## Matthieu Mangeat

### Publications Scientifiques

##### [17] M. Karmakar1, S. Chatterjee2, M. Mangeat2, H. Rieger2,3, and R. Paul1, Jamming and flocking in the restricted active Potts model, submitted (2022).

1School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Kolkata 700032, India.
2Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany.
3INM – Leibniz Institute for New Materials, Campus D2 2, D-66123 Saarbrücken, Germany.

Abstract We study the active Potts model with either site occupancy restriction or on-site repulsion to explore jamming and kinetic arrest in a flocking model. The incorporation of such volume exclusion features leads to a surprisingly rich variety of self-organized spatial patterns. While bands and lanes of moving particles commonly occur without or under weak volume exclusion, strong volume exclusion along with low temperature, high activity, and large particle density facilitates traffic jams. Through several phase diagrams, we identify the phase boundaries separating the jammed and free-flowing phases and study the transition between these phases which provide us with both qualitative and quantitative predictions of how jamming might be delayed or dissolved. We further formulate and analyze a hydrodynamic theory for the restricted APM with that predicts various features of the microscopic model.

##### [16] S. Chatterjee1, M. Mangeat1, C.-U. Woo2, H. Rieger1,3, and J. D. Noh2, Flocking of two unfriendly species: The two-species Vicsek model, submitted (2022).

1Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany.
2Department of Physics, University of Seoul, Seoul 02504, Korea.
3INM – Leibniz Institute for New Materials, Campus D2 2, D-66123 Saarbrücken, Germany.

Abstract We consider the two-species Vicsek model (TSVM) consisting of two kinds of self-propelled particles, A and B, that tend to align with particles from the same species and to anti-align with the other. The model shows a flocking transition that is reminiscent of the original Vicsek model: it has a liquid-gas phase transition and displays micro-phase separation in the coexistence region where multiple dense liquid bands propagate in a gaseous background. The novel feature of the TSVM is the existence of two kinds of bands, one composed of mainly A-particles and one mainly of B-particles and the appearance of two dynamical states in the coexistence region: the PF (parallel flocking) state in which all bands of the two species propagate in the same direction, and the APF (anti-parallel flocking) state in which the bands of species A and species B move in opposite directions. When PF and APF states exist in the low-density part of the coexistence region they perform stochastic transitions from one to the other. The system size dependence of the transition frequency and dwell times shows a pronounced crossover that is determined by the ratio of the band width and the longitudinal system size. Our work paves the way for studying multi-species flocking models with heterogeneous alignment interactions.

##### [15] S. Chatterjee1, M. Mangeat1, and H. Rieger1,2, Polar flocks with discretized directions: the active clock model approaching the Vicsek model, EPL 138, 41001 (2022).

1Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany.
2INM – Leibniz Institute for New Materials, Campus D2 2, D-66123 Saarbrücken, Germany.

Abstract We consider the off-lattice two-dimensional $q$-state active clock model (ACM) as a natural discretization of the Vicsek model (VM) describing flocking. The ACM consists of particles able to move in the plane in a discrete set of $q$ equidistant angular directions, as in the active Potts model (APM), with an alignment interaction inspired by the ferromagnetic equilibrium clock model. We find that for a small number of directions, the flocking transition of the ACM has the same phenomenology as the APM, including macrophase separation and reorientation transition. For a larger number of directions, the flocking transition in the ACM becomes equivalent to the one of the VM and displays microphase separation and only transverse bands, i.e. no re-orientation transition. Concomitantly also the transition of the $q\to\infty$ limit of the ACM, the active XY model (AXYM), is in the same universality class as the VM. We also construct a coarse-grained hydrodynamic description for the ACM and AXYM akin to the VM.

##### [14] A. Alexandre1, M. Mangeat2, T. Guérin1, and D. S. Dean1,3, How Stickiness Can Speed Up Diffusion in Confined Systems, Phys. Rev. Lett. 128, 210601 (2022).

1Univ. Bordeaux, CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, F-33405 Talence, France.
2Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany.
3Team MONC, INRIA Bordeaux Sud Ouest, CNRS UMR 5251, Bordeaux INP, Univ. Bordeaux, F-33400 Talence, France.

