arXiv subjects

Alexandre Nicolas

Publications and source records attributed to Alexandre Nicolas.

46 records · Page 3Linked to original sources

arXiv2016

Statistical fluctuations in pedestrian evacuation times and the effect of social contagion

Mathematical models of pedestrian evacuation and the associated simulation software have become essential tools for the assessment of the safety of public facilities and buildings. While a variety of models are now available, their calibration and test against empirical data are generally restricted to global, averaged quantities, the statistics compiled from the time series of individual escapes (" microscopic " statistics) measured in recent experiments are thus overlooked. In the same spirit, much research has primarily focused on the average global evacuation time, whereas the whole distribution of evacuation times over some set of realizations should matter. In the present paper we propose and discuss the validity of a simple relation between this distribution and the " microscopic " statistics, which is theoretically valid in the absence of correlations. To this purpose, we develop a minimal cellular automaton, with novel features that afford a semi-quantitative reproduction of the experimental " microscopic " statistics. We then introduce a process of social contagion of impatient behavior in the model and show that the simple relation under test may dramatically fail at high contagion strengths, the latter being responsible for the emergence of strong correlations in the system. We conclude with comments on the potential practical relevance for safety science of calculations based on " microscopic " statistics.

nlin.CG↗

arXiv2016

Effects of inertia on the steady-shear rheology of disordered solids

We study the finite-shear-rate rheology of disordered solids by means of molecular dynamics simulations in two dimensions. By systematically varying the damping magnitude $ζ$ in the low-temperature limit, we identify two well defined flow regimes, separated by a thin (temperature-dependent) crossover region. In the overdamped regime, the athermal rheology is governed by the competition between elastic forces and viscous forces, whose ratio gives the Weissenberg number $Wi= ζ\dotγ$ (up to elastic parameters); the macroscopic stress $Σ$ follows the frequently encountered Herschel-Bulkley law $Σ= Σ\_0 + k \sqrt{Wi}$, with yield stress $Σ\_0\textgreater{}0$. In the underdamped (inertial) regime, dramatic changes in the rheology are observed for low damping: the flow curve becomes non-monotonic. This change is not caused by longer-lived correlations in the particle dynamics at lower damping; instead, for weak dissipation, the sample heats up considerably due to, and in proportion to, the driving. By suitably thermostatting more or less underdamped systems, we show that their rheology only depends on their kinetic temperature and the shear rate, rescaled with Einstein's vibration frequency.

cond-mat.soft↗

arXiv2015

Shear-thinning in dense colloidal suspensions and its effect on elastic instabilities: from the microscopic equations of motion to an approximation of the macroscopic rheology

In the vicinity of their glass transition, dense colloidal suspensions acquire elastic properties over experimental timescales. We investigate the possibility of a visco-elastic flow instability in curved geometry for such materials. To this end, we first present a general strategy extending a first-principles approach based on projections onto slow variables (so far restricted to strictly homogeneous flow) in order to handle inhomogeneities. In particular, we separate the advection of the microstructure by the flow, at the origin of a fluctuation advection term, from the intrinsic dynamics. On account of the complexity of the involved equations, we then opt for a drastic simplification of the theory, in order to establish its potential to describe instabilities. These very strong approximations lead to a constitutive equation of the White-Metzner class, whose parameters are fitted with experimental measurements of the macroscopic rheology of a glass-forming colloidal dispersion. The model properly accounts for the shear-thinning properties of the dispersions, but, owing to the approximations, the description is not fully quantitative. Finally, we perform a linear stability analysis of the flow in the experimentally relevant cylindrical (Taylor-Couette) geometry and provide evidence that shear-thinning strongly stabilises the flow, which can explain why visco-elastic instabilities are not observed in dense colloidal suspensions.

cond-mat.soft↗

arXiv2015

Elastic consequences of a single plastic event: towards a realistic account of structural disorder and shear wave propagation in models of flowing amorphous solids

Shear transformations (i.e., localised rearrangements of particles resulting in the shear deformation of a small region of the sample) are the building blocks of mesoscale models for the flow of disordered solids. In order to compute the time-dependent response of the solid material to such a shear transformation, with a proper account of elastic heterogeneity and shear wave propagation, we propose and implement a very simple Finite-Element (FE) -based method. Molecular Dynamics (MD) simulations of a binary Lennard-Jones glass are used as a benchmark for comparison, and information about the microscopic viscosity and the local elastic constants is directly extracted from the MD system and used as input in FE. We find very good agreement between FE and MD regarding the temporal evolution of the disorder-averaged displacement field induced by a shear transformation, which turns out to coincide with the response of a uniform elastic medium. However, fluctuations are relatively large, and their magnitude is satisfactorily captured by the FE simulations of an elastically heterogeneous system. Besides, accounting for elastic anisotropy on the mesoscale is not crucial in this respect. The proposed method thus paves the way for models of the rheology of amorphous solids which are both computationally efficient and realistic, in that structural disorder and inertial effects are accounted for.

cond-mat.soft↗

arXiv2014

Rheology of athermal amorphous solids: Revisiting simplified scenarios and the concept of mechanical noise temperature

We study the rheology of amorphous solids in the limit of negligible thermal fluctuations. On the basis of general arguments, the flow curve is shown to result from an interplay between the time scales of the macroscopic driving and the (cascades of) local particle rearrangements. Such rearrangements are known to induce a redistribution of the elastic stress in the system. Although mechanical noise, i.e., the local stress fluctuations arising from this redistribution, is widely believed to activate new particle rearrangements, we provide evidence that casts severe doubt on the analogy with thermal fluctuations: mechanical and thermal fluctuations lead to asymptotically different statistics for barrier crossing. These ideas are illustrated and supported by a simple coarse-grained model whose ingredients are directly connected with the physical processes relevant for the flow.

