The Turbulence Power Spectrum in Optically Thick Interstellar Clouds

The Fourier power spectrum is one of the most widely used statistical tools to analyze the nature of magnetohydrodynamic turbulence in the interstellar medium. Lazarian & Pogosyan (2004) predicted that the spectral slope should saturate to -3 for an optically thick medium and many observations exist in support of their prediction. However, there have not been any numerical studies to-date testing these results. We analyze the spatial power spectrum of MHD simulations with a wide range of sonic and Alfv\'enic Mach numbers, which include radiative transfer effects of the $^{13}$CO transition. We confirm numerically the predictions of Lazarian & Pogosyan (2004) that the spectral slope of line intensity maps of an optically thick medium saturates to -3. Furthermore, for very optically thin supersonic CO gas, where the density or CO abundance values are too low to excite emission in all but the densest shock compressed gas, we find that the spectral slope is shallower than expected from the column density. Finally, we find that mixed optically thin/thick CO gas, which has average optical depths on order of unity, shows mixed behavior: for super-Alfv\'enic turbulence, the integrated intensity power spectral slopes generally follow the same trend with sonic Mach number as the true column density power spectrum slopes. However, for sub-Alfv\'enic turbulence the spectral slopes are steeper with values near -3 which are similar to the very optically thick regime.Comment: accepted to Ap

State forest resources of the peninsula and their management - past, present and future

Utilisation of forest resources of Tasman Peninsula began during the convict period of Port Arthur settlement and continues today. The Tasmanian Forestry Commission manages State Forests of the peninsula for muiltiple uses including wood production, conservation, recreation, landscape and water

Minimum energy route optimisation of a quad-copter UAV with landing incentivisation

Recent advancements in the technology surrounding UAVs have expanded the possibility of incorporating them into current logistical solutions. In order to accurately assess their capabilities, it is important that minimum energy trajectories can be generated to increase the travel range of a UAV as well as its possible number of visited locations. However, in current formulations of the optimisation problem, UAV dynamics do not incorporate a contact force on the ground. This results in hover-to-hover trajectories where the duration of the journey is exactly equal to an arrival time which is set as one of the problem's parameters. Those solutions are likely to be energetically sub-optimal if an unnecessarily large value of arrival time is chosen. This paper introduces landing capability by modifying gravitational acceleration in the dynamics using a sigmoid function which approaches zero at the destination. In this way, the trip can be conducted in a shorter amount of time if it results in lower energy consumption. The new model is compared against an example from the literature, where the corresponding solution results in a reduction of the travel time and energy consumption by approximately 80%. It is also applied to a real-world example where it is demonstrated that a UAV can provide energy savings if it replaces a van completing a delivery in the Solent region of the UK

Density Studies of MHD Interstellar Turbulence: Statistical Moments, Correlations and Bispectrum

We present a number of statistical tools for obtaining studying turbulence in molecular clouds and diffuse interstellar medium. For our tests we used of three-dimensional 512 cube compressible MHD isothermal simulations performed for different sonic and Alfvenic Mach numbers. We introduce the bispectrum, a new tool for statistical studies of the interstellar medium which, unlike an ordinary power spectrum of turbulence, preserves the phase information of the stochastic field. We show that the bispectra of the 3D stochastic density field and of column densities, available from observations, are similar. We use the bispectrum technique to define the role of non-linear wave-wave interactions in the turbulent energy cascade. We also obtained the bispectrum function for density and column densities with varying magnetic field strength. Larger values of sonic Mach number result in increased correlations for modes with different wavenumbers. This effect becomes more evident with increasing magnetic field intensity. In addition to the bispectrum, we calculated the 3rd and 4th statistical moments of density and column density, namely, skewness and kurtosis, respectively. We found a strong dependence of skewness and kurtosis with the sonic Mach number. In particular, as this number increases, so does the asymmetry of the density distribution. We also studied the correlations of 2D column density with dispersion of velocities and magnetic field, as well as the correlations of 3D density with magentic and kinetic energy and Alfven Mach number for comparison. Our results show that column density is linearly correlated with magnetic field for high sonic Mach number. This trend is independent of the turbulent kinetic energy and can be used to characterize inhomogeneities of physical properties in low density clumps in the ISM.Comment: apj emulated, 18 pages, 11 figures. Accepted to Astrophysical Journa