Posts by Collection


Hysteresis, phase transitions, and dangerous transients in electrical power distribution systems

Published in Phys. Rev. E, 2013

The majority of dynamical studies in power systems focus on the high-voltage transmission grids where models consider large generators interacting with crude aggregations of individual small loads. However, new phenomena have been observed indicating that the spatial distribution of collective, nonlinear contribution of these small loads in the low-voltage distribution grid is crucial to the outcome of these dynamical transients. To elucidate the phenomenon, we study the dynamics of voltage and power flows in a spatially extended distribution feeder (circuit) connecting many asynchronous induction motors and discover that this relatively simple 1+1 (space+time) dimensional system exhibits a plethora of nontrivial spatiotemporal effects, some of which may be dangerous for power system stability. Long-range motor-motor interactions mediated by circuit voltage and electrical power flows result in coexistence and segregation of spatially extended phases defined by individual motor states, a “normal” state where the motors’ mechanical (rotation) frequency is slightly smaller than the nominal frequency of the basic ac flows and a “stalled” state where the mechanical frequency is small. Transitions between the two states can be initiated by a perturbation of the voltage or base frequency at the head of the distribution feeder. Such behavior is typical of first-order phase transitions in physics, and this 1+1 dimensional model shows many other properties of a first-order phase transition with the spatial distribution of the motors’ mechanical frequency playing the role of the order parameter. In particular, we observe (a) propagation of the phase-transition front with the constant speed (in very long feeders) and (b) hysteresis in transitions between the normal and stalled (or partially stalled) phases.

Recommended citation: "Hysteresis, phase transitions, and dangerous transients in electrical power distribution systems", C. Duclut, S. Backhaus, and M. Chertkov, Phys. Rev. E 87, 62802 (2013).

Langevin Equations for Reaction-Diffusion Processes

Published in Phys. Rev. Lett., 2016

For reaction-diffusion processes with at most bimolecular reactants, we derive well-behaved, numerically tractable, exact Langevin equations that govern a stochastic variable related to the response field in field theory. Using duality relations, we show how the particle number and other quantities of interest can be computed. Our work clarifies long-standing conceptual issues encountered in field-theoretical approaches and paves the way for systematic numerical and theoretical analyses of reaction-diffusion problems.

Recommended citation: "Langevin Equations for Reaction-Diffusion Processes", F. Benitez, C. Duclut, H. Chaté, B. Delamotte, I. Dornic, and M. A. Muñoz, Phys. Rev. Lett. 117, 100601 (2016).

Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark

Published in Phys. Rev. E, 2017

We derive the necessary conditions for implementing a regulator that depends on both momentum and frequency in the nonperturbative renormalization-group flow equations of out-of-equilibrium statistical systems. We consider model A as a benchmark and compute its dynamical critical exponent $z$. This allows us to show that frequency regulators compatible with causality and the fluctuation-dissipation theorem can be devised. We show that when the principle of minimal sensitivity (PMS) is employed to optimize the critical exponents $\eta$, $\nu$, and $z$, the use of frequency regulators becomes necessary to make the PMS a self-consistent criterion.

Recommended citation: "Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark", C. Duclut, and B. Delamotte, Phys. Rev. E 95, 12107 (2017).

Nonuniversality in the erosion of tilted landscapes

Published in Phys. Rev. E, 2017

The anisotropic model for landscapes erosion proposed by Pastor-Satorras and Rothman [R. Pastor-Satorras and D. H. Rothman, Phys. Rev. Lett. 80, 4349 (1998)] is believed to capture the physics of erosion at intermediate length scale ($\lesssim$3 km), and to account for the large value of the roughness exponent $\alpha$ observed in real data at this scale. Our study of this model—conducted using the nonperturbative renormalization group—concludes on the nonuniversality of this exponent because of the existence of a line of fixed points. Thus the roughness exponent depends (weakly) on the details of the soil and the erosion mechanisms. We conjecture that this feature, while preserving the generic scaling observed in real data, could explain the wide spectrum of values of α measured for natural landscapes.

