
Ayala, A., Claeys, X., EscapilInchauspé, P., & JerezHanckes, C. (2022). Local Multiple Traces Formulation for electromagnetics: Stability and preconditioning for smooth geometries. J. Comput. Appl. Math., Early Access.
Abstract: We consider the timeharmonic electromagnetic transmission problem for the unit sphere. Appealing to a vector spherical harmonics analysis, we prove the first stability result of the local multiple traces formulation (MTF) for electromagnetics, originally introduced by Hiptmair and JerezHanckes (2012) for the acoustic case, paving the way towards an extension to general piecewise homogeneous scatterers. Moreover, we investigate preconditioning techniques for the local MTF scheme and study the accumulation points of induced operators. In particular, we propose a novel secondorder inverse approximation of the operator. Numerical experiments validate our claims and confirm the relevance of the preconditioning strategies.



Aylwin, R., JerezHanckes, C., & Pinto, J. (2020). On the Properties of Quasiperiodic Boundary Integral Operators for the Helmholtz Equation. Integr. Equ. Oper. Theory, 92(2), 41 pp.
Abstract: We study the mapping properties of boundary integral operators arising when solving twodimensional, timeharmonic waves scattered by periodic domains. For domains assumed to be at least Lipschitz regular, we propose a novel explicit representation of Sobolev spaces for quasiperiodic functions that allows for an analysis analogous to that of Helmholtz scattering by bounded objects. Except for RayleighWood frequencies, continuity and coercivity results are derived to prove wellposedness of the associated first kind boundary integral equations.



Dölz, J., Harbrecht, H., JerezHanckes, C., & Multerer M. (2022). Isogeometric multilevel quadrature for forward and inverse random acoustic scattering. Comput. Methods in Appl. Mech. Eng., 388, 114242.
Abstract: We study the numerical solution of forward and inverse timeharmonic acoustic scattering problems by randomly shaped obstacles in threedimensional space using a fast isogeometric boundary element method. Within the isogeometric framework, realizations of the random scatterer can efficiently be computed by simply updating the NURBS mappings which represent the scatterer. This way, we end up with a random deformation field. In particular, we show that it suffices to know the deformation field’s expectation and covariance at the scatterer’s boundary to model the surface’s Karhunen–Loève expansion. Leveraging on the isogeometric framework, we employ multilevel quadrature methods to approximate quantities of interest such as the scattered wave’s expectation and variance. By computing the wave’s Cauchy data at an artificial, fixed interface enclosing the random obstacle, we can also directly infer quantities of interest in free space. Adopting the Bayesian paradigm, we finally compute the expected shape and variance of the scatterer from noisy measurements of the scattered wave at the artificial interface. Numerical results for the forward and inverse problems validate the proposed approach.



Gonzalez, H., A., & Rojas, F. (2021). The structure of IR divergences in celestial gluon amplitudes. J. High Energy Phys., (6), 171.
Abstract: The allloop resummation of SU(N) gauge theory amplitudes is known to factorize into an IRdivergent (soft and collinear) factor and a finite (hard) piece. The divergent factor is universal, whereas the hard function is a processdependent quantity.We prove that this factorization persists for the corresponding celestial amplitudes. Moreover, the soft/collinear factor becomes a scalar correlator of the product of renormalized Wilson lines defined in terms of celestial data. Their effect on the hard amplitude is a shift in the scaling dimensions by an infinite amount, proportional to the cusp anomalous dimension. This leads us to conclude that the celestialIRsafe gluon amplitude corresponds to a expectation value of operators dressed with Wilson line primaries. These results hold for finite N.In the large N limit, we show that the soft/collinear correlator can be described in terms of vertex operators in a Coulomb gas of colored scalar primaries with nearest neighbor interactions. In the particular cases of four and five gluons in planar N = 4 SYM theory, where the hard factor is known to exponentiate, we establish that the Mellin transform converges in the UV thanks to the fact that the cusp anomalous dimension is a positive quantity. In other words, the very existence of the full celestial amplitude is owed to the positivity of the cusp anomalous dimension.



Gonzalez, H. A., Puhm, A.,, & Rojas, F. (2020). Loop corrections to celestial amplitudes. Phys. Rev. D., 102, 126027.
Abstract: We study the effect of loop corrections to conformal correlators on the celestial sphere at null infinity. We first analyze finite oneloop celestial amplitudes in pure YangMills theory and Einstein gravity. We then turn to our main focus: infrared divergent loop amplitudes in planar N=4
super–YangMills theory. We compute the celestial oneloop amplitude in dimensional regularization and show that it can be recast as an operator acting on the celestial treelevel amplitude. This extends to any loop order, and the resummation of all planar loops enables us to write down an expression for the allloop celestial amplitude. Finally, we show that the exponentiated allloop expression given by the BernDixonSmirnov (BDS) formula gets promoted on the celestial sphere to an operator acting on the treelevel conformal correlation function, thus yielding, the celestial BDS formula.



