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Ce livre propose une étude des façons de mesurer, des unités, de la structure des systèmes d’unités et de leur histoire, afin de permettre une compréhension fine de ce qu’est « faire de la physique ».La première partie est une courte introduction à l’épistémologie de la physique.La seconde explique comment définir une unité et décrit les unités du Système international, en alternant entre éléments historiques et avancées récentes, avec l’importante réforme de 2019.La troisième partie pousse au bout l’étude de la structure d’un système d’unités et décortique ce qu’est une mesure.La quatrième retrace l’histoire des notions d’unité, de dimension, d’homogénéité et de grandeur physique, depuis les Grecs jusqu’à aujourd’hui.

Several attacks based on fault injection have been presented against the AES algorithm. Most of these attacks belong to the class of Differential Fault Analysis. Every attack relies on a specific fault model defined as hypothesis by the authors of the attack. In this paper we analyze the role of the knowledge by the attacker about such fault model on the practical effectiveness of the attacks

Magnetic reconnection is a leading mechanism for magnetic energy conversion and high-energy non-thermal particle production in a variety of high-energy astrophysical objects, including ones with relativistic ion-electron plasmas (e.g., microquasars or AGNs) - a regime where first principle studies are scarce. We present 2D particle-in-cell (PIC) simulations of low $\beta$ ion-electron plasmas under relativistic conditions, i.e., with inflow magnetic energy exceeding the plasma rest-mass energy. We identify outstanding properties: (i) For relativistic inflow magnetizations (here $10 < \sigma_e < 360$), the reconnection outflows are dominated by thermal agitation instead of bulk kinetic energy. (ii) At large inflow electron magnetization ($\sigma_e > 80$), the reconnection electric field is sustained more by bulk inertia than by thermal inertia. It challenges the thermal-inertia-paradigm and its implications. (iii) The inflows feature sharp transitions at the entrance of the diffusion zones. These are not shocks but results from particle ballistic motions, all bouncing at the same location, provided that the thermal velocity in the inflow is far smaller than the inflow E cross B bulk velocity. (iv) Island centers are magnetically isolated from the rest of the flow, and can present a density depletion at their center. (v) The reconnection rates are slightly larger than in non-relativistic studies. They are best normalized by the inflow relativistic Alfv\'en speed projected in the outflow direction, which then leads to rates in a close range (0.14-0.25) thus allowing for an easy estimation of the reconnection electric field., Comment: Submitted to A&A

Collisionless magnetic reconnection is a prime candidate to account for flare-like or steady emission, outflow launching, or plasma heating, in a variety of high-energy astrophysical objects, including ones with relativistic ion-electron plasmas. But the fate of the initial magnetic energy in a reconnection event remains poorly known: what is the amount given to kinetic energy, the ion/electron repartition, and the hardness of the particle distributions? We explore these questions with 2D particle-in-cell simulations of ion-electron plasmas. We find that 45 to 75% of the total initial magnetic energy ends up in kinetic energy, this fraction increasing with the inflow magnetization. Depending on the guide field strength, ions get from 30 to 60% of the total kinetic energy. Particles can be separated into two populations that only weakly mix: (i) particles initially in the current sheet, heated by its initial tearing and subsequent contraction of the islands; and (ii) particles from the background plasma that primarily gain energy via the reconnection electric field when passing near the X-point. Particles (ii) tend to form a power-law with an index $p=-d\log n(\gamma)/d\log\gamma$, that depends mostly on the inflow Alfv\'en speed $V_A$ and magnetization $\sigma_s$ of species $s$, with for electrons $p=5$ to $1.2$ for increasing $\sigma_e$. The highest particle Lorentz factor, for ions or electrons, increases roughly linearly with time for all the relativistic simulations. This is faster, and the spectra can be harder, than for collisionless shock acceleration. We discuss applications to microquasar and AGN coronae, to extragalactic jets, and to radio lobes. We point out situations where effects such as Compton drag or pair creation are important., Comment: 15 pages, submitted to A&A

We present first results of a long-term project which aims at multi-scale, multi-physics simulations of wind accretion in microquasars and high-mass X-ray binaries. The 3D hydrodynamical simulations cover all scales, from the circum-binary environment down to the immediate vicinity of the black hole. We first introduce the numerical method and parallelization strategy of the AMR A-MAZE code. We then discuss some preliminary results of how, and on what scales, an accretion disk is formed around the black hole. We finally present some characteristics of this disk, which is far from Keplerian. We emphasize that on all scales shocks play a decisive role for the accretion process and the process of structure formation -- for the formation of the large scale, nearly coherent structure of the disk, but also for the formation of turbulent fluctuations., Comment: Invited contribution to ASTRONUM 2013

