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Active fluids display spontaneous turbulent-like flows known as active turbulence. Recent work revealed that these flows have universal features, independent of the material properties and of the presence of topological defects. However, the differences between defect-laden and defect-free active turbulence remain largely unexplored. Here, by means of large-scale numerical simulations, we show that defect-free active nematic turbulence can undergo dynamical arrest. We find that flow alignment -- the tendency of nematics to reorient under shear -- enhances large-scale jets in contractile rodlike systems while promoting arrested flow patterns in extensile systems. Our results reveal a mechanism of labyrinthine pattern formation produced by an emergent topology of nematic domain walls that partially suppresses chaotic flows. Taken together, our findings call for the experimental realization of defect-free active nematics, and suggest that topological defects enable turbulence by preventing dynamical arrest.

Active nematics exhibit spontaneous flows through a well-known linear instability of the uniformly-aligned quiescent state. Here we show that even a linearly stable uniform state can experience a nonlinear instability, resulting in a discontinuous transition to spontaneous flows. In this case, quiescent and flowing states may coexist. Through a weakly nonlinear analysis and a numerical study, we trace the bifurcation diagram of striped patterns and show that the underlying pitchfork bifurcation switches from supercritical (continuous) to subcritical (discontinuous) by varying the flow-alignment parameter. We predict that the discontinuous spontaneous flow transition occurs for a wide range of parameters, including systems of contractile flow-aligning rods. Our predictions are relevant to active nematic turbulence and can potentially be tested in experiments on either cell layers or active cytoskeletal suspensions.

Many active systems display nematic order, while interacting with their environment. In this work, we show theoretically how environment-stored memory acts an effective external field that aligns active nematics. The coupling to the environment leads to substantial modifications of the known phase diagram and dynamics of active nematics, including nematic order at arbitrarily low densities and arrested domain coarsening. We are motivated mainly by cells that remodel fibers in their extra-cellular matrix (ECM), while being directed by the fibers during migration. Our predictions indicate that remodeling promotes cellular and ECM alignment, and possibly limits the range of ordered ECM domains, in accordance with recent experiments., Comment: 5 pages main text + 9 pages supplemental material, 3 figures

We formulate an active-gel theory for multicellular migration in the extra-cellular matrix (ECM). The cells are modeled as an active, polar solvent, and the ECM as a viscoelastic solid. Our theory enables to analyze the dynamic reciprocity between the migrating cells and their environment in terms of distinct relative forces and alignment mechanisms. We analyze the linear stability of polar cells migrating homogeneously in the ECM. Our theory predicts that, as a consequence of cell-matrix alignment, contractile cells migrate homogeneously for small wave vectors, while sufficiently extensile cells migrate in domains. Homogeneous cell migration of both extensile and contractile cells may be unstable for larger wave vectors, due to active forces and the alignment of cells with their concentration gradient. These mechanisms are stabilized by cellular alignment to the migration flow and matrix stiffness. They are expected to be suppressed entirely for rigid matrices with elastic moduli of order 10 kPa. Our theory should be useful in analyzing multicellular migration and ECM patterning at the mesoscopic scale.

Topological defects are at the root of the large-scale organization of liquid crystals. In two-dimensional active nematics, two classes of topological defects of charges $\pm 1/2$ are known to play a major role due to active stresses. Despite this importance, few analytical results have been obtained on the flow-field and active-stress patterns around active topological defects. Using the generic hydrodynamic theory of active systems, we investigate the flow and stress patterns around these topological defects in unbounded, two-dimensional active nematics. Under generic assumptions, we derive analytically the spontaneous velocity and stall force of self-advected defects in the presence of both shear and rotational viscosities. Applying our formalism to the dynamics of monolayers of elongated cells at confluence, we show that the non-conservation of cell number generically increases the self-advection velocity and could provide an explanation for their observed role in cellular extrusion and multilayering. We finally investigate numerically the influence of the Ericksen stress. Our work paves the way to a generic study of the role of topological defects in active nematics, and in particular in monolayers of elongated cells., Comment: 15 pages, 4 figures

The mechanical properties of tissues play an essential role for all tissue properties such as cell division, and differentiation or morphogenesis. Here, we study theoretically the rheology of 2-dimensional epithelial tissues described by a discrete vertex-like model, using an analytical coarsegrained continuum formulation. We show that epithelial tissues are most often shear-thinning under constant shear rate, and in certain circumstances cross over from shear thickening at low shear rates to shear thinning at high shear rates. We give an analytical expression of the tissue response in an oscillating strain experiment in the linear regime, and calculate it numerically in the non-linear regime. When the tissue is supported by an oscillating substrate, it reorients depending on frequency and substrate's Poisson's ratio. Reorientation could be gradual or abrupt, depending on tissue and substrate parameters, and the configuration phase space exhibits a tricritical point.

