Local symmetries in gauge theories in a finite-dimensional setting

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge theories, but is already true even for global symmetries when one allows for fields that are sections of bundles with (possibly) non-trivial topology or, even when these are topologically trivial, in the absence of a preferred trivialization. (C) 2012 Elsevier B.V. All rights reserved.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

Adsorption of NO on the Rh-13, Pd-13, Ir-13, and Pt-13 Clusters: A Density Functional Theory Investigation

The adsorption of NO on transition-metal (TM) surfaces has been widely studied by experimental and theoretical techniques; however, our atomistic understanding of the interaction of nitrogen monoxide (NO) with small TM clusters is far from satisfactory, which compromises a deep understanding of real catalyst devices. In this study, we report a density functional theory study of the adsorption properties of NO on the TM13 (TM = Rh, Pd, Ir, Pt) clusters employing the projected augmented wave method. We found that the interaction of NO with TM13 is much more complex than that for NO/TM(111). In particular, for low symmetry TM13 clusters, there is a strong rearrangement of the electronic charge density upon NO adsorption and, as a consequence, the adsorption energy shows a very complex dependence even for adsorption sites with the same local effective coordination. We found a strong enhancement of the binding energy of NO to the TM13 clusters compared with the TM(111) surfaces, as the antibonding NO states are not occupied for NO/TM13, and the general relationship based on the d-band model between adsorption energy and the center of gravity of the occupied d-states does not hold for the studied TM13 clusters, in particular, for clusters with low symmetry. In contrast with the adsorption energy trends, the geometric NO/TM13 parameters and the vibrational N-O frequencies for different coordination sites follow the same trend as for the respective TM(111) surfaces, while the changes in the frequencies between different surfaces and TM13 clusters reflect the strong NO-TM13 interaction.

Recoupled separated-local-field experiments and applications to study intermediate-regime molecular motions

A specific separated-local-field NMR experiment, dubbed Dipolar-Chemical-Shift Correlation (DIPSHIFT) is frequently used to study molecular motions by probing reorientations through the changes in XH dipolar coupling and T-2. In systems where the coupling is weak or the reorientation angle is small, a recoupled variant of the DIPSHIFT experiment is applied, where the effective dipolar coupling is amplified by a REDOR-like pi-pulse train. However, a previously described constant-time variant of this experiment is not sensitive to the motion-induced T-2 effect, which precludes the observation of motions over a large range of rates ranging from hundreds of Hz to around a MHz. We present a DIPSHIFT implementation which amplifies the dipolar couplings and is still sensitive to T-2 effects. Spin dynamics simulations, analytical calculations and experiments demonstrate the sensitivity of the technique to molecular motions, and suggest the best experimental conditions to avoid imperfections. Furthermore, an in-depth theoretical analysis of the interplay of REDOR-like recoupling and proton decoupling based on Average-Hamiltonian Theory was performed, which allowed explaining the origin of many artifacts found in literature data. (C) 2012 Elsevier Inc. All rights reserved.

Hard Thermal Loops in the n-Dimensional phi(3) Theory

We derive a closed-form result for the leading thermal contributions which appear in the n-dimensional I center dot (3) theory at high temperature. These contributions become local only in the long wavelength and in the static limits, being given by different expressions in these two limits.