Collisionless magnetic reconnection is a prime candidate to account for flare-like or steady emission, outflow launching, or plasma heating, in a variety of high-energy astrophysical objects, including ones with relativistic ion-electron plasmas. But the fate of the initial magnetic energy in a reconnection event remains poorly known: what is the amount given to kinetic energy, the ion/electron repartition, and the hardness of the particle distributions? We explore these questions with 2D particle-in-cell simulations of ion-electron plasmas. We find that 45 to 75% of the total initial magnetic energy ends up in kinetic energy, this fraction increasing with the inflow magnetization. Depending on the guide field strength, ions get from 30 to 60% of the total kinetic energy. Particles can be separated into two populations that only weakly mix: (i) particles initially in the current sheet, heated by its initial tearing and subsequent contraction of the islands; and (ii) particles from the background plasma that primarily gain energy via the reconnection electric field when passing near the X-point. Particles (ii) tend to form a power-law with an index $p=-d\log n(\gamma)/d\log\gamma$, that depends mostly on the inflow Alfv\'en speed $V_A$ and magnetization $\sigma_s$ of species $s$, with for electrons $p=5$ to $1.2$ for increasing $\sigma_e$. The highest particle Lorentz factor, for ions or electrons, increases roughly linearly with time for all the relativistic simulations. This is faster, and the spectra can be harder, than for collisionless shock acceleration. We discuss applications to microquasar and AGN coronae, to extragalactic jets, and to radio lobes. We point out situations where effects such as Compton drag or pair creation are important., Comment: 15 pages, submitted to A&A

We present first results of a long-term project which aims at multi-scale, multi-physics simulations of wind accretion in microquasars and high-mass X-ray binaries. The 3D hydrodynamical simulations cover all scales, from the circum-binary environment down to the immediate vicinity of the black hole. We first introduce the numerical method and parallelization strategy of the AMR A-MAZE code. We then discuss some preliminary results of how, and on what scales, an accretion disk is formed around the black hole. We finally present some characteristics of this disk, which is far from Keplerian. We emphasize that on all scales shocks play a decisive role for the accretion process and the process of structure formation -- for the formation of the large scale, nearly coherent structure of the disk, but also for the formation of turbulent fluctuations., Comment: Invited contribution to ASTRONUM 2013

Magnetic reconnection is a leading mechanism for magnetic energy conversion and high-energy non-thermal particle production in a variety of high-energy astrophysical objects, including ones with relativistic ion-electron plasmas (e.g., microquasars or AGNs) - a regime where first principle studies are scarce. We present 2D particle-in-cell (PIC) simulations of low $\beta$ ion-electron plasmas under relativistic conditions, i.e., with inflow magnetic energy exceeding the plasma rest-mass energy. We identify outstanding properties: (i) For relativistic inflow magnetizations (here $10 < \sigma_e < 360$), the reconnection outflows are dominated by thermal agitation instead of bulk kinetic energy. (ii) At large inflow electron magnetization ($\sigma_e > 80$), the reconnection electric field is sustained more by bulk inertia than by thermal inertia. It challenges the thermal-inertia-paradigm and its implications. (iii) The inflows feature sharp transitions at the entrance of the diffusion zones. These are not shocks but results from particle ballistic motions, all bouncing at the same location, provided that the thermal velocity in the inflow is far smaller than the inflow E cross B bulk velocity. (iv) Island centers are magnetically isolated from the rest of the flow, and can present a density depletion at their center. (v) The reconnection rates are slightly larger than in non-relativistic studies. They are best normalized by the inflow relativistic Alfv\'en speed projected in the outflow direction, which then leads to rates in a close range (0.14-0.25) thus allowing for an easy estimation of the reconnection electric field., Comment: Submitted to A&A

The PIC model relies on two building blocks. The first stems from the capability of computers to handle only up to $\sim10^{10}$ particles, while real plasmas contain from $10^4$ to $10^{20}$ particles per Debye sphere: a coarse-graining step must be used, whereby of the order of $p\sim10^{10}$ real particles are represented by a single computer superparticle. The second is field storage on a grid with its subsequent finite superparticle size. We introduce the notion of coarse-graining dependent quantities, i.e. physical quantities depending on the number $p$. They all derive from the plasma parameter $\Lambda$, which we show to be proportional to $1/p$. We explore three examples: the rapid collision- and fluctuation-induced thermalization of plasmas with different temperatures, that scale with the number of superparticles per grid cell and are a factor $p\sim10^{10}$ faster than in real plasmas; the high level of electrostatic fluctuations in a thermal plasma, with corrections due to the finite superparticle sizes; and the blurring of the linear spectrum of the filamentation instability, where the fastest growing modes do not dominate the total energy because of a high level of fluctuations. We stress that the enhanced collisions and correlations of PIC plasmas must be kept negligible toward kinetic physics., Comment: 6 pages, proceedings of High Energy Processes in Relativistic Outflows (HEPRO04)

