ONE‐DIMENSIONAL TEMPORALLY DEPENDENT ADVECTION–DISPERSION EQUATION IN POROUS MEDIA: ANALYTICAL SOLUTION

Abstract Analytical solutions of one‐dimensional advection–dispersion equation in semi‐infinite longitudinal porous domain are obtained in this work. The solute dispersion parameter is considered temporally dependent along uniform flow. The first‐order decay term, which is inversely proportional to the dispersion coefficient, is also considered. Initially, the space domain is not solute free. Analytical solutions are obtained for uniform and varying pulse‐type input. A new time variable is introduced. The Laplace transform technique is used to get the analytical solutions.     

Optimization of process for the production of bio-oil from eucalyptus wood

The pyrolysis of eucalyptus wood was carried out in a batch reactor to optimize the yield of bio-oil.Effect of various parameters like feed(particle) size,temperature,presence of catalyst and heating rate on the yield of bio-oil was investigated.The optimum conditions for high yield of bio-oil are for the particle size 2 mm~5 mm(average l/d=12.84/2.03 mm) at 450 ℃ in high heating rate.The reaction kinetics and the quality of bio-oil produced are independent of the presence of different catalysts like mordenite,kaoline clay,fly ash and silica alumina.The physical properties like odour,colour,PH,viscosity,heating value were determined.The FT-IR analysis of bio-oil indicates the presence of different functional groups such as monomeric alcohol,phenol,ketones,aldehydes,carboxylic acid,amines,and nitro compounds.The composition of the bio-oil at different conditions was analyzed using GC-MS and found that the components are temperature dependent but independent of catalysts used.     

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.     

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.