# publications

## 2021

- Adhesion as a trigger of droplet polarization in flowing emulsionsI. Golovkova, L. Montel, F. Pan, E. Wandersman, A. M. Prevost,
**T. Bertrand**, and L.-L. Pontani*Soft Matter*,**Advance Article**, - (2021)Tissues are subjected to large external forces and undergo global deformations during morphogenesis. We use synthetic analogues of tissues to study the impact of cell–cell adhesion on the response of cohesive cellular assemblies under such stresses. In particular, we use biomimetic emulsions in which the droplets are functionalized in order to exhibit specific droplet–droplet adhesion. We flow these emulsions in microfluidic constrictions and study their response to this forced deformation via confocal microscopy. We find that the distributions of avalanche sizes are conserved between repulsive and adhesive droplets. However, adhesion locally impairs the rupture of droplet–droplet contacts, which in turn pulls on the rearranging droplets. As a result, adhesive droplets are a lot more deformed along the axis of elongation in the constriction. This finding could shed light on the origin of polarization processes during morphogenesis.

## 2020

- Diversity of phase transitions and phase co-existences in active fluids
**T. Bertrand**, and C. F. Lee*arXiv*:2012.05866 (2020)Active matter is not only indispensable to our understanding of diverse biological processes, but also provides a fertile ground for discovering novel physics. Many emergent properties impossible for equilibrium systems have been demonstrated in active systems. These emergent features include motility-induced phase separation, long-ranged ordered (collective motion) phase in two dimensions, and order-disorder phase co-existences (banding and reverse-banding regimes). Here, we unify these diverse phase transitions and phase co-existences into a single formulation based on generic hydrodynamic equations for active fluids. We also reveal a novel co-moving co-existence phase and a putative novel critical point.

- Clustering and ordering in cell assemblies with generic asymmetric aligning interactions
**T. Bertrand**, J. d’Alessandro, A. Maitra, S. Jain, B. Mercier, R.-M. Mège, B. Ladoux, and R. Voituriez*arXiv*:2012.00785 (2020)Collective cell migration plays an essential role in various biological processes, such as development or cancer proliferation. While cell-cell interactions are clearly key determinants of collective cell migration – in addition to individual cells self-propulsion – the physical mechanisms that control the emergence of cell clustering and collective cell migration are still poorly understood. In particular, observations have shown that binary cell-cell collisions generally lead to anti-alignement of cell polarities and separation of pairs – a process called contact inhibition of locomotion (CIL), which is expected to disfavor the formation of large scale cell clusters with coherent motion. Here, we adopt a joint experimental and theoretical approach to determine the large scale dynamics of cell assemblies from elementary pairwise cell-cell interaction rules. We quantify experimentally binary cell-cell interactions and show that they can be captured by a minimal equilibrium-like pairwise asymmetric aligning interaction potential that reproduces the CIL phenomenology. We identify its symmetry class, build the corresponding active hydrodynamic theory and show on general grounds that such asymmetric aligning interaction destroys large scale clustering and ordering, leading instead to a liquid-like microphase of cell clusters of finite size and short lived polarity, or to a fully dispersed isotropic phase. Finally, this shows that CIL-like asymmetric interactions in cellular systems – or general active systems – control cluster sizes and polarity, and can prevent large scale coarsening and long range polarity, except in the singular regime of dense confluent systems.

- Depletion attraction impairs the plasticity of emulsions flowing in a constrictionI. Golovkova, L. Montel, E. Wandersman,
**T. Bertrand**, A. M. Prevost, and L.-L. Pontani*Soft Matter*,**16**, 3294-3302 (2020)We study the elasto-plastic behavior of dense attractive emulsions under a mechanical perturbation. The attraction is introduced through non-specific depletion interactions between the droplets and is controlled by changing the concentration of surfactant micelles in the continuous phase. We find that such attractive forces are not sufficient to induce any measurable modification on the scalings between the local packing fraction and the deformation of the droplets. However, when the emulsions are flowed through 2D microfluidic constrictions, we uncover a measurable effect of attraction on their elasto-plastic response. Indeed, we measure higher levels of deformation inside the constriction for attractive droplets. In addition, we show that these measurements correlate with droplet rearrangements that are spatially delayed in the constriction for higher attraction forces.

