Interplay of superconductivity and magnetism in strong coupling

A model is introduced describing the interplay between superconductivity and spin-ordering. It is characterized by on-site repulsive electron-electron interactions, causing antiferromagnetism, and nearest-neighbor attractive interactions, giving rise to d-wave superconductivity. Due to a special choice for the lattice, this model has a strong-coupling limit where the superconductivity can be described by a bosonic theory, similar to the strongly coupled negative U Hubbard model. This limit is analyzed in the present paper. A rich mean-field phase diagram is found and the leading quantum corrections to the mean-field results are calculated. The first-order line between the antiferromagnetic- and the superconducting phase is found to terminate at a tricritical point, where two second-order lines originate. At these lines, the system undergoes a transition to- and from a phase exhibiting both antiferromagnetic order and superconductivity. At finite temperatures above the spin-disordering line, quantum-critical behavior is found. For specific values of the model parameters, it is possible to obtain SO(5) symmetry involving the spin- and the phase-sector at the tricritical point. Although this symmetry is explicitly broken by the projection to the lower Hubbard band, it survives on the mean-field level, and modes related to a spontaneously broken SO(5) symmetry are present on the level of the random phase approximation in the superconducting phase.Comment: 16 pages Revtex, 5 figure

Multiparadigm modeling of dynamical crack propagation in silicon using a reactive force field

We report a study of dynamic cracking in a silicon single crystal in which the ReaxFF reactive force field is used for several thousand atoms near the crack tip, while more than 100 000 atoms are described with a nonreactive force field. ReaxFF is completely derived from quantum mechanical calculations of simple silicon systems without any empirical parameters. Our results reproduce experimental observations of fracture in silicon including changes in crack dynamics for different crack orientations

Quantization of Crack Speeds in Dynamic Fracture of Silicon: Multiparadigm ReaxFF Modeling

We report a study of dynamic cracking in a silicon single crystal in which the ReaxFF reactive force field is used for about 3,000 atoms near the crack tip while the other 100,000 atoms of the model system are described with a simple nonreactive force field. The ReaxFF is completely derived from quantum mechanical calculations of simple silicon systems without any empirical parameters. This model has been successfully used to study crack dynamics in silicon, capable of reproducing key experimental results such as orientation dependence of crack dynamics (Buehler et al., Phys. Rev. Lett. 2006). In this article, we focus on crack speeds as a function of loading and crack propagation mechanisms. We find that the steady state crack speed does not increase continuously with applied load, but instead jumps to a finite value immediately after the critical load, followed by a regime of slow increase. Our results quantitatively reproduce experimental observations of crack speeds during fracture in silicon along the (111) planes, confirming the existence of lattice trapping effects. We observe similar effects in the (110) crack direction

On General Axial Gauges for QCD

General Axial Gauges within a perturbative approach to QCD are plagued by 'spurious' propagator singularities. Their regularisation has to face major conceptual and technical problems. We show that this obstacle is naturally absent within a Wilsonian or 'Exact' Renormalisation Group approach and explain why this is so. The axial gauge turns out to be a fixed point under the flow, and the universal 1-loop running of the gauge coupling is computed.Comment: 4 pages, latex, talk presented by DFL at QCD'98, Montpellier, July 2-8, 1998; to be published in Nucl. Phys. B (Proc. Suppl.

Threshold Crack Speed Controls Dynamical Fracture of Silicon Single Crystals

Fracture experiments of single silicon crystals reveal that after the critical fracture load is reached, the crack speed jumps from zero to [approximate]2 km/sec, indicating that crack motion at lower speeds is forbidden. This contradicts classical continuum fracture theories predicting a continuously increasing crack speed with increasing load. Here we show that this threshold crack speed may be due to a localized phase transformation of the silicon lattice from 6-membered rings to a 5–7 double ring at the crack tip

Modeling the sorption dynamics of NaH using a reactive force field

We have parametrized a reactive force field for NaH, ReaxFFNaH, against a training set of ab initio derived data. To ascertain that ReaxFFNaH is properly parametrized, a comparison between ab initio heats of formation of small representative NaH clusters with ReaxFFNaH was done. The results and trend of ReaxFFNaH are found to be consistent with ab initio values. Further validation includes comparing the equations of state of condensed phases of Na and NaH as calculated from ab initio and ReaxFFNaH. There is a good match between the two results, showing that ReaxFFNaH is correctly parametrized by the ab initio training set. ReaxFFNaH has been used to study the dynamics of hydrogen desorption in NaH particles. We find that ReaxFFNaH properly describes the surface molecular hydrogen charge transfer during the abstraction process. Results on heat of desorption versus cluster size shows that there is a strong dependence on the heat of desorption on the particle size, which implies that nanostructuring enhances desorption process. To gain more insight into the structural transformations of NaH during thermal decomposition, we performed a heating run in a molecular dynamics simulation. These runs exhibit a series of drops in potential energy, associated with cluster fragmentation and desorption of molecular hydrogen. This is consistent with experimental evidence that NaH dissociates at its melting point into smaller fragments

Parametrization of a reactive force field for aluminum hydride

A reactive force field, REAXFF, for aluminum hydride has been developed based on density functional theory (DFT) derived data. REAXFF_(AlH_3) is used to study the dynamics governing hydrogen desorption in AlH_3. During the abstraction process of surface molecular hydrogen charge transfer is found to be well described by REAXFF_(AlH_3). Results on heat of desorption versus cluster size show that there is a strong dependence of the heat of desorption on the particle size, which implies that nanostructuring enhances desorption process. In the gas phase, it was observed that small alane clusters agglomerated into a bigger cluster. After agglomeration molecular hydrogen was desorbed from the structure. This thermodynamically driven spontaneous agglomeration followed by desorption of molecular hydrogen provides a mechanism on how mobile alane clusters can facilitate the mass transport of aluminum atoms during the thermal decomposition of NaAlH_4