Abstract The paradigmatic model for heterogeneous media used in diffusion studies is built from reflecting obstacles and surfaces. It is well known that the crowding effect produced by these reflecting surfaces slows the dispersion of Brownian tracers. Here, using a general adsorption desorption model with surface diffusion, we show analytically that making surfaces or obstacles attractive can accelerate dispersion. In particular, we show that this enhancement of diffusion can exist even when the surface diffusion constant is smaller than that in the bulk. Even more remarkably, this enhancement effect occurs when the effective diffusion constant, when restricted to surfaces only, is lower than the effective diffusivity with purely reflecting boundaries. We give analytical formulas for this intriguing effect in periodic arrays of spheres as well as undulating microchannels. Our results are confirmed by numerical calculations and Monte Carlo simulations.

##### [13] M. Mangeat1,2, T. Guérin1, and D. S. Dean1,3, Steady state of overdamped particles in the non-conservative force field of a simple non-linear model of optical trap, J. Stat. Mech. 2021, 113205 (2021).

1Univ. Bordeaux, CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, F-33405 Talence, France.
2Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany.
3Team MONC, INRIA Bordeaux Sud Ouest, CNRS UMR 5251, Bordeaux INP, Univ. Bordeaux, F-33400 Talence, France.

Abstract Optically trapped particles are often subject to a non-conservative scattering force arising from radiation pressure. In this paper we present an exact solution for the steady state statistics of an overdamped Brownian particle subjected to a commonly used force field model for an optical trap. The model is the simplest of its kind that takes into account non-conservative forces. In particular, we present exact results for certain marginals of the full three dimensional steady state probability distribution as well as results for the toroidal probability currents which are present in the steady state, as well as for the circulation of theses currents. Our analytical results are confirmed by numerical solution of the steady state Fokker-Planck equation.

##### [12] M. Mangeat1 and H. Rieger1, Narrow escape problem in two-shell spherical domains, Phys. Rev. E 104, 044124 (2021).

1Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany.

Abstract Intracellular transport in living cells is often spatially inhomogeneous with an accelerated effective diffusion close to the cell membrane and a ballistic motion away from the centrosome due to active transport along actin filaments and microtubules, respectively. Recently it was reported that the mean first passage time (MFPT) for transport to a specific area on the cell membrane is minimal for an optimal actin cortex width. In this paper we ask whether this optimization in a two-compartment domain can also be achieved by passive Brownian particles. We consider a Brownian motion with different diffusion constants in the two shells and a potential barrier between the two and investigate the narrow escape problem by calculating the MFPT for Brownian particles to reach a small window on the external boundary. In two and three dimensions, we derive asymptotic expressions for the MFPT in the thin cortex and small escape region limits confirmed by numerical calculations of the MFPT using the finite element method and stochastic simulations. From this analytical and numeric analysis we finally extract the dependence of the MFPT on the ratio of diffusion constants, the potential barrier height and the width of the outer shell. The first two are monotonous whereas the last one may have a minimum for a sufficiently attractive cortex, for which we propose an analytical expression of the potential barrier height matching very well the numerical predictions.

##### [11] M. Mangeat1, S. Chatterjee2, R. Paul2, and H. Rieger1, Flocking with a q-fold discrete symmetry: Band-to-lane transition in the active Potts model, Phys. Rev. E 102, 042601 (2020).

1Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany.
2School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Kolkata 700032, India.

Abstract We study the $q$-state active Potts model (APM) on a two-dimensional lattice in which self-propelled particles have q internal states corresponding to the q directions of motion. A local alignment rule inspired by the ferromagnetic $q$-state Potts model and self-propulsion via biased diffusion according to the internal particle states elicits collective motion at high densities and low noise. We formulate a coarse-grained hydrodynamic theory with which we compute the phase diagrams of the APM for $q=4$ and $q=6$ and analyze the flocking dynamics in the coexistence region, where the high-density (polar liquid) phase forms a fluctuating stripe of coherently moving particles on the background of the low-density (gas) phase. A reorientation transition of the phase-separated profiles from transversal band motion to longitudinal lane formation is found, which is absent in the Vicsek model and the active Ising model. The origin of this reorientation transition is revealed by a stability analysis: for large velocities the transverse diffusivity approaches zero and stabilizes lanes. Computer simulations corroborate the analytical predictions of the flocking and reorientation transitions and validate the phase diagrams of the APM.

##### [10] S. Chatterjee1, M. Mangeat2, R. Paul1, and H. Rieger2, Flocking and reorientation transition in the 4-state active Potts model, EPL 130, 66001 (2020).

1School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Kolkata 700032, India.
2Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany.

