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Test-mass thermal noise is a limiting noise source for current and next-generation ground-based gravitational-wave observatories in their most sensitive frequency band. In addition to ongoing efforts to reduce coating mechanical loss, complementary approaches such as the use of uniform-intensity laser beams, including higher-order Laguerre─Gaussian (LG) and Hermite─Gaussian (HG) modes, have been proposed as alternatives to the fundamental Gaussian beam due to their thermal-noise advantages. As the interferometer operating power increases toward the megawatt regime, as anticipated for next-generation detectors, thermal aberrations arising from absorption in the high-reflectivity coatings of the test masses become an increasingly severe challenge. In parallel, the spatially more extended intensity profiles of higher-order modes, which enable their thermal-noise benefits, modify the thermal loading of the test masses, making it essential to assess their behavior under absorption-induced self-heating. In this work, we quantify the robustness of higher-order incident beams against thermal deformation. We show that, under identical operating conditions, higher-order modes produce significantly more uniform thermally induced mirror distortions compared to the sharply peaked aberrations generated by the fundamental mode. As a result, substantially less thermal compensation power is required for their active correction, with the required optimal curvature correction reduced to 33% of that of the fundamental mode for the <inline-formula><mml:math><mml:msub><mml:mi>LG</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> mode and to 24% for the <inline-formula><mml:math><mml:msub><mml:mi>HG</mml:mi><mml:mrow><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> mode. In addition, we show that the residual thermal deformation for higher-order modes leads to significantly lower optical power loss and enables larger power buildup and enhanced modal purity in an aLIGO-like optical cavity. We further demonstrate that astigmatism compensation enhances the intracavity modal purity of HG modes under self-heating-induced thermal deformation. These results highlight that higher-order laser modes mitigate thermal noise while intrinsically suppressing beam self-heating-induced thermal distortions, making them more thermally robust and well suited for operation in high-power gravitational-wave interferometers.

Neutrino flavor evolution in dense astrophysical environments such as core-collapse supernova (CCSN) is influenced by collective effects. While the Fast Flavor Instability (FFI) and the Collisional Flavor Instability (CFI) are recognized as key drivers of rapid flavor conversion, their nonlinear competition with collisional damping in spatially inhomogeneous systems remains poorly understood. Motivated by recent findings that FFI and resonancelike CFI cooccur in the postbounce phase in CCSN, we scrutinize their dynamic competitions and asymptotic states. To this end, we perform numerical simulations of the quantum kinetic neutrino transport, incorporating both spatial advection and the collision terms. We demonstrate that the interplay between these coexisting neutrino flavor instabilities and collisions leads to rich dynamics. Rather than merely inducing simple decoherence, collisional damping can substantially alter the overall dynamics of collective flavor oscillations, driving the system through complex evolutionary pathways. In all cases where flavor instability develops, we find that the system converges to the same flavor-equilibrated asymptotic state, despite the diversity of intermediate dynamics. Our results suggest that realistic collisional effects drive the system to an asymptotic state distinct from the one predicted by the collisionless FFI picture. This highlights the importance of incorporating collisional effects when modeling the asymptotic outcome of flavor conversion in CCSN models.