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A simple single substrate limiting model of a growing biofilm layer is presented. One-dimensional moving front solutions are analyzed. Under certain conditions these solutions are shown to be linearly unstable to fingering instabilities. Scaling laws for the biofilm growth rate and length scale are derived. The nonlinear evolution of the fingering(More)
For weak solutions of the incompressible Euler equations, there is energy conservation if the velocity is in the Besov space B 3 s with s greater than 1/3. B p s consists of functions that are Lip(s) (i.e., Hölder continuous with exponent s) measured in the L p norm. Here this result is applied to a velocity field that is Lip(α 0) except on a set of(More)
We propose a multidimensional continuum model for heterogeneous growth of biofilm systems with multiple species and multiple substrates. The new model provides a deterministic framework for the study of the interactions between several spe1cies and their effects on biofilm heterogeneity. It consists of a system of partial differential equations derived on(More)
Bacterial biofilms, while made up of microbial-scale objects, also function as meso- and macroscale materials. In particular, macro-scale material properties determine how biofilms respond to large-scale mechanical stresses, e.g. fluid shear. Viscoelastic and other constitutive properties influence biomass structure (through growth and fluid shear stresses)(More)
A scheme is presented for mapping the connectivity of a potential magnetic field arising from an arbitrary distribution of discrete sources. The field lines interconnecting the sources are classified into N d domains, defining the field's connectivity. The number of domains is shown to depend on the number of sources and on the numbers of nulls and(More)
Biofilms, sticky conglomerations of microorganisms and extracellular polymers, are among the Earth's most common life forms. One component for their survival is an ability to withstand external mechanical stress. Measurements indicate that biofilm elastic relaxation times are approximately the same (about 18 min) over a wide sample of biofilms though other(More)
Many arthropods use filiform hairs as mechanoreceptors to detect air motion. In common house crickets (Acheta domestica) the hairs cover two antenna-like appendages called cerci at the rear of the abdomen. The biomechanical stimulus-response properties of individual filiform hairs have been investigated and modeled extensively in several earlier studies.(More)
Progress in microbiology has always been driven by technological advances, ever since Antonie van Leeuwenhoek discovered bacteria by making an improved compound microscope. However, until very recently we have not been able to identify microbes and record their mostly invisible activities, such as nutrient consumption or toxin production on the level of the(More)
A mathematical model describing the constitutive properties of biofilms is required for predicting biofilm deformation, failure, and detachment in response to mechanical forces. Laboratory observations indicate that biofilms are viscoelastic materials. Likewise, current knowledge of biofilm internal structure suggests modeling biofilms as associated polymer(More)