Prawal Sinha

A model for fishery resource with reserve area

In this paper, we propose and analyse a mathematical model to study the dynamics of a fishery resource system in an aquatic environment that consists of two zones: a free fishing zone and a reserve zone where fishing is strictly prohibited. Biological and bionomic equilibria of the system are obtained, and criteria for local stability, instability and global stability of the system are derived. It is shown that even if fishery is exploited continuously in the unreserved zone, fish populations can be maintained at an appropriate equilibrium level in the habitat. An optimal harvesting policy is also discussed using the Pantryagins Maximum Principle.

The three-dimensional Reynolds equation for micro-polar-fluid-lubricated bearings

Abstract The three-dimensional Reynolds equation for micropolar fluids is derived. The balance equations for micropolar fluids are simplified by using traditional lubrication assumptions and order-of-magnitude analysis. The simplified equations are solved to yield expressions for the velocity distribution and the microrotation velocities. A generalized Reynolds equation is subsequently derived in the conventional manner.

Couple stresses in the lubrication of rolling contact bearings considering cavitation

Abstract The effects of couple stresses on the lubrication of rolling contact bearings, including the effects on cavitation, were studied by defining a parameter l which has dimensions of length. It was found that, the larger the chain length of the lubricant or additive molecule, the greater are the effects due to couple stresses. The presence of couple stresses produces an increase in the load capacity. However, cavitation is accelerated.

EXISTENCE AND SURVIVAL OF TWO COMPETING SPECIES IN A POLLUTED ENVIRONMENT: A MATHEMATICAL MODEL

In this paper, a nonlinear mathematical model to study the effect of a toxicant emitted into the environment from external sources on two competing biological species is proposed and analyzed. The cases of constant emission and instantaneous spill of a toxicant are considered in the model study. In the case of constant emission, it is shown that four usual outcomes of competition between two species may be altered under appropriate conditions which are mainly dependent on emission rate of toxicant into the environment, uptake concentrations of toxicant by the two species and their growth rate coefficients and carrying capacities. However, in the case of instantaneous spill, it is found that if the washout rate of toxicant is large, then the four outcomes of competition exist under usual conditions. It is also pointed out that the survival of the competitors, coexisting in absence of the toxicant, may be threatened if the constant emission of toxicant into their environment continues unabatedly.

A RESOURCE DEPENDENT FISHERY MODEL WITH OPTIMAL HARVESTING POLICY

A dynamic model for a single-species fishery, which depends partially on a logistically growing resource with functional response, is proposed using taxation as control instrument to protect fish population from overexploitation. The analysis of the model shows that both the equilibrium density of fish population as well as the maximum sustainable yield increase as resource biomass density increases. The optimal harvesting policy is also discussed with the help of Pontryagins Maximum Principle. It is found that for the optimum equilibrium value of resource biomass density, the total users cost of harvest per unit effort must be equal to the discounted value of future price at the steady state.

Modelling the spread of carrier-dependent infectious diseases with environmental effect

Many infectious diseases spread by carriers such as flies, ticks, mites, snails, etc. In this paper an SIS model for carrier-dependent infectious diseases, like cholera, diarrhea, etc. caused by direct contact of susceptibles with infectives as well as by carriers is proposed and analyzed assuming the growth of both the human and the carrier populations logistic. It is assumed further that the density of carrier population increases with the increase in the cumulative density of discharges by the human population into the environment. The mathematical model is analyzed for the following two cases: (i) the rate of cumulative environmental discharges Q is a constant, and (ii) the rate of cumulative environmental discharges Q is a function of the population density. This model is analyzed using usual theory of differential equations and computer simulation. By computer simulation it is concluded that if the growth of carrier population caused by conducive household discharges increases, the spread of the infectious disease increases.

Effects of couple stresses on the blood flow through an artery with mild stenosis

An analysis of the effects of couple stresses on the blood flow through thin artery in the presence of very mild stenosis has been carried out with the help of two nondimensional parameters, alpha (the length ratio parameter) and eta (the parameter characterizing the antisymmetric property of the couple stress tensor). It is shown that an increase in the couple stress (small value of alpha and eta), increases the resistance to the flow and the wall shear stress. These characteristics are further enhanced by the presence of the stenosis.

Effect of viscosity variation due to lubricant additives in journal bearings

Abstract Micropolar fluid theory, which is a possible non-newtonian model of a suspension of rigid particle additives, is applied to the study of the lubrication of an infinitely long and an infinitesimally short journal bearing. The variation in viscosity along the film thickness is taken into consideration. The prominent feature of the presence of solid particles in the lubricant is an increased effective viscosity which increases the load capacity and decreases the coefficient of friction. Whereas viscosity variation tends to decrease both the load and the coefficient of friction for the non-micropolar case, the combined effect is to increase the load and to decrease the coefficient of friction.

Ferrofluid lubrication of cylindrical rollers with cavitation

SummaryThis paper analyses the ferrofluid lubrication of cylindrical rollers under combined rolling and normal motion. The analysis, which takes into account the rotation of magnetic particles, has been made for general cases where the magnetization vectors need not be parallel to the applied magnetic field. Cavitation boundary conditions are used and the applied magnetic field is assumed to be imposed in a direction transverse to the fluid motion. A perturbation scheme in terms of non-dimensional Brownian time relaxation parameter has been used and the effects of various parameters on bearing characteristics have been studied.

Non-newtonian power law fluid lubrication of lightly loaded cylinders with normal and rolling motion

Abstract The lubrication of lightly loaded cylinders with rotating and normal motion was investigated using a non-newtonian power law fluid under cavitation boundary conditions. The load capacity and frictional drag increase as the squeeze velocity increases. This increase is enhanced by an increase in the flow behaviour index of the lubricant. However, when the two surfaces move apart these results are reversed. The effect of the flow behaviour index on the location of the point of cavitation does not seem to be very significant.