The present work solves two-dimensional Advection-Dispersion Equation (ADE) in a semi-infinite domain. A variable source concentration is regarded as the monotonic decreasing function at the source boundary (x=0). Depth-dependent variables are considered to incorporate real life situations in this modeling study, with zero flux condition assumed to occur at the exit boundary of the domain, i.e....

Lambda words are sequences obtained by encoding the differences between ordered elements of the form i + jθ, where i and j are non-negative integers and 1 < θ < 2. Lambda words are right-infinite words defined over an infinite alphabet that have connections with Sturmian words, Christoffel words, and interspersion arrays. We show that Lambda words are infinite rich words. Furthermore, any Lambd...

This paper presents a finite element-infinite element coupling approach for modeling a spherically symmetric transient flow problem in a porous medium of infinite extent. A finite element model is used to examine the flow potential distribution in a truncated bounded region close to the spherical cavity. In order to give an appropriate artificial boundary condition at the truncated boundary, a ...

Many numerical methods have been developed for the solution of Poisson and Laplace equations such as finite-difference methods, finite-element methods, boundary-element methods, etc. Sinc numerical methods developed recently by Stenger and co-workers excel over other methods for problems involving singularities, infinite or semi-infinite domains as well as boundary layer behaviors. In this pape...

We prove that the abstract commensurator of a nontrivial free group, an infinite surface group, or more generally a group that splits appropriately over a cyclic subgroup is not finitely generated. This applies in particular to all torsion-free word-hyperbolic groups with infinite outer automorphism group and abelianization of rank at least 2. We also construct a finitely generated group which ...