cond-mat.soft↗

arXiv2014

Universal and non-universal features in coarse-grained models of flow in disordered solids

We study the two-dimensional (2D) shear flow of amorphous solids within variants of an elastoplastic model, paying particular attention to spatial correlations and time fluctuations of, e.g., local stresses. The model is based on the local alternation between an elastic regime and plastic events during which the local stress is redistributed. The importance of a fully tensorial description of the stress and of the inclusion of (coarse-grained) convection in the model is investigated; scalar and tensorial models yield very similar results, while convection enhances fluctuations and breaks the spurious symmetry between the flow and velocity gradient directions, for instance when shear localisation is observed. Besides, correlation lengths measured with diverse protocols are discussed. One class of such correlation lengths simply scale with the spacing between homogeneously distributed, simultaneous plastic events. This leads to a scaling of the correlation length with the shear rate as $\dotγ^{\frac{-1}{2}}$ in 2D in the athermal regime, regardless of the details of the model. The radius of the cooperative disk, defined as the near-field region in which plastic events induce a stress redistribution that is not amenable to a mean-field treatment, notably follows this scaling. On the other hand, the cooperative volume measured from the four-point stress susceptibility and its dependence on the system size and the shear rate are model-dependent.

cond-mat.soft↗

arXiv2014

Spatiotemporal correlations between plastic events in the shear flow of athermal amorphous solids

The slow flow of amorphous solids exhibits striking heterogeneities: swift localised particle rearrangements take place in the midst of a more or less homogeneously deforming medium. Recently, experimental as well as numerical work has revealed spatial correlations between these flow heterogeneities. Here, we use molecular dynamics (MD) simulations to characterise the rearrangements and systematically probe their correlations both in time and in space. In particular, these correlations display a four-fold azimuthal symmetry characteristic of shear stress redistribution in an elastic medium and we unambiguously detect their increase in range with time. With increasing shear rate, correlations become shorter-ranged and more isotropic. In addition, we study a coarse-grained model motivated by the observed flow characteristics and challenge its predictions directly with the MD simulations. While the model captures both macroscopic and local properties rather satisfactorily, the agreement with respect to the spatiotemporal correlations is at most qualitative. The discrepancies provide important insight into relevant physics that is missing in all related coarse-grained models that have been developed for the flow of amorphous materials so far, namely the finite shear wave velocity and the impact of elastic heterogeneities on stress redistribution.

cond-mat.soft↗

arXiv2013

A mesoscopic model for the rheology of soft amorphous solids, with application to mi- crochannel flows

We study a mesoscopic model for the flow of amorphous solids. The model is based on the key features identified at the microscopic level, namely peri- ods of elastic deformation interspersed with localised rearrangements of parti- cles that induce long-range elastic deformation. These long-range deformations are derived following a continuum mechanics approach, in the presence of solid boundaries, and are included in full in the model. Indeed, they mediate spatial cooperativity in the flow, whereby a localised rearrangement may lead a distant region to yield. In particular, we simulate a channel flow and find manifestations of spatial cooperativity that are consistent with published experimental obser- vations for concentrated emulsions in microchannels. Two categories of effects are distinguished. On the one hand, the coupling of regions subject to different shear rates, for instance,leads to finite shear rate fluctuations in the seemingly un- sheared "plug" in the centre of the channel. On the other hand, there is convinc- ing experimental evidence of a specific rheology near rough walls. We discuss diverse possible physical origins for this effect, and we suggest that it may be associated with the bumps of particles into surface asperities as they slide along the wall.

cond-mat.mtrl-sci↗

arXiv2013

Spatial cooperativity in microchannel flows of soft jammed materials: A mesoscopic approach

The flow of amorphous solids results from a combination of elastic deformation and local structural rearrangements, which induce non-local elastic deformations. These elements are incorporated into a mechanically-consistent mesoscopic model of interacting elastoplastic blocks. We investigate the specific case of channel flow with numerical simulations, paying particular attention to situations of strong confinement. We find that the simple picture of plastic events embedded in an elastic matrix successfully accounts for manifestations of spatial cooperativity. Shear rate fluctuations are observed in seemingly quiescent regions, and the velocity profiles in confined flows at high applied pressure deviate from those expected in the absence of non-local effects, in agreement with experimental data. However, we suggest a different physical origin for the large deviations observed when walls have rough surfaces, associated with "bumps" of the particles against the asperities of the walls.

cond-mat.soft↗

arXiv2012

Non-axisymmetric instability of shear-banded Taylor-Couette flow

Recent experiments show that shear-banded flows of semi-dilute worm-like micelles in Taylor-Couette geometry exhibit a flow instability in the form of Taylor-like vortices. Here we perform the non-axisymmetric linear stability analysis of the diffusive Johnson-Segalman model of shear banding and show that the nature of this instability depends on the applied shear rate. For the experimentally relevant parameters, we find that at the beginning of the stress plateau the instability is driven by the interface between the bands, while most of the stress plateau is occupied by the bulk instability of the high-shear-rate band. Our work significantly alters the recently proposed stability diagram of shear-banded flows based on axisymmetric analysis.

cond-mat.soft↗