arXiv subjects

Jean-Michel Caillol

Publications and source records attributed to Jean-Michel Caillol.

24 records · Page 2Linked to original sources

arXiv2005

Ionic fluids: charge and density correlations near gas-liquid criticality

The correlation functions of an ionic fluid with charge and size asymmetry are studied within the framework of the random phase approximation. The results obtained for the charge-charge correlation function demonstrate that the second-moment Stillinger-Lovett (SL) rule is satisfied away from the gas-liquid critical point (CP) but not, in general, at the CP. However in the special case of a model without size assymetry the SL rules are satisfied even at the CP. The expressions for the density-density and charge-density correlation functions valid far and close to the CP are obtained explicitely.

cond-mat.stat-mech↗

arXiv2004

Monte Carlo simulations of the critical properties of the restricted primitive model

Recent Monte Carlo simulations of the critical point of the restricted primitive model for ionic solutions are reported. Only the continuum version of the model is considered. A finite size scaling analysis based in the Bruce-Wilding procedure gives critical exponents in agreement with those of the three-dimensional Ising universality class. An anomaly in the scaling of the specific heat with system size is pointed out.

cond-mat.stat-mech↗

arXiv2004

Random Walks on Hyperspheres of Arbitrary Dimensions

We consider random walks on the surface of the sphere $S_{n-1}$ ($n \geq 2$) of the $n$-dimensional Euclidean space $E_n$, in short a hypersphere. By solving the diffusion equation in $S_{n-1}$ we show that the usual law $ \varpropto t $ valid in $E_{n-1}$ should be replaced in $S_{n-1}$ by the generic law $<\cos θ> \varpropto \exp(-t/τ)$, where $θ$ denotes the angular displacement of the walker. More generally one has $ \varpropto \exp(-t/ τ(L,n))$ where $C^{n/2-1}_{L}$ a Gegenbauer polynomial. Conjectures concerning random walks on a fractal inscribed in $S_{n-1}$ are given tentatively.

cond-mat.stat-mech↗

arXiv2004

Sine-Gordon Theory for the Equation of State of Classical Hard-Core Coulomb systems. III Loopwise Expansion

We present an exact field theoretical representation of an ionic solution made of charged hard spheres. The action of the field theory is obtained by performing a Hubbard-Stratonovich transform of the configurational Boltzmann factor. It is shown that the Stillinger-Lovett sum rules are satisfied if and only if all the field correlation functions are short range functions. The mean field, Gaussian and two-loops approximations of the theory are derived and discussed. The mean field approximation for the free energy constitutes a rigorous lower bound for the exact free energy, while the mean field pressure is an upper bound. The one-loop order approximation is shown to be identical with the random phase approximation of the theory of liquids. Finally, at the two-loop order and in the pecular case of the restricted primitive model, one recovers results obtained in the framework of the mode expansion theory.

cond-mat.stat-mech↗

arXiv2003

Some applications of the Lambert W function to classical statistical mechanics

We apply the recently defined Lambert W function to some problems of classical statistical mechanics, i.e. the Tonks gas and a fluid of classical particles interacting via repulsive pair potentials. The latter case is considered both from the point of view of the standard theory of liquids and in the framework of a field theoretical description. Some new mathematical properties of the Lambert W function are obtained by passing.

cond-mat.stat-mech↗

arXiv2002

Transport Coefficients of the Yukawa One Component Plasma

We present equilibrium molecular-dynamics computations of the thermal conductivity and the two viscosities of the Yukawa one-component plasma. The simulations were performed within periodic boundary conditions and Ewald sums were implemented for the potentials, the forces, and for all the currents which enter the Kubo formulas. For large values of the screening parameter, our estimates of the shear viscosity and the thermal conductivity are in good agreement with the predictions of the Chapman-Enskog theory.

cond-mat.stat-mech↗