Table of contents

The scaling function for the asymptotic p → ∞ behaviour of periods-p windows useful to describe the phenomenology of periodic windows in one-dimensional maps is calculated. The window size δμ(p) in parameter space and the width δx(p) at the window crisis are accurately estimated even for small periods. We show that the size of periodic-p windows approaching the final aperiodic regime decreases asymptotically with a geometric rate.

Nonrelativistic energy formulae for the superposition between the attractive potential - λ₀/x² and the repulsive n > 2-potential γ(n)/xⁿ have been established in N space dimensions, both to first and second order in 1/N. One proceeds by combining the analytic continuation towards n > 2 of 1/N energy results obtained previously for n < 2-Hamiltonians, with additional selection criteria implied by the related WKB-description. This leads to well-defined energy-levels relying on supercritical λ₀-values. Finally, we find the 1/N energy formula for a spinless relativistic two-body system, which is subject to the attractive scalar potential - Λ₀/x².

We consider in this letter the pseudo-inverse solution for the learning of a binary classification. We address the problem of overfitting, i.e. the fact that the generalization rate can be relatively low although the learning rate is very high. We interpret this phenomenon with respect to the behaviour of the small eigenvalues of the covariance matrix of the learned patterns. We propose two ways for solving this problem: the first one is linear, the second one is a two-layer perceptron. Numerical simulations are given to illustrate these approaches.

We study the existence of a bifurcation point in the Schwinger-Dyson equation of (2 + 1)-dimensional quantum electrodynamics with N fermions. We find evidence for the existence of a critical behaviour, such that chiral symmetry breaking may occur only for a small number of flavours.

The dimensions of star-branched polymers in dilute solution in a Θ–solvent are considered. It is shown that recent results for the expansion factor of star polymers at the Θ–point from neutron scattering, light scattering, and Monte Carlo studies are all consistent with a simple expression derived from the smoothed density model with 3-body interactions included via a concentration-cubed term in the free energy. The analysis suggests that 3-body interactions are the most important correction to the traditional two-parameter theory, and therefore lends support to the belief that the Θ–point corresponds to a tricritical point.

A liquid drop falling in a lighter miscible fluid either undergoes a cascade of fragmentations, each appearing as a dynamic instability, or it mixes by diffusion, depending on the value of a fragmentation number F. F is the ratio of the diffusion time to the time required for the fluid to convectively mix. We assign an accurate experimental value to the critical fragmentation number F_c, which appears to be universal. When the fragmentation occurs, the interfacial area increases via successive splittings which display striking symmetries. We present experimental evidence and a qualitative explanation of such a phenomenon.

Tripolar coherent vortices are shown to emerge from the unstable evolution of perturbed two-dimensional axisymmetric flows. They are obtained from the nonlinear equilibration of barotropically linearly unstable normal modes, as well as from more general initial perturbations. This instability is proposed as an important mechanism for the generation of both dipolar and tripolar coherent vortex structures.

An efficient strategy is developed for building suitable collision operators, to be used in a simplified version of the lattice gas Boltzmann equation. The resulting numerical scheme is shown to be linearly stable. The method is applied to the computation of the flow in a channel containing a periodic array of obstacles.

A new laser scattering plasma diagnostics method is described. An algorithm for the determination of the static local field correction and the ionic form factor is suggested.

We have measured the frequency shift of the counterflow-induced peak in the NMR spectrum of the flare-out texture in rotating ³He in a vortex-free state. From a comparison with the calculated shifts, the temperature dependence of the dipolar velocity at P = 5.0 and 29.3 bar has been deduced. Our results are in good agreement with theoretical predictions.

We present analytical results for the grand canonical density functional of inhomogeneous fluids by explicitly taking into account the van der Waals tails of interfacial density profiles which are characteristic for systems with long-range forces. Two cases are considered: wetting of a wall by a one-component fluid near its liquid-gas coexistence line and interfacial wetting in a binary liquid mixture along its triple line. We discuss the influence of these van der Waals tails of the order of wetting transition as well as their relevance for the onset of critical adsorption.

While the heavy-fermion compound CeCu₆ has a nonmagnetic ground state, magnetic order is observed in CeCu_6-xAu_x for x > 0.1. Measurements of the specific heat under pressure of an alloy with x = 0.5 show a decrease of the ordering temperature T_N. The volume dependence of T_N obtained from T_N(p) is weaker than that from T_N(x), showing that both, an increase of the sd-f exchange and a decrease of the sd-density of states, are operative in establishing magnetic order.

A systematic comparison between experimental and theoretical photoionization cross-sections is presented for the complete series of 3d substitutional transition metal impurities in InP. Such a complete analysis of trends which has not been performed previously is shown to represent a powerful tool for the understanding of these defects. Our study confirms in detail the existing models for the electronic configurations of Ti, Cr and Fe and reveals new features for V, Mn and Co.

Ideal metallic films are expected to show a thickness-dependent work function at a level of 0.1 eV in a short thickness range (5 nm). We investigated the variation of the work function with film thickness during the evaporation of polycrystalline Cu films on glass and Ni substrates, using the vibrating capacitor (Kelvin-)method. An increase of the work function with increasing film thickness at 0.1 eV level has been observed at the vacuum-metal interface according to the theoretical expectations. The effect, however, ranges over large thicknesses ((10 ÷ 15) nm), i.e. comparable with electronic scattering lengths in metal films. This behaviour can be attributed to the violation of local charge neutrality in films with unlike surfaces.

We investigate the superconducting instability for La_2-xSr_xCuO₄ numerically by diagonalizing a Hamiltonian constructed from basis states that consist of Slater determinants of first-principles band structure eigenfunctions over a mesh of points in k-space. The band structure incorporates the orthorhombicity of the system as well as oxygen orbits perpendicular and in the Cu-O plane. Our result shows that both these effects play important roles, that superconductivity can be enhanced by a Coulomb interaction, that spin fluctuation is stronger than charge fluctuation, and that one is close to an intermediate coupling limit. A way to enhance T_c is suggested.

We present an x-ray study at ambient pressure of the metal complexes TTF(Pd(dmit)₂)₂ and TTF(Ni(dmit)₂)₂ as a function of temperature. At room temperature one-dimensional (1D) fluctuations are observed under the form of diffuse lines on the x-ray patterns. The Ni-derivative exhibits one type of scattering which condenses below about 40 K into satellite reflections. The Pd-derivative shows two kinds of scattering which condense into satellite reflections, respectively, at T₁ ≈ 150 K and T₂ ≈ 105 K. These observations provide evidence of charge density wave instabilities related to the 1D electronic anisotropy of these materials, and which compete with superconductivity under pressure.

Tilted-field cyclotron resonance has been measured in very high-mobility GaAs-GaAlAs single heterojunctions. An unexpected line splitting of the resonance has been observed, in particular in the ultra quantum limit where only the lowest spin-Landau level is populated. The analysis of the possible excitations leads us to propose an explanation in terms of the activation of two-dimensional magnetoplasmons induced by their coupling with the electric intersubband excitation.