Resonant drag instability of grains streaming in fluids

We show that grains streaming through a fluid are generically unstable if their velocity, projected along some direction, matches the phase velocity of a fluid wave (linear oscillation). This can occur whenever grains stream faster than any fluid wave. The wave itself can be quite general--sound waves, magnetosonic waves, epicyclic oscillations, and Brunt-V\"ais\"al\"a oscillations each generate instabilities, for example. We derive a simple expression for the growth rates of these "resonant drag instabilities" (RDI). This expression (i) illustrates why such instabilities are so virulent and generic, and (ii) allows for simple analytic computation of RDI growth rates and properties for different fluids. As examples, we introduce several new instabilities, which could see application across a variety of physical systems from atmospheres to protoplanetary disks, the interstellar medium, and galactic outflows. The matrix-based resonance formalism we introduce can also be applied more generally in other (nonfluid) contexts, providing a simple means for calculating and understanding the stability properties of interacting systems.Comment: 5 Pages. Published in ApJ

Physical models of streaming instabilities in protoplanetary discs

We develop simple, physically motivated models for drag-induced dust–gas streaming instabilities, which are thought to be crucial for clumping grains to form planetesimals in protoplanetary discs. The models explain, based on the physics of gaseous epicyclic motion and dust–gas drag forces, the most important features of the streaming instability and its simple generalization, the disc settling instability. Some of the key properties explained by our models include the sudden change in the growth rate of the streaming instability when the dust-to-gas mass ratio surpasses one, the slow growth rate of the streaming instability compared to the settling instability for smaller grains, and the main physical processes underlying the growth of the most unstable modes in different regimes. As well as providing helpful simplified pictures for understanding the operation of an interesting and fundamental astrophysical fluid instability, our models may prove useful for analysing simulations and developing non-linear theories of planetesimal growth in discs

The distribution of density in supersonic turbulence

We propose a model for the density statistics in supersonic turbulence, which play a crucial role in star-formation and the physics of the interstellar medium (ISM). Motivated by [Hopkins, MNRAS, 430, 1880 (2013)], the model considers the density to be arranged into a collection of strong shocks of width $\sim\! \mathcal{M}^{-2}$, where $\mathcal{M}$ is the turbulent Mach number. With two physically motivated parameters, the model predicts all density statistics for $\mathcal{M}>1$ turbulence: the density probability distribution and its intermittency (deviation from log-normality), the density variance-Mach number relation, power spectra, and structure functions. For the proposed model parameters, reasonable agreement is seen between model predictions and numerical simulations, albeit within the large uncertainties associated with current simulation results. More generally, the model could provide a useful framework for more detailed analysis of future simulations and observational data. Due to the simple physical motivations for the model in terms of shocks, it is straightforward to generalize to more complex physical processes, which will be helpful in future more detailed applications to the ISM. We see good qualitative agreement between such extensions and recent simulations of non-isothermal turbulence

Australia's Prosperous 2000s: Housing and the Mining Boom

The 2000s was a particularly eventful decade for both the international and Australian economies. There were: two recessions in many countries; the largest international financial crisis since the Great Depression; the ongoing rapid development of Asia; asset booms and busts; and, Australia experienced the longest sustained increase in commodity prices and the terms of trade in the nation's history. This paper provides an overview of the Australian economy's performance in the decade. Several key topics are elaborated on, including the development of Asia and implications for Australia, policy frameworks, and the opportunities and challenges facing the Australian economy, with a particular focus on the expansion of household balance sheets and the rapid growth in the mining economy.Australian macroeconomy; economic performance; household balance sheets; terms of trade; monetary policy; fiscal policy

Geometry and Dynamics with Time-Dependent Constraints

We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which require time-dependent gauge fixing conditions in order to reduce them to their physical degrees of freedom. To illustrate our results we discuss the gauge-fixing of relativistic particles and strings moving in arbitrary background electromagnetic and antisymmetric tensor fields.Comment: 8 pages, Plain TeX, CERN-TH.7392/94 and MPI-PhT/94-4

Demographic vital rates and population growth: rethinking the relationship in a harvested elk population

Understanding the nature of the relationship between demographic vital rates and the rate of population change (λ) is important for determining effective strategies for population management and conservation. We examined the relative impacts of various demographic vital rates on λ within the range of temporal vital rate variability observed in a harvested population to test the hypotheses that adult survival rates in ungulates are relatively invariant when compared to other vital rates and that variability in calf survival has a greater influence on rates of population change than adult survival. Vital rates were estimated for an elk (_Cervus elaphus_) population at Fort Riley, Kansas from October 2003 – February 2007. The magnitude of adult survival rates were similar to other harvested populations and models including a negative relationship between survival and age received the highest levels of support. Prime-age adult survival had the highest stage-specific elasticity values, indicating a high contribution of these matrix elements to λ. Life-stage simulation analysis indicated that variation in calf survival had the highest correlation with variation in λ (r^2^ = 0.61). Our results suggest that adult survival rates in harvested populations may experience increased levels of variability, but that calf survival rates have the greatest relative influence on λ due to the wider range of variability observed for this vital rate