R. P. Jaju

Switching Model with Two Habitats and a Predator Involving Group Defence

Switching model with one predator and two prey species is considered. The prey species have the ability of group defence. Therefore, the predator will be attracted towards that habitat where prey are less in number. The stability analysis is carried out for two equilibrium values. The theoretical results are compared with the numerical results for a set of values. The Hopf bifuracation analysis is done to support the stability results.

Stability of a Switching Model with Two Habitats and a Predator

A system of differential equations of dispersion between two populations in habitats separated by a barrier with a predator feeding intensively on the more abundant habitats population has been considered. A comprehensive study has been made when predator feeds prey indiscriminately and when it feeds preferentially on the most numerous prey species. Equilibrium and stability analysis have been carried out for both the models.

Hopf Bifurcation Analysis of a Predator Prey System Involving Switching

This paper complements the analysis of Khan, Bhatt and Jaju [1994]. They have studied non-switching and switching models with one predator and two prey species. In the former model predator feeds prey species indiscriminately while in the second model predator switches from a rare species towards the most abundant one. Using conversion rates of prey to predators as the bifurcation parameter it has been shown that Hopf bifurcation can occur in both models.

Energetics of undercooled liquid metals

Abstract The role of basic interactions (i.e. electrondashelectron, iondashion and electrondashion) on the energetics of undercooled ( T ⪡ T m ) liquid metallic system has been investigated within the firsts-principle approach to pseudopotential perturbation theory and the Gibbs-Bogoliaubov variational method. Its application is made to Na and T -dependence of internal energies, interatomic pair potentials, entropies and heat capacities are obtained in the region T ⪡ T m . Various entropic contributions in the undercooled region decrease much faster than the enthalpic terms. Heat capacities calculated both from entropy and enthalpy terms increase with decreasing T in the undercooled region, and exhibit anomalous behaviour at a temperature which is interpreted as glass transition temperature.

Effective pair potential, structure and heat capacity of undercooled liquid rubidium

Abstract The electronic theory of metallic system is used to investigate the effect of the local-field correction function for electrons screening and of the electron–ion pseudopotentials on the effective pair potential, structure and heat capacity (CPl) of undercooled liquid Rb. CPl is found to increase with decreasing T in the region T T=185 K which is about 59% lower than Tm.

A new computerizable quadrature formula using probabilistic approach

A new quadrature formula has been proposed which uses weight functions derived from a new probabilistic approach. Unlike the complicatedly structured quadrature formulae of Gauss, Hermite and others of similar type, the proposed quadrature formula only needs the values of integrand at user-defined equidistant points in the interval of integration and weight functions are not constants. The quadrature formula has been compared empirically with two other simple fundamental methods of integration. The percentage relative gain in efficiency of the quadrature formula with respect to fundamental methods of integration has been computed for certain selected functions and with different number of node points in the interval of integration. It has been observed that the proposed quadrature formula produces significantly better results than the other simple fundamental methods of integration.

Comparative Study of Two Prey-Predator Switching Models

We present in this paper two switching models with habitat heterogeneity of biologically interesting predator-prey relationship. The prey is more prone to predator at higher densities and vice versa. It has been found that for abundance model, increasing the difference between the feeding rates of the habitats, increases the region of stability, while in the group defence model the region of stability decreases.

On the stagnation point flow of a special class of non-Newtonian fluids

Abstract The two-dimensional boundary layer equations for a class of non-Newtonian fluids, for which the apparent viscosity can be expressed as a polynomial in the second scalar invariant of the rate of strain tensor, have been derived. These equations have been employed to analyse the flow near a stagnation point over a stationary impermeable wall. The non-Newtonian effects on the boundary layer velocity profile and the wall skin friction have been studied, and compared with the corresponding Newtonian fluid. The fluid velocity in the boundary layer has been shown to be retarded by the non-Newtonian effect while the skin friction increases proportionate to it.

Switching Effect of Predation on Prey Species Living in Different Habitats with Arbitrary Predatory Rates II

The present paper extends previous work by Bhatt et al. [J. Phys. Soc. Jpn. 69 (2000) 3133] referred as Part I. It deals with the switching effect of predation on prey species living in two habitats when the predatory rates are arbitrary. The predator feeds preferentially on the more abundant habitats population. Two habitats have been separated by a barrier so that the prey species is able to disperse among them at some cost of the population. The stability analysis has been carried out for non-zero equilibrium values. Using the conversion rate of the prey to predator as a bifurcation parameter, necessary and sufficient conditions for a Hopf bifurcation to occur have been derived. Two particular cases of predatory rates, namely, (i) multiplicative case and (ii) exponential case have been derived.

Undercooled state of liquid rubidium

Abstract A first principle theoretical scheme which is based on pseudopotential perturbation theory, the thermodynamics of hard sphere systems and the variational method based on Gibbs-Bogoliaubov inequality is used to investigate the specific heat of liquid Rb in the undercooled region (T < Tm ). Cl p is found to increase with decreasing T and exhibits a maxima in the vicinity of 60 K. The anomalies in Cl p in the undercooled region are discussed in terms of structure and volume dependent contributions of energies and entropies.