Recommended citation: "Nonuniversality in the erosion of tilted landscapes", C. Duclut, and B. Delamotte, Phys. Rev. E 96, 12149 (2017).

Fluid pumping and active flexoelectricity can promote lumen nucleation in cell assemblies

Published in Proc. Natl. Acad. Sci. U.S.A., 2019

We discuss the physical mechanisms that promote or suppress the nucleation of a fluid-filled lumen inside a cell assembly or a tissue. We discuss lumen formation in a continuum theory of tissue material properties in which the tissue is described as a 2-fluid system to account for its permeation by the interstitial fluid, and we include fluid pumping as well as active electric effects. Considering a spherical geometry and a polarized tissue, our work shows that fluid pumping and tissue flexoelectricity play a crucial role in lumen formation. We furthermore explore the large variety of long-time states that are accessible for the cell aggregate and its lumen. Our work reveals a role of the coupling of mechanical, electrical, and hydraulic phenomena in tissue lumen formation.

Recommended citation: "Fluid pumping and active flexoelectricity can promote lumen nucleation in cell assemblies", C. Duclut, N. Sarkar, J. Prost, and F. Jülicher, Proc. Natl. Acad. Sci. U.S.A. 116, 19264 (2019).

Nonequilibrium polarity-induced chemotaxis: Emergent Galilean symmetry and exact scaling exponents

Published in Phys. Rev. Research, 2021

A generically observed mechanism that drives the self-organization of living systems is interaction via chemical signals among the individual elements—which may represent cells, bacteria, or even enzymes. Here we propose an unconventional mechanism for such interactions, in the context of chemotaxis, which originates from the polarity of the particles and which generalizes the well-known Keller-Segel interaction term. We study the resulting large-scale dynamical properties of a system of such chemotactic particles using the exact stochastic formulation of Dean and Kawasaki along with dynamical renormalization group analysis of the critical state of the system. At this critical point, an emergent “Galilean” symmetry is identified, which allows us to obtain the dynamical scaling exponents exactly. These exponents reveal superdiffusive density fluctuations and non-Poissonian number fluctuations. We expect our results to shed light on how molecular regulation of chemotactic circuits can determine large-scale behavior of cell colonies and tissues.

Recommended citation: "Nonequilibrium polarity-induced chemotaxis: Emergent Galilean symmetry and exact scaling exponents", S. Mahdisoltani, R. Ben Alì Zinati, C. Duclut, A. Gambassi, and R. Golestanian, Phys. Rev. Research 3, 13100 (2021).

Hydraulic and electric control of cell spheroids

Published in Proc. Natl. Acad. Sci. U.S.A., 2021

We use a theoretical approach to examine the effect of a radial fluid flow or electric current on the growth and homeostasis of a cell spheroid. Such conditions may be generated by a drain of micrometric diameter. To perform this analysis, we describe the tissue as a continuum. We include active mechanical, electric, and hydraulic components in the tissue material properties. We consider a spherical geometry and study the effect of the drain on the dynamics of the cell aggregate. We show that a steady fluid flow or electric current imposed by the drain could be able to significantly change the spheroid long-time state. In particular, our work suggests that a growing spheroid can systematically be driven to a shrinking state if an appropriate external field is applied. Order-of-magnitude estimates suggest that such fields are of the order of the indigenous ones. Similarities and differences with the case of tumors and embryo development are briefly discussed.

Recommended citation: "Hydraulic and electric control of cell spheroids", C. Duclut, J. Prost, and F. Jülicher, Proc. Natl. Acad. Sci. U.S.A. 118, e2021972118 (2021).

