We derive the conservation law for nematic polymers in tensorial form valid for quadrupolar orientational order, in contradistinction to the conservation law in the case of polar orientational order. Due to microscopic differences in the coupling between the orientational field deformations and the density variations for polar and quadrupolar order, we find that the respective order parameters satisfy fundamentally distinct constraints. Being necessarily scalar in its form, the tensorial conservation law is obtained straightforwardly from the gradients of the polymer nematic tensor field and connects the spatial variation of this tensor field with density variations. We analyze the differences between the polar and the tensorial forms of the conservation law, present some explicit orientational fields that satisfy the tensorial constraint, and discuss the role of singular hairpins, which do not affect the local quadrupolar order of polymer nematics, but nevertheless influence its gradients.
We set up a macroscopic model of bacterial growth and transport based on a dynamic preferred direction - the collective velocity of the bacteria. This collective velocity is subject to the isotropic-nematic transition modeling the density-controlled transformation between immotile and motile bacterial states. The choice of the dynamic preferred direction introduces a distinctive coupling of orientational ordering and transport not encountered otherwise. The approach can also be applied to other systems spontaneously switching between individual (disordered) and collective (ordered) behavior and/or collectively responding to density variations, e.g., bird flocks, fish schools, etc. We observe a characteristic and robust stop-and-go behavior. The inclusion of chirality results in a complex pulsating dynamics.
Electrostatic properties and stability of charged virus-like nano-shells are examined in ionic solutions with monovalent and multivalent ions. A theoretical model based on a thin charged spherical shell and multivalent ions within the dressed multivalent ion approximation, yielding their distribution across the shell and the corresponding electrostatic (osmotic) pressure acting on the shell, is compared with extensive implicit Monte-Carlo simulations. It is found to be accurate for positive or low negative surface charge densities of the shell and for sufficiently high (low) monovalent (multivalent) salt concentrations. Phase diagrams involving electrostatic pressure exhibit positive and negative values, corresponding to an outward and an inward facing force on the shell, respectively. This provides an explanation for the high sensitivity of viral shell stability and self-assembly of viral capsid shells on the ionic environment.