Abstract We study the active 4-state Potts model (APM) on the square lattice in which active particles have four internal states corresponding to the four directions of motion. A local alignment rule inspired by the ferromagnetic 4-state Potts model and self-propulsion via biased diffusion according to the internal particle states leads to flocking at high densities and low noise. We compute the phase diagram of the APM and explore the flocking dynamics in the region, in which the high-density (liquid) phase coexists with the low-density (gas) phase and forms a fluctuating band of coherently moving particles. As a function of the particle self-propulsion velocity, a novel reorientation transition of the phase-separated profiles from transversal to longitudinal band motion is revealed, which is absent in the Vicsek model and the active Ising model. We further construct a coarse-grained hydrodynamic description of the model which validates the results for the microscopic model.

##### [9] M. Mangeat1, T. Guérin1, and D. S. Dean1, Effective diffusivity of Brownian particles in a two dimensional square lattice of hard disks, J. Chem. Phys. 152, 234109 (2020).

1Univ. Bordeaux, CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, F-33405 Talence, France.

Abstract We revisit the classic problem of the effective diffusion constant of a Brownian particle in a square lattice of reflecting impenetrable hard disks. This diffusion constant is also related to the effective conductivity of non-conducting and infinitely conductive disks in the same geometry. We show how a recently derived Green’s function for the periodic lattice can be exploited to derive a series expansion of the diffusion constant in terms of the disk’s volume fraction φ. Second, we propose a variant of the Fick–Jacobs approximation to study the large volume fraction limit. This combination of analytical results is shown to describe the behavior of the diffusion constant for all volume fractions.

##### [8] M. Mangeat1 and H. Rieger1, The narrow escape problem in a circular domain with radial piecewise constant diffusivity, J. Phys. A: Math. Theor. 52, 424002 (2019).

1Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany.

Abstract The stochastic motion of particles in living cells is often spatially inhomogeneous with a higher effective diffusivity in a region close to the cell boundary due to active transport along actin filaments. As a first step to understand the consequence of the existence of two compartments with different diffusion constant for stochastic search problems we consider here a Brownian particle in a circular domain with different diffusion constants in the inner and the outer shell. We focus on the narrow escape problem and compute the mean first passage time (MFPT) for Brownian particles starting at some pre-defined position to find a small region on the outer reflecting boundary. For the annulus geometry we find that the MFPT can be minimized for a specific value of the width of the outer shell. In contrast for the two-shell geometry we show that the MFPT depends monotonously on all model parameters, in particular on the outer shell width. Moreover we find that the distance between the starting point and the narrow escape region which maximizes the MFPT depends discontinuously on the ratio between inner and outer diffusivity.

##### [7] M. Mangeat1, Y. Amarouchene1, Y. Louyer1, T. Guérin1, and D. S. Dean1, Role of nonconservative scattering forces and damping on Brownian particles in optical traps, Phys. Rev. E 99, 052107 (2019).

1Univ. Bordeaux, CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, F-33405 Talence, France.

Abstract We consider a model of a particle trapped in a harmonic optical trap but with the addition of a nonconservative radiation induced force. This model is known to correctly describe experimentally observed trapped particle statistics for a wide range of physical parameters, such as temperature and pressure. We theoretically analyze the effect of nonconservative force on the underlying steady state distribution as well as the power spectrum for the particle position. We compute perturbatively the probability distribution of the resulting nonequilibrium steady states for all dynamical regimes underdamped through to overdamped and give expressions for the associated currents in phase space (position and velocity). We also give the spectral density of the trapped particle's position in all dynamical regimes and for any value of the nonconservative force. Signatures of the presence of nonconservative forces are shown to be particularly strong for the underdamped regime at low frequencies.

##### [6] Y. Amarouchene1, M. Mangeat1, B. Vidal Montes1, L. Ondic2, T. Guérin1, D. S. Dean1, and Y. Louyer1, Nonequilibrium Dynamics Induced by Scattering Forces for Optically Trapped Nanoparticles in Strongly Inertial Regimes, Phys. Rev. Lett. 122, 183901 (2019).

1Univ. Bordeaux, CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, F-33405 Talence, France.
2Institute of Physics, Academy of Sciences of the Czech Republic, CZ-162 00 Prague, Czech Republic.

Abstract The forces acting on optically trapped particles are commonly assumed to be conservative. Nonconservative scattering forces induce toroidal currents in overdamped liquid environments, with negligible effects on position fluctuations. However, their impact in the underdamped regime remains unexplored. Here, we study the effect of nonconservative scattering forces on the underdamped nonlinear dynamics of trapped nanoparticles at various air pressures. These forces induce significant low-frequency position fluctuations along the optical axis and the emergence of toroidal currents in both position and velocity variables. Our experimental and theoretical results provide fundamental insights into the functioning of optical tweezers and a means for investigating nonequilibrium steady states induced by nonconservative forces.

