A new sigmoid growth equation is presented for curve-fitting, analysis and simulation of growth curves. Like the logistic growth equation, it increases monotonically, with both upper and lower asymptotes. Like the Richards growth equation, it can have its maximum slope at any value between its minimum and maximum. The new sigmoid equation is unique because it always tends towards exponential gr...

abstract spatial variability of soils makes difficult analysis of soil water flow phenomena especially in a large area such as a watershed. using scaling methods is a solution in variability problems. the objective of this study was to investigate the effect of the non-linear variability on performance of the scaling methods of richards’ equation for modeling infiltration in a watershed. the me...

The Richards equation is widely used as a model for the flow of water in unsaturated soils. For modelling one-dimensional flow in a homogeneous soil, this equation can be cast in the form of a specific nonlinear partial differential equation with a time derivative and one spatial derivative. This paper is a survey of recent progress in the pure mathematical analysis of this last equation. The e...

Unsaturated flow of soils in unsaturated soils is an important problem in geotechnical and geo-environmental engineering. Richards’ equation is often used to model this phenomenon in porous media. Obtaining appropriate solution to this equation therefore provides better means to studying the infiltration into unsaturated soils. Available 5 methods for the solution of Richards’ equation mostly f...

We present a heterogeneous domain decomposition approach to the Richards equation coupled with surface water flow. Assuming piecewise constant soil parameters in the constitutive equations for saturation and relative permeability, we present a novel domain decomposition approch to the Richards equation involving on fast and robust subdomain solver based on optimization techniques. The coupling ...

We formulate the 2-Lagrange multiplier method for the Richards equation in heterogeneous soil. This allows a rigorous formulation of a discrete version of the Richards equation on subdomain decompositions involving cross points. Using Kirchhoff transformation, the individual subdomain problems can be transformed to convex minimization problems and solved efficiently using a monotone multigrid m...

The traditional Richards' equation implies that the wetting front in unsaturated soil follows Boltzmann scaling, with travel distance growing as the square root of time. This study proposes a fractal Richards' equation (FRE), replacing the integer-order time derivative of water content by a fractal derivative, using a power law ruler in time. FRE solutions exhibit anomalous non-Boltzmann scalin...