Home  << 1 2 >> 
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., 413, 114356.
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.

Caceres, C., Morgado, M. D. G., Bozo, F. C., Piletsky, S., & Moczko, E. (2022). Rapid Selective Detection and Quantification of betaBlockers Used in Doping Based on Molecularly Imprinted Nanoparticles (NanoMIPs). Polymers, 14(24), 5420.
Abstract: Human performance enhancing drugs (PEDs), frequently used in sport competitions, are strictly prohibited by the World AntiDoping Agency (WADA). Biological samples collected from athletes and regular patients are continuously tested regarding the identification and/or quantification of the banned substances. Current work is focused on the application of a new analytical method, molecularly imprinted nanoparticles (nanoMIPs), to detect and determine concentrations of certain prohibited drugs, such as Bblockers, in water and human urine samples. These medications are used in the treatment of cardiovascular conditions, negative effects of adrenaline (helping to relief stress), and hypertension (slowing down the pulse and softening the arteries). They can also significantly increase muscle relaxation and improve heart efficiency. The new method of the detection and quantification of Bblockers is based on synthesis, characterization, and implementation of nanoMIPs (socalled plastic antibodies). It offers numerous advantages over the traditional methods, including high binding capacity, affinity, and selectivity for target molecules. Additionally, the whole process is less complicated, cheaper, and better controlled. The size and shape of the nanoMIPs is evaluated by dynamic light scattering (DLS) and transmission electron microscope (TEM). The affinity and selectivity of the nanoparticles are investigated by competitive pseudo enzymelinked immunosorbent assay (pseudoELISA) similar to common immunoassays employing natural antibodies. To provide reliable results towards either doping detection or therapeutic monitoring using the minimal invasive method, the qualitative and quantitative analysis of these drugs is performed in water and human urine samples. It is demonstrated that the assay can detect Bblockers in water within the linear range 1 nmolmiddotL(1)1 mmolmiddotL(1) for atenolol with the detection limit 50.6 ng mL(1), and the linear range 1 mmolmiddotL(1)10 mmolmiddotL(1) for labetalol with the detection limit of 90.5 ngmiddotmL(1). In human urine samples, the linear range is recorded in the concentration range 0.1 mmolmiddotL(1)10 nmolmiddotL(1) for atenolol and 1 mmolmiddotL(1)10 nmolmiddotL(1) for labetalol with a detection limit of 61.0 ngmiddotmL(1)for atenolol and 99.4 ngmiddotmL(1) for labetalol.
Keywords: doping in sports; performance enhancing drugs (PEDs); betablockers; atenolol; labetalol; molecularly imprinting nanoparticles (nanoMIPs); enzymelinked immunosorbent assay (ELISA); “pseudo” enzymelinked immunosorbent assay (pseudoELISA); dynamic analysis light scattering (DLS); transmission electron microscope (TEM)

Calderon, F., Lozada, A., Morales, P., BorquezParedes, D., Jara, N., Olivares, R., et al. (2022). Heuristic Approaches for Dynamic Provisioning in MultiBand Elastic Optical Networks. IEEE Commun. Lett., 26(2), 379–383.
Abstract: Multiband elastic optical networks are a promising alternative to meet the bandwidth demand of the evergrowing Internet traffic. In this letter, we propose a family of band allocation algorithms for multiband elastic optical networks. Employing simulation, we evaluate the blocking performance of 3 algorithms of such a family and compare their performance with the only heuristic proposed to date. Results show that the three new algorithms outperform the previous proposal, with up to one order of magnitude improvement. We expect these results to help advance the area of dynamic resource allocation in multiband elastic optical networks.

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.

