Computational and Analytical Investigations of Disordered and Interacting Systems

Localization of particle wavefunctions in quasi-disordered one dimensional incommensurate lattices is studied both numerically and analytically. Through exact diagonalization, we show that energy dependent mobility edges can appear in the case of shallow lattices. We also show that these mobility edges can be studied with a tight-binding model (an extension of the Aubry-Andre model) that has energy dependent mobility edges that can be determined analytically. Topological aspects of the Aubry-Andre/Harper model are also studied by numerically calculating the Chern number. We first verify arguments by numerical calculations that variations in the Chern density decrease with increasing system size when the potential is incommensurate with the lattice. Next we introduce random disorder into the model and study the Chern number and the Chern density as a function of disorder strength by using the non-commutative Brillouin zone. We show that variations of the Chern density take on the same trends for both commensurate and incommensurate potentials after some critical disorder strength is reached. Strongly correlated quantum Hall states are also examined. We numerically examine the entanglement entropy and the entanglement spectrum of fractional quantum hall states as a function of the finite layer thickness $d$ of the quasi-two-dimensional system for a number of filling fractions $\nu$ in the lowest and the second Landau levels: $\nu$ = 1/3, 7/3, 1/2, and 5/2. We observe that the entanglement measures are dependent on which Landau level the electrons fractionally occupy and are completely consistent with the results based on wavefunction overlap calculations. We also compare the ground state energies by variational Monte Carlo of the spin unpolarized Halperin 331 and the spin polarized Moore-Read (MR) Pfaffian fractional quantum Hall states at half filling of the lowest Landau level (LLL) and the second Landau level (SLL) as a function of small deviations around the Coulomb point. Our results suggest that even under moderate deviations in the interaction potential the MR Pfaffian description is more energetically favorable than the Halperin 331 state in the half filled SLL, consistent with recent experimental investigations

Indigenous population projections, 2006-31: Planning for growth

Policy development in Indigenous affairs often proceeds with dated estimates of population and with little understanding of the likely impact of changing demographic parameters on future Indigenous population size and composition. To the extent that policy itself can influence demographic outcomes, this represents a significant deficiency in current planning methodology. To stimulate a dialogue around such issues, this paper models the national and regional population impacts of a continuation of existing mortality and fertility regimes compared to a situation where these converge. The effects of inter-regional migration are also considered. The scenarios presented are heuristic only and reflect the logic of sustaining into the future recently observed demographic trends, compared to following through on the idea of convergence in sociodemographic outcomes over timescales that are commensurate with stated policy ambitions. As such, they are designed to sketch out the effects on the size and composition of Indigenous population of no change in current conditions compared to maximum change. What they show is that while the overall size of the Indigenous population is conservatively projected to be around 830,000 by 2031, regardless of which assumptions are adopted, any movement towards convergence in demographic outcomes, as implied by current Closing the Gap policies, produces a population that is much older and more urban in profile

Estimating the accuracy of geographic variation in Indigenous population counts

The ABS 2006 Post-Enumeration Survey was extended to include a sample of localities from the whole of Australia, thereby providing an estimate of census net undercount reflective of the enumeration in remote Indigenous settlements for the first time. Th

Thermal Conductivity of Supercooled Water

The heat capacity of supercooled water, measured down to -37 {\deg}C, shows an anomalous increase as temperature decreases. The thermal diffusivity, i. e., the ratio of the thermal conductivity and the heat capacity per unit volume, shows a decrease. These anomalies may be associated with a hypothetical liquid-liquid critical point in supercooled water below the line of homogeneous nucleation. However, while the thermal conductivity is known to diverge at the vapor-liquid critical point due to critical density fluctuations, the thermal conductivity of supercooled water, calculated as the product of thermal diffusivity and heat capacity, does not show any sign of such an anomaly. We have used mode-coupling theory to investigate the possible effect of critical fluctuations on the thermal conductivity of supercooled water, and found that indeed any critical thermal-conductivity enhancement would be too small to be measurable at experimentally accessible temperatures. Moreover, the behavior of thermal conductivity can be explained by the observed anomalies of the thermodynamic properties. In particular, we show that thermal conductivity should go through a minimum as temperature is decreased, as Kumar and Stanley observed in the TIP5P model of water. We discuss physical reasons for the striking difference between the behavior of thermal conductivity in water near the vapor-liquid and liquid-liquid critical points.Comment: References added, typos corrected. Extrapolation for viscosity improved; results essentially unchange

Indigenous Participation in Regional Labour Markets, 2001-06

This paper examines the extent to which Indigenous Australians have shared in the large expansion of the Australian workforce that is revealed by a comparison of 2001 and 2006 census results. It considers whether this is reflected in changes to regional patterns of Indigenous labour force status, income, occupation and industry of employment. As such, it provides the first comprehensive assessment of possible impacts of federal Indigenous employment policies introduced just prior to the 2001 Census and it contributes to the policy discourse on 'closing the gap' between Indigenous and other Australians. Conventional census measures of labour force status are established for each of 37 Indigenous Regions and administrative data are also deployed to produce a more accurate picture of the spread of CDEP program employment and the effect of this on labour force outcomes. Changes in occupational and industry segregation are established as is the effect of employment change on the gap in median incomes. In line with previous gap analyses conducted by CAEPR an attempt is made to estimate future job requirements using a projection of the Indigenous working-age population to 2016. This reveals a need for more than 70,000 additional jobs to meet current government target

Two-State Thermodynamics of Supercooled Water

Water has been called the “most studied and least understood” of all liquids, and upon supercooling its behavior becomes even more anomalous. One particularly fruitful hypothesis posits a liquid-liquid critical point terminating a line of liquid-liquid phase transitions that lies just beyond the reach of experiment. Underlying this hypothesis is the conjecture that there is a competition between two distinct hydrogen-bonding structures of liquid water, one associated with high density and entropy and the other with low density and entropy. The competition between these structures is hypothesized to lead at very low temperatures to a phase transition between a phase rich in the high-density structure and one rich in the low-density structure. Equations of state based on this conjecture have given an excellent account of the thermodynamic properties of supercooled water. In this thesis, I extend that line of research. I treat supercooled aqueous solutions and anomalous behavior of the thermal conductivity of supercooled water. I also address supercooled water at negative pressures, leading to a framework for a coherent understanding of the thermodynamics of water at low temperatures. I supplement analysis of experimental results with data from the TIP4P/2005 model of water, and include an extensive analysis of the thermodynamics of this model

Thermodynamic bounds on ultrasensitivity in covalent switching

Switch-like motifs are among the basic building blocks of biochemical networks. A common motif that can serve as an ultrasensitive switch consists of two enzymes acting antagonistically on a substrate, one making and the other removing a covalent modification. To work as a switch, such covalent modification cycles must be held out of thermodynamic equilibrium by continuous expenditure of energy. Here, we exploit the linear framework for timescale separation to establish tight bounds on the performance of any covalent-modification switch, in terms of the chemical potential difference driving the cycle. The bounds apply to arbitrary enzyme mechanisms, not just Michaelis-Menten, with arbitrary rate constants, and thereby reflect fundamental physical constraints on covalent switching.Comment: 29 pages, 6 figure