Nematodynamics with odd and rotational viscosities.

We explore a novel mechanism of interactions between nematic order and flow including odd and rotational viscosities, and investigate activity-induced instabilities in the framework of this model. We show how these modes of viscous dissipation can be incorporated in the Ericksen-Leslie formalism, but it does not eliminate deficiencies of the approach based on Onsager's reciprocal relations that lead to spurious instabilities. The suggested way of deriving nematodynamic equations, based on a specific mechanism applicable to rigid rods, is not universal, but it avoids referring to Onsager's relations and avoids spurious instabilities in the absence of an active inputs. The model is further applied to the analysis of instabilities in active media.

Erratum: Vector formalism for active nematic liquid crystals in two dimensions [Phys. Rev. E 106, 034701 (2022)].

This corrects the article DOI: 10.1103/PhysRevE.106.034701.

Vector formalism for active nematic liquid crystals in two dimensions.

Specific features of two-dimensional nematodynamics give rise to shortfalls of the tensor representation of the nematic order parameter commonly used in computations, especially in theory of active matter. The alternative representation in terms of the vector order parameter follows with small adjustments the classical director-based theory, but is applicable to 2D problems where both nematic alignment and deviation from the isotropic state are variable. Stability analysis of nematic alignment and flow is used as a testing ground. A director-based analysis demonstrates a shortfall of the standard theory, which does not ensure relaxation to equilibrium in a passive system. It also demonstrates the inadequacy of the director-based description, which misses a stabilizing effect of perturbations of the modulus ensuring stability of a passive system on scales far exceeding the healing length.

Reshaping of a Janus ring.

We consider the reshaping of closed Janus filaments acquiring intrinsic curvature upon actuation of a driven component-a nematic elastomer elongating upon phase transition. Linear stability analysis establishes instability thresholds of circles with no imposed twist, dependent on the ratio q of the intrinsic curvature to the inverse radius of the original circle. Twisted circles are proven to be absolutely unstable but the linear analysis well predicts the dependence of the looping number of the emerging configurations on the imposed twist. Modeling stable configurations by relaxing numerically the overall elastic energy detects multiple stable and metastable states with different looping numbers. The bifurcation of untwisted circles turns out to be subcritical, so that nonplanar shapes with a lower energy exist at q below the critical value. The looping number of stable shapes generally increases with q.

Active textiles with Janus fibres.

We describe reshaping of active textiles actuated by bending of Janus fibres comprising both active and passive components. A great variety of shapes, determined by minimising the overall energy of the fabric, can be produced by varying bending directions determined by the orientation of Janus fibres. Under certain conditions, alternative equilibrium states, one absolutely stable and the other metastable coexist, and their relative energy may flip its sign as system parameters, such as the extension upon actuation, change. A snap-through reshaping in a specially structured textile reproduces the Venus flytrap effect.

Textures and shapes in nematic elastomers under the action of dopant concentration gradients.

We explore a novel strategy of patterning nematic elastomers that does not require inscribing the texture directly. It is based on varying the dopant concentration that, beside shifting the phase transition point, affects the nematic director field via coupling between the gradients of concentration and nematic order parameter. Rotation of the director around a point dopant source causes topological modification manifesting itself in a change of the number of defects. A variety of shapes, dependent on the dopant distribution, are obtained by anisotropic deformation following the nematic-isotropic transition.

Phase separation and folding in swelled nematoelastic films.

We explore reshaping of nematoelastic films upon imbibing an isotropic solvent under conditions when isotropic and nematic phases coexist. The structure of the interphase boundary is computed taking into account the optimal nematic orientation governed by interaction of gradients of the nematic order parameter and solvent concentration. This structure determines the effective line tension of the boundary. We further compute equilibrium shapes of deformed thin sheets and cylindrical and spherical shells with the rectilinear or circular shape of the boundary between nematic and isotropic domains. A differential expansion or contraction near this boundary generates a folding pattern spreading out into the bulk of both phases. The hierarchical ordering of this pattern is most pronounced on a cylindrical shell.

Flexible helical yarn swimmers.

We investigate the motion of a flexible Stokesian flagellar swimmer realised as a yarn made of two intertwined elastomer fibres, one active, that can reversibly change its length in response to a local excitation causing transition to the nematic state or swelling, and the other one, a passive isotropic elastomer with identical mechanical properties. A propagating chemical wave may provide an excitation mechanism ensuring a constant length of the excited region. Generally, the swimmer moves along a helical trajectory, and the propagation and rotation velocity are very sensitive to the ratio of the excited region to the pitch of the yarn, as well as to the size of a carried load. External excitation by a moving actuating beam is less effective, unless the direction of the beam is adjusted to rotation of the swimmer.

Nematoelastic crawlers.

A propagating "beam" triggering a local phase transition in a nematic elastomer sets it into a crawling motion, which may morph due to buckling. We consider the motion of the various configurations of slender rods and thin stripes with both uniform and splayed nematic order in cross-section and detect the dependence of the gait and speed on flexural rigidity and substrate friction.

Multiscale modeling of tumor growth induced by circadian rhythm disruption in epithelial tissue.

We propose a multiscale chemo-mechanical model of cancer tumor development in epithelial tissue. The model is based on the transformation of normal cells into a cancerous state triggered by a local failure of spatial synchronization of the circadian rhythm. The model includes mechanical interactions and a chemical signal exchange between neighboring cells, as well as a division of cells and intercalation that allows for modification of the respective parameters following transformation into the cancerous state. The numerical simulations reproduce different dephasing patterns--spiral waves and quasistationary clustering, with the latter being conducive to cancer formation. Modification of mechanical properties reproduces a distinct behavior of invasive and localized carcinoma.

