Remarks on the stability analysis of reactive flows

A simple model of compressible reacting flow is studied. First, a dispersion relation is derived for the linearized problem making a distinction between frozen and equilibrium sound speed. Second, the stability of the Von Neumann-Richtmyer scheme applied to this model is studied. A natural generalization of the C.F.L. condition is found

Centrality and connectivity in public transport networks and their significance for transport sustainability in cities

The promotion of public transport as a backbone of mobility in urban agglomerations, or at least as an alternative to the dominance of the automobile, has become a prominent policy focus in most large cities around the world. However, while some cities have been successful in shifting car journeys onto rail and buses, others are struggling despite considerable effort to make public transport more attractive. This paper provides a brief overview of success factors for public transport and then takes the configuration of public transport networks as a vantage point for policy evaluation. The development of centrality and connectivity indicators for the public transport network of Melbourne's north-eastern suburbs delivers an instrument for assessing the congruence of the systems with the geographical structure of central areas and urban activities in these cities. It is hypothesised that a higher number of convenient transfer points and a choice of routes to users (network connectivity), as well as a high degree of spatial overlap and integration between public transport infrastructure and urban activity centres and corridors (centrality of facilities) will lead to a greater role for public transport in the mobility patterns of the city as a whole

Dimensional crossover and cold-atom realization of topological Mott insulators

We propose a cold-atom setup which allows for a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers. We further show that additional Hubbard onsite interactions can give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of a quantum state of matter which merely exists because of the interplay of the non-trivial topology of the band structure and strong interactions. While the theoretical understanding of this phase has remained elusive, our proposal shall help to shed some light on this exotic state of matter by paving the way for a controlled experimental investigation in optical lattices.Comment: 4+ pages, 3 figures; includes Supplemental Material (3 pages, 1 figure

Hierarchy of Information Scrambling, Thermalization, and Hydrodynamic Flow in Graphene

We determine the information scrambling rate $\lambda_{L}$ due to electron-electron Coulomb interaction in graphene. $\lambda_{L}$ characterizes the growth of chaos and has been argued to give information about the thermalization and hydrodynamic transport coefficients of a many-body system. We demonstrate that $\lambda_{L}$ behaves for strong coupling similar to transport and energy relaxation rates. A weak coupling analysis, however, reveals that scrambling is related to dephasing or single particle relaxation. Furthermore, $\lambda_{L}$ is found to be parametrically larger than the collision rate relevant for hydrodynamic processes, such as electrical conduction or viscous flow, and the rate of energy relaxation, relevant for thermalization. Thus, while scrambling is obviously necessary for thermalization and quantum transport, it does generically not set the time scale for these processes. In addition we derive a quantum kinetic theory for information scrambling that resembles the celebrated Boltzmann equation and offers a physically transparent insight into quantum chaos in many-body systems