We derive a course grained, continuum model of the 2D vertex model, applicable for different underlying geometries, and allowing for analytical analysis of an otherwise numerical model. Using a geometric approach and out--of--equilibrium statistical mechanics, we calculate both mechanical and dynamical instabilities within a tissue, and their dependence on different variables, including activity, and disorder. Most notably, the tissue's response depends on the existence of mechanical residual stresses in the tissue. Thus, even freely growing tissues may exhibit a growth instability depending on food consumption. Using this geometric model we can readily distinct between elasticity and plasticity in a growing, flowing, tissue.

Despite the absence of a membrane-enclosed nucleus, the bacterial DNA is typically condensed into a compact body - the nucleoid. This compaction influences the localization and dynamics of many cellular processes including transcription, translation, and cell division. Here, we develop a model that takes into account steric interactions among the components of the Escherichia coli transcriptional-translational machinery (TTM) and out-of-equilibrium effects of mRNA transcription, translation, and degradation, in order to explain many observed features of the nucleoid. We show that steric effects, due to the different molecular shapes of the TTM components, are sufficient to drive equilibrium phase separation of the DNA, explaining the formation and size of the nucleoid. In addition, we show that the observed positioning of the nucleoid at midcell is due to the out-of-equilibrium process of messenger RNA (mRNA) synthesis and degradation: mRNAs apply a pressure on both sides of the nucleoid, localizing it to midcell. We demonstrate that, as the cell grows, the production of these mRNAs is responsible for the nucleoid splitting into two lobes, and for their well-known positioning to 1/4 and 3/4 positions on the long cell axis. Finally, our model quantitatively accounts for the observed expansion of the nucleoid when the pool of cytoplasmic mRNAs is depleted. Overall, our study suggests that steric interactions and out-of-equilibrium effects of the TTM are key drivers of the internal spatial organization of bacterial cells., Comment: 21 pages, 11 figures

We present a theory of active, permeating, polar gels, based on a two-fluid model. An active relative force between the gel components creates a steady-state current. We analyze its stability, while considering two polar coupling terms to the relative current: a permeation-deformation term, which describes network deformation by the solvent flow, and a permeation-alignment term, which describes the alignment of the polarization field by the network deformation and flow. Novel instability mechanisms emerge at finite wave vectors, suggesting the formation of periodic domains and mesophases. Our results can be used to determine the physical conditions required for various types of multicellular migration across tissues., Comment: 16 pages, 2 figures (Supplemental Material included)

Active fluids exhibit spontaneous flows with complex spatiotemporal structure, which have been observed in bacterial suspensions, sperm cells, cytoskeletal suspensions, self-propelled colloids, and cell tissues. Despite occurring in the absence of inertia, chaotic active flows are reminiscent of inertial turbulence, and hence they are known as active turbulence. Here, we survey the field, providing a unified perspective over different classes of active turbulence. To this end, we divide our review in sections for systems with either polar or nematic order, and with or without momentum conservation (wet/dry). Comparing to inertial turbulence, we highlight the emergence of power-law scaling with either universal or non-universal exponents. We also contrast scenarios for the transition from steady to chaotic flows, and we discuss the absence of energy cascades. We link this feature to both the existence of intrinsic length scales and the self-organized nature of energy injection in active turbulence, which are fundamental differences with inertial turbulence. We close by outlining the emerging picture, remaining challenges, and future directions., Comment: Review for Annu. Rev. Condens. Matter Phys

Evidence suggests that the transport rate of a passive particle at long timescales is enhanced due to interactions with the surrounding active ones in a size- and composition-dependent manner. Using a system of particles with different temperatures, we probe these effects in dilute solutions and derive long-time friction and self-diffusion coefficients as functions of volume fractions, sizes and temperatures of particles in $d=2$ and 3 dimensions. Thus, we model excluded-volume interactions for nonequilibrium systems but also extend the scope to short-range soft potentials and compare our results to Brownian-dynamics simulations. Remarkably, we show that both viscosity and energy flux display a nonlinear dependence on size. The simplicity of our formalism allows to discover various interesting scenarios that can be relevant for biological systems and active colloids., Comment: Published version, main text and supplemental material

