These articles are provided here for convenience and may be downloaded
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authors and publishers, who retain the copyrights to these works.
Velocity fluctuations
in a fluidized bed,
S.-Y. Tee, P. J. Mucha,
M. P. Brenner and D. A. Weitz,
Journal of Fluid Mechanics596, 467-475 (2008). Abstract:
The velocity fluctuations of particles in a low Reynolds number
fluidized bed have important similarities and differences with the
velocity fluctuations in a low Reynolds number sedimenting
suspension. We show that like sedimentation, the velocity fluctuations
in a fluidized bed are well described by the balance between density
fluctuations due to Poisson statistics and Stokes drag. However,
unlike sedimentation, the correlation length of the fluctuations in a
fluidized bed increases with volume fraction. We argue that this
difference arises because the relaxation time of density fluctuations
is completely different in the two systems.
Community
structure in Congressional cosponsorship networks,
Y. Zhang, A. J. Friend, A. L. Traud,
M. A. Porter, J. H. Fowler and P. J. Mucha,
Physica A387, 1705-1712 (2008). Abstract:
We study the United States Congress by constructing networks between Members of
Congress based on the legislation that they cosponsor. Using the concept of
modularity, we identify the community structure of Congressmen, as connected via
sponsorship/cosponsorship of the same legislation, to investigate the collaborative
communities of legislators in both chambers of Congress. This analysis yields an
explicit and conceptually clear measure of political polarization, demonstrating
a sharp increase in partisan polarization which preceded and then culminated in
the 104th Congress (1995-1996), when Republicans took control of both chambers.
Although polarization has since waned in the U.S. Senate, it remains at
historically high levels in the House of Representatives.
Velocity fluctuations
of initially stratified sedimenting spheres,
S.-Y. Tee, P. J. Mucha,
M. P. Brenner and D. A. Weitz,
Physics of Fluids19, 113304 (2007). Abstract:
The study of velocity fluctuations in the sedimentation of spheres
is complicated by the time evolution of the underlying particle
distribution, both at the microscale and in the bulk. We perform a
series of experiments and simulations to isolate the effect of an
initial, stable stratification in the particle concentration. The directly
observed dependence of velocity fluctuations on stratification
agrees with a previously-obtained scaling theory.
Random Walker Ranking for NCAA
Division I-A Football,
T. Callaghan,
P. J. Mucha and M. A. Porter,
American Mathematical Monthly114, 761-777 (2007).
Abstract:
Each December, college football fans and pundits across America debate
which two teams should meet in the NCAA Division I-A National
Championship game. The Bowl Championship Series (BCS) standings employed
to select the teams invited to this game are intended to provide an
unequivocal #1 v. #2 game for the championship; however, this
selection process has itself been highly controversial in four of the
past six years. The computer algorithms that constitute one part of
the BCS standings often act as lightning rods for the controversy, in
part because they are inadequately explained to the public. We
present an alternative algorithm that is simply explained yet remains
effective at ranking the best teams. We define a ranking in terms of
biased random walkers on the graph formed by the schedule of games
played, with two teams (vertices) connected by an edge if they played
each other. Each random walker moves from team to team by selecting a game
and "voting" for its winner with probability p, tracing out a
never-ending path motivated by the "my team beat your team"
argument. We study the statistical properties of a collection of such
walkers, relate the rankings to the community structure of the
underlying network, and compare these rankings for recent NCAA
Division I-A seasons. We also discuss the algorithm's asymptotic
behavior, illustrated with some analytically tractable cases for
round-robin tournaments, and discuss possible generalizations.
Statistical reconstruction
of velocity profiles for nanoparticle image velocimetry,
C. Hohenegger and P. J. Mucha,
SIAM Journal of Applied Mathematics68, 239-252 (2007).
