arXiv subjects

Richard Bonneville

Publications and source records attributed to Richard Bonneville.

8 recordsLinked to original sources

arXiv2021

Conditional entropy; an alternative derivation of the pair correlation function for simple classical fluids

We present an alternative derivation of the pair correlation function for simple classical fluids by using a variational approach. That approach involves the conditional probability p(3,..., N /1, 2) of an undefined system of N particles with respect to a given pair (1,2), and the definition of a conditional entropy $σ$(3,..., N /1, 2). An additivity assumption of $σ$(3,..., N /1, 2) together with a superposition assumption for p(3 / 1, 2) allows deriving the pair probability p(1,2). We then focus onto the case of simple classical fluids, which leads to an integral, non-linear equation that formally allows computing the pair correlation function g(R). That equation admits the one resulting from the hyper netted chain approximation (and the Percus-Yevick approximation) as a limit case.

cond-mat.stat-mech↗

arXiv2020

An independent link model of simple fluids; random close packing limit

A new approach to modelling the behaviour of simple fluids is presented. Starting from the usual expression of the partition function of N molecules, a Fourier transformation is performed. It is argued that the N(N-1)/2 dynamical variables kpq in the reciprocal space featuring the link between 2 molecules p and q can reasonably be considered independent in the thermodynamical limit. Treated as a set of effective independent particles, their statistical behaviour is analogous to a Bose-Einstein gas. Expressions of the partition function, of the radial pair correlation function and of the pressure are derived, and a special attention is given to the mathematical inter-consistency of those quantities. The results, which are independent of the exact shape of the intermolecular potential, are applied to the simple case of hard sphere fluids. An analytical expression of the radial pair correlation function is derived as well as of the equation of state. The model predicts a qualitatively satisfactory behaviour for g(R), and it provides numerically correct values for the equation of state at low and medium densities, although at higher densities the contact value of g(R)is underestimated. Quite interestingly it predicts for the maximum random close packing density the correct value 0.637 .

physics.flu-dyn↗

arXiv2020

An independent pair-link model of simple fluids

A new approach to thermodynamics of simple fluids is presented. The partition function is first expressed in the reciprocal space, it is argued that the links (p,q) between 2 molecules can reasonably in the thermodynamical limit be considered as a set nearly independent objects characterized by the dynamical variables . It is then possible to derive an expression of the pair correlation function. The results, which are independent of the exact shape of the intermolecular potential, are applied to the simple case of hard sphere fluids.

physics.gen-ph↗

arXiv2019

Looking for a compact semi empirical equation of state for hard spheres: possibility of a glassy transition and random loose packing

The equation of state of a hard sphere fluid at high density should exhibit a simple pole at the random close packing limit. Here we show that trying to obtain a compact semi-empirical equation of state simultaneously compatible with that asymptotic behaviour and with the known virial coefficients raises an analytical difficulty which can be solved if a glassy transition occurs in the disordered metastable phase at a density intermediate between the freezing point and the random close packing limit, numerically close to the melting point. The estimated value for the transition point, which is identified with random loose packing, is in good agreement with earlier estimations.

cond-mat.soft↗

arXiv2017

An approximate simple equation of state for model fluids

A new analytical approach to derive an approximate equation of state and the virial coefficients for simple fluids is presented. Starting from the usual expression of the partition function, we first perform a Fourier transformation, and then we implement an original approximation scheme of the correlation terms in the reciprocal space. A procedure involving combinatorial analysis and partial re-summations leads to simple expressions for the virial coefficients, which are effectively calculated for hard sphere fluids. A comparison is made with Carnahan & Starling equation of state and with the available numerical results for the virial coefficients. The virial coefficients calculated within our approximation scheme are in rather good agreement with the known computed values up to order 6, i.e. at low density; if we extrapolate those results for higher orders we obtain a simple equation of state in good agreement with the experimental data for the stable fluid phase.

physics.gen-ph↗

arXiv2016

An alternative model of particle physics in a 10-dimension (pseudo) Euclidian space-time

A consistent description of the fundamental interactions of particle physics based upon the assumption of 6 real extra dimensions is presented. The usual 4-dimension space-time, a curved hypersurface with the Lorentz group as local symmetry, is assumed to be embedded in a larger flat 10-dimension space-time. Two additional assumptions are made: (i) the orthogonal 6-d space in any point of the hypersurface is invariant under the orthogonal group SO(6) or one of its subgroups, (ii) in that space only the invariant, or distinguished, subgroups of SO(6) can be symmetry groups for the physical states. There are only two such possibilities, each of them corresponding to one type of particles: (i) hadrons, experiencing a gauge field associated to a real symmetry group GH(6) , isomorphous to SU(3) and identified with the strong interaction, and (ii) leptons experiencing another gauge field associated with a real symmetry group GL(6), isomorphous to SU(2)xU(1) but different from the usual electro-weak coupling. Moreover both hadrons and leptons are subject to weak and electromagnetic interactions plus a scalar Higgs-type coupling. That description can be extended so as to include gravitation. Postulating a minimal Lagrangian in the full 10-dimension space-time leads to introduce one effective additional vector-type field, which does not act the same way upon hadrons and leptons, thus provoking an apparent violation of the equivalence principle.

hep-ph↗

arXiv2016

A semi empirical expression of the virial coefficients for hard sphere fluids at all density

We propose a new semi empirical expression of the virial coefficients for a hard sphere fluid which is valid in the disordered phase over the whole density range. The results are in good agreement with the numerical data and better than those of the well-known Carnahan & Starling equation of state in the domain of validity of the later; moreover this new expression accounts for the singularity which is required for the equation of state at the close random packing limit.

cond-mat.stat-mech↗

arXiv2015

Asymptotic expression of the virial coefficients for hard sphere systems

We evidence via a computation in the reciprocal space the asymptotic behaviour of the high order virial coefficients for a hard sphere system. These coefficients, if their order is high enough, are those of a geometric series. We thus are able to give an explicit expression of the equation of states of the hard sphere system at high density when the fluid phase is no longer the stable one; in the disordered phase this equation of states exhibits a simple pole at the random close packing density. We can then estimate the packing densities of the freezing point of the disordered phase and also of the melting point of the fcc ordered phase. The results are compared with those of the numerical simulations.

cond-mat.stat-mech↗