%% Papers Published
@article{fds374487,
Author = {Autry, E and Carter, D and Herschlag, GJ and Hunter, Z and Mattingly,
JC},
Title = {METROPOLIZED FOREST RECOMBINATION FOR MONTE CARLO SAMPLING
OF GRAPH PARTITIONS},
Journal = {SIAM Journal on Applied Mathematics},
Volume = {83},
Number = {4},
Pages = {1366-1391},
Year = {2023},
Month = {August},
url = {http://dx.doi.org/10.1137/21M1418010},
Abstract = {We develop a new Markov chain on graph partitions that makes
relatively global moves yet is computationally feasible to
be used as the proposal in the Metropolis-Hastings method.
Our resulting algorithm is able to sample from a specified
measure on partitions or spanning forests. Being able to
sample from a specified measure is a requirement of what we
consider as the gold standard in quantifying the extent to
which a particular map is a gerrymander. Our proposal chain
modifies the recently developed method called recombination
(ReCom), which draws spanning trees on joined partitions and
then randomly cuts them to repartition. We improve the
computational efficiency by augmenting the statespace from
partitions to spanning forests. The extra information
accelerates the computation of the forward and backward
proposal probabilities which are required for the
Metropolis-Hastings algorithm. We demonstrate this method by
sampling redistricting plans on several measures of interest
and find promising convergence results on several key
observables of interest. We also explore some limitations in
the measures that are efficient to sample from and
investigate the feasibility of using parallel tempering to
extend this space of measures.},
Doi = {10.1137/21M1418010},
Key = {fds374487}
}
@article{fds368290,
Author = {Zhao, Z and Hettle, C and Gupta, S and Mattingly, JC and Randall, D and Herschlag, GJ},
Title = {Mathematically Quantifying Non-responsiveness of the 2021
Georgia Congressional Districting Plan},
Journal = {ACM International Conference Proceeding Series},
Year = {2022},
Month = {October},
ISBN = {9781450394772},
url = {http://dx.doi.org/10.1145/3551624.3555300},
Abstract = {To audit political district maps for partisan
gerrymandering, one may determine a baseline for the
expected distribution of partisan outcomes by sampling an
ensemble of maps. One approach to sampling is to use
redistricting policy as a guide to precisely codify
preferences between maps. Such preferences give rise to a
probability distribution on the space of redistricting
plans, and Metropolis-Hastings methods allow one to sample
ensembles of maps from the specified distribution. Although
these approaches have nice theoretical properties and have
successfully detected gerrymandering in legal settings,
sampling from commonly-used policy-driven distributions is
often computationally difficult. As of yet, there is no
algorithm that can be used off-the-shelf for checking maps
under generic redistricting criteria. In this work, we
mitigate the computational challenges in a
Metropolized-sampling technique through a parallel tempering
method combined with ReCom[11] and, for the first time,
validate that such techniques are effective on these
problems at the scale of statewide precinct graphs for more
policy informed measures. We develop these improvements
through the first case study of district plans in Georgia.
