Table of contents

Several operator relations for differential operators on a Riemannian manifold are written down in terms of a set of basis operators which act on an exterior algebra. Differential geometric relations are expressed in terms of these operators. An important relation which connects the Laplace-Beltrami operator on p-forms to the Bochner Laplacian is developed.

By examining the effects of rotational and orbital motions of the Earth on wave propagation in the global positioning system and an intercontinental microwave link, it is pointed out that the Earth's orbital motion has no influence on these earthbound wave propagations, while the Earth's rotation does contribute to the Sagnac effect. As the propagation mechanism in the Michelson-Morley experiment cannot be different from that in the aforementioned ones, it is concluded that due to the Earth's rotation, the shift in interference fringe in this famous experiment is not exactly zero. However, by virtue of the round-trip propagation path, this shift becomes second order and hence is too small to observe within the present precision.

We consider the linear response of a system modelled by continuous-time random walks (CTRW) to an external field pulse of rectangular shape. We calculate the corresponding response function explicitly and show that it exhibits aging, i.e. that it is not translationally invariant in the time domain. This result differs from that of systems which behave according to fractional Fokker-Planck equations.

We show that the Random Energy Model has interesting rejuvenation properties in its frozen phase. Different "susceptibilities" to temperature changes, for the free energy and for other ("magnetic" ) observables, can be computed exactly. These susceptibilities diverge at the transition temperature, as (1 − T/T_c)⁻³ for the free energy.

We present a theory which accounts for the increase in interfacial tension of water due to the presence of 1:1 electrolyte. The agreement between the theory and experiment is excellent, extending all the way to relatively high salt concentrations of 1 M. For low concentrations of electrolyte the theory reduces to the Onsager-Samaras limiting law.

Conformal nonlinear σ-models (NSM) are constructed in arbitrary D-dimensional spaces. For odd D they are always nonlocal. It is shown that the conformal NSM on spaces with π_{D − 1} = have topological solutions of "hedgehog" and "anti-hedgehog" types with logarithmic energies. For spaces with π_D ≠ 0 they have also topological excitations of instanton type with finite energies. The possible interesting manifolds are discussed.

The interfacial structure of physisorbed homopolymers is studied by means of Monte Carlo simulations. The focus is on relatively long chains in an effort to reach the "power law regime" inside the intermediate portion of the solid-polymer interface. The chain lengths required exceed substantially those of polymers typically used for colloid stabilization. Our findings confirm the correctness of the generic -4/3 exponent for long chains. Furthermore, they quantify the difference between mean-field predictions and Monte Carlo data, which is exaggerated for long chains. Finally, these findings illustrate that resolution of the finer trends of interfacial structure requires even longer chain lengths than those studied in this article.

Spectroscopy was performed along three distinct crystallographic axes of a high refractive index contrast photonic crystal and the spectra were compared with theoretical calculations. Deep dips were observed in the experimental spectra at 2.1 and 3.2 μm and predicted by calculations. The photonic crystal was prepared through melt-imbibing of selenium into a self-assembled face-centered-cubic colloidal crystal template.

We report and analyze the results of numerical studies of dense granular flows on an incline with a "rough" bottom in two and three dimensions, using linear damped spring or Hertzian force laws between particles with a Coulomb failure criterion. This flow geometry produces a constant density profile that satisfies scaling relations of the Bagnold, rather than viscous, kind. The type of force law has little impact on the behavior of the system. The bulk and the surface layer differ in their rheology, as evidenced by the change in principal stress directions near the surface. Surface-only flows are not observed for the cases studied.

We have quantitatively investigated the parity-breaking bifurcation in a liquid column pattern with periodic boundary conditions formed below an overflowing dish. For high enough viscosity homogeneous global drifting states can be stabilized within a large range of wavelengths. Data are analyzed in terms of coupled phase and amplitude equations and show that the bifurcation to a global drifting state is supercritical, the flow rate and phase gradient behaving as effective control parameters. The wavelength dependence shows that new non-linearities must be added to the usual model. We also identify at large flow rate a regime of spatio-temporal chaos that mixes oscillations, drifts, coalescences and nucleations of columns.

A new "indirect" laser-driven ultrashort hard-X-ray source based on the combination of a high-repetition rate femtosecond laser system with a conventional X-ray tube is demonstrated. This hard-X-ray source promises an outstanding performance in terms of average X-ray power, simplicity and handling as compared to "direct" X-ray sources based on high-power laser-produced plasmas.

We show, using surface pressure vs. molecular area isotherm measurements and synchrotron grazing X-ray diffraction, that 4BCD12 molecules, which consist of a central flexible bowl-like core to which eight long lateral hydrocarbon chains are bound, form a stable edge-on monolayer. Experimental data indicate that six lateral hydrocarbon chains orient upwards to form a quasi-rectangular lattice of 43° tilted hydrocarbon chains. The obtained axially asymmetric phase, which we label edge₂⁶-on, allows using surface potential measurements, for the validation of literature electric models of a single monolayer spread at the air-water interface.

Resonant X-ray scattering measurements on the energy dependence of multilayer Bragg reflections are presented. It is shown that the deviations from the ideal Bragg law at resonance are due to refraction, which allows a determination of the real part of the extended X-ray absorption fine-structure (EXAFS) function. With this new technique, it is possible to obtain phase-sensitive EXAFS information without the difficult data analysis and absorption corrections required by the diffraction anomalous fine-structure technique.

