David Chopp - US grants

The Department of Engineering Sciences and Applied Mathematics
of Northwestern University propose to purchase a Hewlett Packard
multiprocessor graphics workstation and two X-terminal stations. The
equipment will be used for scientific computation for the following
research projects:

* Numerical simulation of viscous sintering
* Numerical studies of frequency conversion and light propagation
in optical systems
* Complex Structures in Pattern-Forming Systems
* Superlattice wave patterns

The principal investigator is D. Chopp. Co-principal investigators are
G. G. Luther, H. Riecke, and M. Silber. Northwestern University has
agreed to contribute 50% of the cost of the equipment.

[unreadable] DESCRIPTION (provided by applicant): The tendency of bacteria to stick to surfaces and form surface-associated communities called biofilms has been well documented. A hallmark characteristic of biofilms is that they can be up to a thousand times more resistant to antimicrobial stress than free-swimming cells of the same species. Pseudomonas aeruginosa is an opportunistic human pathogen that has been implicated in nosocomial infections as well as chronic lung infections in people suffering from Cystic Fibrosis. P. aeruginosa uses a cell-to-cell signaling mechanism called quorum sensing to regulate virulence factor production, as well as biofilm formation. Therapeutic strategies directed at quorum sensing may be effective at combating P. aeruginosa biofilm infections. The proposed research will develop and utilize mathematical models for predicting acyl-HSL-regulated gene expression in a biofilm system. These models will be tested experimentally against actual biofilms grown under ecologically relevant conditions. The ultimate goal is to generate a versatile, predictive model that will allow clinicians to predict the onset of quorum sensing-regulated gene expression during the course of biofilm infections. A hierarchy of mathematical models will be developed for three different length scales: single unit cell, small clusters of cells, and full biofilm. The objective of these models will be to predict the level of acyl-HSL within an experimentally observed biofilm and its relationship to its environment. New hybrid numerical methods will be employed to simulate the mathematical models which will be based upon a coupling of the Level Set Method and the Extended Finite Element Method. The new method will be uniquely suited for simulating the growth of the biofilm and the synthesis of the signal acyl-HSL. Experimental data for parameter estimation in the models, as well as model testing will be done using a battery of biological reporter systems. These reporter strains utilize transcriptional fusions of quorum sensing-regulated promoters to the green fluorescent protein (GFP). The expression of GFP and the onset of fluorescence coincide with the accumulation of acyl-HSL signal to a critical threshold concentration. Use of these reporter systems in conjunction with scanning confocal laser microscopy will allow the examination of gene expression at the single cell level. Experimental results will be used to refine the mathematical models.

This project incorporates four different applications, which are
related through their common need for high-speed computational
capabilities. The first project involves the simulation of growing
bacterial biofilms. The simulation will couple the extended finite
element method with the level set method in order to capture the
interaction between the growing biofilm and the surrounding fluid
flow. The second project will solve a low Mach number model for
deflagrations in stellar envelopes. By filtering out sound waves from
the model, significantly larger time steps can be achieved than are
possible for full hydrodynamical models, thus making long time
computations feasible. The third project will study the role of
defects in the break-down of ordered structures. Parallelized
Monte-Carlo and Fourier spectral methods will be employed to
investigate defect trajectories in two paradigmatic systems, a
magnetic system and a dynamical system of coupled oscillators in two
dimensions. They exhibit spatially ordered as well as disordered
states. The goal is to identify to what extent various statistical
measures of the trajectories follow universal power laws. The fourth
project will use recently developed importance-sampling methods for
simulating rare events that set the performance of optical fiber
communication systems.

The impact of these projects will be felt across a broad spectrum of
disciplines, and will aid in the training and education of several
graduate students and postdoctoral research associates. In addition
to the scientific areas described above, the training will also
include the efficient use of high-performance parallel computing
architectures. The study of biofilms will improve our understanding
of quourum sensing organisms, and how to treat them. Such organisms
are responsible for a number of diseases, including diseases
associated with cystic fibrosis and deep burn wounds. The study of
deflagrations in stellar envelopes will improve our understanding of
the dynamics of novae of white dwarfs and the nature of X-ray bursts
from neutron stars. Transitions from ordered patterns to disordered
states are observed in many physical systems undergoing phase
transitions as well as in dynamical systems like arrays of coupled
oscillators, various kinds of fluid flow, and optical systems. Often
defects in the patterns are striking features of the disordered
states. The research will elucidate the role the defect dynamics play
in the break-down of the ordered states. The study of rare events in
optical fiber communication systems will lead to the construction of a
set of simulation tools capable of predicting the performance of
lightwave communication systems.

In this project, we will develop computational tools for modeling the complex
interactions between the microbiological, architectural, and mechanical
properties of bacterial biofilms. The tools will combine models for
multi-species biofilm growth and development, elasticity properties that
depend on the different species and their products, e.g. EPS, and the
interaction of the biofilm with overlying fluid flow. As a test case, the
tools will be used to study the behavior of heterotroph/autotroph two-species
biofilms commonly used for nitrogen removal in activated sludge reactors.
These biofilms exhibit complex behavior in their tendency to develop stratified
colonies where the fast growing heterotrophs cover the slow growing and brittle
autotrophs. The heterotrophs protect the autotrophs from fluid stresses, and
also consume the products generated by the autotrophs as they remove nitrogen
from wastewater.

