Table of contents

Physical properties of cages and clusters obey symmetry rules that are extensions of the celebrated Euler-Poincaré theorem on polyhedra. A connection is established between this result and a fundamental topological relationship in the theory of homology groups. The connection allows us to assign symmetry representations to physically relevant topological invariants. The results are illustrated by a derivation of the symmetries of the low-lying empty orbitals in leapfrog fullerenes.

The vibrational dynamics of bodies in cavities filled with liquid and subjected to high-frequency rotational vibrations is investigated. The equations of the average behavior of solid bodies in liquid are obtained by the method of averaging in the range of high frequency of vibrations. The generation of a specific average vibrational force applied to the bodies in the bulk of the cavity is demonstrated. The vibrational effect is strong enough to provide levitation in the gravity field of bodies denser than liquid: in case of horizontal axis of rotational vibration bodies could be lifted from the bottom to the ceiling of the cavity. The conditions for solid-cylindrical-bodies levitation in a sector of a horizontal cylindrical layer subjected to rotational vibration around its axis are found on the basis of these equations. The results of the experimental study of this problem corroborate the theoretical predictions.

We discuss two double-resonance scenarios within the context of laser-assisted electron-atom scattering in which double poles of the S-matrix occur. We demonstrate the effect of the double poles on the resonant contribution to the cross-section as well as on the time delay matrix and we point out that double poles could be observed experimentally at quite modest intensities and at frequencies corresponding to existing lasers.

The hypernetted-chain theory is applied to study the fractional quantum Hall effect with the Laughlin wave functions. A new method is proposed to include the effect of the elementary diagrams, which improves upon the commonly used modified hypernetted-chain approximation. The correlation energy, the pair distribution function, as well as the magnetoroton excitation spectrum have been computed within this method. The results obtained are in very good agreement with the available Monte Carlo estimates. The method is generalizable to treat other wave functions, like those corresponding to the hierarchical states or those of composite fermion type.

Laser velocimetry measurements are presented for transitional pipe. It is shown that a) scaling phenomena appear well before the transition to fully developed turbulence is completed, b) multifractal structures are not a characteristic of fully developed turbulence, but they are already present at Reynolds numbers as low as 1500.

Spontaneous oscillations developing during low-temperature impact ionization breakdown in extrinsic germanium have been shown to obey the characteristic features of the type-I intermittent route to chaos. In this paper we show that the distribution of the laminar phase length remains form invariant under variation of the experimental control parameter, if properly normalized to its variance. This presents the first experimental evidence of a recently proposed critical scaling law for the higher-order moments (Rein et al., Europhys. Lett., 21 (1993) 7).

Electrical-transport measurements are reported on high-purity H₂(pc)I single crystals and their alloys with Ni(pc)I in the temperature range from room temperature to 20 mK and in magnetic fields up to 5.5 T. We have observed a sharp maximum in conductivity at 1.8 K which we attribute to crossover from one- to three-dimensional behavior. The conductivity follows a simple quadratic temperature dependence below 1.8 K and remains metallic ( ≈ 10⁴ Ω⁻¹cm⁻¹) at very low temperatures. A negative contribution to the magnetoresistance appears at 1.8 K consistent with weak-localization theory.

We describe a charged-particle diffusion in unbounded plasma, which is controlled by the temperature gradients of the charged particles. The obtained diffusion coefficient can be negative if the temperature of the electrons is greater than the temperature of the ions. We show that this charged-particle diffusion can cause plasma self-constriction, presented by a bell soliton.

The switching properties of a short pitch (0.43 μm) chiral smectic-C liquid-crystal film in bookshelf orientation were studied. Transient-bistable switching was observed in the smectic-C phase over a broad temperature range. The threshold voltage for transient-bistable switching U_th was strongly dependent on the applied pulse width and on the temperature. The anchoring energy threshold W₀ for bistable switching varies within the experimental error linearly with temperature and changes its sign at a critical temperature T_crit of about 50°C, where no bistable switching could be observed. Above T_crit an electric field induces texture changes, which were investigated using polarizing microscopy.

We prove that the predicted charge transfer state in symmetric bilayers of two-dimensional electron gases is always unstable at zero bias voltage, due to interlayer interactions and/or tunneling. This is most easily seen by resorting to a pseudospin formalism and considering coherent states obtained from the charge transfer state through rotations of the pseudospins. Evidently, the charge transfer state is stabilized by a sufficiently strong gate voltage, as found in recent experiments. We show that a simple model, in which the layers are strictly two-dimensional, is able to account quantitatively for such experimental findings, when correlation is properly included.

We calculate the average polarisability of two-dimensional mesoscopic rings in the presence of an Aharonov-Bohm flux. The screening is taken into account self-consistently within a mean-field approximation. We investigate the effects of statistical ensemble, finite frequency and disorder. We emphasize geometrical effects which make the observation of field-dependent polarisability much more favourable on rings than on disks or spheres of comparable radius. The ratio of the flux-dependent to the flux-independent part is estimated for typical GaAs rings.

We have used a scanning SQUID microscope to directly observe the half-integer flux quantum effect, in epitaxial films of Bi₂Sr₂CaCu₂O_{8 + δ}, at the meeting point of a tricrystal substrate of SrTiO₃ in a geometry chosen to show this effect for a d-wave superconductor. This observation, when considered along with recent photoemission results, proves that the in-plane order parameter for this high-T_c cuprate superconductor closely follows d_{x² − y²} symmetry.

Thin films of DyFe₂ and ErFe₂ have been epitaxially grown along the [110] direction. At 4.2 K, the easy magnetization axis in the films, determined by Mössbauer spectroscopy, is the same as in bulk compounds (i.e. ⟨100⟩ for DyFe₂ and ⟨111⟩ for ErFe₂). At 300 K, the magnetic moments, which remain in the same direction as at 4.2 K in bulk compounds, rotate towards ⟨110⟩ directions in thin films: they are close to the in-plane [10] direction in DyFe₂ films, and close to the perpendicular-to-the-plane [110] direction in ErFe₂ films. These modifications of the magnetic anisotropy are related to the epitaxial strains, and to the sign and the relative importance of the anisotropy and magnetoelastic constants of the compound.

We report an observation of shear-banding, under Couette flow, of the worm-like surfactant system cetyl pyridinium chloride/sodium salicylate (respective concentrations of 100 mM and 60 mM in pure water). The method, based on NMR velocity imaging, allows the direct measurement of velocity, and consequent calculation of shear rate, at a spatial resolution of around 10 μm, sufficient to resolve apparent slip at the inner wall from shear banding within the bulk of the fluid. Above a critical shear rate (around 1 s⁻¹) a high shear rate band is observed in the annulus between concentric rotating cylinders, the width of the band being of order 30 μm with a corresponding shear rate of order 500 s⁻¹. The precise location of the band is sensitive to boundary conditions at the inner wall and is shown to be susceptible to significant broadening.