## 2019

- Nonlinear diffusion and hyperuniformity from Poisson representation in systems with interaction mediated dynamics
**T. Bertrand**, D. Chatenay, and R. Voituriez*New Journal of Physics*,**21**, 123048 (2019)We introduce a minimal model of interacting particles relying on conservation of the number of particles and interactions respecting conservation of the center of mass. The dynamics in our model is directly amenable to simple pairwise interactions between particles leading to particle displacements, ensues from this what we call interaction mediated dynamics. Inspired by binary reaction kinetics-like rules, we model systems of interacting agents activated upon pairwise contact. Using Poisson representations, our model is amenable to an exact nonlinear stochastic differential equation. We derive analytically its hydrodynamic limit, which turns out to be a nonlinear diffusion equation of porous medium type valid even far from steady state. We obtain exact self-similar solutions with subdiffusive scaling and compact support. The nonequilibrium steady state of our model in the dense phase displays hyperuniformity which we are able to predict from our analytical approach. We reinterpret hyperuniformity as stemming from correlations in particles displacements induced by the conservation of center of mass. Although quite simplistic, this model could in principle be realized experimentally at different scales by active particles systems.

- Comparison of shear and compression jammed packings of frictional disksF. Xiong, P. Wang, A. H. Clark,
**T. Bertrand**, N. T. Ouellette, M. D. Shattuck, and C. S. O’Hern*Granular Matter*,**21**, 109 (2019)We compare the structural and mechanical properties of mechanically stable (MS) packings of frictional disks in two spatial dimensions (2D) generated with isotropic compression and simple shear protocols from discrete element modeling (DEM) simulations. We find that the average contact number and packing fraction at jamming onset are similar (with relative deviations <0.5%) for MS packings generated via compression and shear. In contrast, the average stress anisotropy ⟨Σ̂ xy⟩=0 for MS packings generated via isotropic compression, whereas ⟨Σ̂ xy⟩>0 for MS packings generated via simple shear. To investigate the difference in the stress state of MS packings, we develop packing-generation protocols to first unjam the MS packings, remove the frictional contacts, and then rejam them. Using these protocols, we are able to obtain rejammed packings with nearly identical particle positions and stress anisotropy distributions compared to the original jammed packings. However, we find that when we directly compare the original jammed packings and rejammed ones, there are finite stress anisotropy deviations ΔΣ̂ xy. The deviations are smaller than the stress anisotropy fluctuations obtained by enumerating the force solutions within the null space of the contact networks generated via the DEM simulations. These results emphasize that even though the compression and shear jamming protocols generate packings with the same contact networks, there can be residual differences in the normal and tangential forces at each contact, and thus differences in the stress anisotropy.

- Active acoustic switches using two-dimensional granular crystalsQ. Wu, C. Cui,
**T. Bertrand**, M. D. Shattuck, and C. S. O’Hern*Phys. Rev. E*,**99**, 062901 (2019)We employ numerical simulations to study active transistor-like switches made from two-dimensional (2D) granular crystals containing two types of grains with the same size but different masses. We tune the mass contrast and arrangement of the grains to maximize the width of the frequency band gap in the device. The input signal is applied to a single grain on one side of the device, and the output signal is measured from another grain on the other side of the device. Changing the size of one or many grains tunes the pressure, which controls the vibrational response of the device. Switching between the on and off states is achieved using two mechanisms: (1) pressure-induced switching where the interparticle contact network is the same in the on and off states and (2) switching through contact breaking. In general, the performance of the acoustic switch, as captured by the gain ratio and switching time between the on and off states, is better for pressure-induced switching. We show that in these acoustic switches the gain ratio between the on and off states can be larger than 104 and the switching time (multiplied by the driving frequency) is comparable to that obtained recently for sonic crystals and less than that for photonic transistor-like switches. Since the self-assembly of grains with different masses into 2D granular crystals is challenging, we describe simulations of circular grains with small circular knobs placed symmetrically around the perimeter mixed with circular grains without knobs. Using umbrella sampling techniques, we show that grains with six knobs most efficiently form the hexagonal crystals that yield the largest frequency band gap. Using the simulation results, we estimate the time required for vibration experiments to generate granular crystals of millimeter-sized steel beads with maximal band gaps.

## 2018

- Dynamics of run-and-tumble particles in dense single-file systems
**T. Bertrand**, P. Illien, O. Bénichou, and R. Voituriez*New Journal of Physics*,**20**, 113045 (2018)We study a minimal model of self-propelled particle in a crowded single-file environment. We extend classical models of exclusion processes (previously analyzed for diffusive and driven tracer particles) to the case where the tracer particle is a run-and-tumble particle (RTP), while all bath particles perform symmetric random walks. In the limit of high density of bath particles, we derive exact expressions for the full distribution of the RTP position X and all its cumulants, valid for arbitrary values of the tumbling probability α and time n. Our results highlight striking effects of crowding on the dynamics: even cumulants of the RTP position are increasing functions of α at intermediate timescales, and display a subdiffusive anomalous scaling independent of α in the limit of long times . These analytical results set the ground for a quantitative analysis of experimental trajectories of real biological or artificial microswimmers in extreme confinement.

