Learning transport processes with machine intelligence.

Transport processes ruled by complex micro-physics and impractical to theoretical investigation may exhibit emergent behavior describable by mathematical expressions. Such information, while implicitly contained in the results of microscopic-scale numerical simulations close to first principles or experiments is not in a form suitable for macroscopic modelling. Here we present a machine learning approach that leverages such information to deploy micro-physics informed transport flux representations applicable to a continuum mechanics description. One issue with deep neural networks, arguably providing the most generic of such representations, is their noisiness which is shown to break the performance of numerical schemes. The matter is addressed and a methodology suitable for schemes characterised by second order convergence rate is presented. The capability of the methodology is demonstrated through an idealized study of the long standing problem of heat flux suppression relevant to fusion and cosmic plasmas. Symbolic representations, although potentially less generic, are straightforward to use in numerical schemes and theoretical analysis, and can be even more accurate as shown by the application to the same problem of an advanced symbolic regression tool. These results are a promising initial step to filling the gap between micro and macro in this important area of modeling.

Strong suppression of heat conduction in a laboratory replica of galaxy-cluster turbulent plasmas.

In conventional gases and plasmas, it is known that heat fluxes are proportional to temperature gradients, with collisions between particles mediating energy flow from hotter to colder regions and the coefficient of thermal conduction given by Spitzer's theory. However, this theory breaks down in magnetized, turbulent, weakly collisional plasmas, although modifications are difficult to predict from first principles due to the complex, multiscale nature of the problem. Understanding heat transport is important in astrophysical plasmas such as those in galaxy clusters, where observed temperature profiles are explicable only in the presence of a strong suppression of heat conduction compared to Spitzer's theory. To address this problem, we have created a replica of such a system in a laser laboratory experiment. Our data show a reduction of heat transport by two orders of magnitude or more, leading to large temperature variations on small spatial scales (as is seen in cluster plasmas).

Time-resolved turbulent dynamo in a laser plasma.

Understanding magnetic-field generation and amplification in turbulent plasma is essential to account for observations of magnetic fields in the universe. A theoretical framework attributing the origin and sustainment of these fields to the so-called fluctuation dynamo was recently validated by experiments on laser facilities in low-magnetic-Prandtl-number plasmas ([Formula: see text]). However, the same framework proposes that the fluctuation dynamo should operate differently when [Formula: see text], the regime relevant to many astrophysical environments such as the intracluster medium of galaxy clusters. This paper reports an experiment that creates a laboratory [Formula: see text] plasma dynamo. We provide a time-resolved characterization of the plasma's evolution, measuring temperatures, densities, flow velocities, and magnetic fields, which allows us to explore various stages of the fluctuation dynamo's operation on seed magnetic fields generated by the action of the Biermann-battery mechanism during the initial drive-laser target interaction. The magnetic energy in structures with characteristic scales close to the driving scale of the stochastic motions is found to increase by almost three orders of magnitude and saturate dynamically. It is shown that the initial growth of these fields occurs at a much greater rate than the turnover rate of the driving-scale stochastic motions. Our results point to the possibility that plasma turbulence produced by strong shear can generate fields more efficiently at the driving scale than anticipated by idealized magnetohydrodynamics (MHD) simulations of the nonhelical fluctuation dynamo; this finding could help explain the large-scale fields inferred from observations of astrophysical systems.

Self-similar energetics in large clusters of galaxies.

Massive galaxy clusters are filled with a hot, turbulent and magnetized intra-cluster medium. Still forming under the action of gravitational instability, they grow in mass by accretion of supersonic flows. These flows partially dissipate into heat through a complex network of large-scale shocks, while residual transonic (near-sonic) flows create giant turbulent eddies and cascades. Turbulence heats the intra-cluster medium and also amplifies magnetic energy by way of dynamo action. However, the pattern regulating the transformation of gravitational energy into kinetic, thermal, turbulent and magnetic energies remains unknown. Here we report that the energy components of the intra-cluster medium are ordered according to a permanent hierarchy, in which the ratio of thermal to turbulent to magnetic energy densities remains virtually unaltered throughout the cluster's history, despite evolution of each individual component and the drive towards equipartition of the turbulent dynamo. This result revolves around the approximately constant efficiency of turbulence generation from the gravitational energy that is freed during mass accretion, revealed by our computational model of cosmological structure formation. The permanent character of this hierarchy reflects yet another type of self-similarity in cosmology, while its structure, consistent with current data, encodes information about the efficiency of turbulent heating and dynamo action.

Developed turbulence and nonlinear amplification of magnetic fields in laboratory and astrophysical plasmas.

The visible matter in the universe is turbulent and magnetized. Turbulence in galaxy clusters is produced by mergers and by jets of the central galaxies and believed responsible for the amplification of magnetic fields. We report on experiments looking at the collision of two laser-produced plasma clouds, mimicking, in the laboratory, a cluster merger event. By measuring the spectrum of the density fluctuations, we infer developed, Kolmogorov-like turbulence. From spectral line broadening, we estimate a level of turbulence consistent with turbulent heating balancing radiative cooling, as it likely does in galaxy clusters. We show that the magnetic field is amplified by turbulent motions, reaching a nonlinear regime that is a precursor to turbulent dynamo. Thus, our experiment provides a promising platform for understanding the structure of turbulence and the amplification of magnetic fields in the universe.

Strong magnetic fields in normal galaxies at high redshift.

The origin and growth of magnetic fields in galaxies is still something of an enigma. It is generally assumed that seed fields are amplified over time through the dynamo effect, but there are few constraints on the timescale. It was recently demonstrated that field strengths as traced by rotation measures of distant (and hence ancient) quasars are comparable to those seen today, but it was unclear whether the high fields were in the unusual environments of the quasars themselves or distributed along the lines of sight. Here we report high-resolution spectra that demonstrate that the quasars with strong Mg II absorption lines are unambiguously associated with larger rotation measures. Because Mg ii absorption occurs in the haloes of normal galaxies along the sightlines to the quasars, this association requires that organized fields of surprisingly high strengths are associated with normal galaxies when the Universe was only about one-third of its present age.