Our analysis projects that any election in Georgia will
reliably elect 9 Republicans and 5 Democrats under the
enacted plan. This result is largely fixed even as public
opinion shifts toward either party and the partisan outcome
of the enacted plan does not respond to the will of the
people. Only 0.12% of the ∼160K plans in our ensemble were
similarly non-responsive.},
Doi = {10.1145/3551624.3555300},
Key = {fds368290}
}
@article{fds355783,
Author = {Herschlag, G and Lee, S and Vetter, JS and Randles,
A},
Title = {Analysis of GPU Data Access Patterns on Complex Geometries
for the D3Q19 Lattice Boltzmann Algorithm},
Journal = {IEEE Transactions on Parallel and Distributed
Systems},
Volume = {32},
Number = {10},
Pages = {2400-2414},
Year = {2021},
Month = {October},
url = {http://dx.doi.org/10.1109/TPDS.2021.3061895},
Abstract = {GPU performance of the lattice Boltzmann method (LBM)
depends heavily on memory access patterns. When implemented
with GPUs on complex domains, typically, geometric data is
accessed indirectly and lattice data is accessed
lexicographically. Although there are a variety of other
options, no study has examined the relative efficacy between
them. Here, we examine a suite of memory access schemes via
empirical testing and performance modeling. We find strong
evidence that semi-direct is often better suited than the
more common indirect addressing, providing increased
computational speed and reducing memory consumption. For the
layout, we find that the Collected Structure of Arrays
(CSoA) and bundling layouts outperform the common Structure
of Array layout; on V100 and P100 devices, CSoA consistently
outperforms bundling, however the relationship is more
complicated on K40 devices. When compared to
state-of-the-art practices, our recommendations lead to
speedups of 10-40 percent and reduce memory consumption up
to 17 percent. Using performance modeling and computational
experimentation, we determine the mechanisms behind the
accelerations. We demonstrate that our results hold across
multiple GPUs on two leadership class systems, and present
the first near-optimal strong results for LBM with arterial
geometries run on GPUs.},
Doi = {10.1109/TPDS.2021.3061895},
Key = {fds355783}
}
@article{fds360560,
Author = {Autry, EA and Carter, D and Herschlag, GJ and Hunter, Z and Mattingly,
JC},
Title = {METROPOLIZED MULTISCALE FOREST RECOMBINATION for
REDISTRICTING},
Journal = {Multiscale Modeling and Simulation},
Volume = {19},
Number = {4},
Pages = {1885-1914},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2021},
Month = {January},
url = {http://dx.doi.org/10.1137/21M1406854},
Abstract = {We develop a Metropolized Multiscale Forest Recombination
Markov Chain on redistricting plans. The chain is designed
to be usable as the proposal in a Markov Chain Monte Carlo
(MCMC) algorithm. Sampling the space of plans amounts to
dividing a graph into a partition with a specified number of
elements each of which corresponds to a different district
according to a specified probability measure. The districts
satisfy a collection of hard constraints, and the
probability measure may be weighted with regard to a number
of other criteria. The multiscale algorithm is similar to
our previously developed Metropolized Forest Recombination
proposal; however, this algorithm provides improved scaling
properties and may also be used to preserve nested
communities of interest such as counties and precincts. Both
works use a proposal which extends the ReCom algorithm [D.
DeFord, M. Duchin, and J. Solomon, Harvard Data Sci. Rev.,
(2021)] which leveraged spanning trees to merge and split
districts. In this work, we extend the state space so that
each district is defined by a hierarchy of trees. In this
sense, the proposal step in both algorithms can be seen as a
“Forest ReCom.” The collection of plans sampled by the
MCMC algorithm can serve as a baseline against which a
particular plan of interest is compared. If a given plan has
different racial or partisan qualities than what is typical
of the collection of plans, the given plan may have been
gerrymandered and is labeled as an outlier. Metropolizing
relative to a policy driven probability measure removes the
possibility of algorithmically inserted biases.},
Doi = {10.1137/21M1406854},
Key = {fds360560}
}
@article{fds362602,
Author = {Herschlag, G and Mattingly, JC and Sachs, M and Wyse,
E},
Title = {Non-reversible Markov chain Monte Carlo for sampling of
districting maps},
Year = {2020},
Month = {August},
Abstract = {Evaluating the degree of partisan districting
(Gerrymandering) in a statistical framework typically
requires an ensemble of districting plans which are drawn
from a prescribed probability distribution that adheres to a
realistic and non-partisan criteria. In this article we
introduce novel non-reversible Markov chain Monte-Carlo
(MCMC) methods for the sampling of such districting plans
which have improved mixing properties in comparison to
previously used (reversible) MCMC algorithms. In doing so we
extend the current framework for construction of
non-reversible Markov chains on discrete sampling spaces by
considering a generalization of skew detailed balance. We
provide a detailed description of the proposed algorithms
and evaluate their performance in numerical
experiments.},
Key = {fds362602}
}
@article{fds362603,
Author = {Autry, EA and Carter, D and Herschlag, G and Hunter, Z and Mattingly,
JC},
Title = {Multi-Scale Merge-Split Markov Chain Monte Carlo for
Redistricting},
Year = {2020},
Month = {August},
Abstract = {We develop a Multi-Scale Merge-Split Markov chain on
redistricting plans. The chain is designed to be usable as
the proposal in a Markov Chain Monte Carlo (MCMC) algorithm.