Kleanthous, A., Betcke, T., Hewett, D. P., EscapilInchauspe, P., JerezHanckes, C., & Baran, A. J. (2022). Accelerated Calderon preconditioning for Maxwell transmission problems. J. Comput. Phys., 458, 111099.
Abstract: We investigate a range of techniques for the acceleration of Calderon (operator) preconditioning in the context of boundary integral equation methods for electromagnetic transmission problems. Our objective is to mitigate as far as possible the high computational cost of the barycentricallyrefined meshes necessary for the stable discretisation of operator products. Our focus is on the wellknown PMCHWT formulation, but the techniques we introduce can be applied generically. By using barycentric meshes only for the preconditioner and not for the original boundary integral operator, we achieve significant reductions in computational cost by (i) using “reduced” Calderon preconditioners obtained by discarding constituent boundary integral operators that are not essential for regularisation, and (ii) adopting a “biparametric” approach [1,2] in which we use a lower quality (cheaper) Hmatrix assembly routine for the preconditioner than for the original operator, including a novel approach of discarding farfield interactions in the preconditioner. Using the boundary element software Bempp (www.bempp.com), we compare the performance of different combinations of these techniques in the context of scattering by multiple dielectric particles. Applying our accelerated implementation to 3D electromagnetic scattering by an aggregate consisting of 8 monomer ice crystals of overall diameter 1cm at 664GHz leads to a 99% reduction in memory cost and at least a 75% reduction in total computation time compared to a nonaccelerated implementation. Crown Copyright (C) 2022 Published by Elsevier Inc. All rights reserved.



Nastase, H., Rojas, F., & Rubio, C. (2022). Celestial IR divergences in general mostsubleadingcolor gluon and gravity amplitudes. J. High Energy Phys., (1), 136.
Abstract: Gluon amplitudes at mostsubleading order in the 1/N expansion share a remarkable simplicity with graviton amplitudes: collinear divergences are completely absent in both and, as a consequence, their full IR behavior arises from soft gluon/graviton exchange among the external states. In this paper we study the effect of allloop IR divergences of celestial mostsubleading color gluon amplitudes and their similarities with the celestial gravity case. In particular, a simple celestial exponentiation formula for the dipole part can be written. We also analize how this exponentiation is modified by nondipole contributions. Finally we also show that, in the Regge limit, the soft factor satisfies the KnizhnikZamolodchikov equation hinting at the possibility that, in this limit, an effective WessZuminoWitten model would describe the dynamics of the infrared sector.



Pinto, J., Aylwin, R., & JerezHanckes, C. (2021). Fast solver for quasiperiodic 2DHelmholtz scattering in layered media. ESAIMMath. Model. Numer. Anal., 55(5), 2445–2472.
Abstract: We present a fast spectral Galerkin scheme for the discretization of boundary integral equations arising from twodimensional Helmholtz transmission problems in multilayered periodic structures or gratings. Employing suitably parametrized Fourier basis and excluding cutoff frequencies (also known as RayleighWood frequencies), we rigorously establish the wellposedness of both continuous and discrete problems, and prove superalgebraic error convergence rates for the proposed scheme. Through several numerical examples, we confirm our findings and show performances competitive to those attained via Nyström methods.



RamirezCuevas, F. V., Gurunatha, K. L., Parkin, I. P., & Papakonstantinou, I. (2022). Universal Theory of Light Scattering of Randomly Oriented Particles: A FluctuationalElectrodynamics Approach for Light Transport Modeling in Disordered Nanostructures. ACS Photonics, 9(2), 672–681.
Abstract: Disordered nanostructures are commonly encountered in many nanophotonic systems, from colloid dispersions for sensing to heterostructured photocatalysts. Randomness, however, imposes severe challenges for nanophotonics modeling, often constrained by the irregular geometry of the scatterers involved or the stochastic nature of the problem itself. In this Article, we resolve this conundrum by presenting a universal theory of averaged light scattering of randomly oriented objects. Specifically, we derive expansionbasisindependent formulas of the orientationandpolarizationaveraged absorption cross section, scattering cross section, and asymmetry parameter, for single or a collection of objects of arbitrary shape. These three parameters can be directly integrated into traditional unpolarized radiative energy transfer modeling, enabling a practical tool to predict multiple scattering and light transport in disordered nanostructured materials. Notably, the formulas of average light scattering can be derived under the principles of fluctuational electrodynamics, allowing the analogous mathematical treatment to the methods used in thermal radiation, nonequilibrium electromagnetic forces, and other associated phenomena. The proposed modeling framework is validated against optical measurements of polymer composite films with metaloxide microcrystals. Our work may contribute to a better understanding of lightmatter interactions in disordered systems, such as plasmonics for sensing and photothermal therapy, photocatalysts for water splitting and CO2 dissociation, photonic glasses for artificial structural colors, and diffuse reflectors for radiative cooling, to name just a few.



Trifonov, T., Brahm, R., Espinoza, N., Henning, T., Jordan, A., Nesvorny, D., et al. (2021). A Pair of Warm Giant Planets near the 2:1 Mean Motion Resonance around the Kdwarf Star TOI2202*. Astron. J., 162(6), 283.
Abstract: TOI2202 b is a transiting warm Jovianmass planet with an orbital period of P = 11.91 days identified from the Full Frame Images data of five different sectors of the TESS mission. Ten TESS transits of TOI2202 b combined with three followup light curves obtained with the CHAT robotic telescope show strong transit timing variations (TTVs) with an amplitude of about 1.2 hr. Radial velocity followup with FEROS, HARPS, and PFS confirms the planetary nature of the transiting candidate (a (b) = 0.096 +/ 0.001 au, m (b) = 0.98 +/ 0.06 M (Jup)), and a dynamical analysis of RVs, transit data, and TTVs points to an outer Saturnmass companion (a (c) = 0.155 +/ 0.002 au, m (c) = 0.37 +/ 0.10 M (Jup)) near the 2:1 mean motion resonance. Our stellar modeling indicates that TOI2202 is an early Ktype star with a mass of 0.82 M (circle dot), a radius of 0.79 R (circle dot), and solarlike metallicity. The TOI2202 system is very interesting because of the two warm Jovianmass planets near the 2:1 mean motion resonance, which is a rare configuration, and their formation and dynamical evolution are still not well understood.