Nonlinear rheology of cellular networks

Published in Cells & Development, 2021

Morphogenesis depends crucially on the complex rheological properties of cell tissues and on their ability to maintain mechanical integrity while rearranging at long times. In this paper, we study the rheology of polygonal cellular networks described by a vertex model in the presence of fluctuations. We use a triangulation method to decompose shear into cell shape changes and cell rearrangements. Considering the steady-state stress under constant shear, we observe nonlinear shear-thinning behavior at all magnitudes of the fluctuations, and an even stronger nonlinear regime at lower values of the fluctuations. We successfully capture this nonlinear rheology by a mean-field model that describes the tissue in terms of cell elongation and cell rearrangements. We furthermore introduce anisotropic active stresses in the vertex model and analyze their effect on rheology. We include this anisotropy in the mean-field model and show that it recapitulates the behavior observed in the simulations. Our work clarifies how tissue rheology is related to stochastic cell rearrangements and provides a simple biophysical model to describe biological tissues. Further, it highlights the importance of nonlinearities when discussing tissue mechanics.

Recommended citation: "Nonlinear rheology of cellular networks", C. Duclut, J. Paijmans, M. M. Inamdar, C. D. Modes, and F. Jülicher, Cells & Development 168, 203746 (2021).

Stochastic dynamics of chemotactic colonies with logistic growth

Published in EPL, 2022

The interplay between cellular growth and cell-cell signaling is essential for the aggregation and proliferation of bacterial colonies, as well as for the self-organization of cell tissues. To investigate this interplay, we focus here on the collective properties of dividing chemotactic cell colonies by studying their long-time and large-scale dynamics through a renormalization group (RG) approach. The RG analysis reveals that a relevant but unconventional chemotactic interaction – corresponding to a polarity-induced mechanism – is generated by fluctuations at macroscopic scales, even when an underlying mechanism is absent at the microscopic level. This emerges from the interplay of the well-known Keller–Segel (KS) chemotactic nonlinearity and cell birth and death processes. At one-loop order, we find no stable fixed point of the RG flow equations. We discuss a connection between the dynamics investigated here and the celebrated Kardar–Parisi–Zhang (KPZ) equation with long-range correlated noise, which points at the existence of a strong-coupling, nonperturbative fixed point.

Recommended citation: "Stochastic dynamics of chemotactic colonies with logistic growth", R. Ben Alì Zinati, C. Duclut, S. Mahdisoltani, A. Gambassi, and R. Golestanian, EPL 136, 50003 (2022).

Coarse-grained curvature tensor on polygonal surfaces

Published in SciPost Phys. Core, 2022

Using concepts from integral geometry, we propose a definition for a local coarse-grained curvature tensor that is well-defined on polygonal surfaces. This coarse-grained curvature tensor shows fast convergence to the curvature tensor of smooth surfaces, capturing with accuracy not only the principal curvatures but also the principal directions of curvature. Thanks to the additivity of the integrated curvature tensor, coarse-graining procedures can be implemented to compute it over arbitrary patches of polygons. When computed for a closed surface, the integrated curvature tensor is identical to a rank-2 Minkowski tensor. We also provide an algorithm to extend an existing C++ package, that can be used to compute efficiently local curvature tensors on triangulated surfaces.

Recommended citation: "Coarse-grained curvature tensor on polygonal surfaces", C. Duclut, A. Amiri, J. Paijmans, and F. Jülicher, SciPost Phys. Core 5, 11 (2022).

Active T1 transitions in cellular networks

Published in Eur. Phys. J. E, 2022

In amorphous solids as in tissues, neighbor exchanges can relax local stresses and allow the material to flow. In this paper, we use an anisotropic vertex model to study T1 rearrangements in polygonal cellular networks. We consider two different physical realizations of the active anisotropic stresses: (i) anisotropic bond tension and (ii) anisotropic cell stress. Interestingly, the two types of active stress lead to patterns of relative orientation of T1 transitions and cell elongation that are different. Our work suggests that these two realizations of anisotropic active stresses can be observed \textit{in vivo}. We describe and explain these results through the lens of a continuum description of the tissue as an anisotropic active material. We furthermore discuss the energetics of the dynamic tissue and express the energy balance in terms of internal elastic energy, mechanical work, chemical work and heat. This allows us to define active T1 transitions that can perform mechanical work while consuming chemical energy.

