Dr Kirill Glavatskiy

The spatial structure of modern cities exhibits highly diverse patterns and keeps evolving under numerous constraints and sustainability demands. However, it is unclear if there are fundamental physical constraints guiding the evolution of cities. Here, we offer a concise model revealing key invariants within urban forms shaped by human resettlement over the years. In doing so, we assess the heterogeneity and spreading of population density in 25 Australian and 175 US cities. We observe that larger cities tend to form a cluster with low spreading and high heterogeneity, and explain this observation using dynamic properties of the intra-urban migration in these cities. As a result, we report three distinct feasible phases of urban structures: uniform, monocentric, and polycentric, separated by abrupt regime shifts. We demonstrate that transitions between these phases, resulting from the population redistribution, are not necessarily driven by external factors (such as city growth) and can exist even in a closed system. Our analysis reveals that the set of all possible equilibrium configurations ("configurational attractors") form a narrow region in the heterogeneityspreading space, thus explaining the emergence of clustering patterns.

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 longterm predictions of the cities' spatial structures, which define their equilibrium population distribution.

We show that the solvent behaviour in both diffusio-osmosis and Marangoni flow can be derived from a simple model of colloid-interface interactions. We demonstrate that the direction of the flow is regulated by a single value of the attractive parameter covering the purely repulsive and attractive-repulsive interaction cases. The proposed universality between diffusio-osmosis and Marangoni flow is extended further to include diffusio-phoresis. In particular, an object immersed to a colloidal solution moves towards the low concentration of the colloidal particles in the case of colloid-interface repulsion and towards the high concentration of the colloidal particles in the case of colloid-interface attraction. The approach combines the methods of fluid dynamics, molecular physics and transport phenomena and provides a tractable explanation of how the colloid-interface interactions affect the momentum balance and the transport phenomena (interfacially driven transport).

Fluid transport through nanoporous membranes is subject to additional resistance at the membrane interface, a large part of which is due to the difference in thermodynamic states of the fluid inside and outside the membrane. The state of the fluid confined within a membrane depends on the size of the nanopores, which results in a corresponding dependence of the interfacial resistance. We investigate here the dependence of the thermodynamic resistance on the radius of the nanopore and the thickness of the pore wall, considering the transport of carbon dioxide and methane through carbon nanotubes of radii between 4¿Å and 50¿Å at room temperature, and a wide range of pressures. We find that the thermodynamic resistance strongly depends on the state of the fluid adsorbed in the membrane, which is determined by the size of the pores and the external pressure. In particular, for narrow micropores the thermodynamic resistance has two pressure regimes, being constant at low pressures and increasing gradually at high pressures. Furthermore, moderate and wide pores allow presence of multiple fluid phases with distinct condensation. In the corresponding pressure range the thermodynamic resistance is subjected to large fluctuations, which are not observed for small pores. Furthermore, our results reveal strong dependence of the thermodynamic resistance on the pore radius for very narrow pores and large pressures, when the state of the fluid inside of the membrane is most different from that of the external bulk fluid, with the resistance increasing with decrease in pore radius. Our results also indicate that analyzing the pore size dependence of the interfacial resistance makes it possible to distinguish the contribution of the thermodynamic resistance from the other sources of resistance to fluid flow through the membrane, in particular, the hydrodynamic resistance and the internal resistance.

Nanoporous materials are important in industrial separation, but their application is subject to strong interfacial barriers to the entry and transport of fluids. At certain conditions the fluid inside and outside the nanoporous material can be viewed as a two-phase system, with an interface between them, which poses an excess resistance to matter flow. We show that there exist two kinds of phenomena which influence the interfacial resistance: hydrodynamic effects and thermodynamic effects, which are independent of each other. Here, we investigate the role of the thermodynamic effects in carbon nanotubes (CNTs) and slit pores and compare the associated thermodynmic resistance with that due to hydrodynamic effects traditionally modeled by the established Sampson expression. Using CH4 and CO2 as model fluids, we show that the thermodynamic resistance is especially important for moderate to high pressures, at which the fluid within the CNT or slit pore is in the condensed state. Further, we show that at such pressures the thermodynamic resistance becomes comparable with the internal resistance to fluid transport at length scales typical of membranes used in fuel cells, and of importance in membrane-based separation, and nanofluidics in general.