Sampling the space of plans amounts to dividing a graph into
a partition with a specified number of elements which each
correspond to a different district. The districts satisfy a
collection of hard constraints and the measure may be
weighted with regard to a number of other criteria. The
multi-scale algorithm is similar to our previously developed
Merge-Split proposal, however, this algorithm provides
improved scaling properties and may also be used to preserve
nested communities of interest such as counties and
precincts. Both works use a proposal which extends the ReCom
algorithm which leveraged spanning trees merge and split
districts. In this work we extend the state space so that
each district is defined by a hierarchy of trees. In this
sense, the proposal step in both algorithms can be seen as a
"Forest ReCom." We also expand the state space to include
edges that link specified districts, which further improves
the computational efficiency of our algorithm. The
collection of plans sampled by the MCMC algorithm can serve
as a baseline against which a particular plan of interest is
compared. If a given plan has different racial or partisan
qualities than what is typical of the collection of plans,
the given plan may have been gerrymandered and is labeled as
an outlier.},
Key = {fds362603}
}
@article{fds352187,
Author = {Herschlag, G and Kang, HS and Luo, J and Graves, CV and Bangia, S and Ravier, R and Mattingly, JC},
Title = {Quantifying Gerrymandering in North Carolina},
Journal = {Statistics and Public Policy},
Volume = {7},
Number = {1},
Pages = {30-38},
Publisher = {Informa UK Limited},
Year = {2020},
Month = {January},
url = {http://dx.doi.org/10.1080/2330443X.2020.1796400},
Abstract = {By comparing a specific redistricting plan to an ensemble of
plans, we evaluate whether the plan translates individual
votes to election outcomes in an unbiased fashion.
Explicitly, we evaluate if a given redistricting plan
exhibits extreme statistical properties compared to an
ensemble of nonpartisan plans satisfying all legal criteria.
Thus, we capture how unbiased redistricting plans interpret
individual votes via a state’s geo-political landscape. We
generate the ensemble of plans through a Markov chain Monte
Carlo algorithm coupled with simulated annealing based on a
reference distribution that does not include partisan
criteria. Using the ensemble and historical voting data, we
create a null hypothesis for various election results, free
from partisanship, accounting for the state’s
geo-politics. We showcase our methods on two recent
congressional districting plans of NC, along with a plan
drawn by a bipartisan panel of retired judges. We find the
enacted plans are extreme outliers whereas the bipartisan
judges’ plan does not give rise to extreme partisan
outcomes. Equally important, we illuminate anomalous
structures in the plans of interest by developing graphical
representations which help identify and understand instances
of cracking and packing associated with gerrymandering.
These methods were successfully used in recent court cases.