Active fluids exhibit complex turbulent-like flows at low Reynolds number. Recent work predicted that 2d active nematic turbulence follows universal scaling laws. However, experimentally testing these predictions is conditioned by the coupling to the 3d environment. Here, we measure the spectrum of the kinetic energy, $E(q)$, in an active nematic film in contact with a passive oil layer. At small and intermediate scales, we find the scaling regimes $E(q)\sim q^{-4}$ and $E(q)\sim q^{-1}$, respectively, in agreement with the theoretical prediction for 2d active nematics. At large scales, however, we find a new scaling $E(q)\sim q$, which emerges when the dissipation is dominated by the 3d oil layer. In addition, we derive an explicit expression for the spectrum that spans all length scales, thus explaining and connecting the different scaling regimes. This allows us to fit the data and extract the length scale that controls the crossover to the new large-scale regime, which we tune by varying the oil viscosity. Overall, our work experimentally demonstrates the emergence of universal scaling laws in active turbulence, and it establishes how the spectrum is affected by external dissipation.

The internal and external mechanical environment plays an important role in tumorogenesis. As a proxy of an avascular early state tumor, we use multicellular spheroids, a composite material made of cells, extracellular matrix and permeating fluid. We characterize its effective rheology at the timescale of minutes to hours by compressing the aggregates with osmotic shocks and modeling the experimental results with an active poroelastic material that reproduces the stress and strain distributions in the aggregate. The model also predicts how the emergent bulk modulus of the aggregate as well as the hydraulic diffusion of the percolating interstitial fluid are modified by the preexisting active stress within the aggregate. We further show that the value of these two phenomenological parameters can be rationalized by considering that, in our experimental context, the cells are effectively impermeable and incompressible inclusions nested in a compressible and permeable matrix.

The vertex model is widely used to describe the dynamics of epithelial tissues, because of its simplicity and versatility and the direct inclusion of biophysical parameters. Here, it is shown that quite generally, when cells modify their equilibrium perimeter due to their activity, or the tissue is subject to external stresses, the tissue becomes unstable with deformations that couple pure-shear or deviatoric modes, with rotation and expansion modes. For short times, these instabilities deform cells increasing their ellipticity while, at longer times, cells become non-convex, indicating that the vertex model ceases to be a valid description for tissues under these conditions. The agreement between the analytic calculations performed for a regular hexagonal tissue and the simulations of disordered tissues is excellent due to the homogenization of the tissue at long wavelengths.

We consider a cops and robber game where the cops are blocking edges of a graph, while the robber occupies its vertices. At each round of the game, the cops choose some set of edges to block and right after the robber is obliged to move to another vertex traversing at most $s$ unblocked edges ($s$ can be seen as the speed of the robber). Both parts have complete knowledge of the opponent's moves and the cops win when they occupy all edges incident to the robbers position. We introduce the capture cost on $G$ against a robber of speed $s$. This defines a hierarchy of invariants, namely $\delta^{1}_{\rm e},\delta^{2}_{\rm e},\ldots,\delta^{\infty}_{\rm e}$, where $\delta^{\infty}_{\rm e}$ is an edge-analogue of the admissibility graph invariant, namely the {\em edge-admissibility} of a graph. We prove that the problem asking wether $\delta^{s}_{\rm e}(G)\leq k$, is polynomially solvable when $s\in \{1,2,\infty\}$ while, otherwise, it is NP-complete. Our main result is a structural theorem for graphs of bounded edge-admissibility. We prove that every graph of edge-admissibility at most $k$ can be constructed using $(\leq k)$-edge-sums, starting from graphs whose all vertices, except possibly from one, have degree at most $k$. Our structural result is approximately tight in the sense that graphs generated by this construction always have edge-admissibility at most $2k-1$. Our proofs are based on a precise structural characterization of the graphs that do not contain $\theta_{r}$ as an immersion, where $\theta_{r}$ is the graph on two vertices and $r$ parallel edges., Comment: The paper has appeared as "Stratis Limnios, Christophe Paul, Joanny Perret, Dimitrios M. Thilikos: Edge degeneracy: Algorithmic and structural results. Theor. Comput. Sci. 839: 164-175 (2020)". This is a new version where a typo has been corrected. In particular, "$1,2,3$" is now "$1,2$" and "$\Bbb{N}_{\geq 4}$" is now "$\Bbb{N}_{\geq 3}$"