Abstract:
Velocities and Brownian effects at nanoscales near channel walls can
be measured experimentally in an image plane parallel to the wall by
evanescent wave illumination techniques [R. Sadr et al., J. Fluid
Mech. 506, 357-367 (2004)], but the depth of field in this technique
is difficult to modify. Assuming moblility of spherical particles
dominated by hydrodynamic interaction between particle and wall, the
out-of-plane dependence of the mobility and in-plane velocity are
clearly coupled. We investigate such systems computationally, using a
Milstein algorithm that is both weak- and strong-order 1. In particle
image velocimetry (PIV), image pairs are cross-correlated to
approximate the mean displacement of $n$ matched particles between two
windows. For comparison, we demonstrate that a maximum likelihood
algorithm can reconstruct the out-of-plane velocity profile, as
specified velocities at multiple points, given known mobility depend
ence and perfect mean measurements. We then test this reconstruction
for noisy measurements as might be encountered in experimental
data. Physical parameters are chosen to be as close as possible to the
experimental parameters while we consider three types of velocity
profiles (linear, parabolic, and exponentially decaying).
Animating corrosion and
erosion,
C. Wojtan, M. Carlson, P. J. Mucha and G. Turk,
Eurographics Workshop on Natural Phenomena, 15-22 (2007)
[video].
Abstract:
In this paper, we present a simple method for animating natural
phenomena such as erosion, sedimentation, and acidic corrosion. We
discretize the appropriate physical or chemical equations using finite
differences, and we use the results to modify the shape of a solid
body. We remove mass from an object by treating its surface as a level
set and advecting it inward, and we deposit the chemical and physical
byproducts into simulated fluid. Similarly, our technique deposits
sediment onto a surface in a by advecting the level set outward. Our
idea can be used for off-line high quality animations as well as
interactive applications such as games, and we demonstrate both in
this paper.
Community
structure in the United States House of Representatives,
M. A. Porter, P. J. Mucha,
M. E. J. Newman and A. J. Friend,
Physica A386, 414-438 (2007).
Abstract:
We investigate the networks of committee and subcommittee assignments in
the United States House of Representatives from the 101st--108th
Congresses, with the committees connected by ``interlocks'' or
common membership. We examine the community structure in these networks
using several methods, revealing strong links between certain committees
as well as an intrinsic hierarchical structure in the House as a whole.
We identify structural changes, including additional hierarchical levels
and higher modularity, resulting from the 1994 election, in which the
Republican party earned majority status in the House for the first time
in more than forty years. We also combine our network approach with
analysis of roll call votes using singular value decomposition to uncover
correlations between the political and organizational structure of House
committees.
Diffusion-induced bias
in near-wall velocimetry,
R. Sadr, C. Hohenegger, H. Li,
P. J. Mucha and M. Yoda,
Journal of Fluid Mechanics577, 443-456 (2007).
Abstract:
The Brownian fluctuations of the colloidal tracers often used in
microscale velocimetry are typically isotropic in the bulk. In the
near-wall region, however, these fluctuations are strongly affected
by the hydrodynamic interaction with the wall and by the no-flux
condition imposed by the wall. These wall effects can, under
appropriate conditions, bias measurements based on colloidal tracers,
potentially leading to significant overestimation of near-wall
velocities. We use a Fokker-Planck description to generate probability
density functions of the distances from a single wall sampled by the
matched particles that are present in the same window at both the
start and end of a time interval. The importance of the resulting bias
for experimental parameters is then quantified in terms of the size
of the imaged region and measurement interval. We conclude with a
brief discussion of the implications for near-wall velocimetry
measurements.
Community structure in the
U.S. House of Representatives,
M. A. Porter,
A. J. Friend, P. J. Mucha and
M. E. J. Newman, Chaos16, 041106 (2006).
Abstract: This article originated as a winning poster entry in the Gallery
of Nonlinear Images at the 2006 APS March Meeting, demonstrating that
visualization of
the Congressional committee assignment network of the 108th U.S. House of
Representatives uncovers interesting hierarchical structure without
requiring input in the form of political opinions or judgements of the
researcher.
Keyframe control of
complex particle systems using the adjoint method,
C. Wojtan, P. J. Mucha and G. Turk,
ACM SIGGRAPH/Eurographics Symposium on Computer Animation,
15-23 (2006) [main video,
additional video].
