Leonard M. Sander - US grants

They propose projects in condensed matter physics in two general areas: nonequilibrium growth and the theory of quasiperiodic structures. The first area is the main subject of the proposal: they will investigate a model for thin film growth (ballistic aggregation), aspects of diffusion-limited growth, notably a joint experimental and theoretical project in electrodeposition, a model for fracture which maps it onto a DLA type process, flow in porous media, and an investigation of aspects of crystallization. In the second area they will explore the propagation of wavepackets in artificial quasiperiodic supperlattices.

9420335 Sander A series of projects in the theory of statistical physics far from equilibrium will be studied. The growth of random rough surfaces will be considered; new work is proposed in the description of growth by molecular-beam epitaxy. An inverse method will be applied to the generic theory of interface growth, and the Kuramoto-Shivashinsky equation of flame fronts will be investigated using the same techniques. Three problems related to the diffusion-limited aggregation model will be studied: the question of lacunarity, a statistical analysis of the homogenieties of the fractal clusters produced by the model, and the inverse method will be applied to generate a continuum equation. Finally work will be done in the field of patterns and fluctuations in chemical reactions. In the context of two simple statistical models an attempt to understand the effects of noise and disorder on the formation of chemical patterns will be undertaken. %%% A series of projects will be undertaken on systems which are not in equilibrium. Examples of these systems include: the growth of surfaces in materials, the behavior of flames, models of aggregation of particles, pattern formation occuring in chemical reactions and the effects of noise on these systems. Common models which describe these various phenomena will be studied.

Proposal: DMS-0244419
PI: Charles Doering
Institution: University of Michigan
Title: Fronts, Fluctuations, and Growth

ABSTRACT

This interdisciplinary investigation brings together researchers from the University of Michigan's Departments of Mathematics, Physics and Chemical Engineering to study questions of front propagation and pattern formation arising in materials science and chemistry. The central goal of the project is to elucidate, theoretically and mathematically, the roles of fluctuations, noise and disorder on the dynamics of interfaces in nonequilibrium systems such as chemical reactions and thin film growth. This project combines theoretical condensed matter and statistical physics, Kinetic Monte Carlo and numerical simulations, and mathematical modeling and analysis to investigate the interplay of stochastic and nonlinear effects in systems of scientific and technological interest.

With regard to the intellectual merit of this activity, research results from this project will lead to the development of effective mathematical descriptions and efficient computational schemes for problems of increasing importance for small-scale physical and chemical processes in materials science and nanotechnology. With regard to the broader impacts of this activity, it also has a significant advanced training aspect: a graduate student research assistant associated with this project will carry out original PhD thesis research under the guidance of the principal investigators.

Abstract

This Focused Research Group brings together researchers from the
University of Michigan's Departments of Mathematics, Physics and
Chemical Engineering to address important problems of modeling,
simulation and analysis for dynamical processes where underlying
discreteness plays a non-negligible role in large scale descriptions
via deterministic continuum systems (generally systems of ordinary and
partial differential equations). This Focused Research Group combines
the investigators' expertise in theory, modeling, analysis and
scientific computation to study a suite of problems from materials
physics, chemical kinetics and the life sciences to elucidate the
fundamental scientific issues and develop appropriate quantitative
tools to analyze them. The specific problems to be studied are: (1)
Mesoscopic mathematical models of wound healing with cell proliferation
and migration, and including the biologically important effect of
cell-cell adhesion; (2) The application of new and improved simulation
techniques, direct solutions of the Becker-Doering equations, and
simulation and analysis of stochastic models to investigate the role of
microscopic correlations in Ostwald ripening; (3) The development of
analytic asymptotic methods for accurate reduced descriptions of slow
stochastic variables properly incorporating residual fluctuation
effects with applications to (bio)chemical reaction networks possessing
a wide spectrum of reaction rates; (4) An extension of modeling,
analysis and simulation methods developed for simple systems to
increasingly complex stochastic models in population biology and
epidemiology including epidemics in structured populations and
extinction of competing species; (5) Spatial inhomogeneities and
reaction-rate variations in the stochastic Fisher-Kolmogorov equation,
a fundamental paradigm of front propagation and pattern formation.

Results from this project will lead to the development of effective
mathematical descriptions and efficient computational schemes for
problems of increasing importance for small-scale physical and chemical
processes in materials science and nano-technology, and for
quantitative modeling in the life sciences. With regard to the even
broader impact of this project, it contributes to the development of
the scientific workforce by providing advanced training for
postdoctoral researchers and doctoral students in the natural,
engineering and applied mathematical sciences.

The discovery that new neurons are born in adult brains and integrate into functional networks raised questions about the dynamics of this process. Namely, what are the activity dependent queues guiding the integration of the new cells into existing networks and how do these queues depend on the intrinsic properties of the augmented networks? The focus of this project is to develop an integrated computational and experimental framework, which will allow for investigation of dynamical mechanisms underlying migration and incorporation of newly born neurons into existing networks. We specifically want to understand whether, and how, network augmentation depends on the ongoing activity of the original network, and to discern the collective changes in the network activity patterns specifically due to network augmentation. To do so the PI will develop a computational approach that will allow him to elucidate links between cellular mechanisms of network augmentation and their network-wide outcomes. In addition the PI will use an in vitro experimental system based on dissociated cell cultures to monitor patterns of network augmentation and changes in spatio-temporal activity, after GFP labeled neuroblasts are added. The neural activity using multi-electrode arrays and calcium imaging will be recorded, and then labeling studies to elucidate structural patterns of neural augmentation will be performed. The proposed project will provide a better understanding of the interaction of cellular and network mechanisms underlying function-dependent network augmentation. This is critical for identifying dynamical mechanisms of self-reorganization in these types systems.

This project will allow three collaborating laboratories to serve as a training resource for undergraduate and graduate students. The students will have the opportunity to gain experience in truly interdisciplinary research combining theoretical physics, modeling and neurobiology. They will further gain experience in the scientific process through participation in interdisciplinary meetings to present their results. The knowledge gained through this research will be disseminated to members of the scientific community through publications, seminars, and workshops. Additionally, the obtained results will be incorporated in the "Biocomplexity" course that the PI has developed for the advanced undergraduates.