Journal de Mathématiques Pures et Appliquées

Journal: Journal de Mathématiques Pures et Appliquées

Publisher

Elsevier

ISSN

0021-7824
1776-3371

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Publications 1 - 10 of 15

Generalized solutions for the Euler equations in one and two dimensions
Bernot, Marc; Figalli, Alessio; Santambrogio, Filippo (2008)
Journal de Mathématiques Pures et Appliquées
Singular limits for plasmas with thermalised electrons
Griffin-Pickering, Megan; Iacobelli, Mikaela (2020)
Journal de Mathématiques Pures et Appliquées
Towards a description of the double ramification hierarchy for Witten's r-spin class
Buryak, Alexandr; Guéré, Jérémy (2016)
Journal de Mathématiques Pures et Appliquées
Khovanskii bases for semimixed systems of polynomial equations – Approximating stationary nonlinear Newtonian dynamics
Borovik, Viktoriia; Breiding, Paul; del Pino, Javier; et al. (2024)
Journal de Mathématiques Pures et Appliquées
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 nanoparticles
Ammari, Habib; Millien, Pierre (2019)
Journal de Mathématiques Pures et Appliquées
Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
Cohen, Albert; Chkifa, Abdellah; Schwab, Christoph (2015)
Journal de Mathématiques Pures et Appliquées
Stability results on the smoothness of optimal transport maps with general costs
Chen, Shibing; Figalli, Alessio (2016)
Journal de Mathématiques Pures et Appliquées
A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions
Figalli, Alessio; Gigli, Nicola (2010)
Journal de Mathématiques Pures et Appliquées
Topologically protected edge modes in one-dimensional chains of subwavelength resonators
Ammari, Habib; Davies, Bryn; Orvehed Hiltunen, Erik; et al. (2020)
Journal de Mathématiques Pures et Appliquées
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 fields
Bolsinov, Alexey V.; Matveev, Vladimir S.; Mettler, Thomas; et al. (2015)
Journal de Mathématiques Pures et Appliquées

Publications 1 - 10 of 15

Journal: Journal de Mathématiques Pures et Appliquées

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