Reversible and dissipative macroscopic contributions to the stress tensor: active or passive?

The issue of dynamic contributions to the macroscopic stress tensor has been of high interest in the field of bio-inspired active systems over the last few years. Of particular interest is a direct coupling ("active term") of the stress tensor with the order parameter, the latter describing orientational order induced by active processes. Here we analyze more generally possible reversible and irreversible dynamic contributions to the stress tensor for various passive and active macroscopic systems. This includes systems with tetrahedral/octupolar order, polar and non-polar (chiral) nematic and smectic liquid crystals, as well as active fluids with a dynamic preferred (polar or non-polar) direction. We show that it cannot a priori be seen, neither from the symmetry properties of the macroscopic variables involved, nor from the structure of the cross-coupling contributions to the stress tensor, whether the system studied is active or passive. Rather, that depends on whether the variables that give rise to those cross-couplings in the stress tensor are driven or not. We demonstrate that several simplified descriptions of active systems in the literature that neglect the necessary counter term to the active term violate linear irreversible thermodynamics and lead to an unphysical contribution to the entropy production.

Active polar two-fluid macroscopic dynamics.

We study the dynamics of systems with a polar dynamic preferred direction. Examples include the pattern-forming growth of bacteria as well as shoals of fish, flocks of birds and migrating insects. Due to the fact that the preferred direction only exists dynamically, but not statically, the macroscopic variable of choice is the macroscopic velocity associated with the motion of the active units, which are typically biological in nature. We derive the macroscopic equations for such a system and discuss novel static, reversible and irreversible cross-couplings connected to a second velocity as a variable. We analyze in detail how the macroscopic behavior of an active system with a polar dynamic preferred direction compares to other systems with two velocities including immiscible liquids and electrically neutral quantum liquids such as superfluid (4)He and (3)He . We critically discuss changes in the normal mode spectrum when comparing uncharged superfluids, immiscible liquids and active system with a polar dynamic preferred direction. We investigate the influence of a macroscopic hand (collective effects of chirality) on the macroscopic behavior of such active media.

Macroscopic behavior of systems with an axial dynamic preferred direction.

We present the derivation of the macroscopic equations for systems with an axial dynamic preferred direction. In addition to the usual hydrodynamic variables, we introduce the time derivative of the local preferred direction as a new variable and discuss its macroscopic consequences including new cross-coupling terms. Such an approach is expected to be useful for a number of systems for which orientational degrees of freedom are important including, for example, the formation of dynamic macroscopic patterns shown by certain bacteria such a Proteus mirabilis. We point out similarities in symmetry between the additional macroscopic variable discussed here, and the magnetization density in magnetic systems as well as the so-called Î vector in superfluid (3)He-A. Furthermore we investigate the coupling to a gel-like system for which one has the strain tensor and relative rotations between the new variable and the network as additional macroscopic variables.

Dynamics of nematic liquid crystal disclinations: the role of the backflow.

We measure the electric-field-driven annihilation of nematic disclination pairs with strength +/- 1/2 in the 4-cyano-4'-n-pentylbiphenyl (5CB) liquid crystal. The use of a very weak azimuthal anchoring ensures a two-dimensional director field. The relaxation is governed by the formation of a pi wall connecting the two opposite charge defects. The +1/2 disclinations move almost twice as fast as the -1/2 disclinations. The simple used geometry allows a quantitative comparison with numerical studies based on the hydrodynamics of the tensorial order parameter. The simulations show that in the pi wall regime the symmetry breaking is due to the backflow and not to the elastic anisotropy.

Fluctuations of topological disclination lines in nematic liquid crystals: renormalization of the string model.

Using the tensorial Landau-de Gennes theory, we study the fluctuations of a disclination line in a nematic liquid crystal. By analyzing the structure and the spectrum of the eigenmodes of a line of strength +/-1/2 , we reassess the concept of line tension used in the simple string model of the disclination showing that it does not include the complete set of eigenmodes and must be renormalized. In general, the line tension considerably underestimates the thermal amplitude of a disclination and we find that it is only applicable to severely confined disclinations.