Recommended citation: "Active T1 transitions in cellular networks", C. Duclut, J. Paijmans, M. M. Inamdar, C. D. Modes, and F. Jülicher, Eur. Phys. J. E 45, 29 (2022).

Passive odd viscoelasticity

Published in Phys. Rev. E, 2022

Active chiral viscoelastic materials exhibit elastic responses perpendicular to the applied stresses, referred to as odd elasticity. We use a covariant formulation of viscoelasticity combined with an entropy production analysis to show that odd elasticity is not only present in active systems but also in broad classes of passive chiral viscoelastic fluids. In addition, we demonstrate that linear viscoelastic chiral solids do require activity in order to manifest odd elastic responses. In order to model the phenomenon of passive odd viscoelasticity we propose a chiral extension of Jeffreys model. We apply our covariant formalism in order to derive the dispersion relations of hydrodynamic modes and obtain clear imprints of odd viscoelastic behavior.

Recommended citation: "Passive odd viscoelasticity", R. Lier, J. Armas, S. Bo, C. Duclut, F. Jülicher, P. Surówka, Phys. Rev. E 105, 54607 (2022).

Emergent chirality in active solid rotation of pancreas spheres

Published in preprint, 2022

Collective cell dynamics play a crucial role in many developmental and physiological contexts. While two-dimensional (2D) cell migration has been widely studied, how three-dimensional (3D) geometry and topology interplay with collective cell behavior to determine dynamics and functions remains an open question. In this work, we elucidate the biophysical mechanism underlying rotation in spherical tissues, a phenomenon widely reported both in vivo and in vitro. Using murine pancreas-derived organoids as a model system, we find that epithelial spheres exhibit persistent rotation, rotational axis drift and rotation arrest. Using a 3D vertex model, we demonstrate how the interplay between traction force and polarity alignment can account for these distinct rotational dynamics. Furthermore, our analysis shows that the spherical tissue rotates as an active solid and exhibits spontaneous chiral symmetry breaking. Using a continuum model, we demonstrate how the types and location of topological defects in the polarity field underlie this symmetry breaking process. Altogether, our work shows that tissue chirality can arise via topological defects in the pattern of cell traction forces, with potential implications for left-right symmetry breaking processes in morphogenetic events.

Recommended citation: "Emergent chirality in active solid rotation of pancreas spheres", T. H. Tan, A. Amiri, I. Seijo-Barandiarán, M. F. Staddon, A. Materne, S. Tomas, C. Duclut, M. Popović, A. Grapin-Botton, F. Jülicher, bioRxiv:2022.09.29.510101 (2022).

Lift force in odd compressible fluids

Published in Phys. Rev. E, 2023

We compute the response matrix for a tracer particle in a compressible fluid with odd viscosity living on a two-dimensional surface. Unlike the incompressible case, we find that an odd compressible fluid can produce an odd lift force on a tracer particle. Using a "shell localization" formalism, we provide analytic expressions for the drag and odd lift forces acting on the tracer particle in a steady state and also at finite frequency. Importantly, we find that the existence of an odd lift force in a steady state requires taking into account the non-conservation of the fluid mass density due to the coupling between the two-dimensional surface and the three-dimensional bulk fluid.

Recommended citation: "Lift force in odd compressible fluids", R. Lier, C. Duclut, S. Bo, J. Armas, F. Jülicher, P. Surówka, Phys. Rev. E 108, L023101 (2023).

Auxiliary fields approach to shift-symmetric theories: the φ^4 derivative theory and the crumpled-to-flat transition of membranes at two-loop order

Published in Phys. Rev. D, 2023

We introduce a technique relying on the use of auxiliary fields in order to eliminate explicit field-derivatives that plague the high orders renormalization group treatment of shift-symmetric (derivative) theories. This technique simplifies drastically the computation of fluctuations in such theories. This is illustrated by deriving the two-loop renormalization group equations—and the three-loop anomalous dimension—of the φ^4 derivative theory in D=4−ε, which is also relevant to describe the crumpled-to-flat transition of polymerized membranes. Some features of this transition are provided.

