Bonni Kealy-Dichone

Nonlinear stability analyses of Turing patterns for a mussel-algae model

A particular interaction–diffusion mussel-algae model system for the development of spontaneous stationary young mussel bed patterning on a homogeneous substrate covered by a quiescent marine layer containing algae as a food source is investigated employing weakly nonlinear diffusive instability analyses. The main results of these analyses can be represented by plots in the ratio of mussel motility to algae lateral diffusion versus the algae reservoir concentration dimensionless parameter space. Regions corresponding to bare sediment and mussel patterns consisting of rhombic or hexagonal arrays and isolated clusters of clumps or gaps, an intermediate labyrinthine state, and homogeneous distributions of low to high density may be identified in this parameter space. Then those Turing diffusive instability predictions are compared with both relevant field and laboratory experimental evidence and existing numerical simulations involving differential flow migrating band instabilities for the associated interaction–dispersion–advection mussel-algae model system as well as placed in the context of the results from some recent nonlinear pattern formation studies.

On the E-optimality of Blocked Main Effects Plans In Blocks of Different Sizes

ABSTRACT In this article, we consider experimental situations in which m 2-level factors are to be studied using a main effects plan where n runs are to be partitioned into b blocks having both even and odd sizes. For these cases, we give some simple methods for constructing E-optimal designs.

On the Joint Use of the Foldover and Partial Confounding for the Construction of Follow-Up Two-Level Blocked Fractional Factorial Designs

In this article, we consider experimental situations where a regular fractional factorial design is initially used to study m two-level factors using n = 2m−k experimental units arranged in 2p blocks of size 2m−k−p but where a follow-up design is desired to further study main effects and two-factor interactions. A typical follow-up would consist of folding over some of the experimental factors but using the same blocking scheme for the foldover design. Here, we consider the joint use of the foldover and the use of a different blocking scheme in the follow-up design to generate alternative combined designs that outperform the combined designs obtained using previously given procedures in terms of estimability of two-factor interactions, estimation capacity, or both.