Personne :
Dubé, Louis J.

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Date de naissance
Projets de recherche
Structures organisationnelles
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Louis J.
Université Laval. Département de physique, de génie physique et d'optique
Identifiant Canadiana

Résultats de recherche

Voici les éléments 1 - 10 sur 66
  • Publication
    Accès libre
    Targeting unknown and unstable periodic orbits
    (American Institute of Physics, 2002-03-07) Dubé, Louis J.; Doyon, Bernard
    We present a method to target and subsequently control (if necessary) orbits of specified period but otherwise unknown stability and position. For complex systems where the dynamics is often mixed [e.g., coexistence of regular and chaotic regions in area-preserving (Hamiltonian) systems], this targeting algorithm offers a way to not only gently bring the system from the chaotic domain to an unstable periodic orbit (where control is applied), but also to access stable regions of phase space (where control is not necessary) from within the stochastic regions. The technique is quite general and applies equally well to dissipative or conservative discrete maps and continuous flows.
  • Publication
    Accès libre
    Light-induced chaotic rotations in nematic liquid crystals
    (American Physical Society through the American Institute of Physics, 2006-02-23) Brasselet, Étienne.; Dubé, Louis J.
    Various nonlinear rotation regimes are observed in an optically excited nematic liquid-crystal film under boundary conditions for the light and material that are invariant by rotation. The excitation light is circularly polarized, the intensity profile is circularly symmetric, and the beam diameter at the sample location is a few times smaller than the cell thickness. A transition to chaos via quasiperiodicity is identified when the light intensity is taken as the control parameter. Transverse nonlocal effects are suggested to be the cause of the observed dynamics, and a simple model consisting of a collection of coupled rotators is developed to provide a qualitative explanation.
  • Publication
    Accès libre
    Structural preferential aAttachment : network organization beyond the link
    (American Physical Society, 2011-10-06) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.
    We introduce a mechanism which models the emergence of the universal properties of complex networks, such as scale independence, modularity and self-similarity, and unifies them under a scale-free organization beyond the link. This brings a new perspective on network organization where communities, instead of links, are the fundamental building blocks of complex systems. We show how our simple model can reproduce social and information networks by predicting their community structure and more importantly, how their nodes or communities are interconnected, often in a self-similar manner.
  • Publication
    Accès libre
    Time evolution of epidemic disease on finite and infinite networks
    (American Physical Society through the American Institute of Physics, 2009-02-02) Noël, Pierre-André; Davoud, Bahman; Dubé, Louis J.; Brunham, Robert C.; Pourbohloul, Babak
    Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the expense of simplifying the pattern of transmission. The second approach uses network theory to incorporate detailed information pertaining to the underlying contact structure among individuals while disregarding the progression of time during outbreaks. So far, the only alternative that enables the integration of both aspects of disease propagation simultaneously while preserving the variety of outcomes has been to abandon the analytical approach and rely on computer simulations. We offer an analytical framework, that incorporates both the complexity of contact network structure and the time progression of disease spread. Furthermore, we demonstrate that this framework is equally effective on finite- and “infinite”-size networks. This formalism can be equally applied to similar percolation phenomena on networks in other areas of science and technology.
  • Publication
    Accès libre
    Spectral dimension reduction of complex dynamical networks
    (American Physical Society, 2019-03-04) Laurence, Edward; Dubé, Louis J.; Doyon, Nicolas; Desrosiers, Patrick
    Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve (nodes’ dynamics). Despite substantial progress, little is known about why some subtle changes in the network structure, at the so-called critical points, can provoke drastic shifts in its dynamics. We tackle this challenging problem by introducing a method that reduces any network to a simplified low-dimensional version. It can then be used to describe the collective dynamics of the original system. This dimension reduction method relies on spectral graph theory and, more specifically, on the dominant eigenvalues and eigenvectors of the network adjacency matrix. Contrary to previous approaches, our method is able to predict the multiple activation of modular networks as well as the critical points of random networks with arbitrary degree distributions. Our results are of both fundamental and practical interest, as they offer a novel framework to relate the structure of networks to their dynamics and to study the resilience of complex systems.
  • Publication
    Lorenz-Mie theory for 2D scattering and resonance calculations
    (Bristol Institute of Physics Publishing, 2015-09-22) Gagnon, Denis; Dubé, Louis J.