- Stress anisotropy in shear-jammed packings of frictionless disksS. Chen*,
**T. Bertrand***, W. Jin, M. D. Shattuck, and C. S. O’Hern*Phys. Rev. E*,**98**, 042906 (2018)We perform computational studies of repulsive, frictionless disks to investigate the development of stress anisotropy in mechanically stable (MS) packings at jamming onset. We focus on two protocols for generating MS packings at jamming onset: (1) isotropic compression and (2) applied simple or pure shear strain γ at fixed packing fraction ϕ. MS packings of frictionless disks occur as geometric families (i.e., quasiparabolic segments with positive curvature) in the ϕ−γ plane. MS packings from protocol 1 populate parabolic segments with both signs of the slope, dϕ/dγ>0 and dϕ/dγ<0. In contrast, MS packings from protocol 2 populate segments with dϕ/dγ<0 only. For both simple and pure shear, we derive a relationship between the stress anisotropy and local dilatancy dϕ/dγ obeyed by MS packings along geometrical families. We show that for MS packings prepared using isotropic compression, the stress anisotropy distribution is Gaussian centered at zero with a standard deviation that decreases with increasing system size. For shear jammed MS packings, the stress anisotropy distribution is a convolution of Weibull distributions that depend on strain, which has a nonzero average and standard deviation in the large-system limit. We also develop a framework to calculate the stress anisotropy distribution for packings generated via protocol 2 in terms of the stress anisotropy distribution for packings generated via protocol 1.

- Optimized Diffusion of Run-and-Tumble Particles in Crowded Environments
**T. Bertrand**, Y. Zhao, O. Bénichou, J. Tailleur, and R. Voituriez*Phys. Rev. Lett.*,**120**, 198103 (2018)We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of run-and-tumble particles (RTPs) moving in discrete time on a d-dimensional cubic lattice in the presence of diffusing hard-core obstacles. We derive an explicit expression for the diffusivity of the RTP, which is exact in the limit of low density of fixed obstacles. To do so, we introduce a generalization of Kac’s theorem on the mean return times of Markov processes, which we expect to be relevant for a large class of lattice gas problems. Our results show the diffusivity of RTPs to be nonmonotonic in the tumbling probability for low enough obstacle mobility. These results prove the potential for the optimization of the transport of RTPs in crowded and disordered environments with applications to motile artificial and biological systems.

## 2017

- Response of jammed packings to thermal fluctuationsQ. Wu,
**T. Bertrand**, M. D. Shattuck, and C. S. O’Hern*Phys. Rev. E*,**96**, 062902 (2017)We focus on the response of mechanically stable (MS) packings of frictionless, bidisperse disks to thermal fluctuations, with the aim of quantifying how nonlinearities affect system properties at finite temperature. In contrast, numerous prior studies characterized the structural and mechanical properties of MS packings of frictionless spherical particles at zero temperature. Packings of disks with purely repulsive contact interactions possess two main types of nonlinearities, one from the form of the interaction potential (e.g., either linear or Hertzian spring interactions) and one from the breaking (or forming) of interparticle contacts. To identify the temperature regime at which the contact-breaking nonlinearities begin to contribute, we first calculated the minimum temperatures Tcb required to break a single contact in the MS packing for both single- and multiple-eigenmode perturbations of the T=0 MS packing. We find that the temperature required to break a single contact for equal velocity-amplitude perturbations involving all eigenmodes approaches the minimum value obtained for a perturbation in the direction connecting disk pairs with the smallest overlap. We then studied deviations in the constant volume specific heat ¯¯¯CV and deviations of the average disk positions Δr from their T=0 values in the temperature regime T¯¯¯CV<T<Tr, where Tr is the temperature beyond which the system samples the basin of a new MS packing. We find that the deviation in the specific heat per particle Δ¯¯¯C0V/¯¯¯C0V relative to the zero-temperature value ¯¯¯C0V can grow rapidly above Tcb; however, the deviation Δ¯¯¯C0V/¯¯¯C0V decreases as N−1 with increasing system size. To characterize the relative strength of contact-breaking versus form nonlinearities, we measured the ratio of the average position deviations Δrss/Δrds for single- and double-sided linear and nonlinear spring interactions. We find that Δrss/Δrds>100 for linear spring interactions is independent of system size. This result emphasizes that contact-breaking nonlinearities are dominant over form nonlinearities in the low-temperature range Tcb<T<Tr for model jammed systems.