Abstract:
Control of physical simulation has become a popular topic in the field
of computer graphics. Keyframe control has been applied to
simulations of rigid bodies, smoke, liquid, flocks, and finite
element-based elastic bodies. In this paper, we create a framework for
controlling systems of interacting particles -- paying special
attention to simulations of cloth and flocking behavior. We introduce
a novel integrator-swapping approximation in order to apply the
adjoint method to linearized implicit schemes appropriate for cloth
simulation. This allows the control of cloth while avoiding
computationally infeasible derivative calculations. Meanwhile,
flocking control using the adjoint method is significantly more
efficient than currently-used methods for constraining group
behaviors, allowing the controlled simulation of greater numbers of
agents in fewer optimization iterations.
Particle-based simulation of
granular materials,
W. N. Bell, Y. Yu and P. J. Mucha,
ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 77-86
(2005) [video].
Abstract: Granular materials, such as sand and grains, are
ubiquitous. Simulating the 3D dynamic motion of such materials
represents a challenging problem in graphics because of their unique
physical properties. In this paper we present a simple and effective
method for granular material simulation. By incorporating techniques
from physical models, our approach describes granular phenomena more
faithfully than previous methods. Granular material is represented by
a large collection of non-spherical particles which may be in
persistent contact. The particles represent discrete elements of the
simulated material. One major advantage of using discrete elements is
that the topology of particle interaction can evolve freely. As a
result, highly dynamic phenomena, such as splashing and avalanches,
can be conveniently generated by this meshless approach without
sacrificing physical accuracy. We generalize this discrete model to
rigid bodies by distributing particles over their surfaces. In this
way, two-way coupling between granular materials and rigid bodies is
achieved.
Water drops on surfaces,
H. Wang, P. J. Mucha and G. Turk, ACM Transactions on Graphics
(SIGGRAPH)24. 921-929 (2005)
[video].
Abstract: We present a physically-based method to enforce
contact angles at the intersection of fluid free surfaces and solid
objects, allowing us to simulate a variety of small-scale fluid
phenomena including water drops on surfaces. The heart of this
technique is a virtual surface method, which modifies the level set
distance field representing the fluid surface in order to maintain an
appropriate contact angle. The surface tension that is calculated on
the contact line between the solid surface and liquid surface can then
capture all interfacial tensions, including liquid-solid, liquid-air,
and solid-air tensions. We use a simple dynamic contact angle model to
select contact angles according to the solid material property, water
history, and the fluid front's motion. Our algorithm robustly and
accurately treats various drop shape deformations, and handles both
flat and curved solid surfaces. Our results show that our algorithm is
capable of realistically simulating several small-scale liquid
phenomena such as beading and flattened drops, stretched and
separating drops, suspended drops on curved surfaces, and capillary
action.
Modeling of debris
deposition in an extrusion filter medium,
C. L. Cox, E. W. Jenkins and
P. J. Mucha, Proceedings of the 21st Annual Meeting of the
Polymer Processing Society (2005).
Abstract: The goal of this work is to predict reasonable lifetime
of a filter used to remove debris (e.g. foreign particles and gels) from
the melt stream of an extrusion process. We are developing models which
incorporate non-Newtonian porous media flow through a medium whose porosity
changes as debris accumulates. Boundary conditions are based on the
assumption of constant flow rate and coupling with other process stages.
Governing equations consist of a mass balance equation for flow of the
suspension coupled with a Darcy velocity, the non-Newtonian constitutive
equation, and equations for modeling particle transport and deposition.
The model is being developed in a manner which allows for generalization
to various domains in higher dimensions and more complex constitutive
models. One-dimensional Newtonian and non-Newtonian flow models will be
presented and compared to one another. Plans for continuing work will
also be discussed.
A network analysis of
committees in the U.S. House of Representatives,
M. A. Porter, P. J. Mucha, M. E. J. Newman and C. M. Warmbrand,
Proceedings of the National Academy of Sciences102,
7057-7062 (2005).
Abstract: Network theory provides a powerful tool for the
representation and analysis of complex systems of interacting agents.
