Computational methods for sensitivity analysis are invaluable tools for aerodynamics research and engineering design. However, traditional sensitivity analysis methods break down when applied to long-time averaged quantities in turbulent fluid flow fields, specifically those obtained using high-fidelity turbulence simulations. This is because of a number of dynamical properties of turbulent and chaotic fluid flows, most importantly high sensitivity of the initial value problem, popularly known as the "butterfly effect".The recently developed least squares shadowing (LSS) method avoids the issues encountered by traditional sensitivity analysis methods by approximating the "shadow trajectory" in phase space, avoiding the high sensitivity of the initial value problem. The following paper discusses how the least squares problem associated with LSS is solved. Two methods are presented and are demonstrated on a simulation of homogeneous isotropic turbulence and the Kuramoto-Sivashinsky (KS) equation, a 4th order chaotic partial differential equation. We find that while LSS computes fairly accurate gradients, faster, more efficient linear solvers are needed to apply both LSS methods presented in this paper to larger simulations.

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The present study was part of a larger 3-day, 2-night double-blind parallel group design in which 80 young adult men were divided into eight treatment groups to examine the effects of benzodiazepines and caffeine on nocturnal sleep and daytime sleepiness, performance, and mood. The present study was done to examine further the relationship among daytime sleepiness, performance, mood, and nocturnal sleep and to determine if and how these relationships were affected by the nighttime use of benzodiazepine and the ingestion of caffeine in the morning. Subjects received 15 or 30 mg of flurazepam, 0.25 or 0.50 mg of triazolam, or placebo at bedtime and 250 mg of caffeine or placebo in the morning for two treatment days. Two objective (Multiple Sleep Latency Test and lapses) and two subjective (Stanford Sleepiness Scale and Visual Analog Scale) measures of sleepiness, five performance tests, and two mood measures (Profile of Mood Scale and Visual Analog Scale) were administered repeatedly on both days. Electroencephalogram sleep was recorded on both nights. Objective sleep measures of daytime sleepiness were not significantly related to either performance or mood, but subjects with greater daytime sleepiness had significantly longer and more efficient nocturnal sleep. Neither benzodiazepine or caffeine influenced these relationships. In contrast, higher estimates of subjective sleepiness were significantly associated with poorer mood and tended to be related to poorer performance. Caffeine significantly reduced these relationships. Nocturnal sleep measures were not related to subjective estimates of daytime sleepiness.

We present a reformulation of unsteady turbulent flow simulations. The initial condition is relaxed and information is allowed to propagate both forward and backward in time. Simulations of chaotic dynamical systems with this reformulation can be proven to be well-conditioned time domain boundary value problems. The reformulation can enable scalable parallel-in-time simulation of turbulent flows. I. NEED FOR SPACE-TIME PARALLELISMThe use of computational fluid dynamics (CFD) in science and engineering can be categorized into Analysis and Design. A CFD Analysis performs a simulation on a set of manually picked parameter values. The flow field is then inspected to gain understanding of the flow physics. Scientific and engineering decisions are then made based on understanding of the flow field. Analysis based on high fidelity turbulent flow simulations, particular Large Eddy Simulations, is a rapidly growing practice in complex engineering applications 12 .CFD based Design goes beyond just performing individual simulations, towards sensitivity analysis, optimization, control, uncertainty quantification and data based inference. Design is enabled by Analysis capabilities, but often requires more rapid turnaround. For example, an engineer designer or an optimization software needs to perform a series of simulations, modifying the geometry based on previous simulation results. Each simulation must complete within at most a few hours in an industrial design environment. Most current practices of design use steady state CFD solvers, employing RANS (Reynolds Averaged NavierStokes) models for turbulent flows. Design using high fidelity, unsteady turbulent flow simulations has been investigated in academia 3 . Despite their great potential, high fidelity design is infeasible in an industrial setting because each simulation typically takes days to weeks. FIG. 1:Exponential increase of high performance computing power, primarily sustained by increased parallelism in the past decade. Data originate from top500.org. GFLOPS, TFLOPS, PFLOPS and EFLOPS represent 10 9 , 10 12 , 10 15 and 10 18 FLoating point Operations Per Second, respectively.The inability of performing high fidelity turbulent flow simulations in short turnaround time is a barrier to the game-changing technology of high fidelity CFD-based design. Nevertheless, development in High Performance Computing (HPC), as shown in Figure 1, promises to delivery in about ten years computing hardware a thousand times faster than those available today. This will be achieved through extreme scale a) Corresponding

In a double-blind parallel group design, 80 young adult males were divided into eight treatment groups. Subjects received 15 or 30 mg flurazepam, 0.25 or 0.50 mg triazolam, or placebo at bedtime, and 250 mg caffeine or placebo in the morning for 2 treatment days. Two objective (Multiple Sleep Latency Test and lapses) and two subjective (Stanford Sleepiness Scale and Visual Analog Scale) measures of sleepiness, five performance tests, and two mood measures (Profile of Mood Scale and Visual Analog Mood Scale) were administered repeatedly on both days. Significant treatment effects were found for sleepiness but not for performance or mood. Early morning caffeine significantly antagonized next day hypnotic-induced drowsiness and enhanced alertness in the subjects who received bed-time placebo. Flurazepam, 30 mg, subjects were more sleepy than all other groups. Although not significantly different, the flurazepam, 30 mg, group demonstrated a trend toward poorer performance and a more negative mood than all other groups. Caffeine most improved performance of this group. In all groups, sleepiness was greatest and performance and mood poorest in early morning trials and caffeine was most effective at this time.