We propose that the natural tendency of banana-shaped mesogen molecules to induce a local bend of the nematic director can result in pathological elasticity, with negative bend elastic constant. Under this hypothesis, a simple Landau-like phenomenological model predicts a symmetry-breaking transition inside the nematic phase, from uniform textures toward spontaneous periodic distortion, either oscillating splay-bend or conical twist-bend helix. The predicted lower symmetry nematic phases are expected to show interesting polar properties, similar to those already reported for banana-shaped smectogens.

Scanning tunneling microscopy of low coverages of 1-nitronaphtalene (NN) on reconstructed Au(111) reveals that the face-centered-cubic (fcc) reconstruction domains of steps are densely and selectively decorated. Molecular dynamics simulations identify this phenomenon as the self-assembly of hydrogen-like bonded supramolecular chains driven by the step electrostatic potential. First principles calculations predict weak adsorption at domain boundaries, and stable adsorption at the step edge of the fcc domains, explaining the selective decoration.

The low and glasslike thermal conductivity of metal-doped semiconductor clathrate compounds makes them potentially high-efficiency thermoelectric materials. The cause of this unique and remarkable property has been postulated to be due to resonant scattering of lattice phonons by localized vibrations of the dopants. We present theoretical evidence in support of this hypothesis through the analysis of electronic and vibrational interactions between dopant atoms with the host framework. In particular, the contrasting behavior of two clathrates: the glasslike thermal conductivity in Na₈Si₄₆ and the normal behavior in Cs₈Sn₄₄ can be rationalized.

We report results from a systematic strong-coupling expansion of a spin-½ Heisenberg chain coupled to Einstein phonons and a frustrating next-nearest-neighbor spin interaction. It is not obvious which interaction dominates in the regime of small coupling constants. In the non-adiabatic regime (ℏΩ ≈ J) this model is used to describe the zero-temperature properties of CuGeO₃. The linked cluster expansion allows the determination of observables in the thermodynamic limit preserving the full lattice dynamics without a truncation of the phononic Hilbert space. We show that the spin-phonon coupling leads to a renormalization of the elementary triplet dispersion. Surprisingly, in the non-adiabatic regime a substantial renormalization of the spin gap only sets in at much larger couplings than those proposed for CuGeO₃. The ground-state magnetic correlations are found to be hardly affected by the spin-phonon coupling, but dominated by the frustrating magnetic interaction in the parameter regime relevant for CuGeO₃.

The lattice dynamics of the antiferromagnetic FeBO₃ crystal has been calculated by ab initio density-functional theory and measured by nuclear inelastic absorption spectroscopy. The calculations for the antiferromagnetic phase reproduce the experimental lattice parameters of the unit cell and provide phonon dispersion relations which agree well with the measured partial density of phonon states for the Fe atoms. Calculations for the nonmagnetic configuration lead to a smaller crystal volume and drastically higher phonon frequencies for the Fe atoms.

We present calculations of the non-collinear magnetic structure in Fe/Cr superlattices having imperfect interfaces modeled by considering atomic steps in the Cr layers and Fe/Cr interfacial ordered compounds. The magnetic moments maps and the interlayer couplings are obtained directly from self-consistent tight-binding band structure calculations allowing to discuss the results in the proximity magnetism framework. We show that the bilinear-biquadratic expression for the coupling energy fits nicely the calculated interlayer couplings curves in all considered cases.

Using high-resolution X-ray scattering techniques, we have measured the wave vector of the sliding charge density wave as a function of beam position, along the length of NbSe₃ whiskers. We show that structural imperfections and radiation-induced defects increase locally the CDW pinning force, and give rise to CDW phase distortions. Using the semi-microscopic model of Brazovskii et al. (Phys. Rev. B, 61 (2000) 10640) describing the normal ↔ condensed carrier conversion, with spatially varying parameters, we account for the experimental spatial dependence of the CDW phase gradient near both types of defects.

We performed point-contact spectroscopy on the binary superconductor MgB₂. The differential conductance shows gap-related structures which vary in width and position from contact to contact. The distribution of energy gaps shows a distinct accumulation around 1.7 and 7 meV which is associated with the occurrence of a small and a large energy gap in MgB₂. While with increasing T the structure in dI/dV associated with the small gap is present up to T_c, in magnetic field it is suppressed well below B_c2.

Single-phase, textured samples of a new orthorhombic intermetallic compound Ho₂Ni₂Pb have been fabricated (space group Cmmm). Here the bulk magnetic properties are presented as determined via magnetization, susceptibility, heat capacity and resistivity measurements. The results exhibit two distinct magnetic transitions and large metamagnetic effects. Such behaviour is related to the unusual rare-earth symmetry of the highly anisotropic crystal structure.

Nuclear resonant scattering of synchrotron radiation from the 25.6 keV level of ¹⁶¹Dy is studied with two techniques: nuclear forward scattering (NFS) and nuclear incoherent scattering (NIS). NFS time spectra of Dy metal are measured at temperatures ranging from 15 K to 80 K. They reveal electron spin relaxation in ferromagnetic dysprosium with long relaxation times of ≃ 10–30 ns. NIS energy spectra of Dy₂O₃ at room temperature are measured with meV resolution. Scattering accompanied by phonon excitation is observed.