Electron acceleration in vacuum by ultrashort and tightly focused radially polarized laser pulses

Exact closed-form solutions to Maxwell's equations are used to investigate electron acceleration driven by radially polarized laser beams in the nonparaxial and ultrashort pulse regime. Besides allowing for higher energy gains, such beams could generate synchronized counterpropagating electron bunches.Comment: 3 pages, 3 figures. To appear in the proceedings of the Ultrafast Phenomena XVIII conferenc

Exact solution of bond percolation on small arbitrary graphs

We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution of the node partitions (i.e., the constrained distribution of the size of each component) in undirected graphs. Besides opening the way to the theoretical prediction of percolation on arbitrary graphs of large but finite size, we show how our results find application in graph theory, epidemiology, percolation and fragmentation theory.Comment: 5 pages and 3 figure

Adaptive networks: coevolution of disease and topology

Adaptive networks have been recently introduced in the context of disease propagation on complex networks. They account for the mutual interaction between the network topology and the states of the nodes. Until now, existing models have been analyzed using low-complexity analytic formalisms, revealing nevertheless some novel dynamical features. However, current methods have failed to reproduce with accuracy the simultaneous time evolution of the disease and the underlying network topology. In the framework of the adaptive SIS model of Gross et al. [Phys. Rev. Lett. 96, 208701 (2006)], we introduce an improved compartmental formalism able to handle this coevolutionary task successfully. With this approach, we analyze the interplay and outcomes of both dynamical elements, process and structure, on adaptive networks featuring different degree distributions at the initial stage.Comment: 11 pages, 8 figures, 1 appendix. To be published in Physical Review

Accélération d'électrons à l'aide d'impulsions laser ultrabrèves et fortement focalisées

Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2015-2016Lorsque fortement focalisées, les impulsions laser de haute puissance génèrent des champs électromagnétiques d’amplitude gigantesque. Ces derniers peuvent être mis à profit pour accélérer des électrons à une grande énergie sur une très courte distance. Les progrès récents dans le domaine des lasers de haute puissance laissent ainsi entrevoir des perspectives excitantes dans le développement d’une nouvelle génération d’accélérateurs laser qui seraient beaucoup plus compacts et moins dispendieux que les accélérateurs d’électrons conventionnels. Parmi les différents schémas d’accélération laser proposés, l’utilisation d’impulsions laser de polarisation radiale s’avère prometteuse. Cette méthode tire profit de la composante longitudinale du champ électrique au centre d’un faisceau laser de type TM01 afin d’accélérer des électrons le long de l’axe optique. L’objectif spécifique du projet de doctorat présenté dans cette thèse est d’étudier l’accélération d’électrons par impulsions TM01 dans le régime des impulsions ultrabrèves et fortement focalisées. Dans ces conditions extrêmes, les impulsions laser doivent impérativement être modélisées à l’aide de solutions exactes aux équations de Maxwell. Nous présentons d’abord une technique permettant d’obtenir une solution exacte sous forme fermée aux équations de Maxwell pour décrire le champ électromagnétique de l’impulsion TM01. Cette solution exacte nous permet de modéliser rigoureusement la dynamique en régime d’impulsions ultrabrèves et fortement focalisées et d’en faire ressortir les caractéristiques intéressantes. Il est également mis en évidence qu’une solution exacte pour le champ électromagnétique n’est pas seulement utile en régime non paraxial, mais qu’elle est également nécessaire pour modéliser correctement la dynamique dans des conditions de faible focalisation. Une partie de cette thèse s’intéresse finalement à une application intéressante de l’accélération par impulsions TM01 ultrabrèves et fortement focalisées, soit la production d’impulsions ultrabrèves d’électrons sous-relativistes. À l’aide de simulations particle-in-cell, nous démontrons la possibilité d’accélérer des impulsions d’électrons d’une durée de l’ordre de la femtoseconde à quelques centaines de keV d’énergie lorsqu’une impulsion TM01 de quelques centaines de gigawatts est focalisée dans un gaz de faible densité. Étant situées dans la fenêtre énergétique adéquate, ces impulsions d’électrons pourraient permettre d’améliorer significativement la résolution temporelle dans les expériences d’imagerie atomique et moléculaire par diffraction électronique ultrarapide.When focused on a tiny spot, high-power laser pulses generate gigantic electromagnetic fields. Under these strong field conditions, charged particles can be accelerated up to high energies over short distances. Recent advances in high-power laser technology hint at exciting new possibilities in the development of a new generation of laser-driven electron accelerators that are expected to offer a robust, compact, and low-cost alternative to conventional linear accelerators. Among the many proposed laser-driven acceleration schemes, the use of radially polarized laser pulses is very promising. In this method, the electrons are accelerated along the optical axis by the strong longitudinal electric field component at the center of a TM01 beam. The main objective of this thesis is to investigate electron acceleration driven by TM01 pulses under ultrashort pulse and strong focusing conditions. In this nonparaxial and ultrashort pulse regime, the laser pulses must be rigorously modeled as exact solutions to Maxwell’s equations. We first present the tools that are used to obtain an exact closed-form solution to Maxwell’s equations for a TM01 pulse. This exact solution allows us to accurately model the acceleration process and to highlight several interesting properties of the dynamics in the nonparaxial and ultrashort pulse regime. It is also shown that an exact solution is not only useful to investigate electron acceleration under nonparaxial conditions, but also necessary to correctly describe the dynamics in the weak focusing limit. A part of this thesis is also concerned with an interesting property of the acceleration driven by ultrashort and tightly focused TM01 pulses, namely the generation of ultrashort bunches of subrelativistic electrons. Using particle-in-cell simulations, we demonstrate the possibility of generating one-femtosecond electron pulses at few-hundred-keV energies when a few-hundred-GW TM01 pulse is tightly focused in a low-density gas. Since they are located in the appropriate energy window, these electron pulses could potentially lead to a significant improvement in the time resolution of atomic and molecular imaging experiments based on ultrafast electron diffraction

