Growth and Approximation of Generalized Bi-Axially Symmetric Potentials

The paper deals with growth estimates and approximation (not necessarily entire) of solutions of certain elliptic partial differential equations. These solutions are called generalized bi-axially symmetric potentials (GBASP's). To obtain more refined measure of growth, we have defined $q$-proximate order and obtained the characterization of generalized $q$-type and generalized lower $q$-type with respect to $q$-proximate order of a GBASP in terms of approximation errors and ratio of these errors in sup norm.     

DYNAMICAL BEHAVIOR OF AN INNOVATION DIFFUSION MODEL WITH INTRA-SPECIFIC COMPETITION BETWEEN COMPETING ADOPTERS

In this paper,we proposed an innovation diffusion model with three compartments to investigate the diffusion of an innovation（product） in a particular region.The model exhibits two equilibria,namely,the adopter-free and an interior equilibrium.The existence and local stability of the adopter-free and interior equilibria are explored in terms of the effective Basic Influence Number（BIN） R_A.It is investigated that the adopter free steady-state is stable if R_A <1.By conside...     

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.     

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.     

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.