Differences in activities in colloidal particles are sufficient to drive phase separation between active and passive (or less active) particles, even if they have only excluded volume interactions. In this paper, we study the phase separation kinetics and propose a theory of phase separation of colloidal mixtures in the diffusive limit. Our model considers a mixture of diffusing particles coupled to different thermostats, it thus has a non-equilibrium nature due to the temperature differences. However, we show that indeed the system recovers an effective equilibrium thermodynamics in the dilute limit. We obtain phase diagrams showing the asymmetry in concentrations due to activity differences. By using a more general approach, we show the equivalence of phase separation kinetics with the well known Cahn-Hilliard theory. On the other hand, higher order expansions in concentration indicate the emergence of non-equilibrium effects leading to a breakdown of the equilibrium analogy. We lay out the general theory in terms of accessible parameters which we demonstrate by several applications. In this simple formalism, we capture a positive surface tension for hard spheres}, and interesting scaling laws for interfacial properties, droplet growth dynamics, and phase segregation conditions. \rev{Several of our results are in agreement with existing numerical simulations while we also propose testable predictions., Comment: Published version, 19 pages (main text+appendix), 4 figures

A landmark of turbulence is the emergence of universal scaling laws, such as Kolmogorov's $E(q)\sim q^{-5/3}$ scaling of the kinetic energy spectrum of inertial turbulence with the wave vector $q$. In recent years, active fluids have been shown to exhibit turbulent-like flows at low Reynolds number. However, the existence of universal scaling properties in these flows has remained unclear. To address this issue, here we propose a minimal defect-free hydrodynamic theory for two-dimensional active nematic fluids at vanishing Reynolds number. By means of large-scale simulations and analytical arguments, we show that the kinetic energy spectrum exhibits a universal scaling $E(q)\sim q^{-1}$ at long wavelengths. We find that the energy injection due to activity has a peak at a characteristic length scale, which is selected by a nonlinear mechanism. In contrast to inertial turbulence, energy is entirely dissipated at the scale where it is injected, thus precluding energy cascades. Nevertheless, the non-local character of the Stokes flow establishes long-ranged velocity correlations, which lead to the scaling behavior. We conclude that active nematic fluids define a distinct universality class of turbulence at low Reynolds number., Comment: Updated journal version

We calculate the Casimir stresses in a thin layer of active fluid with nematic order. By using a stochastic hydrodynamic approach for an active fluid layer of finite thickness $L$, we generalize the Casimir stress for nematic liquid crystals in thermal equilibrium to active systems. We show that the active Casimir stress differs significantly from its equilibrium counterpart. For contractile activity, the active Casimir stress, although attractive like its equilibrium counterpart, diverges logarithmically as $L$ approaches a threshold of the spontaneous flow instability from below. In contrast, for small extensile activity, it is repulsive, has no divergence at any $L$ and has a scaling with $L$ different from its equilibrium counterpart.

We analyze the collective behavior of hydrodynamically coupled molecular motors. We show that the local fluxes induced by motors displacement can induce the experimentally observed bidirectional motion of cargoes and vesicles. By means of a mean--field approach we show that sustained oscillations as well as bistable collective motor motion arise even for very large collection of motors, when thermal noise is irrelevant. The analysis clarifies the physical mechanisms responsible for such dynamics by identifying the relevant coupling parameter and its dependence on the geometry of the hydrodynamic coupling as well as on system size. We quantify the phase diagram for the different phases that characterize the collective motion of hydrodynamically coupled motors and show that sustained oscillations can be reached for biologically relevant parameters, hence demonstrating the relevance of hydrodynamic interactions in intracellular transport.

Microscopic swimming particles, which dissipate energy to execute persistent directed motion, are a classic example of a non-equilibrium system. We investigate the non-interacting Ornstein--Uhlenbeck Particle (OUP), which is propelled through a viscous medium by a force which is correlated over a finite time. We obtain an exact expression for the steady state phase-space density of a single OUP confined by a quadratic potential, and use the result to explore more complex geometries, both through analytical approximations and numerical simulations. In a "Casimir"-style setup involving two narrowly-spaced walls, we describe a particle-trapping phenomenon, which leads to a repulsive effective interaction between the walls; while in a two-dimensional annulus geometry, we observe net stresses which resemble the Laplace pressure., Comment: Main text six pages, four figures

In many adult tissues, stem cells and differentiated cells are not homogeneously distributed : stem cells are arranged in periodic "niches", and differentiated cells are constantly produced and migrate out of these niches. In this article, we provide a general theoretical framework to study mixtures of dividing and actively migrating particles, which we apply to biological tissues. We show in particular that the interplay between the stresses arising from active cell migration and stem cell division give rise to robust stem cell patterns. The instability of the tissue leads to spatial patterns which are either steady or oscillating in time. The wavelength of the instability has an order of magnitude consistent with the biological observations. We also discuss the implications of these results for future in vitro and in vivo experiments.

