@article{22027,
  abstract     = {We demonstrate that in three space dimensions, the scattering behaviour of semilinear wave equations with quintic-type nonlinearities uniquely determines the nonlinearity. The nonlinearity is permitted to depend on both space and time.},
  author       = {Hu, Nicholas and Killip, Rowan and Visan, Monica},
  issn         = {2578-5885},
  journal      = {Pure and Applied Analysis},
  keywords     = {dispersive equations, nonlinear wave equation, semilinear wave equation, scattering, inverse scattering, deconvolution},
  number       = {1},
  pages        = {1--17},
  publisher    = {Mathematical Sciences Publishers},
  title        = {{Deconvolutional determination of the nonlinearity in a semilinear wave equation}},
  doi          = {10.2140/paa.2025.7.1},
  volume       = {7},
  year         = {2025},
}

@article{9301,
  abstract     = {Electrodepositing insulating lithium peroxide (Li2O2) is the key process during discharge of aprotic Li–O2 batteries and determines rate, capacity, and reversibility. Current understanding states that the partition between surface adsorbed and dissolved lithium superoxide governs whether Li2O2 grows as a conformal surface film or larger particles, leading to low or high capacities, respectively. However, better understanding governing factors for Li2O2 packing density and capacity requires structural sensitive in situ metrologies. Here, we establish in situ small- and wide-angle X-ray scattering (SAXS/WAXS) as a suitable method to record the Li2O2 phase evolution with atomic to submicrometer resolution during cycling a custom-built in situ Li–O2 cell. Combined with sophisticated data analysis, SAXS allows retrieving rich quantitative structural information from complex multiphase systems. Surprisingly, we find that features are absent that would point at a Li2O2 surface film formed via two consecutive electron transfers, even in poorly solvating electrolytes thought to be prototypical for surface growth. All scattering data can be modeled by stacks of thin Li2O2 platelets potentially forming large toroidal particles. Li2O2 solution growth is further justified by rotating ring-disk electrode measurements and electron microscopy. Higher discharge overpotentials lead to smaller Li2O2 particles, but there is no transition to an electronically passivating, conformal Li2O2 coating. Hence, mass transport of reactive species rather than electronic transport through a Li2O2 film limits the discharge capacity. Provided that species mobilities and carbon surface areas are high, this allows for high discharge capacities even in weakly solvating electrolytes. The currently accepted Li–O2 reaction mechanism ought to be reconsidered.},
  author       = {Prehal, Christian and Samojlov, Aleksej and Nachtnebel, Manfred and Lovicar, Ludek and Kriechbaum, Manfred and Amenitsch, Heinz and Freunberger, Stefan Alexander},
  issn         = {1091-6490},
  journal      = {Proceedings of the National Academy of Sciences of the United States of America},
  keywords     = {small-angle X-ray scattering, oxygen reduction, disproportionation, Li-air battery},
  number       = {14},
  publisher    = {National Academy of Sciences},
  title        = {{In situ small-angle X-ray scattering reveals solution phase discharge of Li–O2 batteries with weakly solvating electrolytes}},
  doi          = {10.1073/pnas.2021893118},
  volume       = {118},
  year         = {2021},
}

@article{22084,
  abstract     = {We consider the nonlinear Schrödinger equation in three space dimensions with combined focusing cubic and defocusing quintic nonlinearity. This problem was considered previously by Killip et al. [Arch. Ration. Mech. Anal., 225 (2017), pp. 469--548], who proved scattering for the whole region of the mass/energy plane where the virial quantity is guaranteed to be positive. In this paper, we prove scattering in a slightly larger region where, in particular, the virial quantity is no longer guaranteed to be sign definite.},
  author       = {Killip, Rowan and Murphy, Jason and Visan, Monica},
  issn         = {1095-7154},
  journal      = {SIAM Journal on Mathematical Analysis},
  keywords     = {NLS, scattering, viral},
  number       = {5},
  pages        = {5803--5812},
  publisher    = {Society for Industrial & Applied Mathematics},
  title        = {{Scattering for the cubic-quintic NLS: Crossing the virial threshold}},
  doi          = {10.1137/20m1381824},
  volume       = {53},
  year         = {2021},
}

@article{21642,
  abstract     = {By codesigning a metaoptical front end in conjunction with an image‐processing back end, we demonstrate noise sensitivity and compactness substantially superior to either an optics‐only or a computation‐only approach, illustrated by two examples: subwavelength imaging and reconstruction of the full polarization coherence matrices of multiple light sources. Our end‐to‐end inverse designs couple the solution of the full Maxwell equations—exploiting all aspects of wave physics arising in subwavelength scatterers—with inverse‐scattering algorithms in a single large‐scale optimization involving  degrees of freedom. The resulting structures scatter light in a way that is radically different from either a conventional lens or a random microstructure, and suppress the noise sensitivity of the inverse‐scattering computation by several orders of magnitude. Incorporating the full wave physics is especially crucial for detecting spectral and polarization information that is discarded by geometric optics and scalar diffraction theory.},
  author       = {Lin, Zin and Roques-Carmes, Charles and Pestourie, Raphaël and Soljačić, Marin and Majumdar, Arka and Johnson, Steven G.},
  issn         = {2192-8614},
  journal      = {Nanophotonics},
  keywords     = {computational imaging, end-to-end photonic inverse design, inverse scattering, meta-optics, polarimetry},
  number       = {3},
  pages        = {1177--1187},
  publisher    = {Wiley},
  title        = {{End‐to‐end nanophotonic inverse design for imaging and polarimetry}},
  doi          = {10.1515/nanoph-2020-0579},
  volume       = {10},
  year         = {2020},
}

@article{22045,
  abstract     = {We consider the initial-value problem for the cubic-quintic nonlinear Schrödinger equation (𝑖𝜕𝑡+Δ)⁢𝜓 =𝛼1⁢𝜓 −𝛼3⁢|𝜓|2⁢𝜓 +𝛼5⁢|𝜓|4⁢𝜓 in three spatial dimensions in the class of solutions with |𝜓⁡(𝑥)| →𝑐 >0 as |𝑥| →∞. Here 𝛼1, 𝛼3, 𝛼5, and 𝑐 are such that 𝜓⁡(𝑥) ≡𝑐 is an energetically stable equilibrium solution to this equation. Normalizing the boundary condition to 𝜓⁡(𝑥) →1 as |𝑥| →∞, we study the associated initial-value problem for 𝑢 =𝜓 −1 and prove a scattering result for small initial data in a weighted Sobolev space.},
  author       = {Killip, Rowan and Murphy, Jason and Visan, Monica},
  issn         = {0036-1410},
  journal      = {SIAM Journal on Mathematical Analysis},
  keywords     = {cubic-quintic NLS, nonvanishing boundary conditions, space-time resonances, scattering},
  number       = {3},
  pages        = {2681--2739},
  publisher    = {Society for Industrial & Applied Mathematics},
  title        = {{The initial-value problem for the cubic-quintic NLS with nonvanishing boundary conditions}},
  doi          = {10.1137/17m1116702},
  volume       = {50},
  year         = {2018},
}