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Modern urban science views differences in attractiveness of residential suburbs as the main driver of resettlement within a city. In particular, certain suburbs may attract residents due to lower commute costs, and this is believed to lead to compactification of a city, with highly populated central business district and sprawled suburbia. In this paper we assess residential resettlement patterns in Australian capital cities by analyzing the 2011 and 2016 Australian Census data. Rather than explicitly defining a residential attractiveness of each suburb in subjective terms, we introduce and calibrate a model which quantifies the intra-city migration flows in terms of the attractiveness potentials (and their differences), inferring these from the data. We discover that, despite the existence of well-known static agglomeration patterns favouring central districts over the suburbia, the dynamic flows that shape the intra-city migration over the last decade reveal the preference directed away from the central districts with a high density of jobs and population, towards the less populated suburbs on the periphery. Furthermore, we discover that the relocation distance of such resettlement flows plays a vital role, and explains a significant part of the variation in migration flows: the resettlement flow markedly decreases with the relocation distance. Finally, we propose a conjecture that these directional resettlement flows are explained by the cities' structure, with monocentric cities exhibiting outward flows with much higher reluctance to long-distance relocation. This conjecture is verified across the major Australian capitals: both monocentric (Sydney, Melbourne, Brisbane, Adelaide, Perth, Hobart) and polycentric (Darwin and Canberra). The modern world undergoes rapid urbanisation 1. Growing complexity of cities demands new fundamental understanding and rigorous models of the urban dynamics, including diverse and transient intra-urban migration patterns. At the same time, the increasing availability of large-scale spatiotemporal data (e.g., from censuses or surveys) provides an additional impetus for quantitative modelling of urban development and related dynamics 2-4. A consistent modeling framework for settlement formation does not yet exist 2 , despite an abundance of stable empirical patterns 5-12 and theoretical insights 13-22 that can potentially improve our understanding of how cities grow and self-organise. Contemporary cities are shaped by the long process of settlement formation and evolution which involves multiple types of migration and resettlement. In social sciences it is common to investigate population migration in the context of individual motivation and social consequences 23-25. However, heterogeneous preferences of individual residents cannot be easily integrated into their aggregate migration flows. The latter is a collective phenomenon which we believe is determined mainly by the spatial city structure 2. Furthermore, such migration patterns are usually persistent in time. In particular, w...

We propose a non-equilibrium framework for modelling the evolution of cities, which describes intra-urban migration as an irreversible diffusive process. We validate this framework using the actual migration data for the Australian capital cities. With respect to the residential relocation, the population is shown to be composed of two distinct groups, exhibiting different relocation frequencies. In the context of the developed framework, these groups can be interpreted as two components of a binary fluid mixture, each with its own diffusive relaxation time. Using this approach, we obtain long-term predictions of the cities’ spatial structures, which define their equilibrium population distribution.

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