Supplementary materials for this article are available
online.},
Doi = {10.1080/2330443X.2020.1796400},
Key = {fds352187}
}
@article{fds352188,
Author = {Carter, D and Hunter, Z and Teague, D and Herschlag, G and Mattingly,
J},
Title = {Optimal Legislative County Clustering in North
Carolina},
Journal = {Statistics and Public Policy},
Volume = {7},
Number = {1},
Pages = {19-29},
Year = {2020},
Month = {January},
url = {http://dx.doi.org/10.1080/2330443X.2020.1748552},
Abstract = {North Carolina’s constitution requires that state
legislative districts should not split counties. However,
counties must be split to comply with the “one person, one
vote” mandate of the U.S. Supreme Court. Given that
counties must be split, the North Carolina legislature and
the courts have provided guidelines that seek to reduce
counties split across districts while also complying with
the “one person, one vote” criterion. Under these
guidelines, the counties are separated into clusters; each
cluster contains a specified number of districts and that
are drawn independent from other clusters. The primary goal
of this work is to develop, present, and publicly release an
algorithm to optimally cluster counties according to the
guidelines set by the court in 2015. We use this tool to
investigate the optimality and uniqueness of the enacted
clusters under the 2017 redistricting process. We verify
that the enacted clusters are optimal, but find other
optimal choices. We emphasize that the tool we provide lists
all possible optimal county clusterings. We also explore the
stability of clustering under changing statewide populations
and project what the county clusters may look like in the
next redistricting cycle beginning in 2020/2021.
Supplementary materials for this article are available
online.},
Doi = {10.1080/2330443X.2020.1748552},
Key = {fds352188}
}
@article{fds347398,
Author = {Herschlag, G and Gounley, J and Roychowdhury, S and Draeger, EW and Randles, A},
Title = {Multi-physics simulations of particle tracking in arterial
geometries with a scalable moving window
algorithm},
Journal = {Proceedings - IEEE International Conference on Cluster
Computing, ICCC},
Volume = {2019-September},
Year = {2019},
Month = {September},
ISBN = {9781728147345},
url = {http://dx.doi.org/10.1109/CLUSTER.2019.8891041},
Abstract = {In arterial systems, cancer cell trajectories determine
metastatic cancer locations; similarly, particle
trajectories determine drug delivery distribution.
Predicting trajectories is challenging, as the dynamics are
affected by local interactions with red blood cells, complex
hemodynamic flow structure, and downstream factors such as
stenoses or blockages. Direct simulation is not possible, as
a single simulation of a large arterial domain with explicit
red blood cells is currently intractable on even the largest
supercomputers. To overcome this limitation, we present a
multi-physics adaptive window algorithm, in which individual
red blood cells are explicitly modeled in a small region of
interest moving through a coupled arterial fluid domain. We
describe the coupling between the window and fluid domains,
including automatic insertion and deletion of explicit cells
and dynamic tracking of cells of interest by the window. We
show that this algorithm scales efficiently on heterogeneous
architectures and enables us to perform large,
highly-resolved particle-tracking simulations that would
otherwise be intractable.},
Doi = {10.1109/CLUSTER.2019.8891041},
Key = {fds347398}
}
@article{fds368291,
Author = {Herschlag, G and Gounley, J and Roychowdhury, S and Draeger, EW and Randles, A},
Title = {Multi-physics simulations of particle tracking in arterial
geometries with a scalable moving window
algorithm},
Journal = {2019 IEEE INTERNATIONAL CONFERENCE ON CLUSTER COMPUTING
(CLUSTER)},
Pages = {396-406},
Publisher = {IEEE},
Year = {2019},
Month = {January},
Key = {fds368291}
}
@article{fds347399,
Author = {Chin, A and Herschlag, G and Mattingly, J},
Title = {The Signature of Gerrymandering in Rucho v. Common
Cause},
Journal = {South Carolina Law Review},
Volume = {70},
Year = {2019},
Key = {fds347399}
}
@article{fds340184,
Author = {Herschlag, G and Lee, S and Vetter, JS and Randles,
A},
Title = {GPU data access on complex geometries for D3Q19 lattice
boltzmann method},
Journal = {Proceedings - 2018 IEEE 32nd International Parallel and
Distributed Processing Symposium, IPDPS 2018},
