Table of contents

Using the replica method, we derive quantitative information about the clustering into 2 subgroups of data lying on the surface of an N-dimensional hypersphere. Various clustering algorithms are considered, including the one corresponding to competitive learning.

Under a constant flow velocity V, a flexible polymer (in steady state) is expected to display three types of conformation: 1) unperturbed at low V; 2) "trumpet": partly stretched, with certain scaling laws (F. Brochard-Wyart, Europhys. Lett., 23 (1993) 105) at intermediate V; 3) "stem and flower" with a completely stretched portion (the stem) at high V. We discuss regime 3) here. We also consider transients where (starting from regime 3)) the flow is abruptly suppressed and the resulting decay law for the stem is of the Rouse type.

The sintering of aerogels is modelled by combining two known methods: the method of the array of cylinders used by Scherer and the dressing of particles of fractal aggregates. In this paper, bonds between particles of an on-lattice computed gel are replaced by cylinders. During sintering, the radius of the cylinders increases. We compute this radius vs. the renormalized concentration of the gel, in a first step by an analytical method and then by a numerical method. By deriving the volume as a function of the concentration, we also obtain the specific surface during sintering.

The anharmonicity and lifetime of the CH stretching vibration of the H-terminated diamond H/C(111)-(1 × 1) surface are investigated. It is found that the ν_1→2 transition is 110 cm^-1 lower than the ν_0→1 fundamental. Theoretical calculations show good agreement with the experimental observations and predict the existence of a strongly bound two-phonon bound state. A vibrational lifetime of 19 ps and a similar ground-state recovery time are measured.

A physical consideration is given to reinforce, interpret and generalize the result of Shepelyansky that a not too weak short-range interaction can cause correlated two-electron states to be substantially delocalized with respect to single-electron ones. A generalization of the Thouless block-scaling picture is used and its wide applicability is pointed out. A similar effect for correlated electron-hole pairs is also found. Some physical applications are briefly discussed.

We demonstrate experimentally with an STM operating in ultra-high vacuum and with model calculations that the current-voltage characteristics of a single C₆₀ molecule are linear at low voltage. This is shown to prevail for tip-surface separations larger than the electrical contact point down to when the molecule is physically compressed by the tip. This linear I(V) relationship of a single molecule holds in general as long as its HOMO-LUMO gap in the junction exceeds the voltage used to define the junction electrical resistance and if the molecule is enough coupled to the electrodes.

We give a simple demonstration that anisotropy (of arbitrary strength) in the pairing interaction (of arbitrary origin) always enhances the superconducting temperature T_c, thanks to a general theorem in matrix theory. Moreover, such an anisotropic interaction also gives rise to different partial-wave pairings than in the corresponding isotropic cases. A particular example, treated rigorously in the weak-coupling regime, explicitly exhibits, depending on the anisotropy parameters, either singlet pairing (as an admixture of s (l = 0) and d (l = 2) waves), or triplet (l = 1) pairings. We discuss the possible implications of our results for actual physical systems as well as their plausible link with d-wave pairing often invoked for high-T_c materials.

The upper critical field and the density of states of d_x²-y²-wave superconductor in the vortex state are determined. The temperature dependence of the upper critical field of d-wave superconductor without Pauli term appears to be consistent with the one observed in YBCO. Except in the immediate vicinity of T_c (T ⩾ 0.88T_c) a square vortex lattice tilted by 45° from the a-axis is more favored than a triangular lattice. If we extrapolate the present density of states in the low-field region (B ≪ H_c2 (T)), we obtain the residual density of states proportional to (B)^1/2 consistent with an earlier Volovik's analysis.

The energy dependences of nuclear forward scattering and nuclear 4π scattering of 14.4 keV synchrotron radiation were studied with an energy resolution of 6 meV. Nuclear 4π scattering resulted from internal conversion and therefore represents the energy dependence of resonant nuclear absorption. In the case of the [57Fe(bpp)₂][BF₄]₂ sample the energy dependence of nuclear 4π scattering revealed a 13 meV inelastic broadening of the absorption line. This indicates an excitation of lattice motions in the nuclear absorption process. The technique allows the direct measurement of the energy distribution of nuclear recoil.

We report for the first time a phase transformation from the f.c.c.-like L1₂ structure to the b.c.c. structure induced by mechanical milling. This is found in Fe₃Ge. X-ray diffraction shows that after short periods of milling, anti-site disorder is created in L1₂-Fe₃Ge indicated by the disappearance of superlattice reflections and that after long periods of milling, a nanocrystalline b.c.c. solid solution of Ge in Fe is obtained. High-field magnetization at 4.2 K increases upon disordering in f.c.c. L1₂ and decreases upon phase transformation from f.c.c. to b.c.c. Thermal analysis of various Fe₃Ge samples gives more insight in the change of magnetic behaviour and the phase transformation during milling.

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