Termproject Topics for 22.00J … IM/S
Martin Bazant
I have two areas of interest which could provide topics for termprojects:
• Diffusion-Limited Aggregation. Develop efficient algorithms to simulate and visualize DLA
clusters. Study the effect of various modifications of the model (noise-control, anisotropy,
sticking probabilty, etc.) on the fractal dimension and structure of the resulting clusters. For
advanced students: use codes based on stochastic conformal mapping to study ADLA (=DLA
in a fluid flow) or DLA on curved surfaces.
• Dense Granular Flow. Choose a simulation approach below and model flows in pebble-bed
nuclear reactors.
a) Statistical simulations based on the Void Model and the Spot Model.
b) Molecular dynamics simulations.
c) Continuum models of the mean flow field.
Student Project Topics:
1. Simulating block copolymer phase transitions with mean field theory
This project uses a C++ program to study the self-assembly of block copolymers. Block
copolymers have sections with different chemical compositions, such that segments from
sections that are unalike tend to avoid each other. Because the sections are connected
covalently, no macroscopic phase separation occurs, but rather the chains self-assemble
into nanoscale structures that minimize contact between unlike components. Recently,
we have been studying the nature of transitions between ordered phases using particlebased simulation, and this project would generate comparable results with mean-field
theory. In mean-field theory, one solves a set of coupled partial differential equations that
govern the equilibrium behavior of the segment density and chemical potential fields.
2. Simulating entangled motion of a polymer chain in a regular network of
obstructions
In this project, the student will be asked to write a program that simulates (using
Brownian dynamics) the motion of polymer chains (linear and branched) in 2-D through
a lattice of obstructions than entangle the chain. The effect of chain length and branching
upon the effect diffusivity constant will then be studied. This problem is at the basis of
technology for DNA analysis using gel electrophoresis.
3. Modeling a falling-film reactive absorber
It is common to treat gas waste streams from manufacturing to remove harmful
components prior to release into the atmosphere. This may be done by bringing the gas
stream into contact with a liquid stream, such that the liquid absorbs the harmful
components. The efficiency of this method is improved when the liquid stream contains
an active species that chemically reacts with the harmful component to bind it within the
liquid phase. This project will model reactive absorption in a falling film of liquid.
4. Modeling sailboat dynamics
Sailboat racing is one of the few sports that actually reward competitors for having an
understanding of physics. This project involves developing simple models of sailboat
dynamics by using macroscopic models of drag and lift from fluid mechanics. This model
will then be used to optimize racing tactics by performing case studies. Given sufficient
interest, the student can go on the water to test the performance of the model by
measuring sailboat dynamics with GPS.
As an example of the problems of interest, consider the selection of an optimum gybing
angle on a downwind run. The standard racing course is comprised of a windward leg
going directly into the wind and a leeward leg with the wind at your back. Sailboats can
only sail to within about 40 degrees of the wind direction, and so on the windward leg
one must sail a zig-zag course to make progress in the wind direction towards the mark.
Going downwind, one could take a direct course (called a run), but it is generally faster
also to zig-zag on the leeward leg. This is because when one sails on a broad reach
(slightly to the left or right of the downwind direction), the apparent air velocity over the
sail is higher than it is on a direct run downwind, and so the sails create more propulsive
force. So one must balance this extra speed gained with the extra distance associated with
the zig-zag path to choose the best angle for the zig-zag course (the gybing angle). The
optimal angle depends upon the type of boat and upon wind conditions. From our
modeling, we wish to see how various factors affect the optimal angle. Other questions of
interest are the optimal strategies for tacking (zig-zaging) on upwind legs when the wind
shifts directions.
Markus J Buehler
My research is focused understand the macroscopic mechanical response of complex materials based
on their fundamental, atomistic ultrastructure. We use large-scale, massively parallelized novel
modeling techniques, including differential multi-scale simulation methods that allow description of
material behavior across hierarchies of scales. We aim towards developing a physics based
understanding of materials failure, while including modeling of the chemistry during formation and
breaking of bonds. A major theme of the research is to understand the generation, nucleation and
propagation dynamics of cracks and other defects in various materials, with a particular focus on
natural and biological materials, such as those based on proteins. New technologies utilizing
engineered protein-based materials, for example those developed by recombinant DNA techniques,
represent a major frontier in materials design. A better understanding of the mechanics of biological
and natural materials, integrated in complex technological systems, helps to combine living and nonliving environments to develop sustainable technologies.
