I'm a Research Scientist in the Biophysical Modeling Group, part of the
Center for Computational Biology
at the
Flatiron Institute.
My research focuses on understanding fluid-structure interactions in complex and active fluids. Understanding the features of such systems requires utilizing a wide range of tools, most of which either do not yet exist or which don’t exist in the required form. Over the past several years, I’ve spent time developing new numerical methods that allow rapid simulations of a wide range of complex or active fluids in nontrivial evolving geometries, deriving continuum models for dense carpets of elastic filaments immersed in fluids, and using these new tools to generate insight into the behavior of the basic mathematical equations used and the biological systems that these equations model.

Research

Aster Rotation

Asters centrate and generate rotational motion when confined to cylinders. This rotation is steady in small cylinders, oscillatory in medium sized cylinders, and ceases in large cylinders. We explain the appearance of switching using a mix of numerical and analytical models, and predict that switching transitions to steady rotation when density is increased, a prediction verified both in silico and in vitro.
Joint work with Sami Bashar, Gokberk Kabacaoglu, John Oakey, Taylor Sulerud, Mike Shelley, and Jay Gatlin.

Closures for active fluid models

Kinetic theories have been successful in modelling the behavior of active nematic and polar fluids, but are high-dimensional, requiring both space and orientational degrees of freedom to be discretized. Coarse-grained models that integrate out the orientational degrees of freedom are cheaper, but necessitate closure assumptions. We have derived a closure model for polar fluids that is analogous to the Bingham closure for nematic fluids, preserving its best analytical qualities, and derived numerical methods for both the nematic and polar Bingham closures that are fast, stable, and accurate, even near alligned states.
Joint work with Scott Weady and Mike Shelley.

Hyperuniformity of rotating ensembles

Ensembles of particles rotating in a two-dimensional fluid can exhibit chaotic dynamics yet develop signatures of hidden order. Initially random distributions of such rotors spontaneously self assemble into distinct arrangements with long-wavelength fluctuations isotropically suppressed --- a hallmark of a disordered hyperuniform material.
Joint work with Naomi Oppenheimer, Matan Yah Ben Zion, and Mike Shelley.

Quadrature by Fundamental Solutions

The evaluation of layer potentials at locations near to their source curves is the cause of a great deal of difficulty, especially in applying boundary integral methods to inhomogeneous problems. I've developed a spectrally accurate and kernel-independent way to evaluate layer potentials from smooth, moderately sized source curves to many nearby targets.
Joint work with Alex Barnett.

Spectral Embedded Boundary Schemes

Embedded boundary schemes enable the solution of PDE on general domains using fast, robust, regular grid solvers. Historically, these have been low order and/or plagued by instability and ill-conditioning. I have developed a novel method which uses Function Intension, or the smooth truncation of function values, combined with techniques from boundary integral methods, to generate solvers that are stable, spectrally accurate, and fast.
Joint work with Alex Barnett and Dan Fortunato.

The Behavior of Deformable Active Droplets

While the behavior of bulk active nematics is reasonably well characterized, the behavior of these complex fluids when confined is poorly understood. Using a combination of numerics and linear stability analysis, we've revealed a pantheon of behaviors accessible to individual active droplets. We've further developed methodology that enables large-scale simulations of many droplets, allowing us to chararcterize the behavior of large and dense ensembles.
Joint work with Yuan-nan Young, and Mike Shelley.

Swirling Flows in Drosophila Oocytes

Cytoplasmic streaming during oocyte development in the fruit fly transitions from a spatially disordered cytoskeleton supporting flows with only short-ranged correlations to an ordered state with a cell-spanning vortical flow. We study a discrete-filament model and a coarse-grained continuum theory for motors moving on a deformable cytoskeleton, both of which exhibit a swirling instability to spontaneous large-scale rotational motion.
Joint work with Gabriele de Canio, Ray Goldstein, Eric Lauga, and Mike Shelley.

Understanding Dense Fiber Beds

Fiber bed behavior changes quantitatively and qualitatively with density. I developed a coarse-grained model where fiber density is a parameter, enabling analytical methods in simple geometries. This has shed light on important phenomenon, including swirling flows in the Drosophila Melanogaster ooocyte and rotation in confined asters.
Joint work with Mike Shelley.