Pages = {825-834},
Publisher = {IEEE},
Year = {2018},
Month = {August},
ISBN = {9781538643686},
url = {http://dx.doi.org/10.1109/IPDPS.2018.00092},
Abstract = {GPU performance of the lattice Boltzmann method (LBM)
depends heavily on memory access patterns. When LBM is
advanced with GPUS on complex computational domains,
geometric data is typically accessed indirectly, and lattice
data is typically accessed lexicographically in the
Structure of Array (SoA) layout. Although there are a
variety of existing access patterns beyond the typical
choices, no study has yet examined the relative efficacy
between them. Here, we compare a suite of memory access
schemes via empirical testing and performance modeling. We
find strong evidence that semi-direct addressing is the
superior addressing scheme for the majority of cases
examined: Semi-direct addressing increases computational
speed and often reduces memory consumption. For lattice
layout, we find that the Collected Structure of Arrays
(CSoA) layout outperforms the SoA layout. When compared to
state-of-The-Art practices, our recommended addressing
modifications lead to performance gains between 10-40%
across different complex geometries, fluid volume fractions,
and resolutions. The modifications also lead to a decrease
in memory consumption by as much as 17%. Having discovered
these improvements, we examine a highly resolved arterial
geometry on a leadership class system. On this system we
present the first near-optimal strong results for LBM with
arterial geometries run on GPUS. We also demonstrate that
the above recommendations remain valid for large scale, many
device simulations, which leads to an increased
computational speed and average memory usage reductions. To
understand these observations, we employ performance
modeling which reveals that semi-direct methods outperform
indirect methods due to a reduced number of total
loads/stores in memory, and that CSoA outperforms SoA and
bundling due to improved caching behavior.},
Doi = {10.1109/IPDPS.2018.00092},
Key = {fds340184}
}
@article{fds330268,
Author = {Cao, Y and Feng, Y and Ryser, MD and Zhu, K and Herschlag, G and Cao, C and Marusak, K and Zauscher, S and You, L},
Title = {Programmable assembly of pressure sensors using
pattern-forming bacteria.},
Journal = {Nat Biotechnol},
Volume = {35},
Number = {11},
Pages = {1087-1093},
Year = {2017},
Month = {November},
url = {http://dx.doi.org/10.1038/nbt.3978},
Abstract = {Biological systems can generate microstructured materials
that combine organic and inorganic components and possess
diverse physical and chemical properties. However, these
natural processes in materials fabrication are not readily
programmable. Here, we use a synthetic-biology approach to
assemble patterned materials. We demonstrate programmable
fabrication of three-dimensional (3D) materials by printing
engineered self-patterning bacteria on permeable membranes
that serve as a structural scaffold. Application of gold
nanoparticles to the colonies creates hybrid
organic-inorganic dome structures. The dynamics of the dome
structures' response to pressure is determined by their
geometry (colony size, dome height, and pattern), which is
easily modified by varying the properties of the membrane
(e.g., pore size and hydrophobicity). We generate resettable
pressure sensors that process signals in response to varying
pressure intensity and duration.},
Doi = {10.1038/nbt.3978},
Key = {fds330268}
}
@article{fds335537,
Author = {Herschlag, G and Ravier, R and Mattingly, JC},
Title = {Evaluating Partisan Gerrymandering in Wisconsin},
Year = {2017},
Month = {September},
Abstract = {We examine the extent of gerrymandering for the 2010 General
Assembly district map of Wisconsin. We find that there is
substantial variability in the election outcome depending on
what maps are used. We also found robust evidence that the
district maps are highly gerrymandered and that this
gerrymandering likely altered the partisan make up of the
Wisconsin General Assembly in some elections. Compared to
the distribution of possible redistricting plans for the
General Assembly, Wisconsin's chosen plan is an outlier in
that it yields results that are highly skewed to the
Republicans when the statewide proportion of Democratic
votes comprises more than 50-52% of the overall vote (with
the precise threshold depending on the election considered).
