Closed-form expressions for correlated density matrices: application to dispersive interactions and example of (He)2

Empirically correlated density matrices of N-electron systems are investigated. Exact closed-form expressions are derived for the one- and two-electron reduced density matrices from a general pairwise correlated wave function. Approximate expressions are proposed which reflect dispersive interactions between closed-shell centro-symmetric subsystems. Said expressions clearly illustrate the consequences of second-order correlation effects on the reduced density matrices. Application is made to a simple example: the (He)2 system. Reduced density matrices are explicitly calculated, correct to second order in correlation, and compared with approximations of independent electrons and independent electron pairs. The models proposed allow for variational calculations of interaction energies and equilibrium distance as well as a clear interpretation of dispersive effects on electron distributions. Both exchange and second order correlation effects are shown to play a critical role on the quality of the results.Comment: 22 page

Fourier-Legendre expansion of the one-electron density-matrix of ground-state two-electron atoms

The density-matrix rho(r, r') of a spherically symmetric system can be expanded as a Fourier-Legendre series of Legendre polynomials Pl(cos(theta) = r.r'/rr'). Application is here made to harmonically trapped electron pairs (i.e. Moshinsky's and Hooke's atoms), for which exact wavefunctions are known, and to the helium atom, using a near-exact wavefunction. In the present approach, generic closed form expressions are derived for the series coefficients of rho(r, r'). The series expansions are shown to converge rapidly in each case, with respect to both the electron number and the kinetic energy. In practice, a two-term expansion accounts for most of the correlation effects, so that the correlated density-matrices of the atoms at issue are essentially a linear functions of P1(cos(theta)) = cos(theta). For example, in the case of the Hooke's atom: a two-term expansion takes in 99.9 % of the electrons and 99.6 % of the kinetic energy. The correlated density-matrices obtained are finally compared to their determinantal counterparts, using a simplified representation of the density-matrix rho(r, r'), suggested by the Legendre expansion. Interestingly, two-particle correlation is shown to impact the angular delocalization of each electron, in the one-particle space spanned by the r and r' variables.Comment: 31 pages, 7 figure

Exact Kohn-Sham versus Hartree-Fock in momentum-space: examples of two-fermion systems

The question of how density functional theory (DFT) compares with Hartree-Fock (HF) for the computation of momentum-space properties is addressed in relation to systems for which (near) exact Kohn-Sham (KS) and HF one-electron matrices are known. This makes it possible to objectively compare HF and exact KS and hence to assess the potential of DFT for momentum space studies. The systems considered are the Moshinsky atom, the Hooke's atom and light two-electron ions, for which expressions for correlated density-matrices or momentum densities have been derived in closed-form. The results obtained show that it is necessary to make a distinction between true and approximate DFT.Comment: 30 pages, accepted for publication in J. Chem. Phys. (2006

Conception robuste de systèmes dynamiques frottants

Le niveau des cycles limites obtenus dans les zones d'instabilité des systèmes frottants dépend fortement de la valeur du coefficient de frottement qui admet des dispersions importantes. Ainsi, l'objectif des travaux est d'étudier le comportement dynamique d'un système frottant afin de pouvoir déterminer la dispersion de l'amplitude des cycles limites lors des instabilités de type sprag-slip en prenant en compte les incertitudes du coefficient de frottement avec une approche par intervalles

Measuring the originality of intellectual property assets based on machine learning outputs

Originality criteria are frequently used to compare assets and, in particular, to assess the validity of intellectual property (IP) rights such as copyright and design rights. In this work, the originality of an asset is formulated as a function of the distances between this asset and its comparands, using concepts of maximum entropy and surprisal analysis. Namely, the originality function is defined according to the surprisal associated with a given asset. Creative assets can be justifiably compared to particles that repel each other via an electrostatic-like pair potential. This allows a very simple, suitably bounded formula to be obtained, in which the originality of an asset writes as the ratio of a reference energy to an interaction energy imparted to that asset. In particular, the originality of an asset can be expressed as a ratio of two average distances, i.e., the harmonic mean of the distances from this asset to its comparands divided by the harmonic mean of the distances between the sole comparands. Accordingly, the originality of objects such as IP assets can be simply estimated based on distances computed thanks to unsupervised machine learning techniques or other distance computation algorithms. Application is made to various types of assets, including emojis, typeface designs, paintings, and novel titles.Comment: 23 pages, 6 tables, 2 figure

La vente de médicaments via Internet (un marché français virtuel)

POITIERS-BU Médecine pharmacie (861942103) / SudocSudocFranceF

Modélisation robuste du comportement dynamique d’un système non-lineaire frottant

Ce travail présente l’étude du comportement dynamique d’un système soumis à des instabilités de type Sprag-Slip générées par du frottement. La mise en équation de ce système conduit à un système d’équations différentielles non linéaire. Dans un premier temps, une approche déterministe du comportement est réalisée : la résolution classique de ces équations différentielles permet de déterminer le comportement dynamique du système étudié, ainsi que sa sensibilité aux différents paramètres. Dans un second temps, une analyse par intervalle permet de prendre en compte la dispersion du coefficient de frottement pour l’intégration des équations différentielles. L’objectif est d’obtenir une modélisation robuste du comportement dynamique de systèmes frottants

Interval approach applied to blades of windscreens wiper

International audienceFriction-induced vibration due to mode coupling is a major concern in a wide variety of mechani cal systems. Stability analysis and the associated non-linear amplitudes around a steady-state equilibrium point actually are two of the most important points in the study of non-linear dynamical systems de­ pending on given control parameters. Determining stable and unstable regions is only one aspect of the problem of friction-induced ftutter instability. The instability magni tude is a more significant design factor than the instability region. In this paper, we propose to apply interval analysis to obtain the ma.ximum and minimum amplitudes of a complete non-linear mechanical system. This approach allows us to avoid numerical procedures that are both time and cast consuming to perform when parametric design studies are needed