Biofilms are a ubiquitous form of life that impact humans in many ways.
Biofilms are responsible for nitrogen loss from agricultural fertilizers,
deplete oxygen in streams, cause disease in humans and plants, and foul pipes,
heat exchangers, and ship hulls. It is estimated that biofilms cost the U.S.
billions of dollars annually in equipment and product damage, energy losses,
and human infections. The tools developed in this project will be general
enough to be applied to a wide range of multi-species biofilm communities, and
will be useful in improving our understanding of these complex systems. In
this project, the tools will be applied to activated sludge reactors,
which are systems used for the treatment of wastewater. In this system,
bacteria and other microorganisms remove harmful substances for purposes
of water reclamation. For maximal efficiency of these reactors, the right
balance of autotrophic and heterotrophic bacteria must be found. The tools
developed in this project will improve our understanding of this system and
aid in the identification of the optimal operating conditions.

This project establishes a flexible, modern training program in applied mathematics within the Research Training Group program.

Mathematics is a central component in physical sciences, biological sciences, and engineering, and many diverse disciplines exhibit common mathematical structures. Work in these fields profits from the involvement of applied mathematicians with broad backgrounds. This program will train such young applied mathematicians at all levels, from undergraduates through postdoctoral researchers.

A significant feature of the program is its interdisciplinary nature -- the group's activities involve not just mathematicians, but engineers and scientists as well. Thus, group members, while trained as applied mathematicians, will be comfortable interacting with non-mathematicians in research teams. The research activities will emphasize breadth and flexibility; trainees will be able to tackle problems involving a wide variety of mathematical techniques, ranging from analytical and computational methods to the development of suitable models of physical processes, and they will be able to adapt their research to diverse areas as opportunities arise.

The group's activities will involve mathematical research ranging from analytical to computational, in application areas including life sciences (particularly microbiology and biological fluids), fluid mechanics, materials science, and combustion. A special focus is on interfacial phenomena and phenomena involving multiple scales.

The project will produce a group of young applied mathematicians who are multifaceted in their scientific knowledge, able to grasp common mathematical features in problems from a diverse range of application areas, comfortable working and interacting with scientists and engineers in an interdisciplinary environment, and sufficiently flexible to pursue productive research in other areas as national priorities evolve.

This project would use mathematical modeling and computer simulations to help evaluate the potential capabilities of a commercial scale implementation of microbial fuel cells. The mathematical modeling we will employ is a continuum model using a combination of the level set method with the extended finite element method for solving a coupled system of reaction diffusion equations that incorporates the diffusion of various elements such as oxygen, substrates, and byproducts, as well as the growth of biomass consisting of multiple bacterial species attached to a fixed surface, or substratum. We have successfully applied this strategy to other biofilm systems such as Pseudomonas aeruginosa, a common bacterium often associated with mortality in people with cystic fibrosis, and heterotroph/autotroph symbiotic systems present in activated sludge water treatment processes. In this project, we will develop the necessary reactions and growth processes to simulate the microbial fuel cell system and use it to study various control strategies for optimizing energy production.

Microbial fuel cells are an attractive potential alternative energy source that are currently only at an experimental stage. These systems take waste water streams, e.g. pig manure, and convert them directly into electricity without the use of combustion. At the same time, the water is being cleaned of harmful elements such as ammonium, that is one stage of a comprehensive water treatment process currently in use. It is estimated that microbial fuel cells have the potential to generate as much as 25% of the current worldwide power demand, all while using a negative cost energy source in waste water.
Experimental systems are currently limited to bench scale reactors in closed systems that have a limited lifespan. To take these systems to the commercial scale, these systems need to be better understood for potential power per cost to demonstrate that they are feasible on that scale.

This project is concerned with an interdisciplinary and multifaceted investigation of the dynamics of particles confined to a fluid interface. Specifically, our proposal considers surface-trapped particles on a drop in an applied flow field and seeks to determine the flow-driven particle organization. These are mathematically challenging multiphase problems with application to the study of emulsions and the development of new novel materials with designed properties. Specific examples include emulsions with effective viscosity tunable by an electric field, the fabrication of colloidal photonic crystals, or the fabrication of "digital colloids" in soft robotics.

The primary focus will be on investigating the dynamics of particle-laden drops at medium to low surface coverage in applied flow fields. The PIs will develop mathematical models, analytical solutions, and accurate and efficient computational solutions of the dynamics of many particles on a moving drop interface. This is a complex free boundary problem that presents several challenges: the dynamics of the three-phase contact line, the curvature and deformability of the interface, and the many-body hydrodynamic interactions mediated by the fluids embedding the interface. The PIs plan to develop a multifaceted approach where analytical solutions using asymptotic methods will be sought for the dynamics of a single particle, a novel numerical approach using chimera grids and level set methods to determine the full-range dynamics of the particle-fluid system, and a point-particle method that efficiently simulates the collective dynamics of large numbers of particles.