Wisconsin's plan acts to preserve the Republican majority by
providing extra Republican seats even when the Democratic
vote increases into the range when the balance of power
would shift for the vast majority of redistricting
plans.},
Key = {fds335537}
}
@article{fds361286,
Author = {Bangia, S and Graves, CV and Herschlag, G and Kang, HS and Luo, J and Mattingly, JC and Ravier, R},
Title = {Redistricting: Drawing the Line},
Year = {2017},
Month = {April},
Abstract = {We develop methods to evaluate whether a political
districting accurately represents the will of the people. To
explore and showcase our ideas, we concentrate on the
congressional districts for the U.S. House of
representatives and use the state of North Carolina and its
redistrictings since the 2010 census. Using a Monte Carlo
algorithm, we randomly generate over 24,000 redistrictings
that are non-partisan and adhere to criteria from proposed
legislation. Applying historical voting data to these random
redistrictings, we find that the number of democratic and
republican representatives elected varies drastically
depending on how districts are drawn. Some results are more
common, and we gain a clear range of expected election
outcomes. Using the statistics of our generated
redistrictings, we critique the particular congressional
districtings used in the 2012 and 2016 NC elections as well
as a districting proposed by a bipartisan redistricting
commission. We find that the 2012 and 2016 districtings are
highly atypical and not representative of the will of the
people. On the other hand, our results indicate that a plan
produced by a bipartisan panel of retired judges is highly
typical and representative. Since our analyses are based on
an ensemble of reasonable redistrictings of North Carolina,
they provide a baseline for a given election which
incorporates the geometry of the state's population
distribution.},
Key = {fds361286}
}
@article{fds340185,
Author = {Herschlag, G and Liu, JG and Layton, AT},
Title = {Fluid extraction across pumping and permeable walls in the
viscous limit},
Journal = {Physics of Fluids},
Volume = {28},
Number = {4},
Pages = {041902-041902},
Publisher = {AIP Publishing},
Year = {2016},
Month = {April},
url = {http://dx.doi.org/10.1063/1.4946005},
Abstract = {In biological transport mechanisms such as insect
respiration and renal filtration, fluid travels along a
leaky channel allowing material exchange with systems
exterior to the channel. The channels in these systems may
undergo peristaltic pumping which is thought to enhance the
material exchange. To date, little analytic work has been
done to study the effect of pumping on material extraction
across the channel walls. In this paper, we examine a fluid
extraction model in which fluid flowing through a leaky
channel is exchanged with fluid in a reservoir. The channel
walls are allowed to contract and expand uniformly,
simulating a pumping mechanism. In order to efficiently
determine solutions of the model, we derive a formal power
series solution for the Stokes equations in a finite channel
with uniformly contracting/expanding permeable walls. This
flow has been well studied in the case in which the normal
velocity at the channel walls is proportional to the wall
velocity. In contrast we do not assume flow that is
proportional to the wall velocity, but flow that is driven
by hydrostatic pressure, and we use Darcy's law to close our
system for normal wall velocity. We incorporate our flow
solution into a model that tracks the material pressure
exterior to the channel. We use this model to examine flux
across the channel-reservoir barrier and demonstrate that
pumping can either enhance or impede fluid extraction across
channel walls. We find that associated with each set of
physical flow and pumping parameters, there are optimal
reservoir conditions that maximize the amount of material
flowing from the channel into the reservoir.},
Doi = {10.1063/1.4946005},
Key = {fds340185}
}
@article{fds316988,
Author = {Herschlag, G and Liu, J-G and Layton, AT},
Title = {Optimal reservoir conditions for fluid extraction through
permeable walls in the viscous limit},
Year = {2015},
Month = {November},
url = {http://arxiv.org/abs/1511.01469v1},
Abstract = {In biological transport mechanisms such as insect
respiration and renal filtration, fluid travels along a
leaky channel allowing exchange with systems exterior the
the channel. The channels in these systems may undergo
peristaltic pumping which is thought to enhance the material
exchange. To date, little analytic work has been done to
study the effect of pumping on material extraction across