High-order Immersed Boundary methods

Immersed Boundary methods are applicable to a wide range of problems but suffer from low-order accuracy and the inability to impose Neumann boundary conditions. We developed a high-order version of the IB method that allows a wider range of physical boundary conditions to be imposed, and have used this method to study complex fluid flows and dissolution problems.
Joint work with Mac Huang, Robert Guy, and Becca Thomases.

Selected Papers

David B Stein,
Spectrally accurate solutions to inhomogeneous elliptic PDE in smooth geometries using function intension,
Journal of Computational Physics, 2022.
JCParXivPDF

David B Stein, Alex H Barnett,
Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects,
Advances in Computational Math, 2022.
ACOMarXivPDF

Scott Weady, David B Stein, Michael J Shelley,
Thermodynamically consistent coarse-graining of polar active fluids,
Physical Review Fluids, 2022.
PRFarXivPDF

Scott Weady, Michael J Shelley, David B Stein,
A fast Chebyshev method for the Bingham closure with application to active nematic suspensions,
Journal of Computational Physics, 2022.
JCParXivPDF

Naomi Oppenheimer, David B Stein, Matan YB Zion, Michael J Shelley,
Hyperuniformity and phase enrichment in vortex and rotor assemblies,
Nature Communications, 2022.
NaturearXivPDF

Jinzi (Mac) Huang, Michael J Shelley, David B Stein,
A stable and accurate scheme for solving the Stefan problem coupled with natural convection using the Immersed Boundary Smooth Extension method,
Journal of Computational Physics, 2021.
JCParXivPDF

David B Stein, Gabriele de Canio, Michael J Shelley, Raymond E Goldstein,
Swirling Instability of the Microtubule Cytoskeleton,
Physical Review Letters, 2021.
PRLarXivPDF

Yuan-nan Young, Michael J Shelley, David B Stein,
The many behaviors of deformable active droplets,
Mathematical Biosciences and Engineering, 2021.
MBEPDF

Reza Farhadifar, Che-Hang Yu, Gunar Fabig, Hai-Yin Wu, David B Stein, Matthew Rockman, Thomas Müller-Reichert, Michael J Shelley, Daniel J Needleman,
Stoichiometric interactions explain spindle dynamics and scaling across 100 million years of nematode evolution,
eLife, 2020.
eLifePDF

Naomi Oppenheimer, David B Stein, Michael J Shelley,
Rotating Membrane Inclusions Crystallize Through Hydrodynamic and Steric Interactions,
Physical Review Letters, 2019.
PRLarXivPDF

David B Stein, Michael J Shelley,
Coarse-graining the dynamics of immersed and driven fiber assemblies,
Physical Review Fluids, 2019.
PRFarXivPDF

David B Stein, Robert D Guy, Becca Thomases,
Convergent solutions of Stokes Oldroyd-B boundary value problems using the Immersed Boundary Smooth Extension (IBSE) method,
Journal of Non-Newtonian Fluid Mechanics, 2019.
JNNFMPDF

David B Stein, Robert D Guy, Becca Thomases,
Immersed Boundary Smooth Extension (IBSE): A high-order method for solving incompressible flows in arbitrary smooth domains,
Journal of Computational Physics, 2017.
JCParXivPDF

David B Stein, Robert D Guy, Becca Thomases,
Immersed boundary smooth extension: a high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods,
Journal of Computational Physics, 2016.
JCParXivPDF

Stephen K Peck, Dong-Kun Kim, David Stein, Doug Orbaker, Andrew Foss, Matthew T Hummon, Larry R Hunter,
Limits on local Lorentz invariance in mercury and cesium,
Physical Review A, 2012.
PRAarXivPDF

Stephen S Lim, David B Stein, Alexandra Charrow, Christopher JL Murray,
Tracking progress towards universal childhood immunisation and the impact of global initiatives: a systematic analysis of three-dose diphtheria, tetanus, and pertussis immunisation coverage,
The Lancet, 2008.
LancetPDF