The competing roles of extensional viscosity and normal stress differences in complex flows of elastic liquids

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N(1) and N(2) especially N(1), and the extensional viscosity eta(E). In this paper, we shall be mainly interested in `constant-viscosity` Boger fluids, and, accordingly, we shall limit attention to N(1) and eta(E). We shall concentrate on two important flows - axisymmetric contraction flow and ""splashing"" (particularly that which arises when a liquid drop falls onto the free Surface of the same liquid). Modem numerical techniques are employed to provide the theoretical predictions. It is shown that the two obvious manifestations of viscoelastic rheometrical behaviour can sometimes be opposing influences in determining flow characteristics. Specifically, in an axisymmetric contraction flow, high eta(E) , can retard the flow, whereas high N(1) can have the opposite effect. In the splashing experiment, high eta(E) can certainly reduce the height of the so-called Worthington jet, thus confirming some early suggestions, but, again, other rheometrical influences can also have a role to play and the overall picture may not be as clear as it was once envisaged.

Reappraisal of the effective elastic thickness for the sub-Andes using 3-D finite element flexural modelling, gravity and geological constraints

P>Estimates of effective elastic thickness (T(e)) for the western portion of the South American Plate using, independently, forward flexural modelling and coherence analysis, suggest different thermomechanical properties for the same continental lithosphere. We present a review of these T(e) estimates and carry out a critical reappraisal using a common methodology of 3-D finite element method to solve a differential equation for the bending of a thin elastic plate. The finite element flexural model incorporates lateral variations of T(e) and the Andes topography as the load. Three T(e) maps for the entire Andes were analysed: Stewart & Watts (1997), Tassara et al. (2007) and Perez-Gussinye et al. (2007). The predicted flexural deformation obtained for each T(e) map was compared with the depth to the base of the foreland basin sequence. Likewise, the gravity effect of flexurally induced crust-mantle deformation was compared with the observed Bouguer gravity. T(e) estimates using forward flexural modelling by Stewart & Watts (1997) better predict the geological and gravity data for most of the Andean system, particularly in the Central Andes, where T(e) ranges from greater than 70 km in the sub-Andes to less than 15 km under the Andes Cordillera. The misfit between the calculated and observed foreland basin subsidence and the gravity anomaly for the Maranon basin in Peru and the Bermejo basin in Argentina, regardless of the assumed T(e) map, may be due to a dynamic topography component associated with the shallow subduction of the Nazca Plate beneath the Andes at these latitudes.

A computational study of some rheological influences on the ""splashing experiment""

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N(1) and N(2), especially N(1), the extensional viscosity, and the dynamic moduli G` and G ``. In this paper, we shall confine attention to `constant-viscosity` Boger fluids, and, accordingly, we shall limit attention to N(1), eta(E), G` and G ``. We shall concentrate on the ""splashing"" problem (particularly that which arises when a liquid drop falls onto the free surface of the same liquid). Modern numerical techniques are employed to provide the theoretical predictions. We show that high eta(E) can certainly reduce the height of the so-called Worthington jet, thus confirming earlier suggestions, but other rheometrical influences (steady and transient) can also have a role to play and the overall picture may not be as clear as it was once envisaged. We argue that this is due in the main to the fact that splashing is a manifestly unsteady flow. To confirm this proposition, we obtain numerical simulations for the linear Jeffreys model. (C) 2010 Elsevier B.V. All rights reserved.

Instabilities in thermal gravity with a cosmological constant

It is shown that in quantum gravity at finite temperature, the effective potential evaluated in the tadpole approximation can have a local minimum below a certain critical temperature. However, when the leading higher order thermal loop corrections are included, one finds that no static solution exists at high temperature. (C) 2008 Elsevier B.V. All rights reserved.

Influence of the halo upon angular distributions for elastic scattering and breakup

The angular distributions for elastic scattering and breakup of halo nuclei are analysed using a near-side/far-side decomposition within the framework of the dynamical eikonal approximation. This analysis is performed for (11)Be impinging on Pb at 69 MeV/nucleon. These distributions exhibit very similar features. In particular they are both near-side dominated, as expected from Coulomb-dominated reactions. The general shape of these distributions is sensitive mostly to the projectile-target interactions, but is also affected by the extension of the halo. This suggests the elastic scattering not to be affected by a loss of flux towards the breakup channel. (C) 2010 Elsevier B.V. All rights reserved.