##### [PhD] M. Mangeat1, De la dispersion aux vortex browniens dans des systèmes hors-équilibres confinés, Thèse de doctorat, Université de Bordeaux (soutenue le 25 Sept. 2018).

1Univ. Bordeaux, CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, F-33405 Talence, France.

Résumé Cette thèse vise à caractériser la dynamique stochastique hors-équilibre de particules browniennes sous l’effet de confinement. Ce confinement est appliqué ici par des potentiels attractifs ou des frontières imperméables créant des barrières entropiques. Dans un premier temps, nous regardons la dispersion de particules sans interactions dans les milieux hétérogènes. Un nuage de particules browniennes s’étale au cours du temps sans atteindre la distribution d’équilibre de Boltzmann, et son étalement est alors caractérisé par une diffusivité effective inférieure à la diffusivité microscopique. Dans un premier chapitre, nous nous intéressons au lien entre la géométrie de confinement et la dispersion dans le cas particulier des microcanaux périodiques. Pour cela, nous calculons la diffusivité effective sans hypothèse de réduction de dimensionnalité, contrairement à l’approche standard dite de Fick-Jacobs. Une classification des différents régimes de dispersion est alors réalisée, pour toute géométrie autant pour les canaux continus que discontinus. Dans un second chapitre, nous étendons cette analyse à la dispersion dans les réseaux périodiques d’obstacles sphériques attractifs à courte portée. La présence d’un potentiel attractif peut, de manière surprenante, augmenter la dispersion. Nous quantifions cet effet dans le régime dilué, et montrons alors son optimisation pour plusieurs potentiels ainsi que pour une diffusion médiée par la surface des sphères. Ensuite, nous étudions la dynamique stochastique de particules browniennes dans un piège optique en présence d’une force non conservative créée par la pression de radiation du laser. L’expression perturbative des courants stationnaires, décrivant les vortex browniens, est dérivée pour les basses pressions en conservant le terme inertiel dans l’équation de Langevin sous-amortie. L’expression de la densité spectrale est également calculée permettant d’observer les anisotropies du piège et les effets de la force non conservative. La plupart des expressions analytiques obtenues durant cette thèse sont asymptotiquement exactes et vérifiées par des analyses numériques basées sur l’intégration de l’équation de Langevin ou la résolution d’équation aux dérivées partielles.

##### [5] M. Mangeat1, T. Guérin1, and D. S. Dean1, Dispersion in two-dimensional periodic channels with discontinuous profiles, J. Chem. Phys. 149, 124105 (2018).

1Univ. Bordeaux, CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, F-33405 Talence, France.

Abstract The effective diffusivity of Brownian tracer particles confined in periodic micro-channels is smaller than the microscopic diffusivity due to entropic trapping. Here, we study diffusion in two-dimensional periodic channels whose cross section presents singular points, such as abrupt changes of radius or the presence of thin walls, with openings, delimiting periodic compartments composing the channel. Dispersion in such systems is analyzed using the Fick-Jacobs (FJ) approximation. This approximation assumes a much faster equilibration in the lateral than in the axial direction, along which the dispersion is measured. If the characteristic width a of the channel is much smaller than the period L of the channel, i.e., $\varepsilon = a/L$ is small, this assumption is clearly valid for Brownian particles. For discontinuous channels, the FJ approximation is only valid at the lowest order in $\varepsilon$ and provides a rough, though on occasions rather accurate, estimate of the effective diffusivity. Here we provide formulas for the effective diffusivity in discontinuous channels that are asymptotically exact at the next-to-leading order in $\varepsilon$. Each discontinuity leads to a reduction of the effective diffusivity. We show that our theory is consistent with the picture of effective trapping rates associated with each discontinuity, for which our theory provides explicit and asymptotically exact formulas. Our analytical predictions are confirmed by numerical analysis. Our results provide a precise quantification of the kinetic entropic barriers associated with profile singularities.

##### [4] M. Mangeat1, T. Guérin1, and D. S. Dean1, Dispersion in two dimensional channels—the Fick–Jacobs approximation revisited, J. Stat. Mech. (2017) 123205.

1Univ. Bordeaux, CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, F-33405 Talence, France.

