MIT Open Access Articles
http://hdl.handle.net/1721.1/49433
2018-06-23T18:44:54ZHigher Critical Points in an Elliptic Free Boundary Problem
http://hdl.handle.net/1721.1/116541
Higher Critical Points in an Elliptic Free Boundary Problem
Jerison, David S; Perera, Kanishka
We study higher critical points of the variational functional associated with a free boundary problem related to plasma confinement. Existence and regularity of minimizers in elliptic free boundary problems have already been studied extensively. But because the functionals are not smooth, standard variational methods cannot be used directly to prove the existence of higher critical points. Here we find a nontrivial critical point of mountain pass type and prove many of the same estimates known for minimizers, including Lipschitz continuity and nondegeneracy. We then show that the free boundary is smooth in dimension 2 and prove partial regularity in higher dimensions.
2017-05-01T00:00:00ZMathematicians’ Central Role in Educating the STEM Workforce
http://hdl.handle.net/1721.1/116540
Mathematicians’ Central Role in Educating the STEM Workforce
Friedlander, Eric M.; Holm, Tara S.; Ewing, John; Goldin, Rebecca; Jaco, William H.; Stevens, T. Christine; Thompson, Abigail; Vogan, David A
In the recent report Engage to Excel,1 President Obama’s Council of Advisors on Science and Technology (PCAST) identifies mathematics as a bottleneck in undergraduate Science, Technology, Engineering, and Mathematics (STEM) education. Among PCAST’s recommendations are ones
calling for the development and teaching of college-level mathematics courses “by faculty from mathematics-intensive disciplines other than mathematics” and for “a new pathway for producing K–12 mathematics teachers…in programs in mathematics-intensive fields other than mathematics.”2 While we are in sharp disagreement with these specific recommendations, we do share PCAST’s concern for the state of STEM education. We encourage the mathematics
community to focus constructively on the broad view the report sketches. We appeal to the community to amplify its communications with other STEM disciplines, to publicize its teaching innovations, and to redouble its efforts to meet the challenges discussed by PCAST.
2012-10-01T00:00:00ZBacterial Succession on Sinking Particles in the Ocean's Interior
http://hdl.handle.net/1721.1/116539
Bacterial Succession on Sinking Particles in the Ocean's Interior
Pelve, Erik A.; DeLong, Edward F.; Fontanez, Kristina M
Sinking particles formed in the photic zone and moving vertically through the water column are a main mechanism for nutrient transport to the deep ocean, and a key component of the biological carbon pump. The particles appear to be processed by a microbial community substantially different from the surrounding waters. Single cell genomics and metagenomics were employed to describe the succession of dominant bacterial groups during particle processing. Sinking particles were extracted from sediment traps at Station Aloha in the North Pacific Subtropical Gyre (NPSG) during two different trap deployments conducted in July and August 2012. The microbial communities in poisoned vs. live sediment traps differed significantly from one another, consistent with prior observations by Fontanez et al. (2015). Partial genomes from these communities were sequenced from cells belonging to the genus Arcobacter (commensalists potentially associated with protists such as Radiolaria), and Vibrio campbellii (a group previously reported to be associated with crustacea). These bacteria were found in the particle-associated communities at specific depths in both trap deployments, presumably due to their specific host-associations. Partial genomes were also sequenced from cells belonging to Idiomarina and Kangiella that were enriched in live traps over a broad depth range, that represented a motile copiotroph and a putatively non-motile algicidal saprophyte, respectively. Planktonic bacterial cells most likely caught in the wake of the particles belonging to Actinomarina and the SAR11 clade were also sequenced. Our results suggest that similar groups of eukaryote-associated bacteria are consistently found on sinking particles at different times, and that particle remineralization involves specific, reproducible bacterial succession events in oligotrophic ocean waters.
2017-11-01T00:00:00ZTheory of Water Desalination with Intercalation Materials
http://hdl.handle.net/1721.1/116538
Theory of Water Desalination with Intercalation Materials
Singh, K.; Bouwmeester, H. J. M.; de Smet, L. C. P. M.; Biesheuvel, P. M.; Bazant, Martin Z
We present a porous electrode theory for capacitive deionization with electrodes containing nanoparticles that consist of a redox-active intercalation material. A geometry of a desalination cell is considered which consists of two porous electrodes, two flow channels, and an anion-exchange membrane, and we use the Nernst-Planck theory to describe ion transport in the aqueous phase in all these layers. A single-salt solution is considered, with unequal diffusion coefficients for anions and cations. Similar to previous models for capacitive deionization and electrodialysis, we solve the dynamic two-dimensional equations by assuming that the flow of water, and thus the advection of ions, is zero in the electrode, and in the flow channel only occurs in the direction along the electrode and membrane. In all layers, diffusion and migration are only considered in the direction perpendicular to the flow of water. Electronic as well as ionic transport limitations within the nanoparticles are neglected, and instead the Frumkin isotherm (or regular solution model) is used to describe local chemical equilibrium of cations between the nanoparticles and the adjacent electrolyte, as a function of the electrode potential. Our model describes the dynamics of key parameters of the CDI process with intercalation electrodes, such as effluent salt concentration, the distribution of intercalated ions, cell voltage, and energy consumption.
2018-06-01T00:00:00Z