Analogies between growing dense active matter and soft driven glasses

We develop a minimal model to describe growing dense active matter such as biological tissues, bacterial colonies, and biofilms, which are driven by a competition between particle division and steric repulsion. We provide a detailed numerical analysis of collective and single-particle dynamics. We show that the microscopic dynamics can be understood as the superposition of an affine radial component due to the global growth, and of a more complex nonaffine component that displays features typical of driven soft glassy materials, such as aging, compressed exponential decay of time correlation functions, and a crossover from superdiffusive behavior at short scales to subdiffusive behavior at larger scales. This analogy emerges because particle division at the microscale leads to a global expansion, which then plays a role analogous to shear flow in soft driven glasses. We conclude that growing dense active matter and sheared dense suspensions can generically be described by the same underlying physics

Phenomenology and simulations of active fluids

Active fluids are an interesting new class of non-equilibrium systems in physics. In such fluids, the system is forced out of equilibrium by the individual active particles - in contrast to driven systems where the system is forced out of equilibrium by some external forces. Some biological examples of active fluids are bacterial suspensions and actomyosin solutions inside eukaryotic cells. In the case of bacterial suspensions, the fluid is stirred internally by the swimming bacteria and as a consequence of this, active fluids can have some interesting physics of their own such as hydrodynamic instabilities and spontaneous symmetry breaking. Here, in particular, we study how such instabilities may arise and how they may lead to a non-equilibrium steady state. We also study numerically a droplet of active matter as a simple representation of cell extract comprising actomyosin solution bounded by a cell membrane. It is widely believed that cell motility is driven only by actin polymerization pushing against the cell membrane. However, we show that even in the absence of actin polymerization, actin-myosin contraction alone can also generate a unidirectional motion. This happens due to the spontaneous breakdown of a discrete symmetry at large enough activity (i.e. actomyosin contraction). This non-equilibrium phase transition from stationary to motile state is somewhat similar to the second order phase transition in equilibrium thermodynamics. Finally, we studied the behaviour of an active droplet on a two-dimensional surface to mimic cell crawling. Whereas cell migration in 3D environment maybe driven mainly by actin-myosin contraction (described above), cell crawling on a 2D surface is driven mainly by actin polymerisation. Here we find that localised actin polymerisation can cause protrusion in the cell membrane which is qualitatively similar to lamellipodium formation in cell crawling

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing, for simplicity, on models with a purely diffusive scalar field, such as ‘Model B’ which describes phase separation in binary fluid mixtures. We address the requirement that the steady-state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in a thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for ‘active field theories’ in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR), we must make a careful treatment of so-called ‘spurious drift’ and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative via off-diagonal couplings to additional fields that thermodynamically encode the underlying chemical processes responsible for activity. In this case, the spurious drift terms need careful accounting, not just to evaluate correctly the EPR but also to numerically implement the Langevin dynamics itself

Hydrodynamics of a disk in a thin film of weakly nematic fluid subject to linear friction

To make progress towards the development of a theory on the motion of inclusions in thin structured films and membranes, we here consider as an initial step a circular disk in a two-dimensional, uniaxially anisotropic fluid layer. We assume overdamped dynamics, incompressibility of the fluid, and global alignment of the axis of anisotropy. Motion within this layer is affected by additional linear friction with the environment, for instance, a supporting substrate. We investigate the induced flows in the fluid when the disk is translated parallel or perpendicular to the direction of anisotropy. Moreover, expressions for corresponding mobilities and resistance coefficients of the disk are derived. Our results are obtained within the framework of a perturbative expansion in the parameters that quantify the anisotropy of the fluid. Good agreement is found for moderate anisotropy when compared to associated results from finite-element simulations. At pronounced anisotropy, the induced flow fields are still predicted qualitatively correctly by the perturbative theory, although quantitative deviations arise. We hope to stimulate with our investigations corresponding experimental analyses, for example, concerning fluid flows in anisotropic thin films on uniaxially rubbed supporting substrates

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production.

Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing, for simplicity, on models with a purely diffusive scalar field, such as 'Model B' which describes phase separation in binary fluid mixtures. We address the requirement that the steady-state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in a thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for 'active field theories' in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR), we must make a careful treatment of so-called 'spurious drift' and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative via off-diagonal couplings to additional fields that thermodynamically encode the underlying chemical processes responsible for activity. In this case, the spurious drift terms need careful accounting, not just to evaluate correctly the EPR but also to numerically implement the Langevin dynamics itself

Bayes' Theorem and positive confirmation An experimental economic analysis

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Criticality and correlated dynamics at the irreversibility transition in periodically driven colloidal suspensions

27 pages, 12 figures; J. Stat. Mech. (in press)International audienceOne possible framework to interpret the irreversibility transition observed in periodically driven colloidal suspensions is that of a non-equilibrium phase transition towards an absorbing reversible state at low amplitude of the driving force. We consider a simple numerical model for driven suspensions which allows us to characterize in great detail a large body of physical observables that can be experimentally determined to assess the existence and universality class of such a non-equilibrium phase transition. Characterizing the behaviour of static and dynamic correlation functions both in real and Fourier space we determine in particular several critical exponents for our model, which take values that are in good agreement with the universality class of direct ed percolation. We also provide a detailed analysis of single-particle and collective dynamics of the system near the phase transition, which appear intermittent and spatially correlated over diverging timescales and lengthscales, and provide clear signatures of the underlying criticality