Robert Fisher – Statement of Research Accomplishments 1. Overview The incorporation of turbulent processes into theoretical and computational models has enabled remarkable progress on a wide range of topics in fundamental science. This has par- ticularly been true in astrophysics, where turbulence is now understood to play an essential role in processes ranging from the formation of stars to supernovae explosions. Despite the apparent complexity of the turbulent flows at work in these disparate phenomena, the tur- bulent cascade concept originally proposed by Kolmogorov endows them with a deep under- lying universal scale-invariant structure within the inertial range, independent of the driving mechanism [1]. Zwicky, von Weizsäcker, and later authors (in particular Larson) noted the significance of this powerful concept, and applied it within an astrophysical context to galax- ies and clusters of galaxies, the interstellar medium, and accretion disks [2, 3, 4, 5]. Their seminal work has provided an overarching framework with which we can begin to understand the role turbulence plays in astrophysical processes. Thanks to the monumental advances in parallel supercomputers over the past decade, we can now directly simulate turbulent processes in astrophysics in fully three-dimensional cal- culations, coupled with other key physics, such as self-gravity, radiative transfer, and nuclear burning. These advances in computing come at the same time as a powerful new genera- tion of observational instruments across the entire spectrum – including SCUBA, IRAM, CARMA, SMA, ALMA, Spitzer, SOFIA, LMT, James Webb, and Chandra. As the result of this tremendous progress, we are in a now at an exciting point in time where we can now begin to address how turbulence plays a crucial role in answering fundamental, long-standing questions which have long vexed astrophysicists. My own work has focused on two endpoints of stellar evolution – star formation and su- pernovae. In the context of star formation, these outstanding questions include : How is turbulence within star-forming giant molecular clouds (GMCs) generated and sustained? What sets the stellar initial mass function (IMF)? What sets the rate at which stars are formed? How are brown dwarfs formed? How are binary stars formed? In the context of su- pernovae, these questions include : How does a Chandrasekhar-mass white dwarf first ignite and initiate a subsonic deflagration front that becomes a type Ia supernova? What is the nature of turbulent deflagration within Ia supernovae? Does the deflagration front transi- tion into a supersonic detonation, and if so, how? What is the origin of the Phillips relation, and is it possible to obtain an even-tighter relation using first principles simulations of Ia supernovae, and thereby provide even tighter constraints on the properties of dark energy? Successfully addressing these fundamental questions though computation hinges crucially upon efficient, scalable parallel algorithms to treat the essential physics; a portion of my research is devoted to the development of such algorithms. In addition, computation at the petascale and beyond leads to challenging informatics problems in the analysis of large-scale datasets, which must be solved in order to produce scientific results. I outline our research accomplishments in §2. 2. Key Accomplishments to Date Fisher Research Statement 2 (a) (b) (c) Figure 1: The sequence of events leading up to a type Ia supernova in our recent 3D sim- ulations. (a) Carbon burning on the interior of a Chadrasekhar-mass white dwarf leads to the ignition of a nuclear flame bubble, slightly offset from the center of the star. (b) The bubble rises from the point of ignition, buoyed by the hot nuclear ash, becomes turbulent, and breaks out of the surface of the star about one second later. (c) The hot ash remains gravitationally confined to the surface of the star, generating a surface flow which rushes over the surface of the star in another 1-2 seconds, setting off a detonation. 3D Simulations of Type Ia Supernovae. Type Ia supernovae have received increased in- terest because of their importance as “standard candles” for cosmology. Observations using type Ia supernovae as standard candles have revealed that the ex- pansion rate of the universe is accelerating and have led to the discovery of dark energy. However, the basic explosion mechanism of type Ia supernovae is not fully understood. A fundamental question is how the transi- tion from a subsonic deflagration to a super- sonic detonation occurs in a white dwarf [6]. In collaboration with colleagues (C. Jor- dan, D. Townsley, A. Calder, C. Graziani, S. Asida, D. Lamb, & J. Truran), we were the first to demonstrate successful self- consistent detonations in three-dimensional