Reshaping nemato-elastic sheets.

We consider three-dimensional reshaping of thin nemato-elastic sheets containing half-charged defects upon nematic-isotropic transition. Gaussian curvature, that can be evaluated analytically when the nematic texture is known, differs from zero in the entire domain and has a dipole or hexapole singularity, respectively, at defects of positive or negative sign. The latter kind of defects appears in not simply connected domains. Three-dimensional shapes dependent on boundary anchoring are obtained with the help of finite element computations.

Correction: Step-emulsification in a microfluidic device.

Correction for 'Step-emulsification in a microfluidic device' by Z. Li et al., Lab Chip, 2015, 15, 1023-1031.

Step-emulsification in a microfluidic device.

We present a comprehensive study of the step-emulsification process for high-throughput production of colloidal monodisperse droplets. The 'microfluidic step emulsifier' combines a shallow microchannel operating with two co-flowing immiscible fluids and an abrupt (step-like) opening to a deep and wide reservoir. Based on Hele-Shaw hydrodynamics, we determine the quasi-static shape of the fluid interface prior to transition to oscillatory step-emulsification at low capillary numbers. The theoretically derived transition threshold yields an excellent agreement with experimental data. A closed-form expression for the size of the droplets generated in the step-emulsification regime and derived using geometric arguments also shows a very good agreement with the experiment.

Metric theory of nematoelastic shells.

We consider three-dimensional reshaping of a thin nematoelastic film upon nematic-isotropic transition in the field of a charge one topological defect, leading to either cone or anticone (d-cone) shells. The analysis is based on the relation between the shell metric and the tensor order parameter under the assumption of no elastic deformation and volume change. The shape of the shell can be modified by doping, creating cones with curved generatrices. Anticones necessarily have an even number of radial creases. The curvature singularity at the apex is resolved due to decay of the nematic order parameter at the defect core.

Dynamics of defects in an active nematic layer.

Defect dynamics in a thin active nematic layer is studied by asymptotic matching of solutions in the defect core and the far field. The analysis is facilitated by the correspondence between the two-dimensional nematic and complex scalar field models. Self-propulsion and topological interactions are identified as the primary drivers of the defect motion, surpassing the influence of both passive backflow and active flow induced by other defects.

Phase separation and disorder in doped nematic elastomers.

We formulate and analyse a model describing the combined effect of mechanical deformation, dynamics of the nematic order parameter, and concentration inhomogeneities in an elastomeric mixture of a mesogenic and an isotropic component. The uniform nematic state may exhibit a long-wave instability corresponding to nematic-isotropic demixing. Numerical simulations starting from either a perfectly ordered nematic state or a quenched isotropic state show that coupling between the mesogen concentration and the nematic order parameter influences the shape and orientation of the domains formed during the demixing process.

Chemical and mechanical signaling in epithelial spreading.

We propose a minimal mathematical model to explain long-range coordination of dynamics of multiple cells in epithelial spreading, which may be induced, under different conditions, by a chemical signal, or mechanically induced strain, or both. The model is based on chemo-mechanical interactions including a chemical effect of strain, chemically induced polarization and active traction, and interaction between polarized cells. The results, showing kinase concentration distribution and cell displacement, velocity, and stress fields, allow us to reproduce qualitatively available experimental data and distinguish between distinct dynamical patterns observed under conditions of injury or unconstraining.

Genesis of two-dimensional patterns in cross-gradient fields.

Tissue morphogenesis is controlled by the two-dimensional patterning of gene expression in epithelial layers, that determines cell fates. The mechanisms of pattern formation involve intracellular regulatory networks controlled by paracrine and autocrine signaling. We develop a general logical scheme to deduce the morphology of two-dimensional patterns in the field of two crossed morphogen gradients enriched by the action of autocrine signaling that may subdivide expression domains in nontrivial ways. A variety of persistent patterns, either stationary or oscillatory, are generated using the various interaction schemes, some of which have been generated by a special algorithm including random inputs and selected according to suitable criteria. We give the full classification of a variety of stationary and oscillatory expression patterns in the presence of a single autocrine signal based on logical arguments. These results are further confirmed by numerical computations based on reaction-diffusion equations for morphogens and ligands and the discrete (cell-level) description of intracellular dynamics. Model simulations also elucidate transient processes, in particular interaction schemes. Different internal schemes may lead to identical persistent patterns, although relaxation may proceed in distinct ways. As an illustration of the general method, we test a particular scheme suggested by genetic studies of dynamic gene expression patterns in the follicular epithelium of the Drosophila eggshell.

Do small swimmers mix the ocean?

In this communication we address some hydrodynamic aspects of recently proposed drift mechanism of biogenic mixing in the ocean [K. Katija and J. O. Dabiri, Nature (London) 460, 624 (2009)10.1038/nature 08207]. The relevance of the locomotion gait at various spatial scales with respect to the drift is discussed. A hydrodynamic scenario of the drift based on unsteady inertial propulsion, typical for most small marine organisms, is proposed. We estimate its effectiveness by taking into account interaction of a swimmer with the turbulent marine environment. Simple scaling arguments are derived to estimate the comparative role of drift-powered mixing with respect to the turbulence. The analysis indicates substantial biomixing effected by relatively small but numerous drifters, such as krill or jellyfish.