Theoretical approach to the masses of the elementary fermions

International audienceWe made the hypothesis that, if spacetime is composed of small hypercubes of one Planck length edge, it exists elementary wavefunctions which are equal to √ 2 exp(ix j) if it corresponds to a space dimension or equal to √ 2 exp(it) if it corresponds to a time dimension. The masses of fermions belonging to the first family of fermions are equal to integer powers of 2 (in eV/c 2) [1]. We make the hypothesis that the fermions of the 2nd and 3rd families are excited states of the fermions of the 1st family. Indeed, the fermions of the 2nd and 3rd families have masses equal to 2 n .(p 2)/2 where n is an integer [1] calculated for the first family of fermions and p is another integer. p is an integer which corresponds to the excited states of the elementary wavefunctions (the energy of the excited elementary wave functions are equal to p 2 /2; using normalized units)

Micrometric particles twodimensional self-assembly during drying of liquid film

We computed the self-organisation process of a monodisperse collection of spherical micrometric particles trapped in a two-dimensional (2D) thin liquid film isothermally dried on a chemically inert substrate. The substrate is either flat or indented to create linear stripes on its surface. The numerical results are illustrated and discussed in the light of experimental ones obtained from the drying of diamond particles water based suspension ($d_{50} = 10 \mu m$) on a glass substrate. The drying of the suspension on a flat substrate leads to the formation of linear patterns and small clusters of micrometric particles distributed over the whole surface of the substrate, whereas the drying of the suspension on a indented substrate leads to the aggregation of the particles along one side of the stripe which has a higher roughness than the other side of the stripe. This is an easy experimental way to obtain colloidal selforganized patterns.Comment: 16 pages 7 figure

Analysis of a Lennard-Jones fcc structure melting to the corresponding frozen liquid: differences between the bulk and the surface

We computed a Lennard Jones frozen liquid with a free surface using classical molecular dynamics. The structure factor curves on the free surface of this sample was calculated for different depths knowing that we have periodic boundary conditions on the other parts of the sample. The resulting structure factor curves show an horizontal shift of their first peak depending on how deep in the sample the curves are computed. We analyze our resulting curves in the light of spatial correlation functions during melting and at when the liquid is frozen. The conclusion is that near the free surface the sample is less dense than in the bulk and that the frozen liquid surface has a spatial correlation which does not differ very much from that of the bulk. This result is intrinsic to the melting of the Lennard Jones liquid and does not depend on any other parameter.Comment: 18 pages 9 figure

What if Our Three Dimensional Curved Universe Was Embedded in Four Dimensional Space? Consequences on the EPR Paradox

Abstract We have shown in a previous article by Olivi-Tran and Gauthier [1] that Heisenberg's uncertainty principle is only an approximation because time can only be equal to zero at the beginning of the constitution of the universe: the Big Bang. Indeed time is related to the local radius of curvature and to the total radius of curvature of the universe for a given location. Moreover, we have shown (see Olivi-Tran's referenc