Here, we investigate the U.S. House of Representatives network of
committees and subcommittees, with committees connected according to
``interlocks, or common membership. Analysis of this network reveals
clearly the strong links between different committees, as well as the
intrinsic hierarchical structure within the House as a whole. We show
that network theory, combined with the analysis of roll-call votes
using singular value decomposition, successfully uncovers political
and organizational correlations between committees in the House
without the need to incorporate other political information.
The Bowl Championship Series: A
Mathematical Review,
T. Callaghan, P. J. Mucha and M. A. Porter,
Notices of the American Mathematical Society51, 887-893 (2004).
Abstract: We discuss individual components of the college
football Bowl Championship Series. Comparing with a simple algorithm
defined by random walks on a biased graph, we attempt to predict whether
the proposed changes will truly lead to increased BCS bowl access for
non-BCS schools. We conclude by arguing that the true problem with
the BCS Standings lies not in the computer rankings, but rather in
misguided addition.
Rigid Fluid: Animating the
interplay between rigid bodies and fluid,
M. Carlson, P. J. Mucha and G. Turk, ACM Transactions on Graphics
(SIGGRAPH)23, 377-384
(2004) [video,
higher resolution pdf and video clips available from
Mark Carlson]. Abstract: We present the Rigid Fluid method, a technique for animating
the interplay between rigid bodies and viscous incompressible
fluid with free surfaces. We use distributed Lagrange multipliers
to ensure two-way coupling that generates realistic motion for
both the solid objects and the fluid as they interact with one
another. We call our method the rigid fluid method because
the simulator treats the rigid objects as if they were
made of fluid. The rigidity of such an object is maintained by
identifying the region of the velocity field that is inside the
object and constraining those velocities to be rigid body motion.
The rigid fluid method is straightforward to implement, incurs very
little computational overhead, and can be added as a bridge
between current fluid simulators and rigid body solvers. Many
solid objects of different densities (e.g., wood or lead) can be
combined in the same animation.
A model for velocity
fluctuations in sedimentation,
P. J. Mucha, S.-Y. Tee,
D. A. Weitz, B. I. Shraiman and M. P. Brenner, Journal of
Fluid Mechanics501, 71-104 (2004)
[sample animation].
Abstract: We present a model for velocity fluctuations of
dilute sedimenting spheres at low Reynolds number. The central
idea is that a vertical stratification causes the fluctuations to
decrease below those of an independent uniform distribution of
particles, such a stratification naturally occurring from the
broadening of the sedimentation front. We use numerical
simulations, scaling arguments, structure factor calculations, and
experiments to show that there is a critical stratification above
which the characteristics of the density and velocity fluctuations
change significantly. For thin cells, the broadening of the
sediment front (and the resulting stratification) is small, so the
velocity fluctuations are predicted by independent Poisson
distribution estimates. In very thick cells, the stratification is
significant, leading to persistent decay of the velocity
fluctuations for the duration of the experiment. Estimated
stratifications quantitatively agree with the simulations, and
indicate the likelihood that previous experimental measurements
were also affected by stratification. The velocity fluctuations in
sedimentation are therefore not universal but instead depend on
both the cell shape and developing stratification.
A Stokes flow boundary integral
measurement of tubular structure cross sections in two
dimensions,
M. Niethammer, E. Pichon, A. Tannenbaum and
P. J. Mucha, Proceedings of the IEEE International
Conference on Image Processing, 825-828 (2003). Abstract: In the paper we will develop a method to
determine cross sections of arbitrary two-dimensional tubular
structures, which are allowed to branch, by means of a Stokes flow
based boundary integral formulation. The measure for the cross
sections for a point on the boundary of a given structure will be
the path obtained by integrating perpendicularly to the flow lines
from one side of the boundary to the other. Special emphasis will be
put on the behavior at branching points, the behavior at vortices,
and the necessary boundary conditions. The method can be extended to
three dimensional problems.
Diffusivities and front
propagation in sedimentation,
P. J. Mucha and M. P. Brenner, Physics
of Fluids15, 1305-1313 (2003). Abstract: Continuum models for particles sedimenting in
a fluid often assume that the diffusivity is a local function of the
particulate volume fraction. Since the hydrodynamically induced
diffusivity is a result of the velocity fluctuations of particles,
the recent identification [e.g., Tee et al., Phys. Rev.