Recommended citation: "Auxiliary fields approach to shift-symmetric theories: the φ^4 derivative theory and the crumpled-to-flat transition of membranes at two-loop order", L. Delzescaux, C. Duclut, D. Mouhanna, and M. Tissier, Phys. Rev. D 108, L081702 (2023).

Random traction yielding transition in epithelial tissues

Published in Phys. Rev. Lett., 2023

We investigate how randomly oriented cell traction forces lead to fluidisation in a vertex model of epithelial tissues. We find that the fluidisation occurs at a critical value of the traction force magnitude $F_c$. We show that this transition exhibits critical behaviour, similar to the yielding transition of sheared amorphous solids. However, we find that it belongs to a different universality class, even though it satisfies the same scaling relations between critical exponents established in the yielding transition of sheared amorphous solids. Our work provides a fluidisation mechanism through active force generation that could be relevant in biological tissues.

Recommended citation: "Random traction yielding transition in epithelial tissues", A. Amiri, C. Duclut, F. Jülicher, M. Popović, Phys. Rev. Lett. 131, 188401 (2023).

Core PCP mutations affect short time mechanical properties but not tissue morphogenesis in the Drosophila pupal wing

Published in eLife, 2023

How morphogenetic movements are robustly coordinated in space and time is a fundamental open question in biology. We study this question using the wing of Drosophila melanogaster, an epithelial tissue that undergoes large-scale tissue flows during pupal stages. We showed previously (Etournay et al., 2015) that pupal wing morphogenesis involves both cellular behaviors that allow relaxation of mechanical tissue stress, as well as cellular behaviors that appear to be actively patterned. The core planar cell polarity (PCP) pathway influences morphogenetic cell movements in many other contexts, which suggests that it could globally pattern active cellular behaviors during pupal wing morphogenesis. We show here, however, that this is not the case: there is no significant phenotype on the cellular dynamics underlying pupal morphogenesis in mutants of core PCP. Furthermore, using laser ablation experiments, coupled with a rheological model to describe the dynamics of the response to laser ablation, we conclude that while core PCP mutations affect the fast timescale response to laser ablation, they do not affect overall tissue mechanics. In conclusion, our work shows that cellular dynamics and tissue shape changes during Drosophila pupal wing morphogenesis are independent of one potential chemical guiding cue, core PCP.

Recommended citation: "Core PCP mutations affect short time mechanical properties but not tissue morphogenesis in the Drosophila pupal wing", R. Piscitello-Gómez, F. S. Gruber, A. Krishna, C. Duclut, C. D. Modes, M. Popović, F. Jülicher, N. A. Dye, S. Eaton, eLife 12, e85581 (2023).

Active shape programming drives Drosophila wing disc eversion

Published in preprint, 2023

How complex 3D tissue shape emerges during animal development remains an important open question in biology and biophysics. In this work, we study eversion of the Drosophila wing disc pouch, a 3D morphogenesis step when the epithelium transforms from a radially symmetric dome into a curved fold shape via an unknown mechanism. To explain this morphogenesis, we take inspiration from inanimate “shape-programmable” materials, which are capable of undergoing blueprinted 3D shape transformations arising from in-plane gradients of spontaneous strains. Here, we show that active, in-plane cellular behaviors can similarly create spontaneous strains that drive 3D tissue shape change and that the wing disc pouch is shaped in this way. We map cellular behaviors in the wing disc pouch by developing a method for quantifying spatial patterns of cell behaviors on arbitrary 3D tissue surfaces using cellular topology. We use a physical shape-programmability model to show that spontaneous strains arising from measured active cell behaviors create the tissue shape changes observed during eversion. We validate our findings using a knockdown of the mechanosensitive molecular motor MyoVI, which we find to reduce active cell rearrangements and disrupt wing pouch eversion. This work shows that shape programming is a mechanism for animal tissue morphogenesis and suggests that there exist intricate patterns in nature that could present novel designs for shape-programmable materials.