- Local and global avalanches in a two-dimensional sheared granular mediumJ. Barés, D. Wang, D. Wang,
**T. Bertrand**, C. S. O’Hern, and R. P. Behringer*Phys. Rev. E*,**96**, 052902 (2017)We present the experimental and numerical studies of a two-dimensional sheared amorphous material composed of bidisperse photoelastic disks. We analyze the statistics of avalanches during shear including the local and global fluctuations in energy and changes in particle positions and orientations. We find scale-free distributions for these global and local avalanches denoted by power laws whose cutoffs vary with interparticle friction and packing fraction. Different exponents are found for these power laws depending on the quantity from which variations are extracted. An asymmetry in time of the avalanche shapes is evidenced along with the fact that avalanches are mainly triggered by the shear bands. A simple relation independent of the intensity is found between the number of local avalanches and the global avalanches they form. We also compare these experimental and numerical results for both local and global fluctuations to predictions from mean-field and depinning theories.

## 2016

- Dynamics of Swelling and Drying in a Spherical Gel
**T. Bertrand**, J. Peixinho, S. Mukhopadhyay, and C. W. MacMinn*Phys. Rev. Applied*,**6**, 064010 (2016)Swelling is a volumetric-growth process in which a porous material expands by spontaneous imbibition of additional pore fluid. Swelling is distinct from other growth processes in that it is inherently poromechanical: local expansion of the pore structure requires that additional fluid be drawn from elsewhere in the material, or into the material from across the boundaries. Here, we study the swelling and subsequent drying of a sphere of hydrogel. We develop a dynamic model based on large-deformation poromechanics and the theory of ideal elastomeric gels, and we compare the predictions of this model with a series of experiments performed with polyacrylamide spheres. We use the model and the experiments to study the complex internal dynamics of swelling and drying, and to highlight the fundamentally transient nature of these strikingly different processes. Although we assume spherical symmetry, the model also provides insight into the transient patterns that form and then vanish during swelling as well as the risk of fracture during drying.

- Protocol dependence of the jamming transition
**T. Bertrand**, R. P. Behringer, B. Chakraborty, C. S. O’Hern, and M. D. Shattuck*Phys. Rev. E*,**93**, 012901 (2016)We propose a theoretical framework for predicting the protocol dependence of the jamming transition for frictionless spherical particles that interact via repulsive contact forces. We study isostatic jammed disk packings obtained via two protocols: isotropic compression and simple shear. We show that for frictionless systems, all jammed packings can be obtained via either protocol. However, the probability to obtain a particular jammed packing depends on the packing-generation protocol. We predict the average shear strain required to jam initially unjammed isotropically compressed packings from the density of jammed packings, shape of their basins of attraction, and path traversed in configuration space. We compare our predictions to simulations of shear strain-induced jamming and find quantitative agreement. We also show that the packing fraction range, over which shear strain-induced jamming occurs, tends to zero in the large system limit for frictionless packings with overdamped dynamics.

## 2015

- Musical Acoustics & Instrument Design: when Engineering meets Music
**T. Bertrand**, K. Kaczmarek, and L. Wilen*In Proceedings of the 41st International Computer Music Conference (ICMC)*(2015)This paper documents an instrument-building course co- developed by the School of Engineering and Applied Science and the Department of Music at Yale University. The course focuses on the fundamentals of musical acoustics, electronic sound production, and instrument design through traditional lecture-based learning as well as a hands-on experimentation and building. The structure of the course, the primary pedagogical objectives, the facilities, and examples of final projects realized by the students are discussed.

## 2014

- Hypocoordinated solids in particulate media
**T. Bertrand**, C. F. Schreck, C. S. O’Hern, and M. D. Shattuck*Phys. Rev. E*,**89**, 062203 (2014)We propose a “phase diagram” for particulate systems with purely repulsive contact forces, such as granular media and colloids. We characterize two classes of behavior as a function of the input kinetic energy per degree of freedom T0 and packing fraction deviation from jamming onset Δϕ=ϕ−ϕJ using simulations of frictionless disks. Isocoordinated solids (ICS) exist above jamming; they possess an average contact number equal to the isostatic value ziso. ICS display “strict” harmonic response, where the density of vibrational modes from the Fourier transform of the velocity autocorrelation function is a set of sharp peaks at eigenfrequencies ωdk of the dynamical matrix. In contrast, hypocoordinated solids (HCS) occur above and below jamming and possess fluctuating networks of interparticle contacts but do not undergo cage-breaking particle rearrangements. The density of vibrational frequencies for the HCS is not a collection of sharp peaks at ωdk, but it does possess a common form over a range of Δϕ and T0.