Contact inhibition is the process by which cells switch from a motile growing state to a passive and stabilized state upon touching their neighbors. When two cells touch, an adhesion link is created between them by means of transmembrane E-cadherin proteins. Simultaneously, their actin filaments stop polymerizing in the direction perpendicular to the membrane and reorganize to create an apical belt that colocalizes with the adhesion links. Here, we propose a detailed quantitative model of the role of the cytoplasmic $\beta$-catenin and $\alpha$-catenin proteins in this process, treated as a reaction-diffusion system. Upon cell-cell contact, the concentration in $\alpha$-catenin dimers increases, inhibiting actin branching and thereby reducing cellular motility and expansion pressure. This model provides a mechanism for contact inhibition that could explain previously unrelated experimental findings on the role played by E-cadherin, $\beta$-catenin and $\alpha$-catenin in the cellular phenotype and in tumorigenesis. In particular, we address the effect of a knockout of the adenomatous polyposis coli tumor suppressor gene. Potential direct tests of our model are discussed.

We consider a mixture of passive (i.e., Brownian) and active (e.g., bacterial or colloidal swimmers) particles, and analyze the stability conditions of either uniformly mixed or phase segregated steady states consisting of phases enriched with different types of particles. We show that in sufficiently dilute mixtures the system behaves as if it were exposed to two separate heat baths of uneven temperatures. It can be described within a second virial approximation neglecting three body and higher order collisions. In this approximation, we define non-equilibrium "chemical potentials" whose gradients govern diffusion fluxes and a non-equilibrium "osmotic pressure", which governs the mechanical stability of the interface., Comment: 5 pages with 2 figures, plus 6 pages and 4 figures of supplementary material

The hair bundle of sensory cells in the vertebrate ear provides an example of a noisy oscillator close to a Hopf bifurcation. The analysis of the data from both spontaneous and forced oscillations shows a strong violation of the fluctuation-dissipation theorem, revealing the presence of an underlying active process that keeps the system out of equilibrium. Nevertheless, we show that a generalized fluctuation-dissipation theorem, valid for non-equilibrium steady states, is fulfilled within the limits of our experimental accuracy and computational approximations, when the adequate conjugate degrees of freedom are chosen., Comment: 5 pages, 3 figures

In order to extend the investigation of laser-assisted cleaning of ITER-relevant first mirror materials to the picosecond regime, a commercial laser system delivering 10 picosecond pulses at 355 nm at a frequency of up to 1 MHz has been used to investigate the ablation of mixed aluminium (oxide) / tungsten (oxide) layers deposited on poly- and nanocrystalline molybdenum as well as nanocrystalline rhodium mirrors. Characterization before and after cleaning using scanning electron microscopy (SEM) and spectrophotometry shows heavy dust formation, resulting in a degradation of the reflectivity. Cleaning using a 5 nanosecond pulses at 350 and 532 nm, on the other hand, proved very promising. The structure of the film remnants suggests that in this case buckling was the underlying removal mechanism rather than ablation. Repeated coating and cleaning using nanosecond pulses is demonstrated., Comment: Accepted in Fusion Science and Technology. Fusion Science and Technology 2014

We study a model of cell motility where the condition of optimal trade-off between performance and metabolic cost can be made precise. In this model a steadily crawling fragment is represented by a layer of active gel placed on a frictional surface and driven by contraction only. We find analytically the distribution of contractile elements (pullers) ensuring that the efficiency of self-propulsion is maximal. We then show that natural assumptions about advection and diffusion of pullers produce a distribution that is remarkably close to the optimal one and is qualitatively similar to the one observed in experiments on fish keratocytes.

Using active gel theory we study theoretically the properties of the cortical actin layer of animal cells. The cortical layer is described as a non-equilibrium wetting film on the cell membrane. The actin density is approximately constant in the layer and jumps to zero at its edge. The layer thickness is determined by the ratio of the polymerization velocity and the depolymerization rate of actin., Comment: submitted to Eur Phys Jour E