Swarm behavior of self-propelled rods and swimming flagella

Systems of self-propelled particles are known for their tendency to aggregate and to display swarm behavior. We investigate two model systems, self-propelled rods interacting via volume exclusion, and sinusoidally-beating flagella embedded in a fluid with hydrodynamic interactions. In the flagella system, beating frequencies are Gaussian distributed with a non-zero average. These systems are studied by Brownian-dynamics simulations and by mesoscale hydrodynamics simulations, respectively. The clustering behavior is analyzed as the particle density and the environmental or internal noise are varied. By distinguishing three types of cluster-size probability density functions, we obtain a phase diagram of different swarm behaviors. The properties of clusters, such as their configuration, lifetime and average size are analyzed. We find that the swarm behavior of the two systems, characterized by several effective power laws, is very similar. However, a more careful analysis reveals several differences. Clusters of self-propelled rods form due to partially blocked forward motion, and are therefore typically wedge-shaped. At higher rod density and low noise, a giant mobile cluster appears, in which most rods are mostly oriented towards the center. In contrast, flagella become hydrodynamically synchronized and attract each other; their clusters are therefore more elongated. Furthermore, the lifetime of flagella clusters decays more quickly with cluster size than of rod clusters

Modeling the dynamical interaction between epidemics on overlay networks

Epidemics seldom occur as isolated phenomena. Typically, two or more viral agents spread within the same host population and may interact dynamically with each other. We present a general model where two viral agents interact via an immunity mechanism as they propagate simultaneously on two networks connecting the same set of nodes. Exploiting a correspondence between the propagation dynamics and a dynamical process performing progressive network generation, we develop an analytic approach that accurately captures the dynamical interaction between epidemics on overlay networks. The formalism allows for overlay networks with arbitrary joint degree distribution and overlap. To illustrate the versatility of our approach, we consider a hypothetical delayed intervention scenario in which an immunizing agent is disseminated in a host population to hinder the propagation of an undesirable agent (e.g. the spread of preventive information in the context of an emerging infectious disease).Comment: Accepted for publication in Phys. Rev. E. 15 pages, 7 figure