Lett. 89, 054501 (2002)] of particle density stratification
as a controlling parameter for the velocity fluctuations also
extends to the diffusivities. In particular, the stratification
control strongly affects the diffusivity in the vicinity of the
falling sediment front between particle-laden fluid below and
clarified fluid above. The resulting scaling for
stratification-controlled diffusivities in creeping flow
sedimentation is presented and compares favorably with measurements
from dilute-limit particle simulations. Steadily-falling
concentration profiles for dilute sedimentation with these
diffusivities are then presented, and an extension of the model to
higher volume fractions is discussed.
Melting and Flowing,
M. Carlson, P.
J. Mucha, B. Van Horn and G. Turk, ACM SIGGRAPH Symposium on
Computer Animation, 167-174 (2002)
[video clips available from
Mark Carlson]. Abstract: We present a fast and stable system for
animating materials that melt, flow, and solidify. Examples of
real-world materials that exhibit these phenomena include melting
candles, lava flow, the hardening of cement, icicle formation, and
limestone deposition. We animate such phenomena by physical
simulation of fluids -- in particular the incompressible viscous
Navier-Stokes equations with free surfaces, treating solid and
nearly-solid materials as very high viscosity fluids. The
computational method is a modification of the Marker-and-Cell (MAC)
algorithm in order to rapidly simulate fluids with variable and
arbitrarily high viscosity. This allows the viscosity of the
material to change in space and time according to variation in
temperature, water content, or any other spatial variable, allowing
different locations in the same continuous material to exhibit
states ranging from the absolute rigidity or slight bending of
hardened wax to the splashing and sloshing of water. We create
detailed polygonal models of the fluid by splatting particles into a
volumetric grid and we render those models using ray tracing with
sub-surface scattering. We demonstrate the method with examples of
several viscous materials including melting weax and sand drip
castles.
Nonuniversal velocity fluctuations
of sedimenting particles,
S.-Y. Tee, P. J. Mucha, L. Cipelletti,
S. Manley, M. P. Brenner, P. N. Segre and D. A. Weitz, Physical
Review Letters89, 054501 (2002). Abstract: Velocity fluctuations in sedimentation are studied to
investigate the origin of a hypothesized universal scale
[P. N. Segre, E. Herbolzheimer, and P. M. Chaikin, Phys. Rev. Lett.
79, 2574 (1997)]. Our experiments show that fluctuations decay
continuously in time for sufficiently thick cells, never reaching
steady state. Simulations and scaling arguments suggest that the
decay arises from increasing vertical stratification of particle
concentration due to spreading of the sediment front.
The results suggest that the velocity fluctuations in
sedimentation depend sensitively on cell geometry.
Fast fluid analysis for multibody
micromachined devices,
X. Wang, P. J. Mucha and J. White,
Technical
Proceedings of the Fourth International Conference on Modeling and
Simulation of Microsystems, 19-22 (2001). Abstract: Recently developed fast integral equation methods for
computing solutions to the Stokes' equations have proven to be a
valuable tool for micromachined device designers. The speed of these
fast codes make it possible to simulate multiple interacting 3-D
structures, but issues associated with the singularity of the
integral form of Stokes' equation have not been sufficiently
carefully addressed to reliably perform such simulations. In this
paper we describe the issue and show a remedy.
That sinking feeling,
M. P. Brenner and P. J. Mucha, Nature409, 568-570
(2001) [News & Views]. Abstract: The physics of slowly falling particles in a fluid
remains surprisingly enigmatic. Luckily, laws that work for dilute
suspensions also appear to apply to higher -- and more useful --
particle concentrations.
Partial screening in dense
lattice-configuration suspensions,
P. J. Mucha, I. Goldhirsch, S. A. Orszag and M. Vergassola, Physical Review Letters83,
3414-3417 (1999). Abstract: Hydrodynamically-mediated particle interactions in
creeping flows of
suspensions are investigated to address the open question as to
whether they are screened. A numerical study of lattice
configurations, over the full range of volume fractions, reveals
that only the longitudinal part (in wavevector space) of the
force-velocity interaction is unscreened, and the general lattice
form of the long-range interaction is found to be in qualitative but
not quantitative agreement with a mean field result.
