Comparative efficiency of finite, boundary and hybrid element methods in elastostatics

The comparative computational efficiencies of the finite element (FEM), boundary element (BEM), and hybrid boundary element-finite element (HBFEM) analysis techniques are evaluated for representative bounded domain interior and unbounded domain exterior problems in elastostatics. Computational efficiency is carefully defined in this study as the computer time required to attain a specified level of solution accuracy. The study found the FEM superior to the BEM for the interior problem, while the reverse was true for the exterior problem. The hybrid analysis technique was found to be comparable or superior to both the FEM and BEM for both the interior and exterior problems

Chemical Differences between K and Na in Alkali Cobaltates

K$_x$CoO$_2$ shares many similarities with Na$_x$CoO$_2$, as well as some important differences (no hydration-induced superconductivity has been reported). At $T_{c2}$=20 K, K$_{0.5}$CoO$_2$ becomes an insulator with a tiny optical gap as happens in Na$_{0.5}$CoO$_2$ at 52 K. This similarity, with a known common structure, enables direct comparisons to be made. Using the K-zigzag structure recently reported and the local density approximation, we compare and contrast these cobaltates at x=0.5. Although the electronic structures are quite similar as expected, substantial differences are observed near the Fermi level. These differences are found to be attributable mostly to the chemical, rather than structural difference: although Na is normally considered to be fully ion, K has somewhat more highly ionic character than does Na in these cobaltates.Comment: 5 paper

The Proposed Quadruple System SZ Herculis: Revised LITE Model and Orbital Stability Study

In a recent study, Lee et al. presented new photometric follow-up timing observations of the semi-detached binary system SZ Herculis and proposed the existence of two hierarchical cirumbinary companions. Based on the light-travel time effect, the two low-mass M-dwarf companions are found to orbit the binary pair on moderate to high eccentric orbits. The derived periods of these two companions are close to a 2:1 mean-motion orbital resonance. We have studied the stability of the system using the osculating orbital elements as presented by Lee et al. Results indicate an orbit-crossing architecture exhibiting short-term dynamical instabilities leading to the escape of one of the proposed companions. We have examined the system's underlying model parameter-space by following a Monte Carlo approach and found an improved fit to the timing data. A study of the stability of our best-fitting orbits also indicates that the proposed system is generally unstable. If the observed anomalous timing variations of the binary period is due to additional circumbinary companions, then the resulting system should exhibit a long-term stable orbital configuration much different from the orbits suggested by Lee et al. We, therefore, suggest that based on Newtonian-dynamical considerations, the proposed quadruple system cannot exist. To uncover the true nature of the observed period variations of this system, we recommend future photometric follow-up observations that could further constrain eclipse-timing variations and/or refine light-travel time models.Comment: 24 pages, 2 tables, 8 figures (bw), submitted to A

Large-N Yang-Mills Theory as Classical Mechanics

To formulate two-dimensional Yang-Mills theory with adjoint matter fields in the large-N limit as classical mechanics, we derive a Poisson algebra for the color-invariant observables involving adjoint matter fields. We showed rigorously in J. Math. Phys. 40, 1870 (1999) that different quantum orderings of the observables produce essentially the same Poisson algebra. Here we explain, in a less precise but more pedagogical manner, the crucial topological graphical observations underlying the formal proof.Comment: 8 pages, 3 eps figues, LaTeX2.09, aipproc macros needed; conference proceeding of MRST '99 (10-12 May, 1999, Carleton University, Canada

Unitary Irreducible Representations of a Lie Algebra for Matrix Chain Models

There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way. Moreover, they are the only states with a finite number of non-zero quantum numbers with respect to a certain set of maximally commuting linearly independent quantum observables. Any other state is a tensor product of a multiple meson state and a state coming from a representation of a quotient algebra that extends and generalizes the Virasoro algebra. We expect the representation theory of this quotient algebra to describe physical systems at the thermodynamic limit.Comment: 46 pages, no figure; LaTeX2e, amssymb, latexsym; typos correcte

Integrability of Supersymmetric Quantum Matrix Models in the Large-N Limit

Many physical systems like supersymmetric Yang-Mills theories are formulated as quantum matrix models. We discuss how to apply the Beth ansatz to exactly solve some supersymmetric quantum matrix models in the large-N limit. Toy models are constructed out of the one-dimensional Hubbard and t-J models as illustrations.Comment: 11 pages, LaTeX2e; minor changes, citations adde

Unified description of pairing, trionic and quarteting states for one-dimensional SU(4) attractive fermions

Paired states, trions and quarteting states in one-dimensional SU(4) attractive fermions are investigated via exact Bethe ansatz calculations. In particular, quantum phase transitions are identified and calculated from the quarteting phase into normal Fermi liquid, trionic states and spin-2 paired states which belong to the universality class of linear field-dependent magnetization in the vicinity of critical points. Moreover, unified exact results for the ground state energy, chemical potentials and complete phase diagrams for isospin $S=1/2, 1, 3/2$ attractive fermions with external fields are presented. Also identified are the magnetization plateaux of $m^z=M_s/3$ and $m^z=2M_s/3$, where $M_s$ is the magnetization saturation value. The universality of finite-size corrections and collective dispersion relations provides a further test ground for low energy effective field theory.Comment: 13 pages, 4 figure

Nonmonotonic behavior of resistance in a superconductor-Luttinger liquid junction

Transport through a superconductor-Luttinger liquid junction is considered. When the interaction in the Luttinger liquid is repulsive, the resistance of the junction with a sufficiently clean interface shows nonmonotonic temperature- or voltage-dependence due to the competition between the superconductivity and the repulsive interaction. The result is discussed in connection with recent experiments on single-wall carbon nanotubes in contact with superconducting leads.Comment: Revtex4, 2 eps figure files, slightly revised from an earlier version submitted to PRL on 2001.12.