. The population inversion calculated in this manner along with the relaxation rate of the upper laser level determines the output power of the laser. We have applied the model to an experimental CW laser reported in literature. Our resutls match the experimentally reported power.     

Solutions to the N-dimensional radial Schrödinger equation for the potential ar 2 + br − c/r

Optical fibre probes or optrodes often form the heart of multimode fibre-based measurements and sensors. An optrode usually comprises a bundle of multimode fibres, out of which one or more fibres are used for irradiating the sample, and the remaining fibres are used to collect the light reflected/scattered/fluoresced from the sample containing the measurand(s). The so-collected light carries the characteristic signature of the measurand. Here we present our work on the design and realization of optrodes for the measurement of scattered light from liquid samples. Optical properties of a solution are usually characterized by the parameters absorption coefficient μ _a , scattering coefficient μ _s , and anisotropy factor g. We have developed a simple method to determine μ _a , μ _s , and g, of a turbid medium, and a Monte–Carlo model was used to simulate the light scattering from the turbid medium. As an application, we describe the development of a turbidity sensor that has been designed and realized by employing an optrode in conjunction with a concave mirror. The estimation of turbidity is done on the basis of total interaction, by considering scattering and absorption of light from the sample solution. Details of the experiments and results are presented here.     

HF-based clad etching of fibre Bragg grating and its utilization in concentration sensing of laser dye in dye–ethanol solution

This paper presents a fibre Bragg grating (FBG) based sensor to study the concentration of laser dye in dye–ethanol solution. The FBG used in this experiment is indigenously developed using 255 nm UV radiations from copper vapour laser. The cladding of the FBG was partially removed using HF-based etching to make FBG sensitive to changes in the surrounding refractive index. The experimental results on the shift of the Bragg peak wavelength with HF etching and different dye concentration in ethanol are presented. The Bragg wavelength shifted from 1534.670 nm to 1534.225 nm in 30 min and from this point to 1533.97 in the next 2 min. The clad-etched Bragg peak shifted almost linearly from 1534.056 nm to 1534.162 nm as surrounding dye concentration in ethanol changes from 0 mM to 1.5 mM. It was observed that sensitivity depends on the concentration of the solution and found to be 70 pm/mM.