    This PhD tutorial is concerned with a description of the two-dimensional generalized Lorenz–Mie theory (2D-GLMT), a well-established numerical method used to compute the interaction of light with arrays of cylindrical scatterers. This theory is based on the method of separation of variables and the application of an addition theorem for cylindrical functions. The purpose of this tutorial is to assemble the practical tools necessary to implement the 2D-GLMT method for the computation of scattering by passive scatterers or of resonances in optically active media. The first part contains a derivation of the vector and scalar Helmholtz equations for 2D geometries, starting from Maxwell's equations. Optically active media are included in 2D-GLMT using a recent stationary formulation of the Maxwell–Bloch equations called steady-state ab initio laser theory (SALT), which introduces new classes of solutions useful for resonance computations. Following these preliminaries, a detailed description of 2D-GLMT is presented. The emphasis is placed on the derivation of beam-shape coefficients for scattering computations, as well as the computation of resonant modes using a combination of 2D-GLMT and SALT. The final section contains several numerical examples illustrating the full potential of 2D-GLMT for scattering and resonance computations. These examples, drawn from the literature, include the design of integrated polarization filters and the computation of optical modes of photonic crystal cavities and random lasers
  • Publication
    Accès libre
    Finite-size analysis of the detectability limit of the stochastic block model
    (American Physical Society, 2017-06-19) Young, Jean-Gabriel; Hébert-Dufresne, Laurent; Laurence, Edward; Dubé, Louis J.; Desrosiers, Patrick
    It has been shown in recent years that the stochastic block model is sometimes undetectable in the sparse limit, i.e., that no algorithm can identify a partition correlated with the partition used to generate an instance, if the instance is sparse enough and infinitely large. In this contribution, we treat the finite case explicitly, using arguments drawn from information theory and statistics. We give a necessary condition for finite-size detectability in the general SBM. We then distinguish the concept of average detectability from the concept of instance-by-instance detectability and give explicit formulas for both definitions. Using these formulas, we prove that there exist large equivalence classes of parameters, where widely different network ensembles are equally detectable with respect to our definitions of detectability. In an extensive case study, we investigate the finite-size detectability of a simplified variant of the SBM, which encompasses a number of important models as special cases. These models include the symmetric SBM, the planted coloring model, and more exotic SBMs not previously studied. We conclude with three appendices, where we study the interplay of noise and detectability, establish a connection between our information-theoretic approach and random matrix theory, and provide proofs of some of the more technical results.
  • Publication
    Accès libre
    Geometric evolution of complex networks with degree correlations
    (American Physical Society, 2018-03-19) Allard, Antoine; St-Onge, Guillaume; Laurence, Edward; Dubé, Louis J.; Murphy, Charles
    We present a general class of geometric network growth mechanisms by homogeneous attachment in which the links created at a given time t are distributed homogeneously between a new node and the existing nodes selected uniformly. This is achieved by creating links between nodes uniformly distributed in a homogeneous metric space according to a Fermi-Dirac connection probability with inverse temperature β and general time-dependent chemical potential μ(t). The chemical potential limits the spatial extent of newly created links. Using a hidden variable framework, we obtain an analytical expression for the degree sequence and show that μ(t) can be fixed to yield any given degree distributions, including a scale-free degree distribution. Additionally, we find that depending on the order in which nodes appear in the network—its history—the degree-degree correlations can be tuned to be assortative or disassortative. The effect of the geometry on the structure is investigated through the average clustering coefficient ⟨c⟩. In the thermodynamic limit, we identify a phase transition between a random regime where ⟨c⟩→ 0 when β<βc and a geometric regime where ⟨c⟩ > 0 when β>βc.
  • Publication
    Accès libre
    Threefold 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.
  • Publication
    Bifurcation analysis of optically induced dynamics in nematic liquid crystals : circular polarization at normal incidence
    (Optical Society of America, 2005-08-01) Brasselet, Étienne.; Galstian, Tigran; Dubé, Louis J.; Dmitry, Krimer; Kramer, Lorenz
    We present a detailed bifurcation analysis of the nonlinear reorientation dynamics of a homeotropically aligned nematic liquid-crystal film excited by an elliptically polarized beam at normal incidence with the intensity and the polarization state of light as the control parameters. The asymmetry arising from the elliptical polarization of the excitation lightwave is shown to affect dramatically the dynamics, and various new dynamical behaviors are reported: (i) quasi-periodic rotations for almost circular polarization; (ii) a discontinuous transition, identified as a homoclinic bifurcation, to a largely reoriented state over a large range of ellipticity values; (iii) oscillations associated with large reorientation; and (iv) optical multistability between several distinct dynamical regimes.