## 2013

- Particles accelerate the detachment of viscous liquidsM. S. Deen,
**T. Bertrand**, N. Vu, D. Quéré, E. Clément, and A. Lindner*Rheologica Acta*,**52**, 403–412 (2013)During detachment of a viscous fluid extruded from a nozzle, a filament linking the droplet to the latter is formed. Under the effect of surface tension, the filament thins until pinch-off and final detachment of the droplet. In this paper, we study the effect of the presence of individual particles trapped in the filament on the detachment dynamics using granular suspensions of small volume fractions (ϕ\thinspace<\thinspace6 %). We show that even a single particle strongly modifies the detachment dynamics. The particle perturbs the thinning of the thread, and a large droplet of fluid around the particle is formed. This perturbation leads to an acceleration of the detachment of the droplet compared to the detachment observed for a pure fluid. We quantify this acceleration for single particles of different sizes and link it to similar observations for suspensions of small volume fractions. Our study also gives more insight into particulate effects on detachment of denser suspensions and allows to explain the accelerated detachment close to final pinch-off observed previously (Bonnoit et al. Phys Fluids 24(4):043304, 2012).

## 2012

- Accelerated drop detachment in granular suspensionsC. Bonnoit*,
**T. Bertrand***, Eric Clément, and Anke Lindner*Physics of Fluids*,**24**, 043304 (2012)We experimentally study the detachment of drops of granular suspensions using a density matched model suspension with varying grain volume fraction (ϕ = 15% to 55%) and grain diameter (d = 20 μm to 140 μm). We show that at the beginning of the detachment process, the suspensions behave as an effective fluid. The detachment dynamics in this regime can be entirely described by the shear viscosity of the suspension [R. J. Furbank and J. F. Morris, Int. J. Multiphase Flow 33(4), 448–468 (2007)]. At later stages of the detachment, the dynamics become independent of the volume fraction and are found to be identical to the dynamics of the interstitial fluid. Surprisingly, visual observation reveals that at this stage, particles are still present in the neck. We suspect rearrangements of particles to locally free the neck of grains, causing the observed dynamics. Close to the final pinch off, the detachment of the suspensions is further accelerated, compared to the dynamics of pure interstitial fluid. This acceleration might be due to the fact that the neck diameter gets of the order of magnitude of the size of the grains and a continuous thinning of the liquid thread is not possible any more. The crossover between the different detachment regimes is a function of the grain size and the initial volume fraction. We characterize the overall acceleration as a function of the grain size and volume fraction.

- Dynamics of drop formation in granular suspensions: the role of volume fraction
**T. Bertrand**, C. Bonnoit, E. Clément, and A. Lindner*Granular Matter*,**14**, 169–174 (2012)The presence of grains strongly modifies the detachment of drops of a viscous liquid. We have shown previously that the detachment of drops of granular suspensions takes place via different regimes (Bonnoit et al. submitted, 2011). Here we study the influence of the volume fraction of particles on the formation and shape of the droplets by means of visual observations. We measure the minimal neck diameter as well as the height of the detachment as a function of time to quantify the evolution of the drop shape. We also address the question of the thinning dynamics of the neck in the different regimes. Linking the dynamics to the properties of the effective fluid or to rearrangements of individual grains in the thread gives insights in the origin of the different regimes.

## 2011

- Repulsive Contact Interactions Make Jammed Particulate Systems Inherently NonharmonicC. F. Schreck,
**T. Bertrand**, C. S. O’Hern, and M. D. Shattuck*Phys. Rev. Lett.*,**107**, 078301 (2011)Many jammed particulate systems, such as granular and colloidal materials, interact via repulsive contact forces. We find that these systems possess no harmonic regime in the large system limit (N \to ∞) for all compressions ∆φstudied, and at jamming onset ∆φ\to 0 for all N. We perform fixed energy simulations following perturbations with amplitude δalong eigendirections of the dynamical matrix. The fluctuations abruptly spread to all modes for δ≈\delta_c (where a single contact breaks) in contrast to linear and weakly nonlinear behavior. For δ>\delta_c, all discrete modes disappear into a continuous frequency band. ⟨\delta_c ⟩scales with 1/N and ∆φ$, which limits harmonic behavior to only overcompressed systems. The density of vibrational modes deviates strongly from that predicted from the dynamical matrix when the system enters the nonharmonic regime, which significantly affects its mechanical and transport properties.