the channel walls. In this paper, we examine a fluid
extraction model in which fluid flowing through a leaky
channel is exchanged with fluid in a reservoir. The channel
walls are allowed to contract and expand uniformly,
simulating a pumping mechanism. In order to efficiently
determine solutions of the model, we derive a formal power
series solution for the Stokes equations in a finite channel
with uniformly contracting/expanding permeable walls. This
flow has been well studied in the case of weakly permeable
channel walls in which the normal velocity at the channel
walls is proportional to the wall velocity. In contrast we
do not assume weakly driven flow, but flow driven by
hydrostatic pressure, and we use Dacry's law to close our
system for normal wall velocity. We use our flow solution to
examine flux across the channel-reservoir barrier and
demonstrate that pumping can either enhance or impede fluid
extraction across channel walls. We find that associated
with each set of physical flow and pumping parameters, there
are optimal reservoir conditions that maximizes the amount
of material flowing from the channel into the
reservoir.},
Key = {fds316988}
}
@article{fds316989,
Author = {Herschlag, GJ and Mitran, S and Lin, G},
Title = {A consistent hierarchy of generalized kinetic equation
approximations to the master equation applied to surface
catalysis.},
Journal = {The Journal of chemical physics},
Volume = {142},
Number = {23},
Pages = {234703},
Year = {2015},
Month = {June},
ISSN = {0021-9606},
url = {http://hdl.handle.net/10161/12397 Duke open
access},
Abstract = {We develop a hierarchy of approximations to the master
equation for systems that exhibit translational invariance
and finite-range spatial correlation. Each approximation
within the hierarchy is a set of ordinary differential
equations that considers spatial correlations of varying
lattice distance; the assumption is that the full system
will have finite spatial correlations and thus the behavior
of the models within the hierarchy will approach that of the
full system. We provide evidence of this convergence in the
context of one- and two-dimensional numerical examples.
Lower levels within the hierarchy that consider shorter
spatial correlations are shown to be up to three orders of
magnitude faster than traditional kinetic Monte Carlo
methods (KMC) for one-dimensional systems, while predicting
similar system dynamics and steady states as KMC methods. We
then test the hierarchy on a two-dimensional model for the
oxidation of CO on RuO2(110), showing that low-order
truncations of the hierarchy efficiently capture the
essential system dynamics. By considering sequences of
models in the hierarchy that account for longer spatial
correlations, successive model predictions may be used to
establish empirical approximation of error estimates. The
hierarchy may be thought of as a class of generalized
phenomenological kinetic models since each element of the
hierarchy approximates the master equation and the lowest
level in the hierarchy is identical to a simple existing
phenomenological kinetic models.},
Doi = {10.1063/1.4922515},
Key = {fds316989}
}
@article{fds316991,
Author = {Herschlag, G and Liu, JG and Layton, AT},
Title = {An exact solution for stokes flow in a channel with
arbitrarily large wall permeability},
Journal = {SIAM Journal on Applied Mathematics},
Volume = {75},
Number = {5},
Pages = {2246-2267},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2015},
Month = {January},
ISSN = {0036-1399},
url = {http://arxiv.org/abs/1411.3672},
Keywords = {filtration • permeable boundaries • Stokes
flow},
Abstract = {We derive an exact solution for Stokes flow in a channel
with permeable walls. At the channel walls, the normal
component of the fluid velocity is described by Darcy's law,
and the tangential component of the fluid velocity is
described by the no slip condition. The pressure exterior to
the channel is assumed to be constant. Although this problem
has been well studied, typical studies assume that the
permeability of the wall is small relative to other
nondimensional parameters; this work relaxes this assumption
and explores a regime in parameter space that has not yet
been well studied. A consequence of this relaxation is that
transverse velocity is no longer necessarily small when
compared with the axial velocity. We use our result to
explore how existing asymptotic theories break down in the
limit of large permeability for channels of small
length.},
Doi = {10.1137/140995854},
Key = {fds316991}
}
@article{fds220747,
Author = {G. Herschlag and G.J.M. Garcia and B. Button and R. Tarran and B.