On the Casimir energy for a massive quantum scalar field and the cosmological constant

We present a rigorous, regularization-independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass mu not equal 0 which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field in which the expectation value of the renormalized energy-momentum tensor is, for any fixed time, independent of the space coordinate and of the perfect fluid form g(mu,nu)rho with rho > 0, thus providing a concrete quantum field theoretic model of the cosmological constant. This rho represents the energy density associated to a state consisting of the vacuum and a certain number of excitations of zero momentum, i.e., the constituents correspond to lowest energy and pressure p <= 0. (C) 2009 Elsevier Inc. All rights reserved.

Challenging measurement of the (16)O+(27)Al elastic and inelastic angular distributions up to large angles

The (16)O+(27)Al elastic and inelastic angular distributions have been measured in a broad angular range (13 degrees < theta(lab) < 52 degrees) at about 100 MeV incident energy. The use of the MAGNEX large acceptance magnetic spectrometer and of the ray-reconstruction analysis technique has been crucial in order to provide, in the same experiment, high-resolution energy spectra and cross-section measurements distributed over more than seven orders of magnitude down to hundreds of nb/sr. (C) 2011 Elsevier B.V. All rights reserved.

Effect on the heavy-ion fusion and elastic scattering cross sections of common approximations assumed in coupled-channel calculations

We study the effects of several approximations commonly used in coupled-channel analyses of fusion and elastic scattering cross sections. Our calculations are performed considering couplings to inelastic states in the context of the frozen approximation, which is equivalent to the coupled-channel formalism when dealing with small excitation energies. Our findings indicate that, in some cases, the effect of the approximations on the theoretical cross sections can be larger than the precision of the experimental data.

Study of (9)Be+(12)C elastic scattering at energies near the Coulomb barrier

In this work, angular distribution measurements for the elastic channel were performed for the (9)Be + (12)C reaction at the energies E(Lab) = 13.0, 14.5, 17.3, 19.0 and 21.0 MeV, near the Coulomb barrier. The data have been analyzed in the framework of the double folding Sao Paulo potential. The experimental elastic scattering angular distributions were well described by the optical potential at forward angles for all measured energies. However, for the three highest energies, an enhancement was observed for intermediate and backward angles. This can be explained by the elastic transfer mechanism. (C) 2011 Elsevier B.V. All rights reserved.

Elastic scattering of a proton-halo nucleus: (8)B+(58)Ni

The elastic channel of the (8)B + (58)Ni system has been measured at energies around the Coulomb barrier. An optical potential fi to the experimental angular distributions is obtained. The total reaction cross section consistent with the obtained potential is reported and possible deviations from normal behaviour are discussed.

Temperature Dependence of Rb(2) Molecule Formation Rate Constant in a Magneto-Optical Trap

In this paper, we report the measurement of Rb(2) molecule formation rate constant due to a two body process in a magneto-optical trap as a function of the sample temperature. The ground state molecules are detected by two-photon ionization, through the intermediate a(3)Sigma(+)(u) -> 2(3)Pi(g) molecular band. Our results show that the Rb(2) molecules formed in the MOT could be due to a wave shape resonance, which enhances the molecule formation rate. This effect may be used to enhance the molecule production; and therefore it maybe important to future experiments involving production and trapping of cold ground state molecules.

CONTRA: Improving the performance of dynamic investigations in natural abundance organic solids by mirror-symmetric constant-time CODEX

We present a minor but essential modification to the CODEX 1D-MAS exchange experiment. The new CONTRA method, which requires minor changes of the original sequence only, has advantages over the previously introduced S-CODEX, since it is less sensitive to artefacts caused by finite pulse lengths. The performance of this variant, including the finite pulse effect, was confirmed by SIMPSON calculations and demonstrated on a number of dynamic systems. (C) 2007 Elsevier Inc. All rights reserved.

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

Minimal surfaces in S(3) with constant contact angle

We provide a characterization of the Clifford Torus in S(3) via moving frames and contact structure equations. More precisely, we prove that minimal surfaces in S(3) with constant contact angle must be the Clifford Torus. Some applications of this result are then given, and some examples are discussed.

Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in De Sitter space

In this paper we give a partially affirmative answer to the following question posed by Haizhong Li: is a complete spacelike hypersurface in De Sitter space S(1)(n+1)(c), n >= 3, with constant normalized scalar curvature R satisfying n-2/nc <= R <= c totally umbilical? (C) 2008 Elsevier B.V. All rights reserved.