Donnay, L., Giribet, G., González, H., Puhm, A., & Rojas, F. (2023). Celestial open strings at oneloop. J. High Energy Phys., (10), 47.
Abstract: We study celestial amplitudes in string theory at oneloop. Celestial amplitudes describe scattering processes of boost eigenstates and relate to amplitudes in the more standard basis of momentum eigenstates through a Mellin transform. They are thus sensitive to both the ultraviolet and the infrared, which raises the question of how to appropriately take the field theory limit of string amplitudes in the celestial basis. We address this problem in the context of fourdimensional genusone scattering processes of gluons in open string theory which reach the twodimensional celestial sphere at null infinity. We show that the Mellin transform commutes with the adequate limit in the worldsheet moduli space and reproduces the celestial oneloop field theory amplitude expressed in the worldline formalism. The dependence on alpha ' continues to be a simple overall factor in oneloop celestial amplitudes albeit with a power that is shifted with respect to treelevel, thus making manifest that the dimensionless parameter g102/alpha ' 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{69pt} \begin{document}$$ {g}_{10}<^>2/{\alpha}<^>{\prime 3} $$\end{document} organizes the loop expansion in the celestial basis. The precise way in which the amplitudes scale with this parameter depends on the number of noncompact dimensions in such a way that in 4 dimensions the scaling with alpha ' does agree with that at treelevel.

EspinozaRetamal, J. I., Brahm, R., Petrovich, C., Jordán, A., Stefánsson, G., Sedaghati, E., et al. (2023). The Aligned Orbit of the Eccentric Proto Hot Jupiter TOI3362b. Astrophys. J. Lett., 958(2), L20.
Abstract: Higheccentricity tidal migration predicts the existence of highly eccentric proto hot Jupiters on the “tidal circularization track,” meaning that they might eventually become hot Jupiters, but that their migratory journey remains incomplete. Having experienced moderate amounts of tidal evolution of their orbital elements, proto hot Jupiter systems can be powerful test beds for the underlying mechanisms of eccentricity growth. Notably, they may be used for discriminating between variants of higheccentricity migration, each predicting a distinct evolution of misalignment between the star and the planet's orbit. We constrain the spinorbit misalignment of the proto hot Jupiter TOI3362b with highprecision radialvelocity observations using ESPRESSO at Very Large Telescope. The observations reveal a skyprojected obliquity lambda=1.2+2.8(degrees)/2.7 and constrain the orbital eccentricity to e = 0.720 +/ 0.016, making it one of the most eccentric gas giants for which the obliquity has been measured. Although the large eccentricity and the striking orbit alignment of the planet are puzzling, we suggest that ongoing coplanar higheccentricity migration driven by a distant companion is a possible explanation for the system's architecture. This distant companion would need to reside beyond 5 au at 95% confidence to be compatible with the available radialvelocity observations.
Keywords: INSITU FORMATION; PLANET; TRANSIT; EVOLUTION; BINARY; PHOTOMETRY; SCATTERING; TELESCOPE; MIGRATION; COMPANION

Feinstein, A. D., Radica, M., Welbanks, L., Murray, C. A., Ohno, K., Coulombe, L. P., et al. (2023). Early Release Science of the exoplanet WASP39b with JWST NIRISS. Nature, Early Access.
Abstract: The Saturnmass exoplanet WASP39b has been the subject of extensive efforts to determine its atmospheric properties using transmission spectroscopy(14). However, these efforts have been hampered by modelling degeneracies between composition and cloud properties that are caused by limited data quality(59). Here we present the transmission spectrum of WASP39b obtained using the SingleObject Slitless Spectroscopy (SOSS) mode of the Near Infrared Imager and Slitless Spectrograph (NIRISS) instrument on the JWST. This spectrum spans 0.62.8 mu m in wavelength and shows several waterabsorption bands, the potassium resonance doublet and signatures of clouds. The precision and broad wavelength coverage of NIRISS/SOSS allows us to break model degeneracies between cloud properties and the atmospheric composition of WASP39b, favouring a heavyelement enhancement ('metallicity') of about 1030 times the solar value, a subsolar carbontooxygen (C/O) ratio and a solartosupersolar potassiumtooxygen (K/O) ratio. The observations are also best explained by wavelengthdependent, nongrey clouds with inhomogeneous coverageof the planet's terminator.
Keywords: EXOMOL LINE LISTS; THERMAL STRUCTURE; MODEL; ABUNDANCES; ATMOSPHERE; RETRIEVAL; SCATTERING; EFFICIENT; SPECTRUM; METHANE

