Shear banding in nematogenic fluids with oscillating orientational dynamics

We investigate the occurrence of shear banding in nematogenic fluids under planar Couette flow, based on mesoscopic dynamical equations for the orientational order parameter and the shear stress. We focus on parameter values where the sheared homogeneous system exhibits regular oscillatory orientational dynamics, whereas the equilibrium system is either isotropic (albeit close to the isotropic--nematic transition) or deep in its nematic phase. The numerical calculations are restricted to spatial variations in shear gradient direction. We find several new types of shear banded states characterized by regions with regular oscillatory orientational dynamics. In all cases shear banding is accompanied by a non--monotonicity of the flow curve of the homogeneous system; however, only in the case of the initially isotropic system this curve has the typical $S$--like shape. We also analyze the influence of different orientational boundary conditions and of the spatial correlation length.Comment: 12 pages, 10 figure

Ising-like critical behavior of vortex lattices in an active fluid

Turbulent vortex structures emerging in bacterial active fluids can be organized into regular vortex lattices by weak geometrical constraints such as obstacles. Here we show, using a continuum-theoretical approach, that the formation and destruction of these patterns exhibit features of a continuous second-order equilibrium phase transition, including long-range correlations, divergent susceptibility, and critical slowing down. The emerging vorticity field can be mapped onto a two-dimensional (2D) Ising model with antiferromagnetic nearest-neighbor interactions by coarse-graining. The resulting effective temperature is found to be proportional to the strength of the nonlinear advection in the continuum model

Pattern selection and the route to turbulence in incompressible polar active fluids

Active fluids, such as suspensions of microswimmers, are known to self-organize into complex spatio-temporal flow patterns. An intriguing example is mesoscale turbulence, a state of dynamic vortex structures exhibiting a characteristic length scale. Here, we employ a minimal model for the effective microswimmer velocity field to explore how the turbulent state develops from regular vortex patterns when the strength of activity resp. related parameters such as nonlinear advection or polar alignment strength - is increased. First, we demonstrate analytically that the system, without any spatial constraints, develops a stationary square vortex lattice in the absence of nonlinear advection. Subsequently, we perform an extended stability analysis of this nonuniform "ground state" and uncover a linear instability, which follows from the mutual excitement and simultaneous growth of multiple perturbative modes. This extended analysis is based on linearization around an approximation of the analytical vortex lattice solution and allows us to calculate critical activity parameters. Above these critical values, the vortex lattice develops into mesoscale turbulence in numerical simulations. Utilizing the numerical approach, we uncover an extended region of hysteresis where both patterns are possible depending on the initial condition. Here, we find that turbulence persists below the instability of the vortex lattice. We further determine the stability of square vortex patterns as a function of their wavenumber and represent the results analogous to the well-known Busse balloons known from classical pattern-forming systems. Here, the region of stable periodic patterns shrinks and eventually disappears with increasing activity parameters. Our results show that the strength of activity plays a similar role for active turbulence as the Reynolds number does in driven flow exhibiting inertial turbulence

Anisotropic mesoscale turbulence and pattern formation in microswimmer suspensions induced by orienting external fields

This paper studies the influence of orienting external fields on pattern formation, particularly mesoscale turbulence, in microswimmer suspensions. To this end, we apply a hydrodynamic theory that can be derived from a microscopic microswimmer model (Reinken et al 2018 Phys. Rev. E 97, 022613). The theory combines a dynamic equation for the polar order parameter with a modified Stokes equation for the solvent flow. Here, we extend the model by including an external field that exerts an aligning torque on the swimmers (mimicking the situation in chemo-, photo-, magneto- or gravitaxis). Compared to the field-free case, the external field breaks the rotational symmetry of the vortex dynamics and leads instead to strongly asymmetric, traveling stripe patterns, as demonstrated by numerical solution and linear stability analysis. We further analyze the emerging structures using a reduced model which involves only an (effective) microswimmer velocity field. This model is significantly easier to handle analytically, but still preserves the main features of the anisotropic pattern formation. We observe an underlying transition between a square vortex lattice and a traveling stripe pattern. These structures can be well described in the framework of weakly nonlinear analysis, provided the strength of nonlinear advection is sufficiently weak.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und AnwendungskonzepteDFG, 87159868, GRK 1558: Kollektive Dynamik im Nichtgleichgewicht: in kondensierter Materie und biologischen Systeme

Development of educational video at the technical university

This article discusses the development and production of the main types of video resources on the example of disciplines on technical areas

\u3ci\u3eThe Lord of the Rings\u3c/i\u3e: A Christian Refounding of the Political Order

Examines the “severely classical moral doctrine” of The Lord of the Rings; discusses stewardship as “the proper subordination of Power to Care”; and approves of Tolkien’s “veiling of the Divine” by keeping overt religious references out of the work as a means of leading readers to understanding and affirmation. Reprinted from Christian Perspectives, Winter 1966