We present the parallel particle-in-cell (PIC) code Apar-T and, more importantly, address the fundamental question of the relations between the PIC model, the Vlasov-Maxwell theory, and real plasmas. First, we present four validation tests: spectra from simulations of thermal plasmas, linear growth rates of the relativistic tearing instability and of the filamentation instability, and non-linear filamentation merging phase. For the filamentation instability we show that the effective growth rates measured on the total energy can differ by more than 50% from the linear cold predictions and from the fastest modes of the simulation. Second, we detail a new method for initial loading of Maxwell-J\"uttner particle distributions with relativistic bulk velocity and relativistic temperature, and explain why the traditional method with individual particle boosting fails. Third, we scrutinize the question of what description of physical plasmas is obtained by PIC models. These models rely on two building blocks: coarse-graining, i.e., grouping of the order of p~10^10 real particles into a single computer superparticle, and field storage on a grid with its subsequent finite superparticle size. We introduce the notion of coarse-graining dependent quantities, i.e., quantities depending on p. They derive from the PIC plasma parameter Lambda^{PIC}, which we show to scale as 1/p. We explore two implications. One is that PIC collision- and fluctuation-induced thermalization times are expected to scale with the number of superparticles per grid cell, and thus to be a factor p~10^10 smaller than in real plasmas. The other is that the level of electric field fluctuations scales as 1/Lambda^{PIC} ~ p. We provide a corresponding exact expression. Fourth, we compare the Vlasov-Maxwell theory, which describes a phase-space fluid with infinite Lambda, to the PIC model and its relatively small Lambda., Comment: 24 pages, 14 figures, accepted in Astronomy & Astrophysics

The PIC model relies on two building blocks. The first stems from the capability of computers to handle only up to $\sim10^{10}$ particles, while real plasmas contain from $10^4$ to $10^{20}$ particles per Debye sphere: a coarse-graining step must be used, whereby of the order of $p\sim10^{10}$ real particles are represented by a single computer superparticle. The second is field storage on a grid with its subsequent finite superparticle size. We introduce the notion of coarse-graining dependent quantities, i.e. physical quantities depending on the number $p$. They all derive from the plasma parameter $\Lambda$, which we show to be proportional to $1/p$. We explore three examples: the rapid collision- and fluctuation-induced thermalization of plasmas with different temperatures, that scale with the number of superparticles per grid cell and are a factor $p\sim10^{10}$ faster than in real plasmas; the high level of electrostatic fluctuations in a thermal plasma, with corrections due to the finite superparticle sizes; and the blurring of the linear spectrum of the filamentation instability, where the fastest growing modes do not dominate the total energy because of a high level of fluctuations. We stress that the enhanced collisions and correlations of PIC plasmas must be kept negligible toward kinetic physics., Comment: 6 pages, proceedings of High Energy Processes in Relativistic Outflows (HEPRO04)

We present the parallel particle-in-cell (PIC) code Apar-T and, more importantly, address the fundamental question of the relations between the PIC model, the Vlasov-Maxwell theory, and real plasmas. First, we present four validation tests: spectra from simulations of thermal plasmas, linear growth rates of the relativistic tearing instability and of the filamentation instability, and non-linear filamentation merging phase. For the filamentation instability we show that the effective growth rates measured on the total energy can differ by more than 50% from the linear cold predictions and from the fastest modes of the simulation. Second, we detail a new method for initial loading of Maxwell-J\"uttner particle distributions with relativistic bulk velocity and relativistic temperature, and explain why the traditional method with individual particle boosting fails. Third, we scrutinize the question of what description of physical plasmas is obtained by PIC models. These models rely on two building blocks: coarse-graining, i.e., grouping of the order of p~10^10 real particles into a single computer superparticle, and field storage on a grid with its subsequent finite superparticle size. We introduce the notion of coarse-graining dependent quantities, i.e., quantities depending on p. They derive from the PIC plasma parameter Lambda^{PIC}, which we show to scale as 1/p. We explore two implications. One is that PIC collision- and fluctuation-induced thermalization times are expected to scale with the number of superparticles per grid cell, and thus to be a factor p~10^10 smaller than in real plasmas. The other is that the level of electric field fluctuations scales as 1/Lambda^{PIC} ~ p. We provide a corresponding exact expression. Fourth, we compare the Vlasov-Maxwell theory, which describes a phase-space fluid with infinite Lambda, to the PIC model and its relatively small Lambda., Comment: 24 pages, 14 figures, accepted in Astronomy & Astrophysics