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. 
Han, Z. Y., Chen, H., He, C. L., Dodbiba, G., Otsuki, A., Wei, Y. Z., et al. (2023). Nanobubble size distribution measurement by interactive force apparatus under an electric field. Sci. Rep., 13(1), 3663.
Abstract: Nanobubbles have been applied in many fields, such as environmental cleaning, material production, agriculture, and medicine. However, the measured nanobubble sizes differed among the measurement methods, such as dynamic light scattering, particle trajectory, and resonance mass methods. Additionally, the measurement methods were limited with respect to the bubble concentration, refractive index of liquid, and liquid color. Here, a novel interactive force measurement method for bulk nanobubble size measurement was developed by measuring the force between two electrodes filled with bulk nanobubblecontaining liquid under an electric field when the electrode distance was changed in the nm scale with piezoelectric equipment. The nanobubble size was measured with a bubble gas diameter and also an effective water thin film layer covered with a gas bubble that was estimated to be approximately 10 nm based on the difference between the median diameter of the particle trajectory method and this method. This method could also be applied to the solid particle size distribution measurement in a solution.

JerezHanckes, C., & Labarca, I. (2023). Timedomain multiple traces boundary integral formulation for acoustic wave scattering in 2D. Eng. Anal. Bound. Elem., 157, 216–228.
Abstract: We present a novel computational scheme to solve acoustic wave transmission problems over twodimensional composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. The continuous problem is cast as a local multiple traces timedomain boundary integral formulation. For discretization in time and space, we resort to convolution quadrature schemes coupled to a nonconforming spatial spectral discretization based on second kind Chebyshev polynomials displaying fast convergence. Computational experiments confirm convergence of multistep and multistage convolution quadrature for a variety of complex domains.

JerezHanckes, C., & Pinto, J. (2022). Spectral Galerkin Method for Solving Helmholtz Boundary Integral Equations on Smooth Screens. IMA J. Numer. Anal., 42(4), 3571–3608.
Abstract: We solve firstkind Fredholm boundary integral equations arising from Helmholtz and Laplace problems on bounded, smooth screens in three dimensions with either Dirichlet or Neumann conditions. The proposed GalerkinBubnov methods take as discretization elements pushedforward weighted azimuthal projections of standard spherical harmonics onto the unit disk. By exactly depicting edge singular behaviors we show that these spectral or highorder bases yield superalgebraic error convergence in the corresponding energy norms whenever the screen is an analytic deformation of the unit disk. Moreover, we provide a fully discrete analysis of the method, including quadrature rules, based on analytic extensions of the spectral basis to complex neighborhoods. Finally, we include numerical experiments to support our claims as well as appendices with computational details for treating the associated singular integrals.

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.

McGruder, C. D., LopezMorales, M., Kirk, J., Espinoza, N., Rackham, B. V., Alam, M. K., et al. (2022). ACCESS: Confirmation of a Clear Atmosphere for WASP96b and a Comparison of Light Curve Detrending Techniques. Astron. J., 164(4), 134.
Abstract: One of the strongest Na I features was observed in WASP96b. To confirm this novel detection, we provide a new 475825 nm transmission spectrum obtained with Magellan/IMACS, which indeed confirms the presence of a broad sodium absorption feature. We find the same result when reanalyzing the 400825 nm VLT/FORS2 data. We also utilize synthetic data to test the effectiveness of two common detrending techniques: (1) a Gaussian processes (GP) routine, and (2) commonmode correction followed by polynomial correction (CMC+Poly). We find that both methods poorly reproduce the absolute transit depths but maintain their true spectral shape. This emphasizes the importance of fitting for offsets when combining spectra from different sources or epochs. Additionally, we find that, for our data sets, both methods give consistent results, but CMC+Poly is more accurate and precise. We combine the Magellan/IMACS and VLT/FORS2 spectra with literature 8001644 nm HST/ WFC3 spectra, yielding a global spectrum from 400 to 1644 nm. We used the PLATON and Exoretrievals retrieval codes to interpret this spectrum, and find that both yield relatively deeper pressures where the atmosphere is optically thick at logpressures between 1.3(1.1)(+1.0) and 0.29()(2.02)(+1.86) bars, respectively. Exoretrievals finds solar to supersolar Na I and H2O logmixing ratios of 5.4(1.9)(+2.0) and 4.5(2.0)(+2.0), respectively, while PLATON finds an overall metallicity of log(10) (Z/Z(circle dot)) = 0.49(0.37)(+1.0) dex. Therefore, our findings are in agreement with the literature and support the inference that the terminator of WASP96b has few aerosols obscuring prominent features in the optical to nearinfrared (nearIR) spectrum.

