Publications

Mathematics

General integral identities for bianisotropic media and related equations, properties, and coupling expressions

We consider advanced properties of electromagnetic fields derived from integral identities in bianisotropic media : generalized reciprocity principle for adjoint systems, equivalence of surface sources, uniqueness, links between impedance surface…

J.M.L. Bernard

Electromagnetism

Advanced properties of spectral functions in frequency and time domains for diffraction by a wedge-shaped region

The scattering by objects with singular geometries is a particularly delicate problem, and the Sommerfeld-Maliuzhinets representation of field, when it is associated to Maliuzhinets inversion [3]-[4] and single face representation [7]-[8] methods,…

J.M.L. Bernard

Mathematics

Spectral equations for scattering by impedance polygons : properties and solutions

The Sommerfeld-Maliuzhinets representation of fields is not limited to the study of the diffraction by isolated impedance wedges, and we developed in [1]-[2] an analytical method concerning the determination of spectral function for the scattering…

J.M.L. Bernard

Mathematics

The diffraction by a curved impedance wedge with arbitrary angle and its uniform higher order asymptotics

The methods generally considered for the diffraction by a wedge with curved faces are often different as you consider a wedge of narrow or large angle. An original approach, initiated in [1,2] for faces of constant curvatures, and whose results have…

J.M.L. Bernard

Image Processing

Collaborative Blind Image Deblurring

Blurry images usually exhibit similar blur at various locations across the image domain, a property barely captured in nowadays blind deblurring neural networks. We show that when extracting patches of similar underlying blur is possible, jointly…

Thomas Eboli, Jean-Michel Morel, Gabriele Facciolo

2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) - 2024

Number Theory

Exceptional biases in counting primes over functions fields

We study how often exceptional configurations of irreducible polynomials over finite fields occur in the context of prime number races and Chebyshev's bias. In particular, we show that three types of biases, which we call "complete bias", "lower…

Alexandre Bailleul, Lucile Devin, Daniel Keliher, Wanlin Li

Journal of the London Mathematical Society - 2024

Machine Learning

Graph Cuts with Arbitrary Size Constraints Through Optimal Transport

A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more success…

Chakib Fettal, Lazhar Labiod, Mohamed Nadif

Transactions on Machine Learning Research Journal - 2024

Electromagnetism

Exact and asymptotic reductions of surface radiation integrals with complex phases to contour integrals

We develop here an efficient method for the reduction of surface radiation integrals to non-singular contour integrals, when we suppose known, as in Physical Optics (PO), the analytic expression of surface currents whose electromagnetic radiation is…

J.M.L. Bernard

Electromagnetism

New insights in integral representation theory for the solution of complex canonical diffraction problems

The problem of scattering by 2D and 3D canonical objects with imperfectly conducting surfaces requires some particular efforts on the representation of scattered and incident fields, and we present here some remarkable aspects of them in complex…

J.M.L. Bernard

Fluid Dynamics

Video: FARAMIX: Mixing induced by surface waves in stratified fluids

Standing waves can be observed at the interface between two miscible fluids of small density contrast (liquid-liquid) when subject to a time-periodic vertical acceleration via the Faraday instability. A turbulent mixing zone may develop, grow in…

Andrés Castillo-Castellanos, Benoît-Joseph Gréa, Antoine Briard, Louis Gostiaux