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In this work, we study the time evolution of systems containing a large number of particles interacting via a $1/r$ binary interaction potential, such as Coulombian and self-gravitating systems. In particular, we study the effect on the dynamics of the Holtsmark-Chandrasekhar theory, which describes the static fluctuations of the total force field around the Vlasov mean-field. We derive these effects by developing a new perturbative theory using the fundamental representation of Statistical Mechanics :The BBGKY hierarchy. This leads to a modification of the Vlasov equation by an additional term involving a fractional Laplacian to the power $3/4$ in velocity space, and a fractional iterated time integral of order $1/2$. We show that one of the consequences of this new term for spatially homogeneous systems is the appearance in the velocity distribution of long tails in $v^{-5/2}$. By extension, similar behaviors can be expected for weakly inhomogeneous systems. These long tails correspond to a universal mechanism related to the divergence of the interaction potential in $1/r$. More specifically, they are induced by the long tails of the total force field distribution as described by the Holtsmark-Chandrasekhar theory. Such a result cannot be obtained from theories based on the weak-coupling between particles, which lead to the Vlasov term, and, the Landau collision operator at the next order. We verify numerically these results by means of molecular dynamics simulations. We study the evolution of the velocity distributions for times very short compared to the violent relaxation time. In this particular time regime, we find, as expected, power laws in $v^{alpha}$ for the velocity distribution tail. In particular, when the regularization parameter of the interaction potential tends to $0$, the exponent in the power law indeed tends from below toward the theoretically predicted value $alpha=-5/2$., Doctorat en Sciences, info:eu-repo/semantics/nonPublished

Chacune de ces particularités est discutée en détail dans des chapitres distincts, où l’on applique différentes méthodes de méchanique statistique (équation de Boltzmann, transition de phase, mean field models…) et où l’on vérifie les prédictions théoriques par simulations numériques (MD, Monte Carlo…)., Doctorat en sciences, Spécialisation physique, info:eu-repo/semantics/nonPublished

A nonmarkovian and nonlocal kinetic equation, which is a generalization of the (nonlinear) Balescu-Lenard equation, is derived for a weakly nonuniform multicomponent polarizable plasma. A specific expansion of the plasma resolvent, which allows to separate the dymamic, kinetic and hydrodynamic scales, is proposed. Explicit expressions of the collision integral and of the nonequilibrium pair correlation function are given in an approximation which takes into account the effects of spatial and temporal nonlocality as well as of the polarization. Balance equations for the momentum and energy densities are calculated in the first order in nonlocality, and potential contributions to the fluxes due to polarization are obtained., SCOPUS: ar.j, FLWIN, info:eu-repo/semantics/published

Doctorat en Sciences, info:eu-repo/semantics/nonPublished

A cellular automaton model that simulates the mesoscopic scale behavior of an electrode is presented in this article. Transition rules that mimic anodic and cathodic events corresponding to a simple dissolution mechanism including the presence of adsorbates and charge acceptor cations are introduced. The model focuses essentially on the case of a free corroding electrode, although polarized regimes are also examined. This mesoscopic approach discloses features that are not considered in the standard macroscopic description. First, the metal surface becomes morphologically heterogeneous. Secondly, the degree of roughness is linked to a specific distribution of active dissolution sites, and the resulting interplay between morphology and kinetics carries with it a local segregation of reactants and the detachment of clusters of varying size. Issues concerning these distinguishing properties of the electrode surface are examined using morphogenetic descriptors. Mesoscopic balance equations are established and compared with the macroscopic standard equations for an homogeneous electrode. The influence of those purely mesoscopic features is addressed. We conclude that, although both the descriptions are different, they coexist consistently if a proper approach is chosen. © 2001 Elsevier Science Ltd., SCOPUS: ar.j, info:eu-repo/semantics/published

The nonlinear Balescu-Lenard kinetic equation has been generalised to weakly nonideal spatially nonuniform polarisable plasmas. This is done by including nonlocality in space and time in the collision term. The local laws of conservation for particle, momentum and total energy densities follow. Some outstanding problems are discussed., SCOPUS: ar.j, FLWIN, info:eu-repo/semantics/published

Taking into account the first non-Markovian correction to the Balescu-Lenard equation, we derive an expression for the pair correlation function and a nonlinear kinetic equation valid for a weakly non-ideal polarized classical plasma. This equation allows for the description of the correlational energy evolution and exhibits global conservation of energy with dynamical polarization. © 1998 Cambridge University Press., SCOPUS: ar.j, info:eu-repo/semantics/published

Taking into account the first non-Markovian correction to the Balescu-Lenard equation, we have derived an expression for the pair correlation function and a nonlinear kinetic equation valid for a nonideal polarized classical plasma. This last equation allows for the description of the correlational energy evolution and shows the global conservation of energy with dynamical polarization., SCOPUS: ar.j, info:eu-repo/semantics/published

Ionization of dense hydrogen plasmas is studied from a chemical picture. It is based on a priori existing species: Electrons, protons and hydrogen atoms. All particles are treated as classical point particles interacting through pseudo potentials which account for quantum diffraction effects. Thermodynamics is evaluated by Monte Carlo simulations in a semigrand-canonical ensemble, a suitable method developed for charged fluids. Density effects on the ionization energy are self-consistently introduced in the model. We find that the ionization energy decreases as the density increases and that complete ionization is achieved at densities around 2 g/cm3. © 1994 IOP Publishing Ltd., SCOPUS: ar.j, info:eu-repo/semantics/published

