Dynamic Active Earth Pressure Against Retaining Walls

Equations of equilibrium expressed along the stress characteristics are transformed onto the Zero Extension Line (ZEL) directions. The new dynamic equilibrium equations are then applied to simple ZEL field (composed of Rankine, Goursat, and Coulomb zones) behind retaining walls. Integration of differential equilibrium equations along the assumed field boundary, thus provide the final equations for the active static (Kast) and dynamic (Kady) earth pressure coefficients, which are functions of friction and dilation angles of the soil and friction angle of the wall surface. Numerical evaluation of Kast, and Kady indicates that these coefficients are not sensitive to the wall roughness for practical values of angle of friction of backfill material between 35° and 45°. In this range, the coefficients can be approximated by: Kast=tan2(π/4 -φ/2) and Kady =tan(π/4 - ν/2)

Separating the scales in a compressible interstellar medium

We apply Gaussian smoothing to obtain mean density, velocity, magnetic and energy density fields in simulations of the interstellar medium based on three-dimensional magnetohydrodynamic equations in a shearing box $1\times1\times2 \, \rm{kpc}$ in size. Unlike alternative averaging procedures, such as horizontal averaging, Gaussian smoothing retains the three-dimensional structure of the mean fields. Although Gaussian smoothing does not obey the Reynolds rules of averaging, physically meaningful central statistical moments are defined as suggested by Germano (1992). We discuss methods to identify an optimal smoothing scale $\ell$ and the effects of this choice on the results. From spectral analysis of the magnetic, density and velocity fields, we find a suitable smoothing length for all three fields, of $\ell \approx 75 \, \rm{pc}$. We discuss the properties of third-order statistical moments in fluctuations of kinetic energy density in compressible flows and suggest their physical interpretation. The mean magnetic field, amplified by a mean-field dynamo, significantly alters the distribution of kinetic energy in space and between scales, reducing the magnitude of kinetic energy at intermediate scales. This intermediate-scale kinetic energy is a useful diagnostic of the importance of SN-driven outflows

Statistical properties of Faraday rotation measure from large-scale magnetic fields in intervening disc galaxies

To constrain the large-scale magnetic field strengths in cosmologically distant galax- ies, we derive the probability distribution function of Faraday rotation measure (RM) when random lines of sight pass through a sample of disc galaxies, with axisymmetric large-scale magnetic fields. We find that the width of the RM distribution of the galaxy sample is directly related to the mean large-scale field strength of the galaxy population, provided the dispersion within the sample is lower than the mean value. In the absence of additional constraints on parameters describing the magneto-ionic medium of the intervening galaxies, and in the situation where RMs produced in the intervening galaxies have already been statistically isolated from other RM contributions along the lines of sight, our simple model of the magneto-ionic medium in disc galaxies suggests that the mean large-scale magnetic field of the population can be measured to within ~ 50% accuracy.Comment: 4 pages, Proceedings of FM8 "New Insights in Extragalactic Magnetic Fields", XXXth General Assembly of the IAU, Vienna, August 20-31, 201