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  • 1
    Monograph available for loan
    Monograph available for loan
    Mathematical modelling of environmental and ecological systems : excerpts form an international symposium on 'mathematical modelling of ecological, environmental and biological systems', held from august 27.-30., 1985 in kanpur, india (1987)
    Amsterdam [u.a.] : Elsevier
    Associated volumes
    Details Availability
    Call number: PIK M 370-92-0645
    In: Developments in environmental modelling
    Type of Medium: Monograph available for loan
    Pages: XXI, 254 S. : graph. Darst.
    ISBN: 0444428070
    Series Statement: Developments in environmental modelling
    Location: A 18 - must be ordered
    Branch Library: PIK Library
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  • 2
    Electronic Resource
    Electronic Resource
    Effects of peripheral layer viscosity on blood flow through the artery with mild stenosis (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 797-805 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The effects of peripheral layer viscosity on physiological characteristics of blood flow through the artery with mild stenosis have been studied. It has been shown that the resistance to flow and the wall shear decrease as the peripheral layer viscosity decreases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461059
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  • 3
    Electronic Resource
    Electronic Resource
    Effects of convective and dispersive interactions on the stability of two species (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 593-610 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The evolution and local stability of a system of two interacting species in a finite two-dimensional habitat is investigated by taking into account the effects of self- and cross-dispersion and convection of the species. In absence of cross-dispersion, an equilibrium state which is stable without dispersion is always stable with dispersion provided that the dispersion coefficients of the two species are equal. However, when the dispersion coefficients of the two species are different, the possibility of self-dispersive instability arises. It is also pointed out that the cross-dispersion of species may lead to stability or instability depending upon the nature and the magnitude of the cross-dispersive interactions in comparison to the self-dispersive interactions. The self-convective movement of species increases the stability of the equilibrium state and can stabilize an otherwise unstable equilibrium state. The effect of cross-convection (in absence of self-dispersion and self-convection) is to stabilize the equilibrium state in a prey-predator model with positive cross-dispersion coefficients for the prey species. Finally, it is shown that if the system is stable under homogeneous boundary conditions it remains so under non-homogeneous boundary conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462315
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  • 4
    Electronic Resource
    Electronic Resource
    Models for the effect of toxicant in single-species and predator-prey systems (1991)
    Springer
    Journal of mathematical biology 30 (1991), S. 15-30 
    Details
    ISSN: 1432-1416
    Keywords: Single-species ; Predator-prey ; Toxicants ; Equilibria ; Stability ; Periodic perturbation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Models of single-species and predator-prey systems in a polluted closed environment are developed and partially analyzed. Three cases are considered: a single influx of toxicant, a constant influx of toxicant, and a periodic pollution of the environment. In the case of single-species growth we are able to determine some local and global dynamics. In the case of predator-prey systems, we investigate the existence of steady states for a small constant influx of toxicant. On leave from Department of Mathematics, Indian Institute of Technology, Kanpur, India
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00168004
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  • 5
    Electronic Resource
    Electronic Resource
    Modelling the depletion and conservation of forestry resources: effects of population and pollution (1997)
    Springer
    Journal of mathematical biology 36 (1997), S. 71-94 
    Details
    ISSN: 1432-1416
    Keywords: Key words: Depletion ; Conservation ; Population ; Pollution ; Stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract.  In this paper, a mathematical model is proposed to study the depletion of resources in a forest habitat due to the increase of both population and pollution. It is shown that if the rate of pollutant emission into the environment is either population dependent, constant, or periodic, the equilibrium biomass density of the resource settles down to a lower equilibrium than its original carrying capacity, the magnitude of which decreases as the equilibrium levels of the density of population and the concentration of pollutant increase. However, in the case of an instantaneous spill of pollutant into the environment, the equilibrium biomass density decreases with the increase of the equilibrium density of population only. It is found that if the population density and the emission rate of pollutant increase without control, the forestry resource may become extinct. A conservation model is also proposed, the analysis of which shows that the resource biomass can be maintained at a desired level by conserving the forestry resource and by controlling the growth of population and the emission rate of pollutant in the habitat.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002850050091
