A combined wavelet-element free Galerkin method for numerical calculations of electromagnetic fields

Author name used in this publication: S. L. HoAuthor name used in this publication: J. M. Machado2002-2003 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Families of Graphs with W_r({G},q) Functions That Are Nonanalytic at 1/q=0

Denoting $P(G,q)$ as the chromatic polynomial for coloring an $n$-vertex graph $G$ with $q$ colors, and considering the limiting function $W(\{G\},q) = \lim_{n \to \infty}P(G,q)^{1/n}$, a fundamental question in graph theory is the following: is $W_r(\{G\},q) = q^{-1}W(\{G\},q)$ analytic or not at the origin of the $1/q$ plane? (where the complex generalization of $q$ is assumed). This question is also relevant in statistical mechanics because $W(\{G\},q)=\exp(S_0/k_B)$, where $S_0$ is the ground state entropy of the $q$-state Potts antiferromagnet on the lattice graph $\{G\}$, and the analyticity of $W_r(\{G\},q)$ at $1/q=0$ is necessary for the large-$q$ series expansions of $W_r(\{G\},q)$. Although $W_r$ is analytic at $1/q=0$ for many $\{G\}$, there are some $\{G\}$ for which it is not; for these, $W_r$ has no large-$q$ series expansion. It is important to understand the reason for this nonanalyticity. Here we give a general condition that determines whether or not a particular $W_r(\{G\},q)$ is analytic at $1/q=0$ and explains the nonanalyticity where it occurs. We also construct infinite families of graphs with $W_r$ functions that are non-analytic at $1/q=0$ and investigate the properties of these functions. Our results are consistent with the conjecture that a sufficient condition for $W_r(\{G\},q)$ to be analytic at $1/q=0$ is that $\{G\}$ is a regular lattice graph $\Lambda$. (This is known not to be a necessary condition).Comment: 22 pages, Revtex, 4 encapsulated postscript figures, to appear in Phys. Rev.

Matrix Black Holes

Four and five dimensional extremal black holes with nonzero entropy have simple presentations in M-theory as gravitational waves bound to configurations of intersecting M-branes. We discuss realizations of these objects in matrix models of M-theory, investigate the properties of zero-brane probes, and propose a measure of their internal density. A scenario for black hole dynamics is presented.Comment: 26 pages, harvmac; a few more references and additional comment

Insulator-Superfluid transition of spin-1 bosons in an optical lattice in magnetic field

We study the insulator-superfluid transition of spin-1 bosons in an optical lattice in a uniform magnetic field. Based on a mean-field approximation we obtained a zero-temperature phase diagram. We found that depending on the particle number the transition for bosons with antiferromagnetic interaction may occur into different superfluid phases with spins aligned along or opposite to the field direction. This is qualitatively different from the field-free transition for which the mean-field theory predicts a unique (polar) superfluid state for any particle number.Comment: 10 pages, 2 eps figure

Listening In on the Past: What Can Otolith δ18O Values Really Tell Us about the Environmental History of Fishes?

Oxygen isotope ratios from fish otoliths are used to discriminate marine stocks and reconstruct past climate, assuming that variations in otolith δ18O values closely reflect differences in temperature history of fish when accounting for salinity induced variability in water δ18O. To investigate this, we exploited the environmental and migratory data gathered from a decade using archival tags to study the behaviour of adult plaice (Pleuronectes platessa L.) in the North Sea. Based on the tag-derived monthly distributions of the fish and corresponding temperature and salinity estimates modelled across three consecutive years, we first predicted annual otolith δ18O values for three geographically discrete offshore sub-stocks, using three alternative plausible scenarios for otolith growth. Comparison of predicted vs. measured annual δ18O values demonstrated >96% correct prediction of sub-stock membership, irrespective of the otolith growth scenario. Pronounced inter-stock differences in δ18O values, notably in summer, provide a robust marker for reconstructing broad-scale plaice distribution in the North Sea. However, although largely congruent, measured and predicted annual δ18O values of did not fully match. Small, but consistent, offsets were also observed between individual high-resolution otolith δ18O values measured during tag recording time and corresponding δ18O predictions using concomitant tag-recorded temperatures and location-specific salinity estimates. The nature of the shifts differed among sub-stocks, suggesting specific vital effects linked to variation in physiological response to temperature. Therefore, although otolith δ18O in free-ranging fish largely reflects environmental temperature and salinity, we counsel prudence when interpreting otolith δ18O data for stock discrimination or temperature reconstruction until the mechanisms underpinning otolith δ18O signature acquisition, and associated variation, are clarified

Quantum tunneling across spin domains in a Bose-Einstein condensate

Quantum tunneling was observed in the decay of metastable spin domains in gaseous Bose-Einstein condensates. A mean-field description of the tunneling was developed and compared with measurement. The tunneling rates are a sensitive probe of the boundary between spin domains, and indicate a spin structure in the boundary between spin domains which is prohibited in the bulk fluid. These experiments were performed with optically trapped F=1 spinor Bose-Einstein condensates of sodium.Comment: 5 pages, 4 figure

Quantum metastability in a class of moving potentials

In this paper we consider quantum metastability in a class of moving potentials introduced by Berry and Klein. Potential in this class has its height and width scaled in a specific way so that it can be transformed into a stationary one. In deriving the non-decay probability of the system, we argue that the appropriate technique to use is the less known method of scattering states. This method is illustrated through two examples, namely, a moving delta-potential and a moving barrier potential. For expanding potentials, one finds that a small but finite non-decay probability persists at large times. Generalization to scaling potentials of arbitrary shape is briefly indicated.Comment: 10 pages, 1 figure

Ground State Entropy of Potts Antiferromagnets: Bounds, Series, and Monte Carlo Measurements

We report several results concerning $W(\Lambda,q)=\exp(S_0/k_B)$, the exponent of the ground state entropy of the Potts antiferromagnet on a lattice $\Lambda$. First, we improve our previous rigorous lower bound on $W(hc,q)$ for the honeycomb (hc) lattice and find that it is extremely accurate; it agrees to the first eleven terms with the large-$q$ series for $W(hc,q)$. Second, we investigate the heteropolygonal Archimedean $4 \cdot 8^2$ lattice, derive a rigorous lower bound, on $W(4 \cdot 8^2,q)$, and calculate the large-$q$ series for this function to $O(y^{12})$ where $y=1/(q-1)$. Remarkably, these agree exactly to all thirteen terms calculated. We also report Monte Carlo measurements, and find that these are very close to our lower bound and series. Third, we study the effect of non-nearest-neighbor couplings, focusing on the square lattice with next-nearest-neighbor bonds.Comment: 13 pages, Latex, to appear in Phys. Rev.

Significance of herpesvirus immediate early gene expression in cellular immunity to cytomegalovirus infection

Interstitial pneumonia linked with reactivation of latent human cytomegalovirus due to iatrogenic immunosuppression can be a serious complication of bone marrow transplantation therapy of aplastic anaemia and acute leukaemia1. Cellular immunity plays a critical role in the immune surveillance of inapparent cytomegalovirus infections in man and the mouse1−7. The molecular basis of latency, however, and the interaction between latently or recurrently infected cells and the immune system of the host are poorfy understood. We have detected a so far unknown antigen in the mouse model. This antigen is found in infected cells in association with the expression of the herpesvirus 'immediate early' genes and is recognized by cytolytic T lymphocytes (CTL)8. We now demonstrate that an unexpectedly high proportion of the CTL precursors generated in vivo during acute murine cytomegalovirus infection are specific for cells that selectively synthesize immediate early proteins, indicating an immunodominant role of viral non-structural proteins