Probability

Download Ecole d'Ete de Probabilites de Saint-Flour IV. 1974 by X.M. Fernique, J.P. Conze, J. Gani, P.-L. Hennequin PDF

By X.M. Fernique, J.P. Conze, J. Gani, P.-L. Hennequin

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If our mathematical models incorporating the possible variabilities cannot be solved without significant simplifications and assumptions, and the experiments on real aquifers is prohibitively expensive, where do we turn to understand more about the phenomenon? Computer models built on basic conservation equations incorporating variabilities modeled by known processes would provide us with a tool for experimentation. The whole purpose of the exercise is to develop a tool by looking at the fundamentals of the solute transport process and develop them into mathematical equations and logical relationships with a high degree of flexibility, to incorporate the stochasticity in parameters such as hydraulic conductivity and porosity.

035 cm. 1 m and a =9 cm when the solute plume traveled 5 m. In two-well tests with wells located 8 m apart, the value a =50 cm was obtained. Such variability of a "constant" is very disturbing in a model of which a major merit is intended to be the reduction of a complex phenomenon to simple 22 Stochastic Dynamics - Modeling Solute Transport in Porous Media materials constants. At best, it indicates the presence of a key variable that was not recognized in the first formulation of the model. If this variable can be identified, the situation might be rescued.

This means that while the particle has a position at any moment, and since this position is changing - it 40 Stochastic Dynamics -Modeling Solute Transport in Porous Media is moving - yet no velocity can be defined. e. e. I,u) } are independent for all 0 I tl < t2 . < tk ; P3: {B(t,+, ,w)-B(t, , a ) } is normally distributed with mean 0 and variance (t,+,-t, 1; P4: The stochastic variation of B(t,u) at fixed time t is determined by a Gaussian probability; P5: The Gaussian has a zero mean, E [B( t, u ) ] = 0 for all values of t; P6: B (t,u)are continuous functions o f t for r?

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