Journal: Journal de Mathématiques Pures et Appliquées
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Elsevier
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Publications 1 - 10 of 15
- Generalized solutions for the Euler equations in one and two dimensionsItem type: Journal Article
Journal de Mathématiques Pures et AppliquéesBernot, Marc; Figalli, Alessio; Santambrogio, Filippo (2008) - Singular limits for plasmas with thermalised electronsItem type: Journal Article
Journal de Mathématiques Pures et AppliquéesGriffin-Pickering, Megan; Iacobelli, Mikaela (2020) - Towards a description of the double ramification hierarchy for Witten's r-spin classItem type: Journal Article
Journal de Mathématiques Pures et AppliquéesBuryak, Alexandr; Guéré, Jérémy (2016) - Khovanskii bases for semimixed systems of polynomial equations – Approximating stationary nonlinear Newtonian dynamicsItem type: Journal Article
Journal de Mathématiques Pures et AppliquéesBorovik, Viktoriia; Breiding, Paul; del Pino, Javier; et al. (2024)We provide an approach to counting roots of polynomial systems, where each polynomial is a general linear combination of prescribed, fixed polynomials. Our tools rely on the theory of Khovanskii bases, combined with toric geometry, the Bernstein–Khovanskii–Kushnirenko (BKK) Theorem, and fiber products. As a direct application of this theory, we solve the problem of counting the number of approximate stationary states for coupled driven nonlinear resonators. We set up a system of polynomial equations that depends on three numbers N,n and M and whose solutions model the stationary states. The parameter N is the number of coupled resonators, 2n−1 is the degree of nonlinearity of the underlying differential equation, and M is the number of frequencies used in the approximation. We use our main theorems, that is, the generalized BKK Theorem 2.5 and the Decoupling Theorem 3.8, to count the number of (complex) solutions of the polynomial system for an arbitrary degree of nonlinearity 2n−1⩾3, any number of resonators N⩾1, and M=1 harmonic. We also solve the case N=1,n=2 and M=2 and give a computational way to check the number of solutions for N=1,n=2 and M>2. This extends the results of [1]. - Shape and size dependence of dipolar plasmonic resonance of nanoparticlesItem type: Journal Article
Journal de Mathématiques Pures et AppliquéesAmmari, Habib; Millien, Pierre (2019) - Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEsItem type: Journal Article
Journal de Mathématiques Pures et AppliquéesCohen, Albert; Chkifa, Abdellah; Schwab, Christoph (2015) - Stability results on the smoothness of optimal transport maps with general costsItem type: Journal Article
Journal de Mathématiques Pures et AppliquéesChen, Shibing; Figalli, Alessio (2016) - A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditionsItem type: Journal Article
Journal de Mathématiques Pures et AppliquéesFigalli, Alessio; Gigli, Nicola (2010) - Topologically protected edge modes in one-dimensional chains of subwavelength resonatorsItem type: Journal Article
Journal de Mathématiques Pures et AppliquéesAmmari, Habib; Davies, Bryn; Orvehed Hiltunen, Erik; et al. (2020)The goal of this paper is to advance the development of wave-guiding subwavelength crystals by developing designs whose properties are stable with respect to imperfections in their construction. In particular, we make use of a locally resonant subwavelength structure, composed of a chain of high-contrast resonators, to trap waves at deep subwavelength scales. We first study an infinite chain of subwavelength resonator dimers and define topological quantities that capture the structure's wave transmission properties. Using this for guidance, we design a finite crystal that is shown to have wave localization properties, at subwavelength scales, that are robust with respect to random imperfections. - Four-dimensional Kähler metrics admitting c-projective vector fieldsItem type: Journal Article
Journal de Mathématiques Pures et AppliquéesBolsinov, Alexey V.; Matveev, Vladimir S.; Mettler, Thomas; et al. (2015)
Publications 1 - 10 of 15