From genes to geometry: how visceral organs take form
Visceral organs are composed of multiple tissue layers that interact both mechanically and chemically. During morphogenesis, the initial geometry of visceral organs undergoes a sequence of folding, adopting complex shapes that are vital for function. How do coupled tissue layers choreograph organ shape transformations during embryonic development? Understanding the dynamics of visceral organs has been a formidable challenge, due to both technical and conceptual challenges. We bring advanced microscopy, computational, and theoretical approaches to address how dynamic cellular behaviors generate active stresses to achieve stereotyped shape change in 3D. 
In a recent paper, we show how coupled tissue layers generate complex shape transformations in the fly midgut. We find that calcium mediates the contraction of muscle cells in the outer layer, triggering cellular shape transformations in the endodermal inner layer. These shape transformations give rise at the tissue scale to a convergent extension motif that couples in-plane deformations to out-of-plane motion.
publication: N. P. Mitchell, D. J. Cislo, S. Shankar, Y. Lin, B. I. Shraiman, S. J. Streichan, “Visceral organ morphogenesis via calcium-patterned muscle contractions.” eLife 11:e77355 [biorxiv]
Methods for building quantitative models of morphogenesis
We automatically extract Lagrangian measures of deformation from complex, dynamic tissue surfaces in 3D. This enables whole-organ tracking, quantification of tissue deformation and cell intercalations, tissue anisotropy, and more.
We also develop methods for building atlases of embryonic development based on tissue morphology, enabling a large, unified atlas of gene expression and tissue deformation. This atlas features fly embryos from 0-24 hrs of development, including whole-animal datasets of organ development at high temporal resolution (as low as 30 sec/volume). 
publications:
[1] N. P. Mitchell*, D. J. Cislo*. “TubULAR: Tracking deformations of dynamic tissues and interfaces in 3D.” [biorxiv]
[2] N. P. Mitchell*, M. F. Levebvre*, V. Jain-Sharma*, N. Claussen, M. K. Raich, H. J. Gustafson, A. R. Bausch, S. J. Streichan. “Morphodynamic atlas of Drosophila development.” [biorxiv] *equal contribution
Embryonic gastrulation as condensed matter physics
By careful measurements of the tissue deformations during early embryogenesis in Drosophila, we find that anisotropic myosin patterns in the swirling tissues exhibit remarkable self-similarity over time — far more than would be possible if the tissue was advecting these patterns. This work and ongoing collaborations with Sebastian Streichan’s lab attempt to unravel the different contributions to mechanical deformations in the early embryo.
publication: M. F. Lefebvre*, N. H. Claussen*, N. P. Mitchell, H. J. Gustafson, S. J Streichan. “Geometric control of Myosin-II orientation during axis elongation.” eLife 2023 [biorxiv]
Biological active matter in vitro
How do cytoskeletal components self-organize to generate intricate structures? In joint work with the Dogic Lab (UCSB), we study how reconstituted cytoskeletal components generate contractile gels, extensile fluids, and complex tissue-like 3D shapes, using gels made of microtubules and the molecular motor kinesin-4 as a model system. Unlike some other kinesin motors, kinesin-4 dwells on the tips of microtubules, leading to diverse behaviors for different concentrations of microtubules. 
publication: B. Lemma, N. P. Mitchell, R. Subramanian, D. J. Needleman, Z. Dogic. “Active microphase separation in mixtures of microtubules and tip-accumulating molecular motors.” Physical Review X (2022) [arxiv]
Geometry and topology of colloidal membranes
In a recent study with Dogic Lab, we the geometry and topology of self-assembled membranes composed of viral rods. These colloidal structures form curved surfaces that fuse into catenoids, tri-noids, four-noids, and even system-spanning, sponge-like phases. Tuning temperature controls the geometry of the membranes. 
publication: A. Khanra, L. L. Jia, N. P. Mitchell, A. Balchunas, R. A. Pelcovits, T. R. Powers, Z. Dogic, P. Sharma. “Controlling the shape and topology of two-component colloidal membranes.” PNAS 2022 [arxiv]
PAST RESEARCH
Fluid dynamics
The elementary building blocks of turbulent flow are vortices. We build a blob of turbulence embedded in a non-turbulent fluid environment by repeated injection of vortex rings. This method enables tuning the properties of the flow by tuning the building blocks, such as by adding helicity to the injected rings.
[1] T. Matsuzawa, N. P. Mitchell, S. Perrard, W. T. M. Irvine. “Creation of an isolated turbulent blob fed by vortex rings.” Nature Physics (accepted, 2023). [arxiv]
Topological metamaterials
While traditional materials can often be modeled as networks of masses interacting by springs, highly unusual behavior arises when the masses of such a network are replaced by rapidly spinning tops (gyroscopes). In particular, these networks can exhibit band gaps and uni-directional wave propagation on the network’s edges. Since these behaviors are protected by topological properties of the structures, the waves traverse sharp corners and persist despite impurities in the material.
To our surprise, we found that not only can topological matter have some disorder, but networks with topological band structure can be constructed in a completely amorphous structure. See our paper here for more info.
