Scattering spectra models for physics.

Physicists routinely need probabilistic models for a number of tasks such as parameter inference or the generation of new realizations of a field. Establishing such models for highly non-Gaussian fields is a challenge, especially when the number of samples is limited. In this paper, we introduce scattering spectra models for stationary fields and we show that they provide accurate and robust statistical descriptions of a wide range of fields encountered in physics. These models are based on covariances of scattering coefficients, i.e. wavelet decomposition of a field coupled with a pointwise modulus. After introducing useful dimension reductions taking advantage of the regularity of a field under rotation and scaling, we validate these models on various multiscale physical fields and demonstrate that they reproduce standard statistics, including spatial moments up to fourth order. The scattering spectra provide us with a low-dimensional structured representation that captures key properties encountered in a wide range of physical fields. These generic models can be used for data exploration, classification, parameter inference, symmetry detection, and component separation.

Buoyant crystals halt the cooling of white dwarf stars.

White dwarfs are stellar remnants devoid of a nuclear energy source, gradually cooling over billions of years1,2 and eventually freezing into a solid state from the inside out3,4. Recently, it was discovered that a population of freezing white dwarfs maintains a constant luminosity for a duration comparable with the age of the universe5, signalling the presence of a powerful, yet unknown, energy source that inhibits the cooling. For certain core compositions, the freezing process is predicted to trigger a solid-liquid distillation mechanism, owing to the solid phase being depleted in heavy impurities6-8. The crystals thus formed are buoyant and float up, thereby displacing heavier liquid downward and releasing gravitational energy. Here we show that distillation interrupts the cooling for billions of years and explains all the observational properties of the unusual delayed population. With a steady luminosity surpassing that of some main-sequence stars, these white dwarfs defy their conventional portrayal as dead stars. Our results highlight the existence of peculiar merger remnants9,10 and have profound implications for the use of white dwarfs in dating stellar populations11,12.