Statistical and Biological Physics

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Turbulence is a fundamental and ubiquitous phenomenon in nature, ranging from astrophysical to biophysical scales. At the same time, it is widely acknowledged as one of the key unsolved problems in modern physics. While in the past, most theoretical work in this area has been devoted to simple fluids as described by the Navier-Stokes equations, there is now a growing awareness for the need to extend the research focus to systems with multiscale drive and/or dissipation. This includes various types of complex fluids, plasmas, as well as active systems. One very interesting example of this kind is "low Reynolds number turbulence" in dense bacterial suspensions. Recently, a continuum model has been proposed to describe the experimentally observed flows. It is based on the Navier-Stokes equations, but extends them to include some of the most general terms admitted by the symmetry of the problem, e.g., Swift-Hohenberg terms to represent the drive/dissipation as well as an additional Toner-Tu-type cubic nonlinearity which can interact with the quadratic Navier-Stokes nonlinearity. While developed in the context of living fluids, it is expected to be applicable to many other systems. The present work represents the first systematic study of turbulence described by this model. Our combined numerical and analytical analysis reveals, in particular, that the energy spectrum exhibits a power law at large scales as reported in [1], but that it is not universal and that its slope depends both on finite-size effects of the simulation domain as well as on system parameters. Further investigations even provide a quantitative expression for this dependence which is reinforced by numerical simulations. more

It has been exactly 20 years since the first physical studies which attempted to connect macroscopic collective behaviours in biological active matter systems to phase transitions and nonequilibrium physics. During the years, it has become clear that the precise knowledge of the interaction among the constituents is the key for understanding the emergence of order. In recent years, Boltzmann equations for propelled particles have been developed in order to connect the microscopic dynamics of the individual constituents to the meso- or macroscopic behaviour of the system. However due to the lack of quantitative experimental data, all models relied on very crude assumption of the interaction – most times simple digital interaction were assumed: collisions below 90 degrees align, above they are unaffected by the collision. more