Tidal friction in close-in satellites and exoplanets: The Darwin theory re-visited

This report is a review of Darwin`s classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) capture into the 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.

Sparse partition universal graphs for graphs of bounded degree

In 1983, Chvatal, Trotter and the two senior authors proved that for any Delta there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph K(N) with N >= Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Delta. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and O(N(2-1/Delta)log(1/Delta)N) edges, with N = [B`n] for some constant B` that depends only on Delta. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Delta is O(n(2-1/Delta)log(1/Delta)n) Our approach is based on random graphs; in fact, we show that the classical Erdos-Renyi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Delta. The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed. (C) 2011 Elsevier Inc. All rights reserved.

Balancing the role of the dental school in teaching, research and patient care; including care for underserved areas

Inequalities within dentistry are common and are reflected in wide differences in the levels of oral health and the standard of care available both within and between countries and communities. Furthermore there are patients, particularly those with special treatment needs, who do not have the same access to dental services as the general public. The dental school should aim to recruit students from varied backgrounds into all areas covered by the oral healthcare team and to train students to treat the full spectrum of patients including those with special needs. It is essential, however, that the dental student achieves a high standard of clinical competence and this cannot be gained by treating only those patients with low expectations for care. Balancing these aspects of clinical education is difficult. Research is an important stimulus to better teaching and better clinical care. It is recognized that dental school staff should be active in research, teaching, clinical work and frequently administration. Maintaining a balance between the commitments to clinical care, teaching and research while also taking account of underserved areas in each of these categories is a difficult challenge but one that has to be met to a high degree in a successful, modern dental school.

C(0) and bi-Lipschitz K-equivalence of mappings

In this paper we investigate the classification of mappings up to K-equivalence. We give several results of this type. We study semialgebraic deformations up to semialgebraic C(0) K-equivalence and bi-Lipschitz K-equivalence. We give an algebraic criterion for bi-Lipschitz K-triviality in terms of semi-integral closure (Theorem 3.5). We also give a new proof of a result of Nishimura: we show that two germs of smooth mappings f, g : R(n) -> R(n), finitely determined with respect to K-equivalence are C(0)-K-equivalent if and only if they have the same degree in absolute value.

Intense violet-blue photoluminescence in BaZrO3 powders: A theoretical and experimental investigation of structural order-disorder

Intense violet-blue photoluminescence (PL) emission at room temperature was verified in BaZrO3 (BZO) powders with structural order-disorder. Ab-initio calculations, ultraviolet-visible absorption spectroscopy and PL were performed. Theoretical results showed that the local disorder in the network-formed Zr clusters present an important role in the formation of hole-electron pair. The experimental data and theoretical results are in agreement, indicating that the PL emission in BZO powders can be related to the structural order-disorder degree in the lattice. (C) 2008 Elsevier B.V. All rights reserved.

Spacelike Surfaces in L(4) with Degenerate Gauss Map

In this paper we study and present a complete classification of spacelike surfaces with degenerate Gauss map in the Lorentz-Minkowski space L(4).

Curvature Estimates for Submanifolds in Warped Products

We give estimates of the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of the total space of a Riemannian submersion.

Construction of Hamiltonian-Minimal Lagrangian submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.

Associated Family of G-Structure Preserving Minimal Immersions in Semi-Riemannian Manifolds

We prove the existence of an associated family of G-structure preserving minimal immersions into semi-Riemannian manifolds endowed with a compatible infinitesimally homogeneous G-structure. We will study in more details minimal embeddings into product of space forms.