Next, we demonstrated the ability to create a topological switch using a gyroscopic metamaterial in an experiment. By introducing a patterned magnetic field at every site that interacts with each gyroscope, we break the inversion symmetry (the symmetry under looking at the mirror image) of the network. Once the inversion symmetry breaking is large enough, the edge modes bleed into bulk modes, and the topological waves are shut off. We can control this transition in real time, enabling the use of topological waves for information storage and readout. Read our paper here. Another paper on other topological phase transitions in these systems is here, and an in-depth paper on the symmetries and scaling laws is here.
[1] N. P. Mitchell, L. M. Nash, D. Hexner, A. M. Turner, W. T. M. Irvine. “Amorphous topological insulators constructed from random point sets.” Nature Physics 14, 380–385 (2018). [Full text, arxiv]
[2] N. P. Mitchell, L. M. Nash, W. T. M. Irvine. “Realization of a topological phase transition in gyroscopic lattices.” Physical Review B 97, 100302(R) (2018) [Full text, arxiv]
[3] N. P. Mitchell, L. M. Nash, W. T. M. Irvine. “Tunable band topology in gyroscopic lattices.” Physical Review B, 98, 174301 (2018) [Full text, arxiv]
[4] N. P. Mitchell, A. M. Turner, W. T. M. Irvine. “Real-space origin of topological band gaps, localization, and re-entrant phase transitions in gyroscopic metamaterials.” Physical Review E, 104, 025007 (2021) [arxiv, Full text]
Fracture mechanics on curved surfaces
In recent decades, a deeper understanding of fracture has led to novel tools for controlling cracks. Collaborators and I have uncovered how Gaussian curvature guides material failure in otherwise unstructured or modified elastic sheets. We find that draping an elastic sheet over a curved substrate can trigger or prevent crack growth, direct crack paths, and even arrest cracks. This complex behavior obeys robust geometric principles which should apply to a wide range of systems spanning many scales, from nanoparticle membranes to macroscopic structures.
Fracture and deformation in curved nanoparticle sheets
A useful regime to study the deformation of sheets 
conformed to curved surfaces is on the nanoscale. Nanoparticle monolayer sheets are ultrathin inorganic–organic hybrid materials with broad applications. They combine highly controllable optical and electrical properties with mechanical flexibility and remarkable strength. Like other thin sheets, their low bending rigidity allows them to easily roll into or conform to cylindrical geometries. More important still, they can also cope with strain through local particle rearrangement and plastic deformation. This means that, unlike thin sheets such as paper or graphene, nanoparticle sheets can much more easily conform to surfaces with complex topography characterized by non-zero Gaussian curvature, like spherical caps or saddles. We investigated the limits of nanoparticle monolayers’ ability to conform to substrates with Gaussian curvature by stamping nanoparticle sheets onto lattices of larger polystyrene spheres. We found that tuning the size of the spheres reproducibly changes the behavior of the sheet, and we propose a theoretical account of this behavior that is supported by simulations.
publication: N. P. Mitchell*, R. Carey*, J. Hannah, Y. Wang, M. Cortes, S. McBride, H. Jaeger. “Conforming nanoparticle sheets onto surfaces with Gaussian curvature.” Soft Matter, 14, 9107 – 9117 (2018) [Full text, arxiv] *equal contribution
During my undergraduate years, I worked on a fundamental question in astrophysics: How are nearby dwarf galaxies evolving as new stars are born? Since these small galaxies are less evolved than larger galaxies like the Milky Way, understanding their histories could shed light on the evolution of galaxies formed in the early universe. With Kristen McQuinn and Evan Skillman, I looked at bursts of star formation activity in nearby ‘starburst’ dwarf galaxies, examining their star formation activity with data from Hubble (visible light), MIPS (IR), GALEX (UV), and Chandra (x-ray). By examining the same galaxies through a variety of wavelengths, we characterized star formation in these galaxies and the spatial distribution of galactic superwinds.
publications:
[1] K. B. W. McQuinn, N. P. Mitchell, E. D. Skillman. “The Panchromatic Starburst Irregular Dwarf Survey (STARBIRDS): Observations and Data Archive”, The Astrophysical Journal Supplement Series 218 29 (2015). [Full text, arxiv]
[2] K. B. W. McQuinn, E. D. Skillman, A. E. Dolphin, N. P. Mitchell. “Calibrating UV star formation rates for dwarf galaxies from STARBIRDS.” The Astrophysical Journal 808 109 (2015). [Full text, arxiv]
[3] K. B. W. McQuinn, E. D. Skillman, T. N. Heilman, N. P. Mitchell, T. Kelley. “Galactic outflows, star formation histories, and timescales in starburst dwarf galaxies from STARBIRDS.” Monthly Notices of the Royal Astronomical Society, Volume 477, Issue 3, 1 January 1753, Pages 3164–3177, (2018) [Full text, arxiv]
other loosely-related publication: [4] D. E. Nitz, J. Curry, M. Buuck, A. DeMann, N. P. Mitchell,W. Shull, “Transition probabilities of Ce I obtained from Boltzmann analysis of visible and near-infrared emission spectra.”J. Phys. B: At. Mol. Opt. Phys. 51 045007 (2018) [Full text]
Noah P Mitchell 