McGruder, C. D., LopezMorales, M., Kirk, J., Rackham, B. V., May, E., Ahrer, E. M., et al. (2023). ACCESS, LRGBEASTS, and MOPSS: Featureless Optical Transmission Spectra of WASP25b and WASP124b. Astron. J., 166(3), 120.
Abstract: We present new optical transmission spectra for two hot Jupiters: WASP25b (M = 0.56 M ( J ); R = 1.23 R ( J ); P = 3.76 days) and WASP124b (M = 0.58 M ( J ); R = 1.34 R ( J ); P = 3.37 days), with wavelength coverages of 42009100 & ANGS; and 45709940 & ANGS;, respectively. These spectra are from the ESO Faint Object Spectrograph and Camera (v.2) mounted on the New Technology Telescope and InamoriMagellan Areal Camera & Spectrograph on Magellan Baade. No strong spectral features were found in either spectra, with the data probing 4 and 6 scale heights, respectively. Exoretrievals and PLATON retrievals favor stellar activity for WASP25b, while the data for WASP124b did not favor one model over another. For both planets the retrievals found a wide range in the depths where the atmosphere could be optically thick (& SIM;0.4 & mu;0.2 bars for WASP25b and 1.6 & mu;32 bars for WASP124b) and recovered a temperature that is consistent with the planets' equilibrium temperatures, but with wide uncertainties (up to & PLUSMN;430 K). For WASP25b, the models also favor stellar spots that are & SIM;5003000 K cooler than the surrounding photosphere. The fairly weak constraints on parameters are owing to the relatively low precision of the data, with an average precision of 840 and 1240 ppm per bin for WASP25b and WASP124b, respectively. However, some contribution might still be due to an inherent absence of absorption or scattering in the planets' upper atmospheres, possibly because of aerosols. We attempt to fit the strength of the sodium signals to the aerosolmetallicity trend proposed by McGruder et al., and find WASP25b and WASP124b are consistent with the prediction, though their uncertainties are too large to confidently confirm the trend.

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.
Keywords: Scattering Amplitudes; Conformal Field Theory

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.

Shiranzaei, M., Troncoso, R. E., Fransson, O., Brataas, A., & Qaiumzadeh, A. (2022). Thermal squeezing and nonlinear spectral shift of magnons in antiferromagnetic insulators. New J. Phys., 24(10), 103009.
Abstract: We investigate the effect of magnonmagnon interactions on the dispersion and polarization of magnon modes in collinear antiferromagnetic (AF) insulators at finite temperatures. In twosublattice AF systems with uniaxial easyaxis and biaxial easyplane magnetocrystalline anisotropies, we implement a selfconsistent HartreeFock meanfield approximation to explore the nonlinear thermal interactions. The resulting nonlinear magnon interactions separate into twomagnon intra and interband scattering processes. Furthermore, we compute the temperature dependence of the magnon bandgap and AF resonance modes due to nonlinear magnon interactions for square and hexagonal lattices. In addition, we study the effect of magnon interactions on the polarization of magnon modes. We find that although the noninteracting eigenmodes in the uniaxial easyaxis case are circularly polarized, but in the presence of nonlinear thermal interactions the U(1) symmetry of the magnon Hamiltonian is broken. The attractive nonlinear interactions squeeze the low energy magnon modes and make them elliptical. In the biaxial easyplane case, on the other hand, the bare eigenmodes of low energy magnons are elliptically polarized but thermal nonlinear interactions squeeze them further. Direct measurements of the predicted temperaturedependent AF resonance modes and their polarization can be used as a tool to probe the nonlinear interactions. Our findings establish a framework for exploring the effect of thermal magnon interactions in technologically important magnetic systems, such as magnetic stability of recently discovered twodimensional magnetic materials, coherent transport of magnons, BoseEinstein condensation of magnons, and magnonic topological insulators.
