Personne : Dubé, Louis J.
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Université Laval. Département de physique, de génie physique et d'optique
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- PublicationAccès libreMaster equation analysis of mesoscopic localization in contagion dynamics on higher-order networks(American Physical Society through the American Institute of Physics, 2021-03-01) Hébert-Dufresne, Laurent; Allard, Antoine; St-Onge, Guillaume; Dubé, Louis J.; Thibeault, VincentSimple models of infectious diseases tend to assume random mixing of individuals, but real interactions are not random pairwise encounters: they occur within various types of gatherings such as workplaces, households, schools, and concerts, best described by a higher-order network structure. We model contagions on higher-order networks using group-based approximate master equations, in which we track all states and interactions within a group of nodes and assume a mean-field coupling between them. Using the susceptible-infected-susceptible dynamics, our approach reveals the existence of a mesoscopic localization regime, where a disease can concentrate and self-sustain only around large groups in the network overall organization. In this regime, the phase transition is smeared, characterized by an inhomogeneous activation of the groups. At the mesoscopic level, we observe that the distribution of infected nodes within groups of the same size can be very dispersed, even bimodal. When considering heterogeneous networks, both at the level of nodes and at the level of groups, we characterize analytically the region associated with mesoscopic localization in the structural parameter space. We put in perspective this phenomenon with eigenvector localization and discuss how a focus on higher-order structures is needed to discern the more subtle localization at the mesoscopic level. Finally, we discuss how mesoscopic localization affects the response to structural interventions and how this framework could provide important insights for a broad range of dynamics.
- PublicationAccès libreSocial confinement and mesoscopic localization of epidemics on networks(American Physical Society, 2021-03-01) Hébert-Dufresne, Laurent; Allard, Antoine; St-Onge, Guillaume; Dubé, Louis J.; Thibeault, VincentRecommendations around epidemics tend to focus on individual behaviors, with much less efforts attempting to guide event cancellations and other collective behaviors since most models lack the higher-order structure necessary to describe large gatherings. Through a higher-order description of contagions on networks, we model the impact of a blanket cancellation of events larger than a critical size and find that epidemics can suddenly collapse when interventions operate over groups of individuals rather than at the level of individuals. We relate this phenomenon to the onset of mesoscopic localization, where contagions concentrate around dominant groups.
- PublicationAccès libreDynamical rate equation model for femtosecond laser-induced breakdown in dielectrics(2021-07-06) Varin, Charles; Déziel, Jean-Luc; Dubé, Louis J.Experimental and theoretical studies of laser-induced breakdown in dielectrics provide conflicting conclusions about the possibility to trigger ionization avalanche on the subpicosecond time scale and the relative importance of carrier-impact ionization over field ionization. On the one hand, current models based on a single ionization-rate equation do not account for the gradual heating of the charge carriers, which, for short laser pulses, might not be sufficient to start an avalanche. On the other hand, kinetic models based on microscopic collision probabilities have led to variable outcomes that do not necessarily match experimental observations as a whole. In this paper, we present a rate-equation model that accounts for the avalanche process phenomenologically by using an auxiliary differential equation to track the gradual heating of the charge carriers and define the collisional impact rate dynamically. The computational simplicity of this dynamical rate-equation model offers the flexibility to extract effective values from experimental data. This is demonstrated by matching the experimental scaling trends for the laser-induced damage threshold of several dielectric materials for pulse durations ranging from a few fs to a few ps. Through numerical analysis, we show that the proposed model gives results comparable to those obtained with multiple rate equations and identify potential advantages for the development of large-scale, three-dimensional electromagnetic methods for the modeling of laser-induced breakdown in transparent media.
- PublicationAccès libreThreefold way to the dimension reduction of dynamics on networks : an application to synchronization(American Physical Society, 2020-11-11) Thibeault, Vincent; Desrosiers, Patrick; St-Onge, Guillaume; Dubé, Louis J.Several complex systems can be modeled as large networks in which the state of the nodes continuously evolves through interactions among neighboring nodes, forming a high-dimensional nonlinear dynamical system. One of the main challenges of Network science consists in predicting the impact of network topology and dynamics on the evolution of the states and, especially, on the emergence of collective phenomena, such as synchronization. We address this problem by proposing a Dynamics Approximate Reduction Technique (DART) that maps high-dimensional (complete) dynamics unto low-dimensional (reduced) dynamics while preserving the most salient features, both topological and dynamical, of the original system. DART generalizes recent approaches for dimension reduction by allowing the treatment of complex-valued dynamical variables, heterogeneities in the intrinsic properties of the nodes as well as modular networks with strongly interacting communities. Most importantly, we identify three major reduction procedures whose relative accuracy depends on whether the evolution of the states is mainly determined by the intrinsic dynamics, the degree sequence, or the adjacency matrix. We use phase synchronization of oscillator networks as a benchmark for our threefold method. We successfully predict the synchronization curves for three phase dynamics (Winfree, Kuramoto, theta) on the stochastic block model. Moreover, we obtain the bifurcations of the Kuramoto-Sakaguchi model on the mean stochastic block model with asymmetric blocks and we show numerically the existence of periphery chimera state on the two-star graph. This allows us to highlight the critical role played by the asymmetry of community sizes on the existence of chimera states. Finally, we systematically recover well-known analytical results on explosive synchronization by using DART for the Kuramoto-Sakaguchi model on the star graph. Our work provides a unifying framework for studying a vast class of dynamical systems on networks.