On Zero Reynolds Number Microhydrodynamics
of Particulate Suspensions,
P. J. Mucha, Ph. D. Thesis, Program in
Applied & Computational Mathematics, Princeton University (1998). Abstract: Flows of solids suspended in liquids or gases arise
in many natural and industrial settings, yet basic questions about modeling
and simulating such particulate suspension flows are difficult to
answer, even in the zero Reynolds number limit. In this limit, the
fluid degrees of freedom can be eliminated in favor of effective
hydrodynamically-mediated interparticle interactions that depend on
instantaneous particle positions, velocities, and angular
velocities. The primary difficulty in any such formulation is the
apparent long-ranged nature of this interaction, and the presence or
absence of screening of this interaction due to many-body or other
effects is an open question. By superposition, the problem can be
reduced, at a given time instant, to consideration of states in
which one particle is in motion while the others are at rest, the
solution to which is given in terms of a Green's function that
provides the hydrodynamic force and torque on any particle when only
one particle is in motion. The screening properties of these Green's
functions are investigated using a mean field approximation,
analytic expansions for dilute lattice configurations of particles,
numerical results for dilute random configurations, and numerical
solution for lattice configurations at arbitrary particulate volume
fraction. We find that the interaction is partially screened, and
discuss both configuration-specific and generic properties of the
remaining long-range interaction. The viscosities and permeabilities
of regular arrays of spheres are also calculated from the
appropriate Green's functions, and periodic-in-time shears of
lattice configurations are investigated with attracting periodic
orbits of the particle angular velocities found by numerical
integration. The possible importance of particle angular velocities
in general flows inspires a discussion of macroscopic modeling, and
the long-range properties of the Darcy-like fluid-particle drag term
common in suspension and porous media models is compared with the
screening results. We discuss preliminary attempts to utilize the
partial screening properties to develop more efficient microscopic
simulations. We then present a simple dimensional argument for
determining whether or not the microscopic particle dynamics are
effectively first-order in time, and we propose additional numerical
experiments to further investigate this and other questions which
remain unanswered.
Spectroscopic study of electrons
emitted in Arq+ (8<=q<=16) on Ar at 2.3q keV collision
energy,
J. Vancura, P. J. Mucha and V. O. Kostroun,
Physical Review A53,
2379-2390 (1996). Abstract: The spectra of electrons emitted in Arq+
on Ar (8 <= q <= 16) collisions at 2.3q keV were measured in the
30-400eV energy range. Arq+ ions were produced by the
Cornell superconducting solenoid, cryogenic electron-beam ion
source, and the emitted electrons analyzed by a \sqrt{pi}/2
cylindrical electrostatic analyzer at 900
to the ion beam. The observed spectral features are interpreted in
terms of energy differences between total electronic energies of
final states of the collision system [Arq+ + (electron
configuration)] + Arr+ and the Arq+ + Ar
ground-state total electronic energy. The measured spectra appear to
have a common interpretation.
Finite Deformation of an Elastic Membrane:
A Model for Epiretinal Membrane Separation,
P. J. Mucha, M. Phil. Thesis,
Department of Physics, University of Cambridge (1994). Abstract: As a model of tented-configuration ERM peeling from
the retina, we calculate the deformation of a Gaussian elastic
membrane clamped at its edges with a force applied to a central
attached rigid disk, and with a fluid supported above the
membrane. We develop numerical results and a scaling theory of
membrane profiles. Peeling criteria are developed from energetic
favourability arguments. Addition of a heavier supported fluid
increases the angle of peeling and pushes the retina back down
against the RPE. The net change in the stresses necessary for
peeling, however, slightly increases due to the heavier fluid
load. We conclude that while heavy fluid reduces tenting, and is
thus beneficial, peeling in the tented configuration remains a
dangerous option capable of tearing the retina, and should be
avoided.
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