Abstract We examine the dispersion of Brownian particles in a symmetric two dimensional channel, this classical problem has been widely studied in the literature using the so called Fick–Jacobs’ approximation and its various improvements. Most studies rely on the reduction to an effective one dimensional diffusion equation, here we derive an explicit formula for the diffusion constant which avoids this reduction. Using this formula the effective diffusion constant can be evaluated numerically without resorting to Brownian simulations. In addition, a perturbation theory can be developed in $\varepsilon = h_0/L$ where $h_0$ is the characteristic channel height and $L$ the period. This perturbation theory confirms the results of Kalinay and Percus (2006 Phys. Rev . E 74 041203), based on the reduction, to one dimensional diffusion are exact at least to $\mathcal O(\varepsilon^6)$ . Furthermore, we show how the Kalinay and Percus pseudo-linear approximation can be straightforwardly recovered. The approach proposed here can also be exploited to yield exact results in the limit $\varepsilon \to \infty$ , we show that here the diffusion constant remains finite and show how the result can be obtained with a simple physical argument. Moreover, we show that the correction to the effective diffusion constant is of order $1/\varepsilon$ and remarkably has some universal characteristics. Numerically we compare the analytic results obtained with exact numerical calculations for a number of interesting channel geometries.

##### [3] M. Mangeat1, T. Guérin1, and D. S. Dean1, Geometry controlled dispersion in periodic corrugated channels, EPL 118, 40004 (2017).

1Univ. Bordeaux, CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, F-33405 Talence, France.

Abstract The effective diffusivity $D_e$ of tracer particles diffusing in periodically corrugated axisymmetric two- and three-dimensional channels is studied. The majority of the previous studies of this class of problems are based on perturbative analyses about narrow channels, where the problem can be reduced to an effectively one-dimensional one. Here we show how to analyze this class of problems using a much more general approach which even includes the limit of infinitely wide channels. Using the narrow- and wide-channel asymptotics, we provide a Padé approximant scheme that is able to describe the dispersion properties of a wide class of channels. Furthermore, we systematically identify all the exact asymptotic scaling regimes of $D_e$ and the accompanying physical mechanisms that control dispersion, clarifying the distinction between smooth channels and compartmentalized ones, and identifying the regimes in which $D_e$ can be linked to first passage problems.

##### [2] X. Zhou1, R. Zhao1, K. Schwarz2, M. Mangeat2, E. C. Schwarz1, M. Hamed3,4, I. Bogeski1, V. Helms3, H. Rieger2, and B. Qu1, Bystander cells enhance NK cytotoxic efficiency by reducing search time, Sci. Rep 7, 44357 (2017).

1Biophysics, Center for Integrative Physiology and Molecular Medicine, School of Medicine, Saarland University, D-66421 Homburg, Germany.
2Department of Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany.
3Center for Bioinformatics, Saarland University, D-66041 Saarbrücken, Germany.
4Institute for Biostatistics and Informatics in Medicine and Ageing Research, Rostock University Medical Center, D-18057 Rostock, Germany.

Abstract Natural killer (NK) cells play a central role during innate immune responses by eliminating pathogen-infected or tumorigenic cells. In the microenvironment, NK cells encounter not only target cells but also other cell types including non-target bystander cells. The impact of bystander cells on NK killing efficiency is, however, still elusive. In this study we show that the presence of bystander cells, such as P815, monocytes or HUVEC, enhances NK killing efficiency. With bystander cells present, the velocity and persistence of NK cells were increased, whereas the degranulation of lytic granules remained unchanged. Bystander cell-derived $H_2O_2$ was found to mediate the acceleration of NK cell migration. Using mathematical diffusion models, we confirm that local acceleration of NK cells in the vicinity of bystander cells reduces their search time to locate target cells. In addition, we found that integrin $\beta$ chains ($\beta_1$, $\beta_2$ and $\beta_7$) on NK cells are required for bystander-enhanced NK migration persistence. In conclusion, we show that acceleration of NK cell migration in the vicinity of $H_2O_2$-producing bystander cells reduces target cell search time and enhances NK killing efficiency.

##### [1] M. Mangeat1,2 and F. Zamponi1, Quantitative approximation schemes for glasses, Phys. Rev. E 93, 012609 (2016).

1Laboratoire de Physique Théorique (LPT), École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, F-75005 Paris, France.
2Master ICFP, Département de Physique, École Normale Supérieure, 24 Rue Lhomond, F-75005 Paris, France.

Abstract By means of a systematic expansion around the infinite-dimensional solution, we obtain an approximation scheme to compute properties of glasses in low dimensions. The resulting equations take as input the thermodynamic and structural properties of the equilibrium liquid, and from this they allow one to compute properties of the glass. They are therefore similar in spirit to the Mode Coupling approximation scheme. Our scheme becomes exact, by construction, in dimension $d \to \infty$, and it can be improved systematically by adding more terms in the expansion.