Fluid membranes endowed with tangent-plane order (TPO) such as tilt- and hexatic order afford unique soft matter systems for investigating the interplay between elasticity, shape, topology, and thermal fluctuations. Using the spin-connection formulat
ion of membrane energy we obtain equa- tions of equilibrium together with free boundary conditions for ground states of such membranes. We extend the spin-connection formulation to smectic liquid crystals with TPO and show that for chiral smectics-C* this generalization leads to experimentally verifiable consequences for dispirations having topological indices (helicities) of the same magnitude but opposite signs.
Nonlinearities in constitutive equations of extended objects in shear flow lead to novel phenomena, {it e.g.} rheochaos in solutions of wormlike micelles and elastic turbulence in polymer solutions. Since both phenomena involve anisotropic objects, t
heir contributions to the deviatoric stress are likely to be similar. However, these two fields have evolved rather independently and an attempt at connecting these fields is still lacking. We show that a minimal model in which the anisotropic nature of the constituting objects is taken into account by a nematic alignment tensor field reproduces several statistical features found in rheochaos and elastic turbulence. We numerically analyse the full non-linear hydrodynamic equations of a sheared nematic fluid under shear stress and strain rate controlled situations, incorporating spatial heterogeneity only in the gradient direction. For a certain range of imposed stress and strain rates, this extended dynamical system shows signatures of textit{spatiotemporal chaos} and textit{transient shear banding}. In the chaotic regime the power spectra of the order parameter stress, velocity fluctuations and the total injected power show power law behavior and the total injected power shows a non-gaussian, skewed probability distribution. These dynamical features bear resemblance to textit{elastic turbulence} phenomena observed in polymer solutions. The scaling behavior is independent of the choice of shear rate/stress controlled method.
We study the mechanical response of an open cell dry foam subjected to periodic forcing using experiments and theory. Using the measurements of the static and dynamic stress-strain relationship, we derive an over-damped model of the foam, as a set of
infinitesimal non-linear springs, where the damping term depends on the local foam strain. We then analyse the properties of the foam when subjected to large amplitudes periodic stresses and determine the conditions for which the foam becomes optimally absorbing.
Chemotaxis is typically modeled in the context of cellular motion towards a static, exogenous source of chemoattractant. Here, we propose a time-dependent mechanism of chemotaxis in which a self-propelled particle ({it e.g.}, a cell) releases a chemi
cal that diffuses to fixed particles (targets) and signals the production of a second chemical by these targets. The particle then moves up concentration gradients of this second chemical, analogous to diffusive echolocation. When one target is present, we describe probe release strategies that optimize travel of the cell to the target. In the presence of multiple targets, the one selected by the cell depends on the strength and, interestingly, on the frequency of probe chemical release. Although involving an additional chemical signaling step, our chemical ``pinging hypothesis allows for greater flexibility in regulating target selection, as seen in a number of physical or biological realizations.
