Uniqueness of some cylindrical tangent cones to special Lagrangians by Collins, Tristan C., Li, Yang

“…Abstract We show that if an exact special Lagrangian $$N\subset {\mathbb {C}}^n$$ N ⊂ C n has a multiplicity one, cylindrical tangent cone of the form $${\mathbb {R}}^{k}\times {\textbf{C}}$$ R k × C where $${\textbf{C}}$$ C is a special Lagrangian cone with smooth, connected link, then this tangent cone is unique provided $${\textbf{C}}$$ C satisfies an integrability condition. …”
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An index theorem for end-periodic operators by Ruberman, Daniel, Saveliev, Nikolai, Mrowka, Tomasz S

“…We extend the Atiyah, Patodi, and Singer index theorem for first-order differential operators from the context of manifolds with cylindrical ends to manifolds with periodic ends. This theorem provides a natural complement to Taubes’ Fredholm theory for general end-periodic operators. …”
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Inverse Designed Metalenses with Extended Depth of Focus by Bayati, Elyas, Pestourie, Raphaël, Colburn, Shane, Lin, Zin, Johnson, Steven G., Majumdar, Arka

“…Keywords: diffractive optics; dielectric metasurface; extended depth of focus lens; inverse design; cylindrical lens…”
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Degree reduction and graininess for Kakeya-type sets in R[superscript 3] by Guth, Lawrence

“…Let T be a set of cylindrical tubes in ℝ[superscrpit 3] of length N and radius 1. …”
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Regularity of the Level Set Flow by Colding, Tobias, Minicozzi, William

“…We show here that the second derivative is continuous if and only if the flow has a single singular time where it becomes extinct and the singular set consists of a closed C[superscript 1] manifold with cylindrical singularities. © 2017 Wiley Periodicals, Inc.…”
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Complexity of parabolic systems by Colding, Tobias H, Minicozzi, William P

“…Namely, we prove that in any dimension and codimension any ancient flow that is cylindrical at − ∞ $-\infty $ must be a flow of hypersurfaces in a Euclidean subspace. …”
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Generic mean curvature flow I; generic singularities by Colding, Tobias, Minicozzi, William

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Computational inverse design of non-intuitive illumination patterns to maximize optical force or torque by Lee, Yoonkyung E., Miller, Owen D., Reid, McMahon Thomas Homer, Johnson, Steven G, Fang, Xuanlai

“…The nonconvex optimization is efficiently performed by combining a compact cylindrical Bessel basis representation with a fast boundary element method and a standard derivative-free, local optimization algorithm. …”
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Maximizing Performance of Quantum Cascade Laser-Pumped Molecular Lasers by Wang, Fan, Johnson, Steven G, Everitt, Henry O.

“…Using a validated three-level model that captures the essential collision and saturation behaviors of the QPML gas nitrous oxide (N₂O), we explore how the threshold pump power and output terahertz power depend on the pump power and gas pressure, as well as on the diameter, length, and output-coupler transmissivity of a cylindrical cavity. The analysis indicates that maximum power occurs as pump saturation is minimized in a manner that depends much more sensitively on pressure than on cell diameter, length, or transmissivity. …”
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Scalable numerical approach for the steady-state ab initio laser theory by Esterhazy, S., Liertzer, M., Cerjan, A., Ge, L., Makris, K. G., Stone, A. D., Melenk, J. M., Rotter, S., Liu, David, Johnson, Steven G.

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Scalable numerical approach for the steady-state ab initio laser theory by Esterhazy, S., Liertzer, M., Cerjan, A., Ge, L., Makris, K. G., Stone, A. D., Melenk, J. M., Rotter, S., Liu, David, Johnson, Steven G.

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Lozenge Tilings and the Gaussian Free Field on a Cylinder by Ahn, Andrew, Russkikh, Marianna, Van Peski, Roger

“…Under the first variant, corresponding to random cylindric partitions, the height function converges to a deterministic limit shape and fluctuations around it are given by the Gaussian free field in the conformal structure predicted by the Kenyon-Okounkov conjecture. …”
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