Lindley, B. Reinhardt and T.C. Elston and M.G.
Forest},
Title = {A mechanochemical model for auto-regulation of lung airway
surface layer volume},
Journal = {Journal of Theoretical Biology},
Volume = {325},
Pages = {42-51},
Year = {2013},
Month = {May},
url = {http://www.sciencedirect.com/science/article/pii/S0022519313000489},
Abstract = {http://www.sciencedirect.com/science/article/pii/S0022519313000489},
Key = {fds220747}
}
@article{fds220748,
Author = {G. Herschlag and L. Miller},
Title = {Reynolds number limits for jet propulsion: A numerical study
of simplified jellyfish},
Journal = {Journal of Theoretical Biology},
Volume = {285},
Number = {1},
Pages = {84-95},
Year = {2011},
Month = {September},
url = {http://www.sciencedirect.com/science/article/pii/S0022519311002876},
Abstract = {http://www.sciencedirect.com/science/article/pii/S0022519311002876},
Key = {fds220748}
}
@article{fds316992,
Author = {Herschlag, G and Miller, LA},
Title = {Reynolds number limits for jet propulsion: A numerical study
of simplified jellyfish},
Year = {2010},
Month = {October},
url = {http://arxiv.org/abs/1010.3357v1},
Abstract = {The Scallop Theorem states that reciprocal methods of
locomotion, such as jet propulsion or paddling, will not
work in Stokes flow (Reynolds number = 0). In nature the
effective limit of jet propulsion is still in the range
where inertial forces are significant. It appears that
almost all animals that use jet propulsion swim at Reynolds
numbers (Re) of about 5 or more. Juvenile squid and octopods
hatch from the egg already swimming in this inertial regime.
The limitations of jet propulsion at intermediate Re is
explored here using the immersed boundary method to solve
the two-dimensional Navier Stokes equations coupled to the
motion of a simplified jellyfish. The contraction and
expansion kinematics are prescribed, but the forward and
backward swimming motions of the idealized jellyfish are
emergent properties determined by the resulting fluid
dynamics. Simulations are performed for both an oblate bell
shape using a paddling mode of swimming and a prolate bell
shape using jet propulsion. Average forward velocities and
work put into the system are calculated for Reynolds numbers
between 1 and 320. The results show that forward velocities
rapidly decay with decreasing Re for all bell shapes when Re
< 10. Similarly, the work required to generate the pulsing
motion increases significantly for Re < 10. When compared
actual organisms, the swimming velocities and vortex
separation patterns for the model prolate agree with those
observed in Nemopsis bachei. The forward swimming velocities
of the model oblate jellyfish after two pulse cycles are
comparable to those reported for Aurelia aurita, but
discrepancies are observed in the vortex dynamics between
when the 2D model oblate jellyfish and the
organism.},
Key = {fds316992}
}
@article{fds316993,
Author = {Miller, L and Herschlag, G and Santhanakrishnan,
A},
Title = {Leaf roll-up and aquaplaning in strong winds and
floods},
Year = {2008},
Month = {October},
url = {http://arxiv.org/abs/0810.1975v1},
Abstract = {Flexible plants, fungi, and sessile animals are thought to
reconfigure in the wind and water to reduce the drag forces
that act upon them. In strong winds, for example, leaves
roll up into cone shapes that reduce flutter and drag when
compared to paper cut-outs with similar shapes and
flexibility. During flash floods, herbaceous broad leaves
aquaplane on the surface of the water which reduces drag.
Simple mathematical models of a flexible beam immersed in a
two-dimensional flow will also reconfigure in flow. What is
less understood is how the mechanical properties of a
two-dimensional leaf in a three-dimensional flow will
passively allow roll up and aquaplaning. In this study, we
film leaf roll-up and aquaplaning in tree and vine leaves in
both strong winds and water flows.},
Key = {fds316993}
}
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Mathematics Department