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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, 062802 (2013). https://link.aps.org/doi/10.1103/PhysRevE.87.062802

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). https://link.aps.org/doi/10.1103/PhysRevLett.117.100601

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, 012107 (2017). http://link.aps.org/doi/10.1103/PhysRevE.95.012107

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, 012149 (2017). http://link.aps.org/doi/10.1103/PhysRevE.96.012149

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). http://www.pnas.org/lookup/doi/10.1073/pnas.1908481116

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, 013100 (2021). https://link.aps.org/doi/10.1103/PhysRevResearch.3.013100

Coarse-grained curvature tensor on polygonal surfaces

Published in preprint, 2021

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, arXiv:2104.07988 (2021). https://arxiv.org/abs/2104.07988

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). http://www.pnas.org/lookup/doi/10.1073/pnas.2021972118

Passive odd viscoelasticity

Published in preprint, 2021

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, arXiv:2109.06606 (2021). https://arxiv.org/abs/2109.06606

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 , 203746 (2021). https://linkinghub.elsevier.com/retrieve/pii/S2667290121000802

Stochastic dynamics of chemotactic colonies with logistic growth

Published in preprint, 2021

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, arXiv:2111.08508 (2021). https://arxiv.org/abs/2111.08508

Active T1 transitions in cellular networks

Published in preprint, 2021

In amorphous solids as in tissues, neighbour 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 realization 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 oriented T1 transitions that are different. We describe and explain these observations through the lens of a continuum description of the tissue as an anisotropic active material. We furthermore discuss the energetics of the 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, arXiv:2111.10327 (2021). https://arxiv.org/abs/2111.10327

research

Tissue electrohydraulics

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

talks