A semi-analytical mesh-free series solution method is presented for modeling regional steady-state subsurface saturated-unsaturated flow in 2-D geometrically complex homogenous and stratified hill-slope cross sections. Continuous solutions for pressure in the saturated and unsaturated zone are determined iteratively, as is the location of the water table surface. Mass balance is satisfied exactly over the entire domain except along boundaries and interfaces between layers, where errors are in an acceptable range. The solutions are derived and demonstrated on multiple test cases. The errors for specific cases are assessed and discussed. (C) 2013 Elsevier Ltd. All rights reserved.

In this paper, a two-dimensional analytic series solution for groundwater flow with a free water table condition is derived and demonstrated on a two-layer unconfined aquifer with complex (i.e., natural) stratigraphy. The vertical side and bottom boundaries of the model domain are impermeable, and the water table is a free-boundary condition governed by both Dirichlet and Neumann conditions. Unlike previous investigations, the problem is complicated by the possible intersection of the water table with interfaces between different materials. This challenge can be overcome by intelligently revising the analytic series solution approach previously developed by the authors. The series coefficients are calculated through a least-squares method which minimizes errors. Tests cases are used to demonstrate the effects of both system geometry and lower aquifer conductivity upon the shape of the water table surface.

Many plants reproduce clonally through vegetative extensions. This results in a patch of clones connected through a network of stems (spacers), with some nontrivial spatial pattern. Here, we build on previous work to develop general growth rules that dictate how individual clones under local density-dependent conditions add vegetative extensions, giving rise to emergent population-level spatial patterns. A population subject to these growth rules is simulated in MATLAB as a stochastic individual-based model. The dependence of network architecture on various individual level growth parameters is explored. The growth rules are able to replicate real-world phenomena such as central die-back with regeneration, ‘fairy rings’, and branch entrapment. A shorter spacer length results in higher population density (which may confer resistance to invasion in real populations), while longer spacer length allows exploiting the field more quickly. The number of daughter branches per mother branch follows a power law distribution for certain parameters values, as is observed in some naturally occurring clonal species.

An analytical series solution method is presented for modeling regional steady-state groundwater flow in a two-dimensional stratified aquifer cross-section where the water table is well-characterized. The aquifer system may have any number of contiguous or non-contiguous layers and the geometry of each layer is restricted only by the requirement that the elevation of the stratigraphic unconformities between layers is a function of the x-coordinate alone. Various techniques may be used to handle pinching layers, faults, and other discontinuities. The solutions are obtained by minimizing head and flow continuity errors between layers and errors in the Dirichlet surface at a set of control points along these unconformities; the governing equation is met exactly. The solutions are derived and demonstrated on multiple test cases. The errors for some specific, geometrically challenging cases are assessed and discussed.