Multidimensional Continued Fractions,Dynamical Renormalization and KAM Theory

The disadvantage of ‘traditional’ multidimensional continued fraction algorithms is that it is not known whether they provide simultaneous rational approximations for generic vectors. Following ideas of Dani, Lagarias and Kleinbock-Margulis we describe a simple algorithm based on the dynamics of flows on the homogeneous space (the space of lattices of covolume one) that indeed yields best possible approximations to any irrational vector. The algorithm is ideally suited for a number of dynamical applications that involve small divisor problems. As an example, we explicitly construct a renormalization scheme for the linearization of vector fields on tori of arbitrary dimension.     

Diode-Laser Spectroscopy of the nu(19a) Band of Chlorobenzene in a Supersonic Jet

The diode-laser absorption spectrum of the nu(19a) band of the chlorobenzene molecule cooled in a supersonic jet is presented and transitions from low J, K(a), and K(c) values (0-14) are reported. The C(6)H(5)(35)Cl band center has been found at nu(0) = 1483.894 cm(-1) and rotational constants for the upper state have been determined from a least-squares fitting to experimental data. The band center for the C(6)H(5)(37)Cl isotope has also been obtained. Copyright 2000 Academic Press.     

Improving the 1H indirect dimension resolution of 2D CRAMPS NMR spectra: a simulation and experimental investigation

An experimental and simulation investigation regarding the effect of various CRAMPS parameters (delays interleaved with the decoupling shape, z-rotation symmetry and offset frequency) on the DUMBO decoupling performance is presented using two model compounds, glycine and tyrosine·HCl. Although the conclusions of this work may be extended to the other homonuclear-decoupling schemes, this work focuses essentially on the effect of adding interleaved delays to DUMBO decoupling during the indirect dimension using different 2D pulse-scheme architectures. While the simulations revealed an increasing loss of the spectral resolution with longer delays (from 0 to 6 μs), the experimental 2D (1)H DUMBO NMR correlation spectra revealed that the inclusion of delays, during the indirect dimension, improves the (1)H resolution whether the z-rotation symmetry was used or not. The best experimental spectra are obtained when z-rotation symmetry and windows are combined.     

On the cosmological constant problem and brane-world geometry

The cosmological constant problem is examined within the context of the covariant brane-world gravity, based on Nash’s embedding theorem for Riemannian geometries. We show that the vacuum structure of the brane-world is more complex than General Relativity’s because it involves extrinsic elements, in specific, the extrinsic curvature. In other words, the shape (or local curvature) of an object becomes a relative concept, instead of the “absolute shape” of General Relativity. We point out that the immediate consequence is that the cosmological constant and the energy density of the vacuum quantum fluctuations have different physical meanings: while the vacuum energy density remains confined to the four-dimensional brane-world, the cosmological constant is a property of the bulk’s gravitational field that leads to the conclusion that these quantities cannot be compared, as it is usually done in General Relativity. Instead, the vacuum energy density contributes to the extrinsic curvature, which in turn generates Nash’s perturbation of the gravitational field. On the other hand, the cosmological constant problem ceases to be in the brane-world geometry, reappearing only in the limit where the extrinsic curvature vanishes.     

Crystal microstructure of annealed nanocrystalline Chromium studied by synchrotron radiation diffraction

The microstructure of electrodeposited nanocrystalline chromium (n-Cr) was studied by using synchrotron radiation (SR) diffraction, SEM, TEM, and EDX techniques. The as-prepared n-Cr samples show the standard bcc crystal structure of Cr with volume-averaged column lengths varying from 25 to 30 nm. The grain growth kinetics and the oxidation kinetics were studied by time resolved SR diffraction measurements with n-Cr samples annealed at 400, 600, and 800 °C. The grain growth process is relatively fast and it occurs within the first 10 min of annealing. The final crystallite size depends only on the annealing temperature and not on the initial grain size or on the oxygen content. The final volume-averaged column lengths observed after 50 min annealing are 40(4), 80(1), and 120(2) nm for temperatures 400, 600, and 800 °C, respectively. It is shown that annealing ex situ of n-Cr at 800 °C both under vacuum and in air gives a grain growth process with the same final crystallite sizes. The formation of the Cr₂O₃ and CrH phases is observed during annealing.     

Thermal stability of corrugated epitaxial graphene grown on Re(0001)

We report on a novel approach to determine the relationship between the corrugation and the thermal stability of epitaxial graphene grown on a strongly interacting substrate. According to our density functional theory calculations, the C single layer grown on Re(0001) is strongly corrugated, with a buckling of 1.6 ?, yielding a simulated C 1s core level spectrum which is in excellent agreement with the experimental one. We found that corrugation is closely knit with the thermal stability of the C network: C-C bond breaking is favored in the strongly buckled regions of the moiré cell, though it requires the presence of diffusing graphene layer vacancies.     

A two-Higgs doublet model with remarkable CP properties

We analyze generalized CP symmetries of two-Higgs doublet models, extending them from the scalar to the fermion sector of the theory. We show that, other than the usual CP transformation, there is only one of those symmetries which does not imply massless charged fermions. That single model which accommodates a fermionic mass spectrum compatible with experimental data possesses a remarkable feature. Through a soft breaking of the symmetry it displays a new type of spontaneous CP violation, which does not occur in the scalar sector responsible for the symmetry breaking mechanism but, rather, in the fermion sector.