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In star-forming clouds, high velocity flow gives rise to large fluctuations of density. In this work, we explore the correlation between velocity magnitude (speed) and density. We develop an analytic formula for the joint probability distribution function (PDF) of density and speed, and discuss its properties. In order to develop an accurate model for the joint PDF, we first develop improved models of the marginalized distributions of density and speed. We confront our results with a suite of 12 supersonic isothermal simulations with resolution of $1024^3$ cells in which the turbulence is driven by 3 different forcing modes (solenoidal, mixed, and compressive) and 4 rms Mach numbers (1, 2, 4, 8). We show, that for transsonic turbulence, density and speed are correlated to a considerable degree and the simple assumption of independence fails to accurately describe their statistics. In the supersonic regime, the correlations tend to weaken with growing Mach number. Our new model of the joint and marginalized PDFs are a factor of 3 better than uncorrelated, and provides insight into this important process.

 

The probability distribution of density in isothermal, supersonic, turbulent gas is approximately lognormal. This behaviour can be traced back to the shock waves travelling through the medium, which randomly adjust the density by a random factor of the local sonic Mach number squared. Provided a certain parcel of gas experiences a large number of shocks, due to the central limit theorem, the resulting distribution for density is lognormal. We explore a model in which parcels of gas undergo finite number of shocks before relaxing to the ambient density, causing the distribution for density to deviate from a lognormal. We confront this model with numerical simulations with various rms Mach numbers ranging from subsonic as low as 0.1 to supersonic at 25. We find that the fits to the finite formula are an order of magnitude better than a lognormal. The model naturally extends even to subsonic flows, where no shocks exist.

 

To understand the formation of stars from clouds of molecular gas, one essentially needs to know two things: what gas collapses, and how long it takes to do so. We address these questions by embedding pseudo-Lagrangian tracer particles in three simulations of self-gravitating turbulence. We identify prestellar cores at the end of the collapse, and use the tracer particles to rewind the simulations to identify the preimage gas for each core at the beginning of each simulation. This is the first of a series of papers, wherein we present the technique and examine the first question: What gas collapses? For the preimage gas at t = 0, we examine a number of quantities – the probability distribution function (PDF) for several quantities, the structure function for velocity, several length scales, the volume filling fraction, the overlap between different preimages, and fractal dimension of the preimage gas. Analytical descriptions are found for the PDFs of density and velocity for the preimage gas. We find that the preimage of a core is large and sparse, and we show that gas for one core comes from many turbulent density fluctuations and a few velocity fluctuations. We find that binary systems have preimages that overlap in a fractal manner. Finally, we use the density distribution to derive a novel prediction of the star formation rate.

 

Abstract We present a study of the influence of magnetic field strength and morphology in Type Ia supernovae and their late-time light curves and spectra. In order to both capture self-consistent magnetic field topologies and evolve our models to late times, a two-stage approach is taken. We study the early deflagration phase (∼1 s) using a variety of magnetic field strengths and find that the topology of the field is set by the burning, independent of the initial strength. We study late-time (∼1000 days) light curves and spectra with a variety of magnetic field topologies and infer magnetic field strengths from observed supernovae. Lower limits are found to be 10 6 G. This is determined by the escape, or lack thereof, of positrons that are tied to the magnetic field. The first stage employs 3D MHD and a local burning approximation and uses the code Enzo. The second stage employs a hybrid approach, with 3D radiation and positron transport and spherical hydrodynamics. The second stage uses the code HYDRA. In our models, magnetic field amplification remains small during the early deflagration phase. Late-time spectra bear the imprint of both magnetic field strength and morphology. Implications for alternative explosion scenarios are discussed. 

ABSTRACT We report a facile method to fabricate CuNi nano-octahedra and nanocubes using a colloidal synthesis approach. The CuNi nanocrystals terminated with exclusive crystallographic facets were controlled and achieved by a group of synergetic capping ligands in a hot solution system. Specifically, the growth of {111}-bounded CuNi nano-octahedra is derived by a thermodynamic control, whereas the generation of {100}-terminated CuNi nanocubes is steered by a kinetic capping of chloride. Using a reduction of 4-nitrophenol with sodium borohydride as a model reaction, CuNi nano-octahedra and nanocubes demonstrated a strong facet-dependence due to their different surface energies although both exhibited remarkable catalytic activity with the high rate constant over mass (k/m). A kinetic study indicated that this is a pseudo first-order reaction with an excess of sodium borohydride. CuNi nanocubes as the catalysts showed better catalytic performance (k/m = 385 s -1 •g -1 ) than the CuNi nano-octahedra (k/m = 120 s -1 •g -1 ), indicating that 4-nitrophenol and hydrogen were adsorbed on the {100} facets with their molecules parallel to the surface much easier than those on {111} facets. 

Abstract Background Expiratory muscle weakness leads to difficult ventilator weaning. Maintaining their activity with functional electrical stimulation (FES) may improve outcome. We studied feasibility of breath-synchronized expiratory population muscle FES in a mixed ICU population (“Holland study”) and pooled data with our previous work (“Australian study”) to estimate potential clinical effects in a larger group. Methods Holland: Patients with a contractile response to FES received active or sham expiratory muscle FES (30 min, twice daily, 5 days/week until weaned). Main endpoints were feasibility (e.g., patient recruitment, treatment compliance, stimulation intensity) and safety. Pooled: Data on respiratory muscle thickness and ventilation duration from the Holland and Australian studies were combined ( N  = 40) in order to estimate potential effect size. Plasma cytokines (day 0, 3) were analyzed to study the effects of FES on systemic inflammation. Results Holland: A total of 272 sessions were performed (active/sham: 169/103) in 20 patients ( N  = active/sham: 10/10) with a total treatment compliance rate of 91.1%. No FES-related serious adverse events were reported. Pooled: On day 3, there was a between-group difference ( N  = active/sham: 7/12) in total abdominal expiratory muscle thickness favoring the active group [treatment difference (95% confidence interval); 2.25 (0.34, 4.16) mm, P  = 0.02] but not on day 5. Plasma cytokine levels indicated that early FES did not induce systemic inflammation. Using a survival analysis approach for the total study population, median ventilation duration and ICU length of stay were 10 versus 52 ( P  = 0.07), and 12 versus 54 ( P  = 0.03) days for the active versus sham group. Median ventilation duration of patients that were successfully extubated was 8.5 [5.6–12.2] versus 10.5 [5.3–25.6] days ( P  = 0.60) for the active ( N  = 16) versus sham ( N  = 10) group, and median ICU length of stay was 10.5 [8.0–14.5] versus 14.0 [9.0–19.5] days ( P  = 0.36) for those active ( N  = 16) versus sham ( N  = 8) patients that were extubated and discharged alive from the ICU. During ICU stay, 3/20 patients died in the active group versus 8/20 in the sham group ( P  = 0.16). Conclusion Expiratory muscle FES is feasible in selected ICU patients and might be a promising technique within a respiratory muscle-protective ventilation strategy. The next step is to study the effects on weaning and ventilator liberation outcome. Trial registration: ClinicalTrials.gov, ID NCT03453944. Registered 05 March 2018—Retrospectively registered, https://clinicaltrials.gov/ct2/show/NCT03453944 .