Possible projects include:
- Mechanics of single proteins (e.g. force-displacement response)
- Mechanics of single crystals of metals and semiconductors, for example crack propagation
- Calculation of stress-strain response of metal/semiconductor nanowires or carbon nanotubes
- Atomistic modeling of a one-dimensional model of dynamic fracture (peeling a single
molecule on rigid substrate)
The programming effort can be varied in each project depending on expertise and liking of students.
Additional projects or variations of the above mentioned are possible.
Figure: Stress field near a rapidly moving crack at an interface between two elastically dissimilar
materials (soft/stiff). The crack moves supersonically with respect to the soft material, as can be
confirmed by considering the shock fronts.
Leonid Mirny
I'm working in the fields of biophysics and bioinformatics. My research is aimed at understanding
evolution and dynamics of biological molecules. We also study mechanisms by which large
biological networks (e.g. network of all genes) operate.
I use simulations to study protein folding and protein binding, molecular evolution and genetic
network. Most of these simulations are done by Monte Carlo techniques. Scales covered by the
simulations
range from atom (protein folding) to the whole cell (network simulations) and times covered
range from milliseconds in protein folding to millions of years in the simulations of molecular
evolution.
Possible course projects include:
1. Stochastic simulations of biochemical reactions **
2. Protein aggregation **
3. DNA folding into chromosomes ***
4. Optimal ordering of genes from a DNA-chip experiment *
5. Genetics algorithms to solve genetic problems ***
Complexity: (*) (**) (***)
Adam Powell
My work focuses on "meso-scale" simulations of the processes of formation and evolution of
materials microstructures. I focus on processes at the micron or millimeter scale, where atomistic
simulations are prohibitively expensive, so continuum approaches are necessary. The approaches
are useful for a wide range of materials, from membrane-forming polymers to solidifying metals
and even electrochemical systems. IM/S project topics for this semester could include:
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Solidification of liquid metals
Polymer structures made by phase inversion
Modeling of defects in continuous casting
Liquid free surface shapes, from solder to natural systems
Raul Radovitzky
My main area of interest is in making the connection between microstructure and resulting
effective mechanical response of materials by modeling and simulation. Usually, this amounts to
linking the "meso" (several to many micron) scale to the "macro" (millimeter and larger) or
continuum scale by some averaging or homogenization approach or by direct (large-scale)
numerical simulation. I am particularly interested in the response of engineering materials to
extreme loading conditions such as produced by shocks and detonation waves. The main focus
area at the present time is on crystalline (metallic) materials. Surface roughening, formability
limits and other important issues in material processing are examples of the applications we are
currently investigating. Another important area of research focus in my group is in the continuum
description of some anomalies observed experimentally and in atomistic simulations in the
deformation of nanocrystals. The following list of topics illustrates the type of projects I could
supervise:
Comparisons between atomistic and continuum simulations
Plastic Deformation of polycrystals, direct numerical simulations
Plastic Deformation of polycrystals, averaging approaches
Thermoplastic deformations in metallic materials
Sidney Yip
My interests are primarily in atomistic modeling - theory and simulation - of materials using the
techniques of molecular dynamics and Monte Carlo. At present I am focusing on understanding
mechanical and thermal behavior of crystalline and amorphous solids (metals, semiconductors,
and ceramics). Examples of problems which my graduate students and I are investigating are
physical properties of strength, deformation, and fracture. I also have interests in other areas, such
as radiation transport and statistical mechanics. Typical term project topics which I could
supervise include (programming ability would be helpful but not all topics require a great deal of
programming):
Learning how to do atomistic simulations
Understanding melting and freezing
Ideal strengths of crystals under tension or compression
Shear deformation of crystals and nanocrystals
Cracking in glassy materials
Atomic-level visualization of materials failure
Anything else in atomistic simulation a student would like to propose
None of these topics are very specific which is intentional. Once a student makes a selection,
then we will start talking about what would be involved in building a term-project on that topic.
Much will depend on the student's ability to program or use an existing code. The expectation is
that each project will be customized to suit the student's interest and ability.