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  • 6
    Electronic Resource
    Electronic Resource
    Multispecies food webs with diffusion (1982)
    Springer
    Journal of mathematical biology 13 (1982), S. 339-344 
    Details
    ISSN: 1432-1416
    Keywords: Food web ; Functional response ; Nonlinear stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Using Liapunov's direct method, in this paper, it has been shown that the general Lotka-Volterra food web is stable without and with diffusion under each case of homogeneous reservoir and flux boundary conditions. However, for a three species food web with Holling's functional response the above general result regarding stability is not necessarily true. In such a case, conditions and regions for non-linear stability, without and with diffusion, have been derived. It is shown that such an otherwise unstable system may become stable with diffusion at least in a subregion of the positive octant of the state space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276068
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  • 7
    Electronic Resource
    Electronic Resource
    Dispersion in non-Newtonian fluids: Effects of chemical reaction (1979)
    Springer
    Rheologica acta 18 (1979), S. 740-748 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Die Verteilung eines gelösten Stoffes in nicht-newtonschen Flüssigkeiten, die durch Kanäle und Rohre fließen, wird unter Zugrundelegung einer homogenen chemischen Reaktion erster Ordnung untersucht. Es wird gezeigt, daß bei gleicher mittlerer Strömungsgeschwindigkeit der äquivalente Verteilungskoeffizient abnimmt, wenn die Reaktionsgeschwindigkeit zunimmt. Diese Abnahme wird bei nicht-newtonschen Flüssigkeiten noch verstärkt.
    Notes: Summary The dispersion of a solute in non-Newtonian fluids flowing through channels and pipes has been studied by taking into account the homogeneous first-order chemical reaction. It is shown that for the same mean velocity of the flow the equivalent dispersion coefficient decreases as the rate of the chemical reaction increases. This decrease is enhanced due to non-Newtonian nature of the fluid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01533349
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  • 8
    Electronic Resource
    Electronic Resource
    Dispersion in a Bingham plastic fluid: Effects of peripheral layer (1982)
    Springer
    Rheologica acta 21 (1982), S. 713-719 
    Details
    ISSN: 1435-1528
    Keywords: Dispersion ; peripheral layer ; Bingham plastic fluid ; molecular diffusion coefficient ; tube flow ; channel flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract The dispersion of a soluble matter in a plastic fluid flowing through a tube and a channel has been analysed by taking into account the variations of viscosity, diffusivity and yield stress. It has been shown that in the special case of a Bingham fluid, surrounded by a peripheral layer of a Newtonian fluid, the effective dispersion coefficient with which the solute disperses across a plane moving with the mean speed of the flow decreases with the viscosity of the peripheral layer fluid but increases as the molecular diffusion coefficient of this layer decreases. Further, the effective dispersion coefficient also decreases as the yield stress of the Bingham fluid increases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01524515
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  • 9
    Electronic Resource
    Electronic Resource
    Magneto-hydrodynamically lubricated externally pressurised bearing with variable film thickness (1965)
    Springer
    Flow, turbulence and combustion 11 (1965), S. 453-460 
    Details
    ISSN: 1573-1987
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary This paper studies theoretically the use of a conducting lubricant in an externally pressurised bearing with variable film-thickness in the presence of an axial magnetic field. The flow and other characteristics are determined and it is shown that the pressure and load capacity can be increased by increasing the strength of the applied magnetic field at a given flow rate. But at a given feeding pressure the load capacity and pressure do not depend upon the magnetic field. The load capacity of this bearing is greater than that of a bearing having a constant film-thickness. It is also pointed out that the frictional drag on the rotor can be minimised by supplying electrical energy to the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00384046
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  • 10
    Electronic Resource
    Electronic Resource
    The flow of incompressible immiscible fluids between two plates (1964)
    Springer
    Flow, turbulence and combustion 13 (1964), S. 55-60 
    Details
    ISSN: 1573-1987
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary The flow of layers of different heights of n incompressible immiscible fluids between two plates has been considered and it has been shown that whatever be the number of fluids and whatever be their heights, a unique velocity maximum always exists and a formula for finding the layer in which this maximum occurs has been given. For the particular case of two layers it has been shown that the curve of total flux against the ratio of the heights of the fluids has always a point of inflexion. Further this ratio has been determined so that the fluxes of the two fluids are equal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00382036
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