Annihilation of edge dislocations in smectic-A liquid crystals.

This paper presents a theoretical study of the annihilation of edge dislocations in the same smectic plane in a bulk smectic-A phase. We use a time-dependent Landau-Ginzburg approach where the smectic ordering is described by the complex order parameter psi( r--> ,t) =eta e(iphi) . This quantity allows both the degree of layering and the position of the layers to be monitored. We are able to follow both precollision and postcollision regimes, and distinguish different early and late behaviors within these regimes. The early precollision regime is driven by changes in the phi ( r--> ) configuration. The relative velocity of the defects is approximately inversely proportional to the interdefect separation distance. In the late precollision regime the symmetry changes within the cores of defects also become influential. Following the defect collision, in the early postcollision stage, bulk layer order is approached exponentially in time. At very late times, however, there seems to be a long-time power-law tail in the order parameter fluctuation relaxation.

Instability modes of high-strength disclinations in nematics.

We solve the complete tensor fluctuation problem of a long and straight nematic disclination line with a general winding number in the one elastic constant approximation. Focusing on the eigenmodes growing in time, we show that the disclination with strength higher than 1/2 is unstable with respect to the splitting and for integer strength also to the escape--in both cases there is no metastability. Numerically we show that a moderate elastic anisotropy, e.g., as found in thermotropic liquid crystals like 5CB or MBBA, does not introduce any metastability either.

Hydrodynamics of pair-annihilating disclinations in SmC films.

The pair annihilation of smectic c-director defects with winding numbers +/-1 in a freestanding SmC film as a representative of the XY model is studied numerically, considering a full coupling of orientational degrees of freedom and hydrodynamics. A reduction of the annihilation time compared to the nonhydrodynamic treatment is observed. It is demonstrated that the +1 disclination moves considerably faster than the -1 one primarily due to hydrodynamic flow, weakly assisted also by elastic anisotropy. The stress tensor terms and material parameters relevant for this effect are identified.

Hydrodynamics of pair-annihilating disclination lines in nematic liquid crystals.

The pair annihilation of straight line defects with strength +/-1/2 in bulk nematic systems is studied numerically, considering a full coupling of orientational degrees of freedom and hydrodynamics. This work is based on the generalization of the Ericksen-Leslie theory to the tensor order parameter as proposed by Qian and Sheng [T. Qian and P. Sheng, Phys. Rev. E 58, 7475 (1998)]. The approach is particularly suited for the late stages of the annihilation process. It is confirmed that the +1/2 disclination line moves considerably faster than the -1/2 one (e.g., twice as fast) due to the hydrodynamic flow. Symmetries of the important stress tensor terms upon inverting the sign of the winding number and performing a homogeneous in-plane rotation of the Q-tensor eigensystem are discussed. The stress tensor terms that dominantly contribute to the advective flow and to the flow asymmetry are identified.

Buckling, fluctuations, and collapse in semiflexible polyelectrolytes.

We present a systematic statistical mechanical analysis of the conformational properties of a stiff polyelectrolyte chain with intrachain attractions that are due to counterion correlations. We show that the mean-field solution corresponds to an Euler-like buckling instability. The effect of the conformational fluctuations on the buckling instability is investigated, first, qualitatively, within the harmonic ("semiclassical") theory, then, systematically, within a 1/d expansion, where d denotes the dimension of embedding space. Within the "semiclassical" approximation, we predict that the effect of fluctuations is to renormalize the effective persistence length to smaller values, but not to change the nature of the mean-field (i.e., buckling) behavior. Based on the 1/d expansion we are, however, led to conclude that thermal fluctuations are responsible for a change of the buckling behavior which is turned into a polymer collapse. A phase diagram is constructed in which a sequence of collapse transitions terminates at a buckling instability that occurs at a place that varies with the magnitude of the bare persistence length of the polymer chain, as well as with the strength and range of the attractive potential.