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1.
In this paper, a nonlinear mathematical model is proposed and analyzed to study the removal of gaseous pollutants and particulate matters from the atmosphere of a city by precipitation. The atmosphere consists of four interacting phases i.e. the raindrops phase, the gaseous pollutants phase, the phase of gaseous pollutants absorbed (dissolved) in rain drops and the phase of particulate matters. The dynamics of these phases is assumed to be governed by ordinary differential equations with source, interaction, removal and recycle terms. The proposed model is analyzed by using stability theory of differential equations. It is shown that the pollutants can be removed from the atmosphere and their removal rates depend mainly upon the rates of emission of the pollutants, rate of rain drops formation and the rate of falling rain drops on the ground. If the rate of precipitation is very high, the pollutants may be removed completely from the atmosphere.  相似文献   

2.
In this paper we analyze a stochastic model for interactions of hot gases with cloud droplets and raindrops. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic hot gases modelling. We show that the model established in this paper possesses non-negative solutions as this is essential in any hot gas dynamics model. We also carry out analysis on the stochastically ultimate boundedness, extinction and stability of the hot gases model.  相似文献   

3.
Abstract In this paper, a nonlinear mathematical model is proposed and analyzed to study the formation of acid rain in the atmosphere because of precipitation and its effect on plant species. It is considered that acid‐forming gases such as SO2 , NO2 emitted from various sources combine with water droplets (moisture) during precipitation and form acid rain affecting plant species. It is assumed that the biomass density of plant species follows a logistic model and its growth rate decreases with increase in the concentration of acid rain. The model is analyzed by using stability theory of differential equations and numerical simulation. The model analysis shows that as the concentration of acid rain increases because of increase in the cumulative emission rates of acid forming gases, the biomass density of plant species decreases. It is noted that if the amount of acid formed becomes very large, the plant species may become extinct.  相似文献   

4.
A non-linear mathematical model for rain making from water vapor in the atmosphere is proposed and analyzed. The model considers the process of artificial rain by introducing two kinds of aerosol particles conducive to nucleation of cloud droplets and formation of rain drops. The model analysis shows that, for uninterrupted rain, the water vapor in the atmosphere must be formed continuously with the required rate of rainfall. It is shown further that the intensity of rainfall increases as the concentrations of externally introduced aerosols, as well as the density of water vapor in the atmosphere, increase. Numerical simulation is also performed to see the effect of various parameters on the process of artificial rain making leading to rainfall.  相似文献   

5.
In this paper, a nonlinear mathematical model is proposed and analyzed to study the depletion of dissolved oxygen caused by interactions of organic pollutants with bacteria in a water body, such as lake. The system is assumed to be governed by three dependent variables, namely, the cumulative concentration of organic pollutants, the density of bacteria and the concentration of dissolved oxygen. In the model, the coefficient of interaction of organic pollutants with bacteria depends upon the concentration of dissolved oxygen nonlinearly and explicitly, which is the main focus of this paper, has never been studied before. The stability theory of differential equations is used to analyze the model and to confirm the analytical results numerical simulation is performed. The model analysis shows that if the coefficient of interaction mentioned above depends upon dissolved oxygen explicitly, the decrease in its concentration is more than the case when the interaction does not depend on dissolved oxygen and consequently the depletion of organic pollutants is also more in such a case.  相似文献   

6.
We investigate a generalized form of a partial differential equation governing the diffusion of heavy pollutants into the atmosphere. In earlier treatments of the equation, the vertical component of turbulent exchange coefficient was assumed to be linear. Our generalization takes into account the nonlinear case of this component. Furthermore, two general identities involving the confluent hypergeometric function of the second kind are derived in the course of solving the given PDE.  相似文献   

7.
Summary The influence of combustion on heat and mass transfer is investigated on the following model. A mixture of an inert with a combustible gas (air) flows in steady, laminar flow over a flat plate. A mass flux of gaseous fuel away from the plate surface is produced by some means. Combustion is assumed to occur with very fast reaction rate so that the process is purely controlled by diffusion and the equilibrium is assumed as very close to complete combustion. It is studied under which conditions the combustion occurs at the surface or when the flame is displaced into the boundary layer. The influence of combustion on the heat transfer from a hot gas to the plate surface is calculated, for the condition that combustion occurs at the surface.   相似文献   

8.
This paper presents a weakly nonlinear analysis for one scenario for the development of transversal instabilities in detonation waves in two space dimensions. The theory proposed and developed here is most appropriate for understanding the behavior of regular and chaotically irregular pulsation instabilities that occur in detonation fronts in condensed phases and occasionally in gases. The theory involves low-frequency instabilities and through suitable asymptotics yields a complex Ginzburg-Landau equation that describes simultaneously the evolution of the detonation front and the nonlinear interactions behind this front. The asymptotic theory mimics the familiar theory of nonlinear hydrodynamic instability in outline; however, there are several novel technical aspects in the derivation because the phenomena studied here involve a complex free boundary problem for a system of nonlinear hyperbolic equations with source terms.  相似文献   

9.
We propose and analyze, a nonlinear mathematical model of the spread of HIV/AIDS in a population of varying size with immigration of infectives. It is assumed that susceptibles become infected via sexual contacts with infectives (also assumed to be infectious) and all infectives ultimately develop AIDS. The model is studied using stability theory of differential equations and computer simulation. Model dynamics is also discussed under two particular cases when there is no direct inflow of infectives. On analyzing these situations, it is found that the disease is always persistent if the direct immigration of infectives is allowed in the community. Further, in the absence of inflow of infectives, the endemicity of the disease is found to be higher if pre-AIDS individuals also interact sexually in comparison to the case when they do not take part in sexual interactions. Thus, if the direct immigration of infectives is restricted, the spread of infection can be slowed down. A numerical study of the model is also carried out to investigate the influence of certain key parameters on the spread of the disease.  相似文献   

10.
A multi-phase framework is typically required for the CFD modelling of metals reduction processes. Such processes typically involve the interaction of liquid metals, a gas (often air) top space, liquid droplets in the top space and injection of both solid particles and gaseous bubbles into the bath. The exchange of mass, momentum and energy between the phases is fundamental to these processes. Multi-phase algorithms are complex and can be unreliable in terms of either or both convergence behaviour or in the extent to which the physics is captured. In this contribution, we discuss these multi-phase flow issues and describe an example of each of the main “single phase” approaches to modelling this class of problems (i.e., Eulerian–Lagrangian and Eulerian–Eulerian). Their utility is illustrated in the context of two problems – one involving the injection of sparging gases into a steel continuous slab caster and the other based on the development of a novel process for aluminium electrolysis. In the steel caster, the coupling of the Lagrangian tracking of the gas phase with the continuum enables the simulation of the transient motion of the metal–flux interface. The model of the electrolysis process employs a novel method for the calculation of slip velocities of oxygen bubbles, resulting from the dissolution of alumina, which allows the efficiency of the process to be predicted.  相似文献   

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