Recommended citation: "Active shape programming drives Drosophila wing disc eversion", J. F. Fuhrmann, A. Krishna, J. Paijmans, C. Duclut, S. Eaton, M. Popović, F. Jülicher, C. D. Modes, N. A. Dye, bioRxiv:2023.12.23.573034 (2023).

Fluctuation-Induced First Order Transition to Collective Motion

Published in preprint, 2024

The nature of the transition to collective motion in assemblies of aligning self-propelled particles remains a long-standing matter of debate. In this article, we focus on dry active matter and show that weak fluctuations suffice to generically turn second-order mean-field transitions into a "discontinuous" coexistence scenario. Our theory shows how fluctuations induce a density-dependence of the polar-field mass, even when this effect is absent at mean-field level. In turn, this dependency on density triggers a feedback loop between ordering and advection that ultimately leads to an inhomogeneous transition to collective motion and the emergence of non-linear travelling "flocks". Importantly, we show that such a fluctuation-induced first order transition is present in both metric models, in which particles align with neighbors within a finite distance, and in topological ones, in which alignment is not based on relative distances. We compute analytically the noise-induced renormalization of the polar-field mass using stochastic calculus, which we further back up by a one-loop field-theoretical analysis. Finally, we confirm our analytical predictions by numerical simulations of fluctuating hydrodynamics as well as of topological microscopic models with either k-nearest neighbors or Voronoi alignment.

Recommended citation: "Fluctuation-Induced First Order Transition to Collective Motion", D. Martin, G. Spera, H. Chaté, C. Duclut, C. Nardini, J. Tailleur, F. van Wijland , arXiv:2402.05078 (2024).

Nematic Torques in Scalar Active Matter: When Fluctuations Favor Polar Order and Persistence

Published in Phys. Rev. Lett., 2024

We study the impact of nematic alignment on scalar active matter in the disordered phase. We show that nematic torques control the emergent physics of particles interacting via pairwise forces and can either induce or prevent phase separation. The underlying mechanism is a fluctuation-induced renormalization of the mass of the polar field that generically arises from nematic torques. The correlations between the fluctuations of the polar and nematic fields indeed conspire to increase the particle persistence length, contrary to what phenomenological computations predict. This effect is generic and our theory also quantitatively accounts for how nematic torques enhance particle accumulation along confining boundaries and opposes demixing in mixtures of active and passive particles

Recommended citation: "Nematic Torques in Scalar Active Matter: When Fluctuations Favor Polar Order and Persistence", G. Spera, C. Duclut, M. Durand, J. Tailleur, Phys. Rev. Lett. 132, 078301 (2024).

Probe particles in odd active viscoelastic fluids: How activity and dissipation determine linear stability

Published in Phys. Rev. E, 2024

Odd viscoelastic materials are constrained by fewer symmetries than their even counterparts. The breaking of these symmetries allows these materials to exhibit different features, which have attracted considerable attention in recent years. Immersing a bead in such complex fluids allows for probing their physical properties, highlighting signatures of their oddity and exploring the consequences of these broken symmetries. We present the conditions under which the activity of an odd viscoelastic fluid can give rise to linear instabilities in the motion of the probe particle, and we unveil how the features of the probe particle dynamics depend on the oddity and activity of the viscoelastic medium in which it is immersed.

Recommended citation: "Probe particles in odd active viscoelastic fluids: How activity and dissipation determine linear stability", C. Duclut, S. Bo, R. Lier, J. Armas, F. Jülicher, P. Surówka, Phys. Rev. E 109, 044126 (2024).


Tissue electrohydraulics

In addition to their mechanical properties, cell tissues have the ability to actively transport ions and fluids.