Ionization of dense hydrogen plasmas is studied from a chemical picture. It is based on a priori existing species: electrons, protons and hydrogen atoms. All particles are treated as classical point particles interacting through pseudo‐potentials which account for quantum diffraction effects. Thermodynamics is evaluated by Monte Carlo simulations in a semi‐grand‐canonical ensemble, a suitable method developed for charged fluids. Density effects on the ionization energy are self consistently introduced in the model. The static equilibrium correlation functions are used as input in kinetic theory for the evaluation of the electrical conductivity. On the other hand, a new collision operator is derived; it is suited to treat collisions between neutral as well as between charged particles. Copyright © 1993 WILEY‐VCH Verlag GmbH & Co. KGaA, SCOPUS: ar.j, FLWNA, info:eu-repo/semantics/published

A new method to calculate ionization properties of very dense correlated plasmas is proposed. In this early stage a mixture composed of hydrogen atoms in their ground state and unbounded protons and electrons is studied. All species are treated as classical point particles interacting through pseudo-potentials. As an effect of the strong correlation between hydrogen atoms it is found that the ionization can decrease as the temperature increases. All the correlation functions, excess chemical potentials and equilibrium ionization are evaluated in the HNC approximation. © 1991 IOP Publishing Ltd., SCOPUS: ar.j, info:eu-repo/semantics/published

A kinetic theory is presented for the thermal conductivity of a strongly coupled, fully ionized hydrogen plasma of typical temperature and density 10T104 eV, 1020n1027 cm-3. This theory gives results in good agreement with molecular dynamics and recovers weak-coupling-theory values at high temperature. The theory has then been generalized to a three-component hydrogen plasma made up of protons and electrons of spin up and spin down. It is found that the ionic part of the thermal conductivity cannot be neglected in the high-temperature high-density domain of the parameters. © 1986 The American Physical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

The self-diffusion, shear viscosity and thermal conductivity coefficients of a strongly coupled one-component plasma (OCP) are calculated from kinetic theory without any adjustable parameter: approximate collisional memory functions (or collision operators) which generalise the Balescu-Guernsey-Lennard (BGL) operator to finite wavelengths, finite frequencies and finite coupling constants are used for the microscopic definition of the transport coefficients; some further operational approximations are discussed and compared with the molecular-dynamics results obtained by Hansen and co-workers (1973, 1975). Good agreement is achieved for the self-diffusion and shear viscosity coefficients in the whole fluid phase and for the thermal conductivity in the weak and moderately strong coupling range of the OCP. © 1985 The Institute of Physics., SCOPUS: ar.j, info:eu-repo/semantics/published

Using a simple model of a plasma between two boundaries at which temperature is fixed, we investigate the thermal transport in the collisionless limit, relaxing the usual local neutrality assumption. For physically relevant external parameters, an analytical solution is found where the heat flux is reduced with respect to its value when local electroneutrality is assumed. © 1984 The American Physical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

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A semi-classical (SC) kinetic theory and its purely quantum-mechanical analog are used to calculate the thermal conductivity of a weakly-coupled one-component plasma. The quantum diffraction and symmetry effects are properly taken into account in the quantum theory by the Wigner functions formalism. These effects are included in the temperature dependent effective potentials in the SC theory. Comparison between the two methods shows that diffraction effects are qualitatively well described by the SC framework. On the contrary the quantum symmetry effects are not recovered by the corresponding effective potential as far as the SC dynamics is concerned. © 1987 IOP Publishing Ltd., SCOPUS: ar.j, info:eu-repo/semantics/published

Doctorat en Sciences, info:eu-repo/semantics/nonPublished

In this paper we express the dressed-particle theory of Prigogine and coworkers in terms of reduced distribution functions. The reduced dressed-particle distribution functions are factorized (statistical independence of dressed particles) at thermal equilibrium if a formal condition (the so-called "equilibrium condition") is satisfied. The dressed one-particle distribution function is then sufficient to characterize all thermodynamic quantities; in particular, the entropy takes the same form as that of a perfect gas. We discuss our results and indicate how to generalize them out of equilibrium. © 1972., SCOPUS: ar.j, info:eu-repo/semantics/published

The microscopic definition of entropy as introduced by Prigogine, Henin and George, in terms of a quasi-particle description is used to derive the entropy balance equation for a moderately strong coupled classical non-uniform gas. Both entropy flow and entropy production are found to agree with the expressions postulated by non-equilibrium theory on the basis of the Gibbs entropy law. © 1968., SCOPUS: ar.j, info:eu-repo/semantics/published

We describe an electron gas in the equilibrium Debye approximation in terms of dressed particles as introduced by the Brussels school. We use the Mandel-Turner definition of the dressing operator and show the validity of the so-called equilibrium condition for our model. We show graphically the dependence of the dressed-particle energy on velocity. Finally, as expected from our preceding paper, we recover the correct value of all thermodynamic quantities by using only the dressed one-particle distribution function. © 1972., SCOPUS: ar.j, info:eu-repo/semantics/published

The statistical mechanical definition of entropy introduced by Prigogine et al. is used to derive the entropy balance equation for an arbitrary non-uniform system. It is shown that in the linear domain of irreversible processes Gibbs' entropy law is verified to all orders in the intermolecular interactions and to all orders in the density. © 1969., SCOPUS: ar.j, info:eu-repo/semantics/published

SCOPUS: ar.j, info:eu-repo/semantics/published

SCOPUS: ar.j, info:eu-repo/semantics/published