Figure 2: A close-up demonstrating the GCD simulations of type Ia supernovae [7]. We mechanism in detail. The white dwarf sur- began our simulations with ignition at an face is shown as an isocontour of density, while off-center point in the white dwarf interior, the heated material in the incoming jet gener- resulting in a turbulent burning bubble of ated by the convergence of swept-up unburned hot ash that rose rapidly, broke through surface flow is volume-rendered temperature. the surface of the star, and collided at a The intersection of these two surfaces satisfies point opposite breakout on the stellar sur- a conservative detonation criterion. face – a “gravitationally-confined detona- tion” (GCD). We found that detonation conditions were robustly reached in our three-dimensional simu- Fisher Research Statement 3 lations for a range of initial conditions and resolutions. These conditions were achieved as the result of an inwardly-directed jet that is produced by the compression of unburnt surface material when the surface flow collides with itself (figure 2). Observations of type Ia super- novae imply properties that are consistent with those expected from these 3D simulations of the GCD model. Eulerian and Lagrangian Properties of Homogeneous, Isotropic Weakly Com- pressible Turbulence. Recent experiments involving tracer particles within turbulent flows have sparked considerable interest in the topic of Lagrangian properties of turbulence. Beginning in December 2005, I have led a large, interdisciplinary, international group of over twenty-five computer scientists, applied mathematicians, and physicists at the University of Chicago, Argonne National Laboratory, and the Università di Roma on a project studying the Eulerian and Lagrangian properties of weakly-compressible turbulence through numerical simulation. Our largest simulation was run at a grid resolution of 18563 on the Lawrence Liv- ermore BG/L supercomputer, and utilized 2563 Lagrangian tracer particles. Approximately one week of CPU time on 65,536 processors was used to complete our highest-resolution simulation, which produced over 100 TB of data. Figure 3: A nonlinear mapping of the density gradient within a single cut plane of our large-scale homogeneous isotropic turbulence simulation, revealing the rich network of vortex filament cores in weakly-compressible turbulence. When we initiated this project, we had the vision to release the full dataset under an open data model, allowing open access to any and all interested parties. Designing the hardware Fisher Research Statement 4 and software systems to meet this vision was a major challenge which we successfully ad- dressed in collaboration with a team of computer scientists from the joint Argonne/University of Chicago Computation Institute (CI) [8]. We chose to collocate storage and analysis com- putation, which is the natural solution for a large dataset. The full dataset is served to the community from the CI’s mass datastore, which was custom-designed to meet our specifi- cations. The system currently is a scalable high-performance storage resource that has 75 TB of raw storage configured in an 8+2 RAID array, allowing up to 48 drives to fail with no impact to performance, stability, or reliability. It can deliver a sustained throughput of 3 GB/s. It can also be scaled to 480 TB of raw storage. Five I/O servers are connected to storage system by five fiber channels and then connected to the outside world via 1 Gb/s Ethernet connections to the CI’s 10 Gb/s I-WIRE link. Collocated with the storage resource is the CI’s TeraPort compute resource; a 244-processor AMD Opteron cluster that is used for local processing of the data. Custom parallel software tools were written to handle the data analysis. Over 1015 points were computed when determining the Eulerian structure functions while writing the first papers from this run. In a recent paper we have examined the Eulerian scaling properties within this weakly- compressible flow [9]. One remarkable property of weakly-compressible turbulence emerged during our analysis of the scaling exponents of the pth order density structure function p Sp(r) [δρ(r)] (where ρ(x) is the spatial density field, δρ(r) = ρ(x + r) ρ(x), and ≡ " # − denotes average over points x in the volume and over time). In the inertial regime, the "# ζp structure functions are scale-invariant and therefore follow the power-law Sp(r) r . We ∝ have shown that although no shock waves are produced in the simulation, the density fluc- tuations are characterized by front-like structures that determine the tail of the probability distribution of density increments δρ(r). Accordingly, the scaling exponents ζp of the density structure functions saturate at large moments p. An additional paper currently